"Eureka!" says a 1 dimensional being in a 1 dimensional world. "I have proved conclusively that points cannot exist. To prove this," he says to another 1 dimensional being, "lets imagine a point here but it has no 1D'ness, no height (that is what they describe and measure their sole dimension by). I can pass right through it, so with no points, I don't have to do math anymore." 

         The other says to him, "Yes, we know points cannot exist in space, they are mathematical constructs but we imagine they exist by cheating and giving them minimal height." 

         At the same time in a 2D world sometimes referred to as Flatland for some strange reason, a 2D being realizes lines cannot exist. "Look, lines with length but without width cannot exist if you look at them head on. I can make a square prison made out of lines but they could not hold me. I could pass right through them as if they were only made of laser light. Since lines cannot exist in reality, they must be mathematical constructs, therefore I do not have to learn geometry," he says. 

         "No duh," says another Flatlander. "We know pure lines cannot exist without width but we make them by cheating and giving them a minimal amount of width in addition to their length to imagine and construct them." 

         Unfortunately for them, simultaneously a 3D person reading "Flatland" realizes planes, and therefore 2D worlds, cannot exist. 

         "Look," he says to the ever present other person in this analogy (it is nice to save words to have another present without having to go look for another to enlighten him or her), "without having any thickness, a box made up of 6 planes in 2 parallel planes in 3 pairs would not confine me. It would be like squares of lines with only 1 dimension, width but without length or length without width. A prison made up solely of opposing planes would confine no one!" 

         "Idiot", says the other. "We do not make prisons out of planes, we make them out of walls. Walls like the area they confine or wall off have height and length and width. We call it thickness, dummy. Though a pure plane of just length and width cannot exist without cheating or giving it minimal height so we can draw, imagine, or work with it, we know pure planes of anything exist solely in our minds. They are dimensions of nothing until we oppose them with something to make them stand out against it, a slight width though mathematically zero for a vertical plane, or a microscopic height for a horizontal plane to keep it from vanishing from existence from another perspective. 

1.2:  In which Flatlanders meet and trap jumping circles

         In Flatland of a 2 dimensional plane which has seemingly no height and therefore cannot to us exist, Flatlanders are having to deal with an invasion of circles which behave like fireflies. They seem to disappear for a few seconds and then reappear slightly further along in the direction they were heading. They seem to go out of phase momentarily with existence and then reappear somewhere else. Though they appear quite of Flatlander origin, this weird act of being able to disappear and reappear somewhere else on the other side of lines, Flatland's minimally thick walls (since we have already learned must have length and at least minimal width to confine anything), makes them a scientific curiosity. Grants were approved to study this new and weird phenomena. Since they could only disappear for a few seconds at a time, one smart researcher reasoned, if the walls were thick enough and the circles were intelligent, and perceived they could not disappear long enough to get through they might not try and one could capture one to study it. 

         Around the same time in 3D space, a university received a grant to study a new weird but similar phenomena in their Universe, balls floating about most of the time but disappearing and reappearing seemingly at will on the other sides of walls, which as we previously noted are more than 0" thick or they are not very good at keeping anything in. By making walls much thicker, one could conceivably trap one of these balls to study it if the balls knew they could not move quickly enough and disappear long enough to pass through without rematerializing inside the wall (that would be bad). 

         Both in Flatland and in the 3D world, both coincidentally (and conveniently) they realized their "walls" would have to be 1 meter thick. Both wanted to study the movements of the balls or circles in a confined square of opposing sides, a square in Flatland, a cube in 3D land. Both needed to see the object through the thick walls with the least amount of distortion. A mythical, but expensive, substance, we will call it Mythite, was considered the only viable alternative. In Flatland they constructed a square 3 by 3 meters in each direction, or a 9 section larger square with the middle square empty for the subject. Similarly in 3D world, they built a 3 by 3 by 3 meter cube made of 1 meter cubes, and left the center cube empty for the object to study. 

         In Flatland the researcher speculated that the circles were momentarily moving into something called 3D space. The objects, he postulated, were not disappearing but moving into or through space he could not see. He reasoned if the Universe was not 2D, something which everything his senses told him to be the case, but actually contained a 3rd dimension in which his Universe was sandwiched between or contained within, the object could be briefly moving through this 3rd dimension he could not see and go "over" or "jump" as he phrased it, through the walls and appear on the other side. Since all dimensions have 2 directions, he speculated his Universe or World would have not one but two other ways to do this, 2 other directions to go in to bypass the line wall. The object could go "up and over" the wall, or "down and under" the wall. These were new and radical concepts but seemed to fit the facts to describe the circles behaviors. Luckily the walls he had were sufficiently thick that the circle could not go over and across fast enough to make it to the other side without rematerializing into the wall. 

         In the 3D world, their researcher made a similar conclusion. The spheres obviously were not disappearing and reappearing on the other side but were temporarily moving through a apace or dimension he could not perceive. If the sphere could disappear and reappear at will anywhere else, it could not be trapped. Since its ability to disappear seemed limited to a few seconds and its speed seemed limited too, that 1 meter wall all around it of solid Mythite could hold it. 

1.3:  In which Mythos goes to war and shortages lead to new inventions

         In both the 2D and 3D worlds, also coincidentally, the land of Mythos, the only place Mythite can be found (which is why it is so expensive), there was civil war around the same time both researchers needed to build a second device so they could study the objects or creatures in pairs nearby each other but separately confined. Each researcher was given an amount of Mythite insufficient to make a complete container. In Flatland, a larger grant was issued for anyone who could make a container that could hold the creature with less Mythite. One method proposed was, since the square seemed adequate in size, perhaps one could cut off diagonally half of the corner squares. Instead of 8 (9 - 1 in the center), only 6 squares would be needed. However, the researcher was adamant that the 1 meter perimeter be persevered. Though rare, it might be possible for the circle to move at full speed diagonally toward the corner which would not be fully 1 meter across at that point if the corners were cut rounded off. 

         One brilliant student speculated he could achieve the full effect of the 1 meter containment on all sides using only 6 squares worth of Mythite by folding the walls into another dimension using a mathematical model of the mysterious "3rd" dimension. If 1 meter squares went "up" and "down" 1 meter on each side of the creature in a dimension opposed to both length and width, they could conceivably wall off the creature from escaping through the mysterious but unprovable "height" dimension. Only the north, south, east, and west squares would be needed, each only 1 meter thick, but now their north and south, east and west sides would be in contact all immediately beside the creature, extending a half meter "up" and half meter "below" the creature. 

        "But," said the researcher studying the circles, "I know the math of a 3rd dimension makes a cube theoretically possible. After all, I surmised that the 3rd dimension can be used to describe how these creatures can disappear and reappear at a predictable rate based on speed, time, and distance from when they disappear and reappear. I am not questioning the possibility of a third dimension. What I want to know is how you can envision what this cube will look like, no less how you intend to build one. We are, after all, Flatlanders and not supposed to be able to conceive of what a cube would look like." 

1.4:  In which the student demonstrates 3 dimensionality to Flatlanders

        "Here", says the brilliant student,"is where we Flatlanders are not as dimensionally ignorant and less intelligent as 3D world people might imagine us to be. We can easily envision a 3 dimensional cube using a 1 dimensional world. Though only a construct, since a line must have width to exist, imagine if our world were flat like a line. To someone in a that 1D world, our square would be conceivable as a com- bination of 3 of their worlds all at once in other dimensions or in the same dimension over time. Here is our 3 by 3 square as shown in 3 different 1 dimensional worlds, or on the same 1 dimensional world in 3 different time periods. In the first example we have all three of the base. In the second we have only 2 units each one apart (in the middle) and unit one wide. In the third, we have another 3, the same as the base. Since we live in the real world of 2 dimensionality, we call see all of these 3 levels or dimensions of 1D worlds at once. They could know it over time, putting them together mentally. By recognizing the pattern of the 3 together, then the 3 with the middle one missing, then the three seemingly back again, in a repeatable succession, a 1D person could know it as we know it, as a square." 

         "We can," he continued, "use the same logic to represent our 2 dimensional world. Imagine if our 2D world were really flat like a 1D world to those in a 3rd dimension. By using the time analogy instead of dimensions, we can as yet only guess about where they might be located, for as we well know, ordinary space is only 2 dimensional, by switching these "stacked" Flatlands into a third dimension which we cannot see all "sides" of a cube at once, into a time dimension, we can "see" what it would look like. Instead of 3 for a base, it would have 9 and each of those 9 units would have an extra unit of measurement in the extra dimension. As we know them, our squares are exactly that, one measurement of height times one measurement of width, but the 9 squares that make up the base would have to have an extra measurement, in that other dimension, ideally all cubes by themselves, or 1 meter by 1 meter by 1 meter, or length times width times "height" for lack of a better word."

         "So to imagine", he continued, "what this cube would look like, imagine not 3 at the base each 1 by 1 units of measurement but 9 in 1 by 1 by 1 units of  measurement. These would be stacked solid like the base of our square is solid. Next would come the midsection of another level exactly as we see of our square, one of 8 squares, not 9 for we are leaving the middle empty for the circles to go into. And just like the 1D example, we would have an identical top to match the base with the middle filled in again, to completely seal it off in all, now in 3 different directions at once! All together it would take 26 cubes of solid Mythite."

         "Wait", said the researcher, "I know that if there is such a thing as a third dimension and we only perceive two by comparison, we still have math, and know that the cube of the number 3 is 27, or 3x3x3, not 26!"

         "You forgot the center needs to be empty if you want to put anything in it", he replied. 

         "Ok, my mistake. I do remember you said you could decrease the number of squares we needed to house the circles so we could study them from the 8 we are presently using to only 6. So far all you have done is tell us how you could do it with 26. We don’t have 26, don’t even have 8. That is why you were working on lessening the amount we need, not drastically increasing it!" 

         To this the student replied, "I was only showing how I can conceive of what a solid cube would look like in folded or stacked 2D space or in our 2D space over time. The cube made of 26, of 3 by 3 by 3 cubes with the middle cube empty, would require much more than 26 sheets of Mythite. Each "block" would be not be a square or hollow cube even, but countless sheets of our squares of Mythite stacked into each block to make it solid in the 3rd dimension, and even that giant number just for each block, and then that number you would have to multiply by 26! No, that is not the cube I am proposing to build, nor is there enough Mythite in the entire Universe to build one (The 3D world's 3D cube of 26 blocks of solid Mythite not withstanding, though that is a different Universe). That would be for a cube of the area you have now, the outer edge of the 3 by 3 square with the 1 block hole in the middle for the circles. We would only need to cover the inner 1 meter square’s area because 4 of the square walls we use now would be "turned" sideways folded into another dimension, and stay joined all along the "up and down" sides now to us invisible. These sides will stay together by adding 2 more to join them together at each of the ends where these four sides meet in the other dimension, one square panel joining them together in the "up" direction, the other holding them together in the "down" direction. You would only need 6 squares, not 8, and the outer edge would shrink from 3 meters across now, to only 1. Plus since the only reason we use Mythite now is so you can see clearly through the 1 meter walls without distortion, and the circles would not be contained because of the width or thickness of the walls, but instead by being contained or walled off in each of the directions of the 3D space they travel in, and since the walls could now be much thinner, they could be made any substance, even glass." 

         The disappearing circles researcher was impressed. Only 6 square panels needed now instead of 8 and cheaper and more plentiful materials could be used. Folding the walls into a 3rd dimension sounded promising. He could get closer to the creatures, have lots more room to walk in the lab as the "cage" would now be still the same size on the inside but shrink to only 1 meter across on the outside instead of 3 meters across now. 

         He asked, "What's the catch? That is besides I presume you don’t know how to fold the walls into the 3rd dimension?"

1.5:  In which we first confront the concept of Suchness

         "Suchness," the student replied. "back when I first encountered the example of a 1D Universe of more limited dimensions than our 2 real dimensions, I ignored the implications it was based on a line which is a mathematical abstraction. I used the 1D world example to show how they could understand squares if shown a little bit of them at a time and how they could, if they had memory and intellect enough, remember and recognize this as a representation of a square spread out over time, and then used that to show how we predict what a cube would look like, I left out one key point, or cheated so to speak. To apply the 1D world to our world, you must give them some additional length or width in addition to their regular measured dimensionality since we know the Universe is really at least 2 dimensional. Without some even microscopic length or width opposed to the other which you choose to measure, the line disappears in the other direction or the other means to measure. Lines are to us like points are to them, mathematical abstractions with zero for the value in one dimension but with a real or positive value in the other. To exist as a physical entity or thing requires Suchness. If I have a value for a line in one direction but zero for width of that line in the other of our two real dimensions, its total mass would be the length times zero. It would not be able to exist in our world. Now imagine that the world where the circles go is 3 dimensional. We or whatever we wish to send there would need to have a non-zero 3rd value of measurement in addition to length and width to exist there. If even one of those 3 values equals zero our total mass would equal zero and we could not exist there. Without that third value we would be a mathematical abstraction without form. If any of the values needed in however many dimensions actually exist, if any one of them equals zero, everything that it describes cannot exist in its space unless it extends to a minimal degree in each of the dimensions of its reality." 

         "If," he continued, "if I were to turn a 1 meter by 1 meter wall we now use to hold the circles confined, and turn it 90 degrees into the 3rd dimension, and if it is not minimally 3 dimensional, the wall would disappear since once upturned its width now becomes its "height" and requires the "height" it had before to now become its width. Unless the object we are trying to fold into another dimension already has a value greater than zero in that dimension, it would vanish from our level of existence, but not exist there either." 

         "I think I understand," said the researcher. "It is like spinning a line or a rectangle since lines technically have no width. Its length becomes its width and its width becomes its length, and back again. Though its shape never changes, the angle we view it from is shifted so what was once the height now seems to be the width, and vice versa." 

         "Correct," said the student. "By rotating an object such as your walls for the creatures up and down into the other 3rd dimension, it does not change their shape either, just the part of it we see in our dimension. If it has some measurement in a 3rd dimension, parts of it would vanish to us or from our perspective, but if it had height to begin with, that would become its width. Unless how we perceive the Universe is wrong and we have some even minute 3 dimensionality already, we cannot rotate objects into it without having them disappear completely, which is another story altogether and not very good for building walls out of. We know all walls must have length and width because we know for a fact that the world or our portion of it is at least 2 dimensional. Without length AND width, our walls become lines and mathematical abstractions which cannot exist. Likewise if the world were really 3 dimensional, all walls would need length, width, and a 3rd value I call "height" to keep anything contained within them. All of these values would need to exist or it would vanish without a little of each value in each of its 3 directions." 

         "So in other words," the researcher reasoned, "unless we are 3 dimensional already and other objects are 3 dimensional, the world is really 3 or more dimensional already even if we cannot perceive them. If some objects are 3 dimensional and we are not, our Universe is either a mathematical abstraction like a 1D world is to us, or we cannot in fact, exist in or with their Universe?" 

         "Not necessarily," said the student. "Different regions of the Universe may have different numbers of localized dimensions, but in the case of trying to fence off an area around you by rotating things into another dimension, as I said are possible with your walls, you can only hope to get them back or have them have existence there if they have a value of that dimensional "width" or measurement already higher than zero. The upside is that if they do have a value higher than zero in another physical dimension, things could disappear from one reality while still existing within another, and return again. It is like the circles you are studying. Unless they are really disappearing and reappearing, a neat trick if you can do it, they are moving their whole bodies momentarily out of what is to us the real world, and then returning as you have already surmised or speculated they could be doing. This would mean the world is really at least 3 dimensional and that they, and possibly we, must be also. They must have that 3rd value in addition to length and width which I call height. As we need our length and width to be constant joined together in our world, to exist as a single body in a definite shape, if we had a height aspect or ratio that keeps the edges of the circle glued together when it leaves momentarily our plane of existence. Without having that 3rd value, it would dissipate if moving above or below our 2D world!" 

         The researcher shrugged."Now you are getting over my head. I understand that the circle would not be able to do what it does, namely disappear and reappear intact, without having a non-zero number or size in the dimension it is entering into momentarily to keep its structural integrity intact as you describe your cube should have for it to be stronger or stay together as a form. As long as it is connected with "height" in theory, if there is such a 3rd dimension, it can be partly in our 2D world, or most of it here at once, or all out of it, above it or below it, and still be connected to itself. If it did not have a height value at the bottom of a V, it could not stay a V shape and would break into 2 parts if the bottom were to be moved up or down into another dimension. What I don’t understand though, is how can we be any different. If these circles can move into a 3rd dimension, and though I have not proved it yet, seem to come back again unchanged, the Universe must be 3 dimensional, therefore we must have a non-zero height number as well for we exist as surely as those circles do though we do not know how to do what they do." 

         "That is not necessarily the case," said the student. "We know or can guess that if they are really moving into a 3rd dimension briefly that they must have a non-zero dimensional value of height to keep themselves together outside of our 2 dimensions and return to our 2 dimensional world. Though by some counts, if some objects are 3 dimensional one can reason all objects can or must be 3 dimensional, there are representations which can state otherwise. As we know as 2 dimensional beings, we have real 1 dimensional shadows which fool us 2 dimensional people all the time when they hit walls and freak us out. What we see as our reality might be a 2 dimensional representation of a three or higher dimensional reality. Though the Universe may have higher dimensions, our perceptions of it are decidedly 2 dimensional plus time. We may or may not have a 3rd dimensional aspect to ourselves as these circles seem to do because we do not, in so far as we know, leave it and return as they do. Our existences and our minds are defined by our perceptions of a world of 2 dimensions plus time. Into that world we were born, or seem to have been born into, and possibly will live our entire lives based on a 2 dimensional understanding of things. While we exist here we do not need that third aspect of height. If we try to leave here, we better have it or else."

         "So you are saying," the researcher replied, "that we are defined by our world. Because we perceive 2 dimensions plus time, that is the world we exist in, even if parts of us stick out into a dimension we cannot perceive. You say it is possible that some things can be 3 dimensional and some things might not be. Three dimensional objects can intersect 2 dimensional Universes, and objects can have zero for a third dimension of height and be fine, so long as they never leave their 2D region of space?"

         "Precisely," answered the student. "Objects or whatever gain the number of attributes they need to function or exist within that Universe. If the entire Universe had 20 dimensions, everything in it would need to have 20 non-zero dimensions for height, length, width, and seventeen other names for other dimensional values. However within or beside that 20 dimensional bigger Universe, parts of it or others might function well with 5, 4, 3, or 2 dimensions. Objects or beings within them would only comprehend or need to comprehend as many dimensions as they themselves seem to have, and the objects that surround them seem to have. If the objects that surround them or they themselves exist in more dimensional planes they can perceive, if they cannot perceive it, it is irrelevant." 

         "I’m a Doctor, not a Philosopher damn it!" said the researcher. "Nothing is irrelevant, especially if whether the Universe is 3 dimensional or not, if I and everything around me is 3 dimensional or not, and especially since I am being paid to explain if these disappearing circles are 3 dimensional or not! If I say now, yes, they must be, people are going to legitimately start asking what else might be 3 dimensional and if the Universe itself is 3 dimensional as some science fiction writer crackpots now say."

         The student corrected himself. "I only meant it is relevant to some things but not to others. If the world is 3 dimensional and we always have and possibly always will perceive only 2 of them, in a sense that is, if not our physical Universe, our perceptual one. If you go out and say tomorrow that these circles movements into and out of existence in a predictable fashion is proof of a 3rd dimension, who will believe it? Not most people who only perceive 2 dimensions. If you wish to win over most scientists such as yourself, most might believe you or become less skeptical. Being able to razzle dazzle audiences by sending things into the 3rd dimension and having them come back again might help or hurt your case too. Some might be won over by it. Others would call you a trickster or a fraud. Without the abilities of others to directly perceive this 3rd dimension, it is to most people scientific mumbo jumbo they can’t understand and rightly wonder if it will be believed tomorrow or abandoned in favor of a 4 dimensional reality, or one higher than that." 

         "We as scientists", the student continued, "might find understanding these higher dimensions to be better understanding ourselves and our Universe but others will see it as more and more abstractions less relatable to their everyday lives unless those perceptions are direct and real to them. Maybe our Universe began as 2 dimensional and is growing now outward into a 3rd and we will all one day be able to do what these circles can do or even spend longer time, perhaps our entire lives above or below this Universe’s "floor" we are now limited to. Maybe we will evolve a new way of understanding it, in a world of height, when we can experience it as the circles might see it now. Maybe the world was 3 dimensional once and is collapsing into 2 and we are the more evolved because we have adapted to 2 dimensionality whereas these circles find it necessary to pop in and out of existence, not for fun or freedom as we suppose, but because they cannot fully enter into and stay in this one as we can." 

1.6:  In which 3D people argue, show off their multidimensional thinking and trip over more dimensions than they can make sense of

         Meanwhile in the 3 dimensional world where the researcher studying the spheres that seem to come and go from existence in which he successfully trapped in a 3 by 3 by 3meter solid cube of Mythite, he came back from lunch. 

         His research assistant commented, "Boy, that student sure was smart."

         "What student?" asked the researcher, obviously puzzled. 

        "The one in the story we are in. The one in the 2 dimensional world who successfully imagined our cube to house the spheres right down to the exact dimensions, though he said it probably could never be built," the assistant replied. 

         The researcher was obviously annoyed. "I expected you," he said, "to work while I went to lunch. I worked while you went to lunch. Besides, it is against causality for you to be reading any story you are in while you are still within it if it is ongoing and you are not dead yet!" 

         To this the assistant replied, "It is not against causality. I did not read the parts I was in, nor past now, only what happened previously in an alternate 2 dimensional Universe. Since that was in another Universe, it cannot be against causality." 

         "I did not mean here or there," responded the irate researcher. "If you are a character in a story as you claim, there would conceivably be a 3rd Universe of someone reading the story of you reading the story of them in the story in which you are a part of. You would be violating causality in that Universe." 

        "Why would I care about causality in that or those possible Universes? Besides I was bored, we were left out for so long. You weren’t tempted to read it too?"

         "What do you mean "we" were left out. You weren’t even a character before. No wonder you did not read any parts with you in it!" 

         "I thought you said you did not read it?" the assistant chimed. 

         "Shut up. Now lets get on with it or this will all get edited out. While I was at lunch I thought about a story I read somewhere else, not here...." The researcher eyed warily his fidgeting assistant. "Don’t say it. Now where was I," he continued, "oh yes, a story about a 2 dimensional researcher who conceived of how to build a cube using a model based on super-imposing squares stacked over successive 2 dimensional worlds stacked on top of each other or in the same dimensional world over time. Using the same principles, we could build a Tesseract or 4 dimensional cube to house these spheres since our own supply of Mythite has (conveniently) also run dry, and we need a second one just as they did." 

         The assistant interrupted politely, "I thought it was the student who thought it up and was explaining it to the researcher?" 

         "I said be quiet," the researcher sternly retorted. "I am telling this story and if I say it was the researcher who thought it up, leave it alone. Again, where was I? By folding the cubes of our container into the 4th dimension which the spheres seem to be disappearing into, we should be able to reduce the number of cubes down to 8. Like the Flatlanders did, we start by removing the corner cubes, in their case 4 of a 3 by 3 square. Since ours is 3 by 3 by 3, we can also start by throwing them out. So without the 8 corners, and the 12 edge pieces, we don’t need them either, that leaves the six blocks immediately around the creature. Now without the other 20 blocks around those 6, it would easily be able to slip through a 4th dimension around those blocks and escape. We need 2 more blocks to seal off escape routes "top" and "bottom" relative to that other dimension. If we fold the blocks we have now, if they have a little 4th dimensionality, it would leave a mostly 2 dimensional square remaining in this reality where each cube rotated into the other dimension, just as when the square panels surrounding the captive circles get rotated into what we know as true "up/down" directions, with half going up and half going down. It would look to them to be turning into a thin line. By rotating our 1 by 1 by 1 by .2 meter cubes into 4D space, half of its volume here will go in that dimensions equivalent of up, the other half will block its escape "down", leaving only what looks like ordinary squares here. If we put six of these "turned" squares into a cube shape around the spheres, though it will look completely surrounded, we would still leave it a means of escape in 2 directions we cannot perceive, that dimension’s straight "up" and "down". By rotating 6 cubes we would now perceive as squares and aligning them into a cube formation from our point of view we would have the beginnings of a formidable 4D wall, but then we are still left with a 4D equivalent of a 3D cube with no top or bottom, just sides, as the Flatlanders might build if they forgot they needed more than just 4 sides with 2 completely away and out of their sight in addition to the 4 they can touch. But the squares would still be squares, though the Flatlanders would see them only as lines, they know them to be somehow still squares joining up somehow to form a more narrow but more efficient barrier above and below them somehow." 

         "The smart student," he continued, "ahem, researcher, realized this super-barrier of all wide squares they could see immediately surrounding the circles turned upwards seemingly into thin lines, needed a top and bottom they could not visualize except that it would block 2 more routes of escape they could not imagine, and that it would attach at regular and even angles with the four rotated sides they could visualize as squares seemingly also turned in a direction they could not perceive into lines. They knew once 2 more sides were attached to these mysterious "top" and "bottom" directions, a full cube would be formed. The Flatlander demonstrated how this would look using parallel dimensions of stacked Flatland "Universes" and how it might appear if part of it existed only in each over time, then one could conceive of the whole as they could demonstrate it the same as they could demonstrate the concept of a square to 1 dimensional people using patterns of a line over time. Using this example on themselves, they would first know a cube as a solid square, then as a hollow square in the same place made of turned mostly away from them sides, then a solid square again. To us, the same example would be a solid cube, then a hollow cube made of turned cube "sides" placed around its edges, then a solid cube again in the same place as the first cube and inside of the six previous cube "sides" which we perceive as squares. Where those extra 2 squares to a complete their cube would go, they did not know but knew their size and that they would affix to the edges or tips of the squares not already touching another square directly in the "above" and "below" directions, as these top and bottom cap cubes would be touching or pressing all of their its six outer sides at once against the six cubes we do see partly, in the "up" and "down" directions of we of 4D space we cannot visualize." 

         "They knew," he continued, "each 1 meter square would form a seal with a square of the one to its right and left on 2 sides extending half a meter in one direction and have a meter in the other, and since they know every square has 4 sides not 2, and each square was joined up (from a warped to them viewpoint) fully only with each one beside it, 2 super squares would be need to connect the ends of the 4 squares which they could see directly "above" and "below" the circles, fully out of existence on their Universe or point of view. Likewise our "turned" 6 cubes join up with fully square sides touching in what to us seems a warped space kind of way each with 4 sides of each cubes directly lining up with square sides on the 4 cubes around it where we see only edges touching, not sides. This leaves 2 sides for each cube not touching another other cube directly, thus 12 sides unmatched on untouched sides for the remaining for 2 "cap" cubes 6 sides to touch from 2 more directions in that dimensional version of "up" and "down", each on an opposite sides of the four sides that do touch, which to us looks like "inner" and "outer" but neither term actually can or does apply though we can think of them in that light if we keep in mind that is also very wrong and not the case either. Since the whole 4 dimensional object can be turned on any of the 4 axises, and any side or direction is equally any other side or direction, neither is really inner nor outer but both are equally moving "away" from our seemingly 3 dimensional space or perception, or seemingly getting smaller in both directions at once." 

         The researcher’s assistant said to this, "The way I heard it was different. They never actually built it, nor could they have if the squares were squares only and not partially 3 dimensional already." 

         "That is correct," said the researcher. "If the squares had no height to begin with they could not be rotated up and down as we know it, width and height become transposed and changed to the other. If the squares were purely 2 dimensional, they could no more enter a 3D world than can my shadow. If we rotate the six 1 meter cubes into 4 dimensional space and move them closer to form the beginnings of a 4D wall, to work correctly to see them at all, they could need to be partially 4 dimensional to begin with or they would vanish completely instead of seeming to become squares. Like Flatlanders knew the size, shape, and relative dimensions of what would be needed to cap the remaining 2 spaces they could not reach by simply rotating the squares which they could see, so too can we know the size, shape, and relative location of what it would take for us to cap our six turned cubes which are still cubes just like they were before they were turned, but now would seem like squares making a new 1 by 1 by 1 meter cube actually made of 6 1 meter cubes, though still uncapped at 2 ends completely outside our dimension. Like the Flatlanders, we know we need to take 2 more cubes like they needed 2 more squares, move 1 cube completely out of our 3D Universe directly "above" whatever that means to us as we are as lost as Flatlanders on imagining what that means, throw another cube "below", equally in unknown space to us in the opposite direction on the other side of our 3D space, and then each of the six sides of the 2 additional cubes completely out of our Universe will fit perfectly in place with the 12 remaining sides of the "side turned" cubes we can see which are left exposed by not being sealed off completely by touching another cube. Of the side turned cubes we can see partially, where their ends which we only see as lines at the edges of where we see them touching in this reality, where those edges end in another dimension, at those two places the extra cubes will meet with the 6 we can see. The 2 extra cubes cover the remaining gaps unable to be sealed by the first six cubes directly, though those two extra cubes become completely invisible to us in 2 different and opposite directions "away" from our space or world."(I thought I would break in here since this is hard to visualize. I have added the Tesseract from the cover of Quadranine at the bottom of the page to help explain it. You have to be able to see our 3D plane as sandwiched between 2 others away in 2 different directions. The "edges" where six "turned" cubes touch would be the middles of those sides shown well in this image as being where they intersect our world in the middle and seeming to be bending away into and away from it equally. Again, in the yellow image at the bottom, you need to see the middle cube as being as our "shell" 3D world in a larger dimensional context. The inner and outer cubes away from that center cube would be interchangeable, with either seeming to be on the inside depending on what angle you viewed it from)

         "But," the assistant replied, "to us, though the 2 other solid cubes are completely out of our sight, we like the Flatlanders, must know where, if not how, they went."

         "Exactly," said the researcher. "The two solid cubes must reside directly "over" and "under" in another dimensional sense, the sides we can still see as squares forming what looks to us to be a different cube of 1 meter by 1 meter by 1 meter, but with this "other" cube, each square side to us is really a folded or flipped cube half "up" and half "down" in a direction we can’t see. We see a new cube made up of 6 turned cubes we do see, which may be capped or uncapped since we can’t see those ends lying outside of our space. Though the 2 ends we cannot perceive lie completely outside of our space, the "outer" cap cube's outer six sides would seemingly from our points of view be bent all the way around, turned inside out really, to touch the outermost edges of six sides of the cubes we do see if we imagine them still protruding half outward into our space, or the "outward" invisible half. The "inner" cap cube, to us we would not need to imagine it bent, still looking like a cube, but so tiny as to seemingly disappear into a point in the center if the Tesseract was completely the same dimensions in all of its 4 values. This "too small" cube from our point of view, would touch what appears to us as the "inner" six sides not touching another cube directly away from our space in the opposite direction, not away but seemingly inside (though invisible) though only from our point of view, the hollow middle between the six solid turned cubes which make the comprise the sides of a new hollow cube we could see." See bottom image

        "And that is exactly how a 2 dimensional person could conceive of a cube looking in 2 dimensions without using perspective drawing. They could conceive of the 4 squares they see bending inwards together diagonally, imagine an "inner" square touching those 4 sides where it bends inwards, and an "outer" touching all of the outside 4 edges all at once though it would look impossibly bent outwards in all directions always from the other 4 squares, or have itself turned inside out like a popped soccer ball so the outside of it is inverted inwards to touch the outside of the more normal but slightly bent other 4 regular sides all at once," the assistant added eagerly now seeing the point clearly. See bottom image

         "If," he continued, "all six of the sides we can see push inwards half a meter towards the center from all six directions at once, not to mention the full size inner cube at the central point, doesn’t it get a little crowded in there?"

         "Yes," said the researcher, "it does seem to get crowded in there but on two counts, "in there" is not just "in there". You have to think of adding one new dimension as like an increase in all the other ones combined. To be able to be turned at all, our cubes would have to already have a non-zero value of the 4th dimensional value, or be 4 dimensional already. If we turn a cube mostly out of our space at its apex where it is thinnest in a 4th dimensional value, we can fit a similar amount of full sized cubes into the same space. For example, if Flatlanders turned their 1 meter by 1 meter, by 1 centimeter square at a right angle to their world, but stacking together 100 squares to us what we call "vertically", to them turned sideways out of their dimension into just lines extending away in directions they cannot comprehend, this would mean from their point of view, they could fit 100 panels in the same amount of floor space, to them floor space is total space, in the same space as 1 panel! Storage space would be plentiful and cheap as large objects could be rotated into and out of their Universe and returned at will." 

         "Provided there are no occupants in parallel Universe and down where the objects are rotated to that might damage them," added the assistant. 

         "Yes, though the majority of the mass would seem to magically disappear somewhere, they could deduce as we could that it must be going somewhere. So by comparison, if we rotate a 1 meter by 1 meter by 1 meter by 1cm cube into a 1 cm thick square panel in our space, we know the rest of its mass has gone somewhere, space there is not a problem unless it goes into a parallel 3D world where that space is already occupied by another object. Each integer value "away" from our 3D space could seem like another complete 3D world unto itself, stretching itself "outwards" in "inwards" into multiple 3D Universes at once depending on its thickness in those values, how many Universes or 3D worlds "away" it exists in at once. To trap something in 1 dimension, you need 2 walls, on in both directions it can go at once. With 2 dimensions you could trap something with 3 walls, with 3 dimensions, 4 walls. With 4 dimensions you would need 5 walls," Researcher remarked. 

         "Wait a minute," said the assistant. "We need 8 cube walls!"

         "That is because we are going on the square model," the researcher replied. "A square has four lines, a cube has six squares, and a Tesseract, which is what we are building is called, has 8 cubes for "sides". If we started with a triangle, it would have been smaller from the start and at each step it would have been smaller as well but the square model is easier for most people to understand because we see squares and cubes everywhere. Most people live and work in cubical shaped rooms with square and rectangular walls, ceilings, and floors. Understanding square and cubical shaped things are much easier than triangles and tetrahedrons which are simpler shapes but outside of our everyday experiences much more than squares, square grids such as maps, and stacked cubes as rooms in buildings with many floors."

         "Building up is a good example," he continued. "If you lived in 1 dimension, everything would be really crowded and far apart in different ways. It would get crowded as with only 1 dimension, everything would have to be stacked end to end, like when you hear if your brain cells were stacked end to end they would reach around the world many times over. If the world were 1 dimensional, space would fill up fast yet everything, even most of your brain, would be far away. With 2 dimensions, space is not doubled, it increases many times more. Things can beside each other, not everything in the Universe in one long line. If the Universe was 1 dimensional and infinitely wide, it still might seem small and not very easy to get around it. With 2 dimensions, the inverse can be infinitely wide AND infinitely long, in length spacially that is. Everything can go around each other and it is easier get around and support larger numbers of things. In a 3 dimensional world, it can have infinite height, length, and width. Things can not only go around but also over each other. One person’s home no longer has to dominate all the land as a Flatlanders home would. Many people could live in apartments stacked right on top of each other, all sharing the same 2D footprint or land area. Growing upwards or stacking people over other people seems crowded on one hand but creates more space out of smaller spaces." 

         "In a 4 dimensional sense, right near a 3D world or room, you could have many other 3D worlds or rooms only steps away in a four dimensional sense, both giving far greater room to grow or build outwards into on one hand, or seeming more crowded on the other hand with all of them sharing the same 3D footprint or spacial area." 

         "As long as they keep the noise down from their 4D stereos and TV’s, I could use all those extra rooms in dimensions I would only have to move slightly to go to. My apartment is kind of small," the assistant mused. 

         "Yes, having more room only seems like more room instead of being more crowded when there is complete separation between them. Noisy neighbors in 3 dimension world’s only inches away in another dimensional direction would suck if they were not inter-dimensionally sight and sound proofed." 

1.8:  Where 3 + 1 definitely is not 6 but really really looks that way

         "If you are 3 dimensional and you are standing in the same spot as the 3 dimensional block turn into the 4th dimension, isn’t that 2 dimensions too crowded?" asked the assistant. 

         "Yes, that does seem to be getting a bit too tight if there are only 4 dimensions plus time. In 4D space, it is possible for 2 seemingly 3D objects to exist at the same time in the same spot sort of.  Since I said every time you add 1 new dimension, it is like you add a new set of the number of all previous dimensions. To understand how 3 dimensions + 1 seems to equal 6, and 4 dimensions + 1 seems to equal 8, let’s go back one step. Let’s give Flatland some real depth! Flatland is a 2 dimensional. Let’s give it a height of multiple planes of 2 dimensionality. Now they can have multiple Universes of 2 dimensional worlds, but that is too confusing. Let’s go to them and tell them, if they were able to build their cube out of their 2D Universe, saying if you can build a 3 dimensional cube you are not really flat but partially 3D like us. We could show them how to use their cube building skills to have multiple layers on top of their 2D world. This new 3rd dimension lets one Flatlander stand directly above another, and yet another directly above him. The world is not really flat at all. This new 3rd dimension actually to the Flatlander appears to enable mostly 2D people to share the same space. Now let’s go back to the 3 dimensions + 1 = 6 dimensions example. We cannot have 4 and 6 dimensions at the same time though it can appear as such by some angles.  If the Flatlanders were not 3 dimensional already, we could not teach them how to build up out of their 2D Universe. Without a height in a 3D world or Universe, no more Flatlander, Flatlander flat-lined! If they were really 3D we could show them how to seemingly reproduce their 2D world on another level above the one they know now, to put their height or 3Dness to use." 

         "For me to stand where the block appears to be "above" or "below" in another dimension, it would appear that 2 3D objects are sharing the same space but that can only happen if space were more than 3 dimensional and the block was slightly 4 dimensional to be able to be turned and stay intact somewhere else. A 4D being could show me how I only think or perceive of myself or the block as 3 dimensional, as I could show a Flatlander his perceptions of only being 2 dimensional and the world only being 2 dimensional really do not apply to a 3D world as we experience it, and know they could possibly experience it too if they have some 3 dimensionality to themselves and therefore might be able to build above it, as we know we can in 3 dimensionality, though to a Flatlander it would be confusing and look like 2 objects in the same space, though we know they are not, just above and below, but in normal 2D conceptuality, there is no such thing as above or below. For me to be shown how my block or me only seem to be 3 dimensional, it would be the same as my teaching a 2D person to comprehend 3 dimensionality. None of the rules I understand would apply at first. I would be amazed at how I and the block, both I previously assumed were 3 dimensional, were both actually 4 dimensional, and though it looked to me like I was a 3D person within the space of a 3D turned block into a fourth dimension, the reality would be just two 4 dimensional objects only seeming to exist in the same space from a limited 3D perspective. From that 4th dimensional point of view, my narrow understanding of how 2, many, or infinite 3D planes can exist within the same space would be much the same, and as narrow, as a 2D person not understanding how another 2D world or plane could exist on top of his own 2D world or plane of existence. It would be as confusing as the concept of going "over" something would appear to a 2D person. "Over where" or "over how" they would think. Though 2 dimensions + 1 <> 4 (or more), to a 2D person’s level of understanding it would appear so. For a 3D person experiencing a 4D experience, it can seem like standing in the same place at the same time as another 3D object is not possible. But if the 3D person were really 4D and only understood or perceived 3 spacial dimensions, standing where he knew another 3D object stood in another extra one dimension would be as confusing as "over where" and "over how" to a Flatlander. To us we might call it "through where" or "through how" with no explanation, concept or grasp for what "through" means as a Flatlander could never grasp "over". Once better understanding how a 3D world is not "flat" in a fourth dimension, one could learn to function with these new rules of Physics. It would seem to him like a whole new or multiple new 3 dimensional worlds stacked "within" each other, as a newbie Flatlander would interpret the 3rd dimension as multiple 2 dimensional worlds." 

         "So you are saying that perception defines our world, right?"said the assistant.

         "No," said the researcher, "Perception defines what we believe to be possible. What we believe to be possible is what defines our world. Now get back to work!" 

         "One last question," said the assistant. "If two dimensionality can be shown to or demonstrated to a one dimensional person by a repeating pattern of lines and dots of a square, and a cube can be deduced by a Flatlander as different patterns of a square over time, doesn’t that mean we might be able to deduce some aspects of a four or more dimensional Universe by using patterns of 3 dimensional shapes changing over a period of time?" 

         "Why limit yourself to 3 dimensional shapes for clues," the researcher replied with a wink and a smile. "To the 1 dimensional person, the pattern of the square was simply in the only 2 shapes he knew, lines and dots. With memory and intellect, he could have envisioned a square from it but also could have seen it as anything else. Though the pattern of the square was there to be found, it was more apparent to a Flatlander than it would seem to a 1 dimensional person. "What is it with these repeating patterns of lines and dots?" he might think, and think nothing more of it. A different 1 dimensional person might pick up on it right away. The  Flatlander student who correctly deduced what our complex-by- their-standards 3 by 3 by 3 cube here with an empty cube in the middle would look like if he could imagine seeing it all at once, he was truly exceptional. He knew of squares in a relational sense right off the bat as a scientist or mathematician in training. He was able to take that understanding of the properties of a square and use it to understand square-like things existing in another realm he could imagine but not directly experience. We know from our experiences that a 3D world can exist, at least for us. If he never is able to build his 3D cube, many might think with good reason it was impossible and could not be done, and that their world only really had 2 dimensions. Other explanations having nothing to do with a 3rd dimension might better or more accurately explain the disappearing circles. It is even possible that he could have been able to build his 3 dimensional cube and been able to convince a few he had indeed achieved the feat without having something or someway of proving it to be more than just the square it would appear to them to be."

         "Turning," he continued, "1 meter squares into 1 centimeter wide lines might impress others or his peers but just as likely, they could think of it as a cheap parlor trick, without a full grasp of the science behind it. You or I might see this sphere blinking in and out as a clue to something possibly existing in and moving slightly through some "4th" dimension unknown to us because we are trained to think in those terms or see it in that light. If it were something purposely trying to get us thinking in terms unfamiliar to us to begin to be able to explain it and expand our perceptions, it would have that effect on us. Others might pay it no mind at all. Others still yet might see it as a sign from God to do this or that." 

         "Through time," he went on, "anything can seem to mean anything to anyone. Higher dimensions need not be divined from geometric shapes for someone to see a pattern that makes them think other dimensions exist. They might see it in a rise and fall of species over time, or the beginning and ending of Universes, or in the stages of life they have lived through. When time itself can be thought to be the medium by which 1D people can envision 2Dness, or 2D people can imagine or deduce 3Dness, anything and everything we experience is as valid as any square or triangle, cube, tetrahedron or Tesseract, for opening our minds to dimensions beyond what we perceive." 

         "As scientists we see the logic in understanding or communicating knowledge of our dimensions through shapes down to other lower dimensions when possibly only other scientists would make the connection. Life itself might be the means to convey such information. Life itself is not only to be lived, but begs to be understood. It may be an answer in the form of a question, a question with no definite answers, or nothing needed to be understood at all, just lived. If it does have a point of view to be conveyed, it is best apparent or easiest to understand if it is within all we experience, not hidden in complex numbers or geometric shapes. As a scientist, I might choose to start communicating with a Flatlander or one of lower dimensions by use of number or shapes over time but many other 3D beings might take a different approach entirely." 

         "Yes,  I think", he concluded, "that life itself is the best thing to use to open up 2D beings to the possibilities of the more confusing to them but simple to us, realities of life in our world. If it was in every aspect of their and our lives, everyone would have an equal chance of realizing, if not by one method, then another. Yet it is not for me to enlighten 2D beings on 3D realities. I as always am content to solve the puzzle immediately before me. As always that is to understand everything or my part in everything. Today however, more specifically that means these damn disappearing spheres which I am expected to explain and that unfortunately, as my assistant, yours is trying to help me explain that. Now get back to work!"

          "It is no truer testament to what you just said," the assistant said, "that the lesson or answer you seek might be found in everything you do, not where you look. We have done little since you got back from lunch in studying them, but I can scarcely see what we have talked about to be anything but the only path in trying to understand them, by trying to do what the Flatland student did and imagine new ways of looking at them or new ways of interpreting this strange spheres event we are being paid to try to explain."

         "I thought," the researcher replied wryly, "that the researcher was going to be the smarter one in this section. After all the "student said this" and the "student said that" of the last section, I thought it was going to be different this time." 

         To which the assistant replied sagaciously, "You got to make the most and best points this time and should be grateful to be left that. However, the younger generation will always get the last word in." 

         To that he could only shrug and nod in approval.

 2.1: Building the machine

 (Note: For those who might not understand without being told, most of section 2 regarding machines for turning matter into another higher dimension is simply allegorical for providing a jumping off point for discussing different multi-dimensional states. The ideas provided for how one might do that are not supposed to be taken seriously, nor are the ideas explaining the logic and theories of how such machines work, or why they work. If you must believe everything you read, section 2 is not for you.) 

         Eventually the Flatlander student who envisioned the idea of a cube and folding squares into the bizarre concept of 3D space got funding to build such a machine. Because he was no longer a student at this point it is now necessary to give him, or refer to him by, his proper name, Inventor. Inventor defined the problem quite simply. To turn an object into another dimension, it needs to already be 3 dimensional or put another way, have 3 opposing angles or dimensions of Suchness. Objects have solidity or coherence in the 2D world because of a balance of forces within it pushing outward from it into two dimensions, and pushing inward into it. It wants to explode and implode at the same time. By these forces remaining equal, it just sits there. Though Inventor knows this as Suchness, it is his term for it. In both his 2D world and the 3D world stealing his ideas, they have other names for it. Plus, he has reasoned that because all the rules of 2D physics that most use will not apply for what he is trying to do, Suchness, though not a technical term, is convenient for treating all of the dimensions used to describe something the same. It means in his world, length and width, though opposing or angled on different axises, are essentially the same thing. If it were 3 dimensional, it would have 3 opposing but interchangeable units of measurement, 3 levels of Suchness, all essentially measuring the same property in different ways. 

         Most math in his 2D world describes things as having only 2 dimensions, or 2 levels of Suchness. The forces of the atoms that hold objects together can be described as pushing outward in all directions and inward toward its center in all directions. Because he readily understands 2 dimensions of length and width, he can measure these movements or attempted movements to both explode outward and implode inward, in 2 different ways or along 2 axises, north/south and east/west. Though few of the atoms of the square he intends to flip are actually trying to move north, south, east, or west exclusively, by combining the north/south or X coordinate, with its east/west or Y coordinate, these 2 numbers can describe any attempted movements in both of the 2 dimensions his math describes his world as having. Because he needs to assume what he intends to flip has another dimension of height, he needs to assume it has atoms wanting to go in 2 other direction also, up and down. It not only must have a center point lengthwise and widthwise, but also heightwise as well. It needs a non-zero number of this new height value or the whole idea will not work. 

         To make his experiments easier to achieve (mainly for us to visualize) he needs to use objects with a large number for that 3rd value, its height. His first attempts to expand objects height uniformly and evenly did not go so well. This attempt to pump up their volume so to speak, did not increase the square shape evenly into the 3rd dimension. Instead of gradually adding equal height uniformly over the entire square getting thicker, it bulged in the middle above and below, expanding upward and downward creating matching 4-sided pyramids above and below. Though he could not see these shapes, his math confirmed it was not a uniform increase of height. After much trouble, he found a way to pull the center bulges back towards his world, and have an even value of height all around it. Though this increased height he could not see, he could measure, for he was able to add a predictable amounts of matter to it. After initial testing to see what measurement of height it already had (which was not much, but without even that much, he could not have been able to increase it), he decided it should have a height 20% of its length and width. This is quite thick but still left a lot of room inside in the middle and would be solid enough to use cheaper materials. Each square would be 1 meter wide by 1 meter long by 20 centimeters high. 

         To turn this square upwards he set up 2 sets of lasers at each end of the square. He also needed to invent a new type of charge. He called it Mystericity. Like common electricity to power the lasers, Mystericity has both positive and negative charges. The lasers on the left or west end would fire a positive charge, the lasers on the right or east end would fire a negative charge, and simultaneously a pivot point in the middle was measured and secured for the panel to pivot or turn on. The point and value of Mystericity was to subdue attempted movements of atoms in-between each set of lasers. Since Inventor could not climb on top of it to tip it, he would need to try to get it to tip itself. The positive charge would on the left would try to slow down the naturally downward attempted movements of atoms or ideally have them wish to go upward instead. The negative charge at the opposite end would simultaneously try to subdue the upward movement tendencies or turn them downward instead. 

         Getting it to turn out of his two dimensions into 3D space was difficult. Getting it to stop straight up and down at a 90 degree angle to his 2 dimensional world was even more difficult. Luckily the thickness of the height made it possible to fine-tune it while still partially turned and it had no significant tendency to want to snapback into place as he feared. It tended to be fine at whatever angle it stopped at. 

         He also discovered something that perplexed him greatly. At one point while stuck partway in-between straight up/down and straight left/right, they adjusted the charges to return it more fully into their world to try again only to find they had reversed it. Markings previously on the west side were now on the east side and though they had been on the north end of the west side, they still were on the north end, only on the east side of the north end. It seemed to be a physical mirror image of itself. 

         Back in the 3D world, the researcher merely gained insight on what Inventor was doing and applied the same concepts to fit the situation of expanding them into one more dimension.  He increased the mass of the cubes’ 4th dimensionality to 20 centimeters. It now was 1 meter high, by 1 meter wide, by 1 meter long, by 20 centimeters in the fourth dimensional value of its Suchness. He attached 8 similar lasers, 4 on the left or west side corners positively charged, 4 on the east side corners negatively charged and secured a band from the north to the south directly at the halfway point between its east and west sides. He also found he could "turn" the block completely through the band and make what seemed to go into the band heading west come out backwards while same thing occurred with the east side going through the middle and coming out the west side backwards. Turning it 90 degrees into 4D space, he would get the 20 cm thick 1 meter by 1 meter panel he desired. Turning it again 90 degrees he would get a mirror cube. Another 90 degree turn yielded the same panel as the first panel but reversed. Yet another 90 degree turn and the original cube came back as it looked before the turning began. 

2.2:  Where did the cubes go: Everyone freaks out

         Inventor, ever true to his name, later developed a method of attaching a square panel to a turned square panel and placing ones directly above and below his four turned sides. This technique was promptly adapted by Researcher for cubes. Of all the 2D people or 3D people who marveled at the 3D cube or the 4D Tesseract, it was a long time before anyone but Inventor really understood where the squares or the cubes went. Inventor was born with a 3D brain in a 2D world. Every Flatlander who ever read science fiction books, which were very popular in Flatland, knew or thought they knew the location of the top and bottom squares. When Inventor said they had the same location and shape of the outer square itself but in some invisible other dimension, younger people had no problem with that. Even those who could not understand it could accept it. The four walls were another matter. To everyone but Inventor, the turned walls were a mystery for the longest time, or so it seemed anyway to him. That they could still see them both added to their confusion and was the main source for it as well. "Where did the rest of it go?" everyone who watched the process would say. They would see both the east and west ends of the square get slightly bigger followed by a rapid shrinking into a 20 cm by 1 meter line in the middle. Inventor eventually gave up trying to explain it, simply saying he made it more dense which everyone readily accepted, except it was not true. When Inventor came across someone he thought might understand he would answer truthfully and hope for the best. 

         "It still has a square shape though we can no longer see it from that perspective," he would say. He would then take a 20 cm by 1 meter sample stick and turn it in front of someone. 

         "Watch as I spin it," he would say. "See how it appears to grow into 1 meter when both ends are at an equal distance away from you, but shrink again when pointing directly at you? Notice how the end furthest away from you if I keep turning it eventually becomes the end closest to you?"

         This worked somewhat, but seeing a line in front of them and imagining it to still be a square partly somewhere else was too difficult for them. If the center of the square could have both empty space and 2 solid panels sharing the same space relative to their world but in another dimension, most reasoned the rest of the square that was not visible protruding away from the line was still there, but like the center, they could pass through it unharmed. 

         The 3D researcher did not have much better luck trying to explain where the rest of the cube they could not see went. That he did not fully understand it himself did not help. He was born with a 3D brain in a 3D world. Working with 4D objects was annoying to him, but since he loved to try to figure things out, this gave him plenty to do and enjoy whenever he could overcome his frustration at it not coming as easily and as naturally for him as it did for Inventor. He could understand what Inventor could understand. With his 3D brain raised in a 3D world, he could understand mostly 2D objects flipped upside down through 3D space. 3D objects seemingly turned inside out through 4D space took work for him to understand. Eventually he got there though. 

         For 3D people, they too found it easier to understand the top cap cube and the bottom cap cube were exactly where the visible cube "sides" sat, only in another dimension. That the cube "sides" were visible but seemed thinner was always the hard part. Saying that they were simply made more dense placated most people. They could understand melting or compressing the full cubes mass into a harder, more dense 20 cm by 1 meter by 1 meter square panel. When he tried to explain the square panel visible to them was still a cube, but from another angle, most asked, "From what angle can you view a cube where it does not look like a cube?"

         "From one we can’t see from," was all he could say and knew to be true, but it sounded inadequate even to himself. He too like others was tempted to think when he walked through where a full cube sat whole moments before, that he was standing "inside" or simultaneously existing where the rest of the cube was "above" or ‘below" him but in another dimension, like the old 2 4D objects side by side but seemingly 2 3D objects sharing the same 4D space example. It is not that that is not possible. To be inside the Tesseract at the same time the as the solid top cap and solid bottom cap are in place appears to a 3D mind that 3 3D objects are sharing the same space, but that can only happen if space is really 4 dimensional and only seems 3 dimensional. If people had only a slight 4th dimensional thickness, and a slightly larger 4D cube or Tesseract was 3 meters in all directions but hollow in the middle, they could have a party with over 100 people in what would seem from one point of view a cube only 3 meters by 3 meters by 3 meters. But like Inventor, Researcher eventually realized the full volume of the cube never leaves the edge of the cube you can look at, touch, and carry. The cube turned to a 20 cm by 1 meter by 1meter square, that is the complete border of the cube where it intersects his space, the rest of it is turned on itself up and down into a fourth dimension, but seemingly inward from where a 3D person would be standing. 

         The turning process is what helped Researcher visualize it. He knew what Inventor would see before he turned his square before Inventor did, not because he was smarter, but because he had been turning blocks over since he was a child. From where he was standing, Inventor saw both the east end and west end move slightly outward as the top and bottom edges tilted up and down, and what looked like the square getting smaller was really 2 new edges Inventor never saw before. Top and bottom edges were now the east and west edges, and the east and west edges were now high and low into another dimension. Researcher too saw the edges of his cubes seem to get larger slightly at the beginning of the turn, then seem to get quickly smaller. This new smaller east and west cube halves were the edges he never saw before, and could never see from his current perspective, and that the rest of the cube had switched places with these new parts never seen before in his Universe, just as the smaller line segment to Inventor was really the top and bottom sides never seen before in his Universe. 

         Similarly, only Inventor was not freaked out by mirror images. His 3D brain in a 2D world understood that everything coexisted in and as its own opposite. When people found they could reverse any shape by "flipping it" 180 degrees through its center point, it came out a mirror image of that thing. Inventor understood if his world was really 3D, and Flatlanders can only see or perceive 2 dimensions at a time, the whole of Flatland could be flipped or interchangeable as neither the "top down" or "bottom up" perspective would be the right way to view it from outside it. Both views or perspectives would be equally true though opposite. Seen from above it would look like everyone in Flatland drove on the right side of the road. Seen from below, it would look like everyone drove on the left. East/west,  north/south would be interchangeable. Neither view being the absolute or correct one, except possibly of course, the view from within it. 

         Researcher saw that of Inventor’s world but not his own. He did not want to believe his world could be flipped and no one would ever know, that one day he could be right handed and drive on the right, and the next day he could be left handed and drive on the left side of the road and never know if the whole world were flipped at once. His 4D cube meant he could be flipped as well as the cube and flipped back again. He and a mirror image of himself were the same thing! That bothered him that he could see that he parted his hair on the right but from another view, he parted it on the left. Where he parted his hair was not as worrisome as the implication of looking into a mirror and not knowing which side he was on! Either way it would look the same and not matter from a 4th dimensional point of view. Reality on the left side of the mirror, and image on the right, or reality on the right and the image on the left, both would be true interchangeably from how you looked at it and it would soon cease to matter which way to view it was right because they both are true though opposite interchangeable perspectives. One day while viewing himself in a mirror while shaving he said to his reflection, "Just so long as only one of us is real, I will be grateful!"

 2.3:  Bouncing off of Assistwo

         Back in the 2D world, Inventor’s assistant came in. "Just in time, Assistwo, I needed to bounce some ideas off someone. By the way, how did you get such a strange name?" 

         "My parents said it was to differentiate me from a 3 dimensional researcher’s assistant so other people would not get us confused. They said the "two" could mean either that I am the second assistant in a story or the two could represent our two dimensional world. They are very strange in some ways. I think they did too many drugs in college," Assistwo answered. 

         "Well since you became my assistant, maybe someone someday might understand their logic. Whatever. Anyway, I have been trying to visualize what our 3D panels might look like from 3 different directions at once in 3D space." 

         "Haven’t we all since you built it, but I thought you were so smart you could "visualize" the cube? We keep hearing about how smart you are and all."

         "A little more respect please or you will be Assistnot! Just kidding. Yes, I am pretty sure I can visualize the whole cube at once. It is just "seeing" the 3D properties of the height of the square panels, or trying to visualize it. For instance we know since we can reverse it, these 3 dimensional "tops" and "bottoms" as I call the "up" and "down" sides, also terms I came up with, it has both at once, the top can be the bottom and the bottom can be the top. There is no right way to see it." 

         "I take it you are coming or going from or to the problem of flipping things twice and getting it back backwards," Assistwo surmised. 

         "Yes, by doing a double 90 degree flip, we must be reversing their upness and downness completely. Top we have made the bottom and bottom we have made the top. The pivot points we have attached in the middle of the north and south sides lock those sides to pivot around and keep the whole square from flying off into 3D space, thus keeping the north side on the north and the south side on the south. But even then they are reversed, the marks on the north pointing west now point east, and the ones pointing east now point west. The same happens on the south side." 

         Assistwo said, "Yes and the east and west sides not anchored in our reality change places completely. Haven’t we been over that already?"

         "Not in this much detail. Why is it so hard to get good assistants in this story?" 

         "You are kidding again right?" asked Assistwo. "Right??" 

         "Anyway, we know from the machine that we are altering or messing with their natural tendencies to want to move up and down at once. We know that 3D objects have 3 units of measurement. Normal length and width as we understand it, and the new one I call height. 1 square cm of matter, real matter as we know it, not this stranger 3D kind, well strange to us anyway, that square cm of matter must have equal and opposing sections trying to move left and right, and at the same time, front to back or north and south at the same time." 

         "Yes. Not to sound sarcastic though, I don’t want to be known as Assistnot, but you already covered this with your theory of Suchness. That is that all objects are attempting to push out or expand in all the regions of space they have a positive value in, and likewise trying to contract inward into the same inverse direction. Have you something new to add on this? No, I really mean it. I am not being sarcastic, I really want to know. Please don’t fire me."

         "Trust me, your job is safe, for the moment at least," Inventor said with a grin. "No, I have nothing as such "new" to add to Suchness. It is just by always conceiving of this occurring at the molecular or atomic level, I never tried to visualize it before. Yes, these movements, or these canceling each other out attempted movements by each part first in one direction then the other, are parts of matter far too small to see but we can imagine them to be any size we wish. Instead of very tiny, we can make them big enough to easily see, like 10% if we want to, though that would be a gross overstatement and not really the case." 

2.4:  Flying off the edge: Problems with Suchness

         "But making them that big does bring me to a big problem I have with Suchness,  or that every dimension you mention, height, width, and length, really can be seen as attempted movement of solid matter simultaneously in both directions of that measurement at once. Height like you said exists as height because some parts are trying to go up and some are trying to go down, but they keep bumping into each other so they stay together and appear to be standing still. By breaking or subdividing these sections to be as big as you show now, it becomes obvious that the ones on the ends would fly off and nothing would stay together," Assistwo asked. 

         "Yes, I see what you mean now. We can allow for some very small parts to fly off the edges but looking at it blown up, one would wonder how anything could stay together long," Inventor replied. 

         "We would have asked about this sooner if not for your reputation. At being smart that is, not that it could be taken otherwise. I am shutting up now."

         "Good. Yes, there does need to be some counter force to hold everything together. That things hold together at the atomic levels or smaller we in this 2D world can describe and measure but really can’t explain. We know they want to go every which way at once but can’t, and that simply always getting in each other’s way is not a good enough explanation. There must be a counterforce not simply moving them East, West, Up, Down, and North or South. It, like the idea of Suchness itself, needs to be center oriented. We can measure these movements of attempting to push out in all directions along however many axises we wish to add, but that is just because that is how we go about measuring things, putting a ruler beside it, outside of it, and measure it along imaginary lines or planes. Suchness requires all objects having a center. To understand these forces of positiveness and negativeness of trying to go in both ways at once in every dimension of its existence which creates its positive values in these dimensions, we need to describe it not in terms from measuring it from outside it, but from inside it outwards." 

         "Aren’t they the same thing?" asked Assistwo. 

         "They may have the same values depending on how you want to measure, but they are two different ways of looking at it. Think of gravity or a black hole at the center of every object. Everything not trying to move simply left, right, or up/down, but to and from it." 

         "With a circle I can imagine it," Assistwo said. "With your conceptual models of spheres or 3D circles you say might exist and be as stable a form in a 3D Universe as our circles are to us. I can see why these objects might hold together as you propose but I don’t see how that applies to irregularly shaped objects without a seemingly central point. Would that not mean everything would even out and only circles would exist in our world and only spheres would exist in a 3D world? How do you explain your cube then?" Assistwo was proud of his reasoning on this and knew Inventor was happy he was getting the feedback he needed to shift into high gear. Yes, his job was really safe for now, Assistnot not! But was Inventor stumped at last? 

         "Yes," Researcher replied, "everything 2D would eventually become as circle and everything 3D would eventually become a sphere or ball, as I like to call them. My own cube, if it had intelligence, would say "I’d rather be a ball." Irregularly shaped objects such as my cube exist because each atom is trying not just to fold into a black hole or implode into the center of its mass, both trying to get away from there and go to there at once. They are similarly both attracted and repelled by each other. They can’t stand each other and want to call the whole object off and go their separate ways, and they like each other so much they want to get so close together it would literally create a black hole big enough to swallow all of them." 

         "So existence itself is the ultimate love/hate relationship," Assistwo said smiling. 

         "We don’t have to get that philosophical about it," Inventor continued, "it is enough to say everything, or every part of an object is trying to move away from its center and implode into it, in a larger sense around its whole center if it could, but wherever it is thickest also nearby." 

         "So a cylinder, another of your mathematically possible 3D shapes, would have 2 kinds of centers, the one center of all 3 dimensions and a second center running the entire length of the central circle!" Assistwo said. 

         "I take back what I said about not being able to find good assistants," Inventor exclaimed. "That is both the perfect example to what I was trying to say and a remarkably good understanding of a cylinder, which we have not even tried to build yet. It is hard finding someone who truly seems to grasp 3 dimensionality. Now I remember why I hired you." 

         "You mean the question on the job application, "Describe my concept of a cylinder in complete detail including specifications and possible uses as a metaphor?" I wondered about that question. I thought it was because I am funnier than you, "as such, Suchness". I let that go without remark, you know."

         "That was when you were worried about getting fired. You sure mentioned it quickly enough when that passed," Inventor quipped. "Yes," he continued, "objects can have more than one center of mass in addition to the one in its main center. If the object is irregularly shaped like rope, that main center of mass can shift and even exist outside the object itself, depending on its shape. If I put the line rope into a shape of a circle, though it has a center point running evenly all through it, its absolute center is outside of itself in the middle." 

         "I will now make," he continued, "fully 2 dimensional diagrams using our new extremely expensive laser lines projectors because it is hard to draw it one dimensionally." 

         "I am glad I got this job," Assistwo remarked. "Being able to walk through fully 2D holograms sure is cool. It makes understanding 3D objects easier than our 1D drawings could show." 

         "Yes," Researcher agreed, "holograms are cool and make visualizing it easier. This same concept would apply for a our 3D counterparts. They would have much easier luck understanding 4 dimensionality with 3D holograms made of lasers they could walk through. In the first drawing I have erased all the diagonal movements or desired movements and left only the natural north/south and east/west properties and sub-divided these to squares within squares. Using this we can understand how it would appear to someone 3D looking directly up or down at it. It would look the same from either direction because we know it is even and as I said, its upness and downness are completely reversible to a 3D person from a 3D perspective. That is if it has uniform height throughout its length and width, it would appear the same from the top view and the bottom view. As we see from this drawing, our square can be thought of also as squares within squares all wanting to go in opposite directions. These sections don’t actually exist this big but at a sub-microscopic level of 2D space, and even then mixed in with may more desired movements in all directions not linear. It is just a metaphor for what it means to be 2D. The second drawing I am now showing, I use to imagine what height must look like. It shows opposing squares of upness and downness. We know that when we tip the square panels 90 degrees, the upness and downness become the eastness and westness. Its northness/southness remain north and south, but its eastness/westness displaced now by the old values for upness/downness, now become its new upness/downness."

         "And because these up/down values, the new east/west values, are smaller than the old or original east/west values, it looks smaller from our looking north looking south, or south looking north perspectives, but the old height value now looks larger from a perspective we can’t see," Assistwo added. 

         "Exactly," said Inventor. "These next 2 show it in the 180 degree setting, or completely turned inside out from our points of view. Only the north/south values never changed but because the east/west values are completely reversed in position, the north seems partially reversed with the north left side appearing on the right but still on the north side. The same with the south. The 3rd set shows the thinner to us turned state as before but an exact mirror of the first turned state. Only the 4th turn reverts all values back to normal." 

         "I hate to say it, but this hardly seems to be covering anything new. All you have done is shown proof of what our experiments already have proven out. You may get other Flatlanders to understand now but we already know this stuff," Assistwo said. 

         "You miss the point," Inventor corrected. "We were looking at it from outside of it like a 3D person would see it. That comes naturally for me for some reason. Through working on the cube project, and your cylinder metaphor, you have shown yourself to have picked up the ability to "think" 3 dimensionally as well. This example works so well to explain it to Flatlanders by explaining how it changes as it is turned not from outside looking in, but from inside looking out." 

         "But it does not change from inside out," said Assistwo. 

         "No it does not," Inventor agreed. "Only the way we view it and measure it really changes but by breaking it up into smaller segments, and smaller segments within segments, we can "see" 2 dimensionally as it would seem from inside looking out rather than from outside looking in." 

         "I thought I did that every time I open my eyes. Sorry, I did not mean to leave serious mode. I know this is relative stuff, but I don’t see yet where you are going with this," said Assistwo. 

         "It means "seeing" an object from multiple perspectives at once. From viewing it from its inside multiple dimensional positive and negative values at once, we can more easily understand how everything and its mirror are the same, or stay the same though from any outside perspective they can seem to change when turned or viewed from another angle." After saying this, Inventor got out his 2D replica of a 3D panel in the turned position he loved to use to demonstrate his ideas with, again. 

         "Not the stick example again," Assistwo moaned. 

         "Be quiet. You stand there and watch the stick as I spin it. See how it only appears to get wider and narrower as it moves horizontal to you." 

         "Pleeease. I am not new to perspective. You are not demonstrating anything I do not fully understand already. You admit I am a peer of yours, though I have not heard you use the term "equal", but I can wait for that patiently until or when it ever comes, but surely a peer of yours in the ability to think 3 dimensionally. Why, after all this, demonstrate 2D perspective to me?" Assistwo asked impatiently. 

         "Because you said it yourself. Every time you open your eyes you see the world from inside out. This new example seeks to show the stick and the spinning from inside out irrelevant to position or outside measurement. It seeks to measure the stick only in relation to itself which is how the stick sees itself, to the Universe outside the boundaries of the stick, we don’t matter. We can only understand the matter of anything only from within it out, not from outside trying to measure in, or its shape relative to a world that exists only exists outside its borders, and may not be needed to it at all. I and you saw the stick spinning around because neither you nor I are the stick. The stick saw the room, if it could see, spinning around. It held its shape together perfectly. In this case, it did not matter who was right. Nothing in this minor example was enough to upset the order inherent within the stick." 

         "Ok, I stand corrected, you did have one more metaphor for that thing I did not hear yet. So you are proposing that we turn everything inside out to look at it? I don’t think many things will like that, or our trying to get inside of things so we can measure them. I think that they would prefer that we stay right outside of them where we are now." 

         "True," said Inventor. "If it is true anything of any dimension is simultaneously existing as its own opposite reversible, and constantly reversing itself from one point of view, and irreversible from another, they would not like something outside messing with the order of which is which. But seeing deeper and seeing the reverse image of it in every dimensionality inherent within it regardless of perspective or how many dimensions it is seen from outside of it at once, that is important for 2D people to understand 3 dimensions, and you and I who already know and understand 3, to begin to visualize and really understand 4." 

         "My head hurts, can I have a raise?" Assistwo added. 

2.5:  Confronting your mirror self:  The race toward 4D

         In the 3D world, Researcher was beginning to feel the pressure. Though he succeeded in building the Tesseract, he could not explain what the spheres were and sensed they were becoming unimportant to the storyline anyway. Without an obvious use for the Tesseract, he was endangered of losing his job. Though he thought himself still quite intelligent, he had been reduced to copying all the innovations of some 2 dimensional person and merely adapting them to his 3D world and taking all of the credit. And on top of all that, Inventor now stood poised at explaining even 4 dimensionality better than him. He might even lose that function as well. Worse even than all of that, he was self-aware character in a story who did not even warrant being given a name. 

         "We need to work much faster. We are not making progress fast enough", he snapped at his assistant. 

         "They have not really done much for us to copy..., ahem, I mean "adapt" yet," said his assistant. "All they did was talk and use a bunch of diagrams. Inventor even said we would have a hard time imagining the inside of a Tesseract without a 3D hologram projector. How come we don’t have a hologram projector like they do?"

         "Because they are making progress which is what we have to do. We will just have to make use of 2D drawings and think that much harder to understand and make sense of them." 

         "I don’t have a name either," his assistant said sheepishly. 

         "What?" 

         "I just said, I don’t have a name either. You don’t see me getting upset about it. At least you sort of have a name, you are now capitalized and don’t have a "the" in front. Inventor’s assistant has a name and you don’t see it bothering me any."

         "I am not that upset that I don’t have a name. I understand why and the capital R suits me fine. Don’t believe everything you read."

         "If we warrant names soon, I wonder if that will make me Assistone because I came first, or Assistthree for being 3 dimensional..."

         "I like Assistnot better than either and you know me well enough to know I am NOT joking," Researcher remarked. 

         "You’d make a great one dimensional character," his assistant said so quietly he could not hear it. 

         "What we need to do," Researcher began, "is to understand and explain the essential nature of what makes things 3 dimensional so we can explain reversing it in a way that is intelligible to the 3D people who write our paychecks. If we can explain it like Inventor did, making something its inverse self without resorting to looking at it from a 4th dimensional angle." 

         "Right," his assistant added. "He somewhat explained reversing a 2D object in a way understandable to 2D people without resorting to viewing it as we would, from simply reaching down and turning something over from top to bottom." 

         "Yes, though his way of explaining it seemed limited and lengthy, not once did he say, "You just turn it over." Without resorting to simply viewing it from a 3D perspective, he was able to explain seeming turning things inside out from a 2D person’s perspective. If we can explain how this machine only seems to turn 3D things inside out and backwards, then we will have earned our pay for the week," Researcher concluded. 

         "So what we have to do is adapt his ideas for inner to outer forces trying to both expand and compress the Tesseract into 4 dimensions at once instead of 3. But how do we do that if we can only visualize 3 of those directions," his assistant asked. 

         "What made the most sense to me, and seems like the best place to start is you must understand or "see" into 3D matter and understand or see or visualize its opposite within it. Once you can see it coexisting with its opposite within the same space at once, you are seeing the process under which it goes to seemingly be turned inside out." 

         "I think," his assistant corrected, "you mean see the 4Dness within what appears to us as 3D matter. If it was really 3 dimensional only, we could not seemingly turn it inside out symmetrically through a 4th dimension." 

         "Possibly, possibly not. You might want to ask Inventor that if he passes us. He said the mirror properties, objects have in each of their dimensions of Suchness. He means measurement I guess. That does not necessarily mean only 1 dimension less than the number of real dimensions. Even if we were 3 dimensional only and did not have this machine to prove there is a 4th dimension to seemingly turn things inside out through, the mirror properties would still be there as a direct result of our 3 dimensional nature, not four," Researcher reasoned.

           "Actually I thought we were beyond saying this machine turns things inside out. Didn’t Inventor imply that everything and its mirror image are the same thing and though the cube seems reversed to us, its matter or mass is unchanged within it, and the only thing that is changed is its orientation to this world or the 3 dimensions we perceive?" his assistant asked. 

 "It was implied yes, but worth saying again as you so aptly did. I did not meant to imply that our machine actually turns the cube inside out, though from everything we can see and measure, that does appear to be the case. We may know the cube does not change but we would not have much hope of explaining it or getting anyone else to believe us without being able to give an explanation otherwise." 

         "Yes," his assistant agreed, "you would have a hard time getting anyone to see it is not changed. We might be able to get them to understand how we can seemingly reverse nearly 2D objects (with a non-zero height value) by lifting them out of a 2D world and flipping them over and returning them upside down like flipping a pancake or hamburger, but it does not mean they could necessarily make the leap to understanding how this cube has not seemingly been transformed into its own mirror image." 

         "Unless we figure," Researcher added, "how to use the same method to show how or where an object's 3D mirror exists within it to only seem to change. This does not even require a 4th dimension for it to be turned into to "see" it is in there." 

         "Didn’t Inventor already describe 3Dness when explaining how the panel appeared to be turned into a mirror image of itself?" his assistant asked. 

         "Yes, but only in relation to its 2Dness. That still leaves us the task of explaining 3Dness in relation to its mirror image and in relation to 4Dness if we hope to explain additionally how to seemingly turn it over to its opposite without it actually changing at all from its own point of view." 

         "Then Inventor was right. We need a different way of measuring it from the inside out, instead of from an outside system of measurement of its outer dimensions or projections into "outer" space, outer space meaning any space beyond its edges, be it 2D space, 3D space, or 4D space."

         "Yes," Researcher concluded, "if internal measurements made in relation to itself, if they could be "visualized", we could then see from the objects point of view how it stayed the same and the rest of the world seemed to reverse or spin around."

        "Or," his assistant joked, "you could try getting into a hollow cube yourself while we turn it 180 degrees through the 4 dimension."

         "Don’t," he said tersely, "even joke about that to anyone else. Its only a matter of time before our administration or the military start wanting to us to put puppies or chimpanzees through. I am wondering how we got this far without it ever coming up. If Inventor was wrong and things really do get reversed just like the numbers and measurements of the cube show the cube has changed, not our world in relation to it, if we and he are wrong then I would not want to be here to clean up the mess when something living goes through, and I mean that literally." 

         "Yes, if we are wrong in thinking that the cube never changes or notices anything at all, and something living went through, that could get a little messy. Problem is," the assistant added, "we can’t ask the cube and no one, not even researchers like us, will be satisfied until we can ask the cube, or anything else, what it was like."

3.1:  Contemplating Innerspace and stick spinning in 3D

         "So," the assistant began," as Inventor said, we have to go into the block to understand what happens to it, not literally into the block meaning opening a cover and climbing inside it, but into the matter itself, between its atoms."

         "Simply put, yes we do." Researcher replied. 

         "Yes maybe, but I doubt it will be simple," his assistant remarked.

         "Assistwo was funnier," Researcher said. 

         "Yes, but he was not as confused as me," the assistant said. "If matter is solid, how can we get into it?" 

         "It’s not a matter of us going into it but knowing how it seems to fold around itself from another perspective."

         "From what perspective does matter seem fold around itself?" his assistant asked. 

         "There’s the rub," Researcher said with a smile as wide as his mouth could possibly get. It really freaked his assistant out. He never smiled like that before to his assistant. "From every direction you or anyone could ever possibly see it from." 

         "Why," said the assistant, "do I get the feeling you think you are now over your crisis of confidence of feeling inferior to just copying Inventor’s ideas and applying them to our world? Do you finally see something further than Inventor could see? Have you out invented Inventor? Do you have more insight than him? If you do get a name, will it be Insighter?" 

         "Insighter sounds like someone who would incite a riot," Researcher said. "No matter how big a deal it is to us researchers, we rarely hold riots." 

         "YOU made a joke," his assistant replied, "I think I better sit down for this one. So did you really surpassed Inventor this time?" 

         "We will never know, the story switched back to us before Inventor could explain what he meant. Maybe he saw it fully but I just get to explain what he meant by it. Whether Inventor saw it first or not, I don’t care, that I see it for myself is enough to make me happy." 

         "So tell me then already," his assistant said impatiently. 

         "Within the number of dimensions is the number of directions it can be seen from at 180 degrees opposite. Luckily this book uses squares and cubes for examples instead of triangles and tetrahedrons which I would have preferred. They are simpler shapes and more representative of their respective number of dimensions, but I digress. Here is where using squares and cubes pays off. We can rotate objects any number of degrees in any dimension. 2D people can spin things like Inventor likes to do with his stick. When we play spin the bottle, it is the same thing, spinning it through two dimensions horizontal to the ground, or along a horizontal axis. Inventor’s world only has 2 dimensions so it only has 1 way to spin things. He would love our Universe. He could spin his stick two different ways." 

         "I don’t think I like the sound of that," his assistant remarked. "Don’t we have 3 axises to spin things on? Couldn’t he spin his stick 3 different ways?" 

         "Yes, but only two would seem different. He usually used the stick to demonstrate perspective though more likely it was a model for some other purpose as well. When he spun it most, he was usually trying to show perspective, except that last time when he did it to show how he imagined his panels to be turning on a vertical axis though he could not "see" the vertical axis." 

         "Yes, that really bothered Assistwo. He thought he was doing the other thing with the stick," his assistant said. 

         "Correct, using it to demonstrate perspective on how, when spinning, it only seemed to get larger and smaller when from the stick’s point of view, its shape never changes." 

         "Yes, he hinted that had some meaning toward seeing the Universe from the stick’s perspective outward as well as looking at it from the outside looking in," the assistant added. 

         "Yes," said Researcher, "I will get to that. He had a lot of metaphors for it. But using it to demonstrate perspective in our world, though we have 3 different axises to turn on, only 2 of them appear different. That particular metaphor could make Inventorunderstand stick spinning in a whole new way, that is if he is not so smart he hasn’t thought of it already." 

         "I thought you were over your envy of his intellect," his assistant warned. 

         "Yes, sorry, that was a cheap shot anyway. Even if he had not figured it out yet, it would only be due to a lack of time spent in a 3D world, but he might have figured it out anyway. If he spun the stick on an axis running left to right horizontally opposite to you it would be essentially serve the seemingly getting larger and smaller metaphor. If he spun it on a vertical axis with both tips of the stick taking turns getting closer to you and moving further away, it would be essentially the same metaphor of moving closer to you and further away, thus with the stick only appearing to get larger and smaller," Researcher said. 

         "I get the new way to spin the stick! If it is spun on the axis where all points are equal distance from you, it is not the same metaphor at all, only its position would seem to change, not its size or shape, like looking straight down at a bottle spinning on the ground as seen from directly above. So you have come up with a new way to spin the stick?" 

         "Not for lack of trying. Inventor’s main use was correct in illustrating that its size only appeared to change. He was not from a 2D perspective, able to visualize this like looking down on a top spinning on the ground. He literally mentally had to climb into the stick as it moved through 3D space and see from the stick’s perspective, not itself getting turned inside out, but his world seeming to get turned inside out or get reversed. It appeared as its opposite not because it had changed or reversed, not even that its world changed, but its relationship to that world at every level from inside out was aligned differently." 

         "So without simply describing or imagining just turning it over, he described step by step how its internal orientation to his world changed. Isn’t that the same as turning it over?" 

         "Yes, but from the inside looking out’s point of view," Researcher concluded. 

         "So how many perspectives are there and which are the right ones to look at something through? Well someone had to ask," the assistant said sheepishly. 

         "Obviously, there is no right way to look at something, political beliefs for most not withstanding. There is however how many planes of sight you can line up at once. Inventor could only visually see the stick getting larger and smaller because he only had 2 dimensions, and the minimum required for the stick to spin through is 2, so he could only see it spinning from head on moving toward and away from him. Everything 1 dimensional, 2 dimensional, 3 dimensional, 4, 5 dimensional, 6 dimensional, 7 dimensional, more. Sorry. Everything inherent within its matter, its essence itself, has one common perspective or plane of sight, we can only add to that one." Researcher said. 

         "Away," his assistant said trying to make up for the fact his job sometimes means having to ask the obvious questions. 

3.2:  Away and toward: Love / hate at first line of sight

         "Absolutely," Researcher said. "No matter how many dimensions scientists or mathematicians want to ascribe or believe are within the Universe, there must be one common definition of measuring oneself, from within, and you must too be in that reality to measure it, properties of what existence means. Away, and within. Those are the only 2 choices possible. The way to look at matter best is that to it, there is only an inside and an outside. You don’t encounter the question of how many dimensions exist until you try to go outside out of it." 

         "But I thought matter must have within itself a certain number of preset or prescribed number of dimensions to itself. Isn’t that after all, how all beings must look at it?" the assistant asked now quite pleased with having a better question to ask. 

         "Yes, all beings will see it, no matter how many dimensions they exist in, as having the same number of dimensions as they have to measure it with. A two dimensional being would see it as 2 dimensional because that is how he would measure it. The same is true with 3 or 4 dimensional beings. Find a chunk of matter, take out a ruler, and however many ways you can measure it is how many ways you think there are to measure it by," Researcher said. 

         "It sounds like chicken and egg stuff here," the assistant said. 

         "Anything in existence must be made of at least the number of dimensions it perceives. If the Universe is multi- dimensional beyond that being's perception, it is in a sense irrelevant to that being's perceptual region of space, which is confined to the number of dimensions it perceives. If there are more than such beings might perceive, they should eventually have to understand such dimensions if they are to survive within them. If they could not already survive within it, objects or they themselves, which must be objects within it also, could not exist to be studied. It does not matter if the objects create the number of dimensions of the things which perceive them, or things within them create the number of dimensions through perception. An object contains a scalable number of dimensions," Researcher said. 

         "Dimensionality scalable?" the assistant responded. "I would hate to do the math on that one!"

         "Nor would I," Researcher agreed. "If we are in the dark ages of understanding matter, at least the math is simpler. Getting back to the number of possible perspectives you asked reluctantly, it does hint at a true perspective. Everything in every number of dimensions has an aspect of awayness inherent by existence. Inventor could place the stick, in 2 dimensions, where all points of a long side were equal distance away from him, where it looked widest, and where one point or end was closer and the other furthest away from him. These were the most extremely different ways of viewing the stick. All others can be thought to be a combination of these two ways." 

         "Except that one way you see one side, and the other way you see the other side," the assistant added. 

         "I will get to that in a minute. His reality, and even one dimensional realities, share our, and all realities, away dimension. He could not spin the stick while keeping all points of it relatively equally away from him because the stick needed one more dimension to spin through. Another way to see it is to combine his whole 2D world into a plane we can call a plane of sight. He had one plane of sight, we have 3. To get the math right, we have to understand each plane of sight has 2 dimensional perspectives locked within it. His one plane of sight has 2 dimensions to it, two ways to see something. One of these dimensions we can call the north/south dimension or line. The other is the east/west dimension or line. Along the north/ south line you can be either north looking south or south looking north. Same with the east/west. From all four directions each plane has, is a different way to view something or measure something by. Since we have 3 dimensions, we add to these the up/down direction or top and bottom views. With 4 dimensions, we would add 2 new views, or one more plane of sight. Since only 1 view is common to all dimensions, the measuring of equal distances on a plane of sight all directly away from something, we can line up 2 planes of sight at once. If we could see or experience four dimensional sight or perception, we could line up 3 planes or lines of sight, or 3 planes to measure. Only one, in no matter how many dimensions you add, can never line up with the others, the plane that runs perpendicular to the away from you line of sight, where both ends of the stick are at equal distance from you. That one is always different," Researcher said. 

         "What do you mean by line up?" the assistant asked.

 3.3: Multivision lines of sight coming to a theater near you

         "See from both or all perspectives at once," Researcher said. "Each plane must be at a 90 degree angle to all others. A square extends 90 degrees out from a line or a 2D version of a line. Put a square on the floor and extend it 90 degrees up from the other two lines of sight and you have a cube. Since every plane of sight is like a 2D view of the world and every line of sight is like a 1D view of the world, imagine taking a square card or paper and making a giant plus sign down the middles from left and right and top and bottom so that it looks like 4 squares. When you look at it edge- wise, you can’t see the plus sign on the top or bottom. When you can’t see the plus sign on the top or bottom, you have lined that plane up with your sight. Take 3 square cards with plus signs through the middle of them and cut them and place them at right angles to each other so it looks like a 2 by 2 by 2 cube stack with the outer shell missing, the outer edge that would make it look like a cube. That is what 3 planes of sight look like. You can and must line up 2 whenever you take the 3rd and make its points of equal distance from you, looking at one plane of sight directly head on. The other two come together making straight lines or a cross pointing straight at you. They line up."

         "With 4 dimensions," Researcher continued, "like the others, there is always the away line of sight or dimension. When you when you make all points on that perpendicular plane all equally distant from you from the center, looking at it head on, all 3 other planes line up or appear so thin they virtually disappear because you are seeing them edgewise. No matter how many dimensions you can add that have right angles to each other, if you turn one or see one equally away from you at all its points, all others automatically line up. Using Inventor’s stick, if you had it spinning on a plane like a clock looking straight across from it, all other dimensions would line up perfectly. Stay exactly in that position or view, and measure from that angle spinning sticks on any other planes 90 degrees opposed to all others and they would spin toward and away from you exactly as with Inventor, seeming to get larger and smaller as first one end comes closer to you, then both are equal distances, then the other end comes closer to you. If you are familiar with these dimensions, it is not surprising to you as it would be to a 2D person, knowing he is simply seeing the stick at different angles relative to the away dimension from where he happens to be standing, looking from, or measuring from."

         "So another way to describe planes of sight," the assistant replied, "is the opposite view. Instead of imaging the inside of a 2 by 2 by 2 cube with glass windows instead of walls and 3 different 3D plus signs interjoined which we can visually line up 2 when we see one square head on, we can leave the side on the cube and say the lines of sight run through the middle of the cube between each of the 3 sets of opposing sides."

         "Right, we can keep the sides on the cube if we keep in mind each side of the cube represents half a line of sight when we look at it head on so it looks like a square instead of a cube. If we flip it or go around so that we can see it from the exact opposite side, that is the other half of that line of sight. Each line of sight can be thought to have identical but opposite views, positive going one way, negative when looking back from the opposite way," Researcher said. 

         "So the 4 sides of a square to a Flatlander represent, when seen head on with all points of a side relatively equal in the away direction of measurement, each 2 opposing sides are each halves of 2 possible ways to see it, north/south and east/ west with one way, say north, being positive and south being the negative aspect of the north view. And the same would go for the east/west line of sight, giving one a positive value and one a negative value, but why?" the assistant asked.

         "Because we still think in terms of seeing or measuring everything from outside looking it. That is why we don’t see a square’s opposite sides are different parts or mirror images of the same view to us. Though we readily see and understand each pair’s relationship to its opposite side, we still commonly think of them as four equal sides. The same with a cube or dice, we look at it and see six sides, not 3 views of positive and negative angles." 

         "Aren’t you just dividing everything by two and saying they have positive and negative aspects?" the assistant asked. 

         "No. We may ascribe however many viewpoints or planes of sight at however many right angles (dimensions) to each other we can imagine, but once you add one dimension or way of looking at something, you must see it in terms of a pair possessing an equal but opposite angle or you are not seeing what you added at all." 

         "You can’t add an up direction without creating a down," the assistant said. 

         "Precisely. If Inventor thought he could add a dimension of height without realizing it must run in 2 directions at once, he would not have gotten very far. What goes up must be able to come back down. If something has an upside, it must also have a downside. And he knew when he turned his square and one end went into an upward dimension or area, the other end, if braced in the middle like a see-saw, the other end would go down in an equal amount." 

         "At least with the clichés you were throwing around, you did not say that you can’t imagine good without also creating the notion of bad," the assistant said. 

         "It seemed too obvious to need to be said, but if slightly not completely obvious, that is what you are here for," Researcher said with another big smile. 

         "Another joke, my you must think you have found out something really good today," the assistant remarked. 

3.4:  Researcher’s good day: Positive and negative lines of sight

         "I can understand now why you matched up perspectives or planes of sight into pairs," his assistant said, "but why call them positive and negative?" 

         "When we look closely at mirroring objects or how they can seem to be mirrors of themselves, seeing how the left and right views are not really 2 different views at all, just positive and negative aspects of the same view, it will become critical to reaching any understanding," Researcher said. 

         "How do we decide which to call positive and which to call negative," the assistant asked. "and can it possibly matter?" 

         "Obviously if they are equally matched pairs of a line or plane of sight, either one can be thought to be either positive or negative, but once you decide which is which, you have to keep it that way throughout all subsequent equations or motions through other dimensions. A good way to think of why they are positive and negative is to use the common away plane relative to every dimensional system of measurement common to 2D, 3D, 4D, etc. As I said before, once you map out an away line of sight or unit of measurement with a plane or wall with all points on that wall flat in a perpendicular direction away from you, you have your first best system of measurement."

         "Yes, and all other planes of sight would line up perfectly. We covered that already." 

         "If I may, thank you. Now once you establish that plane you have your first and best line of sight common to every dimensional interpretation. Now put an object in front of you in any dimensional space. Now perpendicular to that plane is a line of sight heading from you to that object at a 90 angle to that plane. We will call this the true view, what we would call head-on. This is the only view we have to it at the moment, so we will call it the right one. This is the positive view of the away direction or dimension or line of sight which can never line up with the others. This line of sight passes through the object. Once exiting, outside the object, as that line of sight continues one can imagine it now has a negative value. Positive values along the line to it, negative values beyond it. We have mentally shishkabobed it!" Researcher said. 

         "That does not seem like a good system of measurement if it only gets negative values when exiting. It is not providing enough info about it," his assistant added. 

         "That zero value," Researcher explained, "between where one end of is mass begins mapping the positive space in front of it and the negative aspect of space behind it is a world unto itself. We need a whole new math for that. All we have done is to have decided on which end to call positive and which end to call negative. To the object, either will do. Along this line sight we have imagined, either can be either but we need to call one positive and the other negative. Now that we have our first plane of measurement, all other planes we can imagine pass through since we can see now how they will line up. Since we can think in 3D, we can imagine we have skewered a ball right through its center directly in front of us, or a dice right through the number one looking straight at the one side directly facing us. The first line of sight runs from us through the center. The second we will imagine is a 9 o’clock or left passing through that center we have established going to 3 o’clock on the right. The third we can have coming top down from 12 o’clock to 6 o’clock. The positive values are 9 and 12 o’clock where we will imagine they seem to go in, and the negative aspects of those views are 3 o’clock and 6 o’clock, where we imagine the lines of sight upon exiting now become the same lines of sight negative aspects, the reverse views." 

         "I fail to see what you are getting at. If we wanted to measure something we don’t need to shishkabob it. We can do that far more accurately from outside of it with a lot less conceptual damage to it, even if hypothetical or allegorical, I doubt anyone would like to be even figuratively speaking, shishkabobed. Besides, all the points between equal zero by this method inside the object, and only have values when leaving it," the assistant concluded. 

         "The idea is that the numbers we give to it match or correspond to its existence in our world, measuring it from the outside we can only do from outside. The units of measurement we shishkabobed only have values outside the object because there are one set of rules for the outside world and another for what goes on inside. We think of dimensionality existing created by objects existing between them. If we see three dimensions in them, we assume they and we, because we are objects we perceive, are also 3 dimensional. In a sense we believe 3 dimensionality lies in there if they come first, or lies out here if space comes first. If space comes first then, we speculate, it is something about the nature of space around the objects  which cause them to take a 3D form. If on the other hand, if matter creates space and objects really are 3 dimensional only, we only perceive space as 3 dimensional because all the objects that we can perceive anyway, say it is. Measure it from out here by the dimensions out here all you want, either way you will get the results you expect. The answer, if any is definitive, cannot be found in the outer space between matter but the inner space of how things look from the inside out." 

         "Ok, if matter really is 3D is what you are trying to prove, isn’t it time to switch back to Inventor? No offense, but he is smarter than you and proving the world was 3D was his job before getting all ambitious and getting into our turf of explaining how the world is 4 dimensional. Remember the Tesseract we built? Explaining that was our job," the assistant said. 

         "Actually, Inventor was onto much more than 4 dimensions. See this Styrofoam ball I stuck with knitting needles and the cube skewered just like I said. I did it while you were talking. I know it is my job to stick in a fourth one at a right angle equally to those 3 which are all at right angles to each other, or I won’t have a job much longer. Watch as I now do the impossible. Tah dah!" 

         "Nothing happened," the assistant exclaimed. 

         "That is because that needle is only imaginary to us. Even Inventor could not have done it any better, except maybe leaving out the "tah dah" part. That needle is not visible to us but watch as I turn the objects with the miniature turning machine based on the big one we have for the blocks. Remember, there is always that line of sight where all points of a plane are equally away from it from the away angle and all other planes match up so perfectly they fit exactly together so they seem to converge? Watch as I attempt to turn these objects to that view in 4D space completely away from us."

         "They disappeared. Cool, now bring them back." 

         "I can’t." Researcher said. 

         "Why not?" 

         "Two reasons possibly, one for sure." 

         "Well, what is the for sure one?" his assistant asked. 

         "The for sure reason I can’t bring them back is that I did not have a pivot point like that band around the block to hold it still while we turn it around keeping part of it always in our space or dimensions. Without that we would not have part of it still anchored in our world at all times to know where it went or how to bring it back. Inventor did the same thing in the middle of the squares to turn them around up and down around the middle like a fulcrum of a see-saw," Researcher answered. 

         "Great, so now we have a ball and cube each with 3 sharp giant needles floating somewhere around us in parallel space. So what’s the other reason in case they come back?" 

         "They won’t come back unless someone in a parallel 3D world or a 4D being knows what we did and knows how to send them back. In that case just watch where you step. The other reason I think they probably can’t come back, besides the fact that I lost track of where they went, was because they might not have been 4 dimensional to begin with. What I did was turn all the angles of the knitting needles 90 degrees at once to our world. With the blocks you remember, we cheated and increased their amount of 4th dimensional volume so we knew it could be done with the blocks, conveniently leaving out how we did that. Since I left out that step this time, if the ball and cube with needles through them did not have enough of that 4th dimensional "width" or whatever you want to call it, they dissipated or disappeared."

           "You bastard!" the assistant exclaimed. "Sorry, now I really miss them knowing they can’t come back." 

3.5:  Finally, let’s get small

         "So how did you do it, add another line of sight at equal right angles to all the other lines of sight, also all at right angles to each other?" the assistant asked. 

         "I couldn’t do it, remember?" Researcher responded. "I didn’t know how to do it 3 dimensionally because you CAN’T do it 3 dimensionally. I can however demonstrate what it would look like if there was a needle in that direction, then grabbed that needle and turned it completely opposite to us in a 4th dimension so that the other dimensions which we can perceive seemed to line up perfectly and therefore vanish completely outside our space as if one of Inventor's panels broke loose and flew off out of his 2D world. Let me show you with the cube of needles where the 4th needle would go if it were not just imaginary. Let’s see, where did I put.... Oh, right. Well, never mind. If we could imagine such a 4 dimensional needle, perspective or viewpoint, like all 3 regular needles, we can see that needle would have to pass through the center and have to be at a 90 degree angle running no closer to any one needle to any other. This can only be done in 4D space or in a 4D object with us perceiving all of its 4 dimensions at once. Since I cannot show the 4th needle passing through the center, I can show where it would be in 3D space if we could see it, or a 3 dimensional shadow of that magic 4th needle." 

         "But that is 4 needles, not one," the assistant remarked. 

         "Yes, since the cube is 3D and the needles representing the 3 possible to us "normal" perspectives look right, the only thing left to be still confusing to us is the 4th needle itself. It thought it best to work up to the rest slowly," Researcher said. 

         "Keeping it simple worked, at least for me," the assistant answered. "Since you said everything else here is 3D conceivable, the 3D cube, the 3 positive/negative needles or perspective angles, the only part that would look strange to a 3D person would be how to show or draw where the 4th needle would actually go. Inventor would have had the same problem. He could show his squares with a giant plus sign in the middle of it representing 2 lines of sight, but he would be hard pressed to draw the 3rd axis or line of sight would go. He would know it passed through the center, but to only make one more line, it could not be equal in angles or distance to the other two. Any place he would put it would not seem right. He could make 2 diagonal lines and say they are both shadows of the same line and still have it look symmetric and equal distances from the other lines at 45 degrees to each. Since each of his diagonal lines is really a mythical half line, they still are mathematically only 90 degrees apart in all directions!" 

         "The same," Researcher concluded, "holds true for these lines. Not one of these lines is actually where the line is but is 1/4 of where it potentially could be seen as a 3 dimensional shadow. Like Inventor’s two half lines are the best symmetrical model he could make of how the 3rd  perspective or viewpoint would run equally in opposition to the others, these quarter lines if you combine them all show our puzzling fourth line or axis viewpoint as Inventor might have drawn his puzzling 3rd line or axis viewpoint." 

4.1:  To confuse or not to confuse: Problems with the 3rd Axis

         Assistwo interrupted Inventor. "I have to demonstrate the positive and negative aspects of the puzzling 3rd axis or viewpoint essential to how your cubes work to a bunch of investors tomorrow, and I was wondering how you used to demonstrate this."

         "Everyone seems to be wondering about that these days." Inventor said. "Everywhere I go all of a sudden people ask, "Explain how you demonstrated the 3rd axis to people so they could understand." It used to be, what is a cube and why did you want to or bother to build one. Either everyone conceivable has already asked me that now or my whole world has gotten thrown off onto that 3rd viewpoint. Hey, that gives me another new idea on how to explain it. For me, there are at least as many ways to imagine and explain that viewpoint or the so-called 3rd axis to people as there are metaphors in this 20cm by 1 meter stick." 

         "Not the stick again," Assistwo moans. "Sheesh, can’t you explain anything without that." 

         "No, none of them include using the stick. I just said there were as many ways I can explain the 3rd axis as there are metaphors I can use that stick to demonstrate with. But now that you mention it, I just thought of one more for each."

         "In answer to your question," Inventor continued, "it would depend on who I am talking to. For awhile I drew a diagonal line from the northwest end to the center and colored it blue for the "above" direction, and one from the center continuing on to the southeast corner but colored in red to signify the "down" direction. Then everyone kept asking "Why are there no lines in the northeast or southwest corners? Does the 3rd axis like the northwest better in the "up" direction?" For awhile I put another blue from the northeast to the center, and another line from the center to the southwest. I said the 2 blue lines were shadows of the same line from 2 lights above and really the same line from different angles at once." 

         "Did that help?" Assistwo asked. 

         "Many just concluded that "up" was really in a somewhat northerly direction up from Flatland and was colder because the lines, if they did indeed converge somewhere, were both headed northwards and were blue, while down must be somewhere in another dimension south of flatland and warmer because the lines were red." 

         "It may sound silly to you that they made that conclusion off of random colors and random orientations. Who knows, maybe in a 3D Universe that is true."

         "You are forgetting," Inventor said, "even if it could be true, which it can’t, it would also have to be opposite as well if the points of view were reversed. "Up" would also mean south and be colder and "down" would also have to mean going north and be warmer from the reversed axis viewpoint or point of view..." 

         "What?" said Assistwo. 

         "I don’t know, I just kept looking at that circle and was thinking of a sphere, and it was kind of making sense to me. Weird. I think I am losing it when I try to makes sense of irrational illogical ideas like that. What if I used purple and orange, and they came up with something for that too? Would I try to make sense out of that too? Still, I keep thinking of a sphere..." 

         Assistwo asked, "You said you explained it different ways to different people?" 

         "Yes, with a group of Physicists, you know how complicated they like everything to be, they asked, "How can the blue line be over here and over there at the same time?" So I said to them, "There is a 50% probability it is over here at any given point in time, and a 50% probability it is exactly there." They like that sort of stuff. Then they asked "What makes it ever be in one place over another?" So I said Measuring it. It is only potentially in either place until you measure it, then it has to decide, the line that is, where it "wants" to be."" 

         "Did they believe you?" Assistwo asked. 

         "You know that great big new building at the college? What is it, yes, the Heisenberg Building. That whole building is filled with scientists studying the idea. I can’t even show my face at the college anymore for fear I might run into one of them." 

         "Why?" Assistwo asked. 

         "I think it would be a little late to have to admit at this point that I was only joking. You know how Physicists don’t have a sense of humor about these things." Inventor said. 

         Assistwo agreed and added, "Do you have any other non-stick related ways of explaining the 3rd viewpoint axis which is invisible from our perspective?"

         "I will ignore the stick comment and show you since I also love to play with this new holograph 2D drawing machine. Now I like to explain the 3rd axis viewpoint using time and these full 2D drawings we can walk through. Here is the square and we see the 2 viewpoints with positive and negative aspects of them that we can visualize because they interact with our perception of space as well." Inventor explained. 

         "I know this from high school geometry, where do you put the mysterious 3rd axis viewpoint now?" Assistwo asked. 

         "I don’t put it anywhere because we can’t see it from our points of view. Actually that is not completely true on two counts. One, it does intersect with our world at a 90 degree angle to the existing real world north/south and east/west viewpoints but only at one point which is not really a point in our world as a point is zero and just a mathematical construct. The other count being, that I have made this center point where all 3 axis or viewpoints merge intersect a little bit brighter to show that at this point, all 3 axis or viewpoints merge, north/south, east/west, and the up/down one we can only imagine where it goes from there." 

         "Though technically more accurate," Assistwo concluded, "by not drawing something we can’t see, it is hardly a more evolved way of representing the 3rd axis. If I started with not drawing it, I think even a flawed attempt at getting people to think "up" was diagonally "up" north, and "down" was really diagonally down south in another dimension and warmer. Heck, even the Physicist’s trying to catch a line that only moves or exists when you try to measure it, everyone has, if not a great rendition of the idea, at least a concept of it. It seems your new idea is just saying the 3rd axis is just an invisible idea or dot which is not a dot which starts here and goes forever in 2 directions at once, neither of which you can or ever will see. I like either of your flawed explanations better." 

         "If you are quite finished, I will continue," Inventor said, knowing what he had in store was worth irritating Assistwo a little bit. "OK, before I show you this demonstration which is really cool, interactive, as well as fully 2D with lots of lasers and cool mind-bending stuff, I must sadly pause because you said something I have to disagree with first. It is not necessarily better that people think they understand something and only understand part of it, than to not think they understand anything and still understand part of it. Both my examples did enlighten others about where the line is in relation to our world, but also gave them misconceptions about it as well. Most people who mentally combined the blue line ended up thinking "up" though not now simply in the northwest, at least vaguely having something to do with the north. The Physicists see clearly neither the northwest nor northeast is representational and is subject to change with your point of view, but they think that "can change" and "does change" are somehow related or the same thing. Yes, both groups know something more about it than simply saying we can’t see it. Each sees it in both a way that is right and wrong at the same time, or part of it. That part of it they do see, my fault partially, also can and will get in the way of seeing it more clearly in the future. Their knowing they don’t have the full picture makes up for my bad examples, but those who simply see it in the center and know it also has to go in two directions from there opposite each other into a place they don’t know where, I believe their imagination alone will get them to a fuller understanding faster than those who already think they know something about it, and do, but will always be tripping over what they think they know while trying to get to what they don’t know. Not knowing anything and starting fresh, often one must come back to again and again anyway, so it is also the best place to always start from." 

         "So if you really believe that your examples might be confusing them as much or more than your are simultaneously enlightening them, why keep trying to improve them then?" Assistwo asked inquiringly. 

         "Because not giving up is important. Sometimes you need to try and fail many times to reach a better solution than if you found one "good enough" right off the bat. Each time also I learned what not to do the next time, and that is as valuable as knowing what to do." 

         "Are you," Assistwo began impatiently, "going to start the as promised super cool fully interactive fully 2D laser new, improved, and not so prone to confuse people into believing wrong things about the up/down axis viewpoint demonstration now?" 

         "Can’t we start now would have sufficed." Inventor said, "I thought you would never ask." 

4.2:  Into the belly of the whale

         Inventor loved showing off his new way of envisioning the up/down axis. In a large room, getting north of a large holographic square, he prepared to follow the north/south laser marking the primary "true" viewpoint for the demonstration and motioned for Assistwo to follow him. He had a small computer readout screen with a keypad he used to control the 2D hologram as they walked through the drawings. For a 3D person, it would be the same as being able to walk through 3 dimensional shapes made of light. As he and Assistwo walked south along the laser marking the north/south axis or viewpoint, he showed Assistwo the closer they neared the square, the keypads numbers kept going down toward zero, finally stopping just above zero as they stood beside the square. 

         "Now what?" Assistwo asked. 

         "Now we go in," Inventor said, and they walked through the laser’s hologram walls into the square. The numbers on the small screen Inventor carried were all over the place, extremely high positive numbers, low numbers, high negative numbers, zero all back and forth in no particular order. "Outside rules don’t apply in here," Inventor said. Up ahead of them they saw a bluish wall made of laser light. "That is the east/west line of sight", he said. 

         Assistwo knew exactly what he meant. It meant that they were nearly halfway through the square. The east/west viewpoint or axis wall was at the exact halfway point between the ends of the square just like the north/south imaginary middle wall they were following. Directly ahead of them was where the east/west view crossed the north/south view they followed, and at the exact point where the two views crossed in the exact center of the square they would be able to "see" where the mysterious north/south axis or viewpoint would intersect their space. As promised, it was only slightly brighter. 

         "That’s it? Make all of this just to show only that? You could have made it another color or blinking or something. With all these fancy lasers, you could have made it stand out a little more," Assistwo said. 

         "It is supposed to be invisible and only a point in our space, but I thought giving it a minor indication was warranted." Inventor continued, "None of this is the drawing. The experience is the drawing. This is "Cube, the ride"."

         "I hope you don’t plan on charging for tickets," Assistwo chimed. 

         As they neared the south wall of the square, Inventor held right the keypad’s screen so Assistwo could see it. "Watch as we prepare to enter real space," he said. 

         Right when they passed through the south wall the screen started back in a normal progression of numbers from zero counting backwards as they moved away from the wall. -1, -2, -3, and so on. 

         "That’s it, that’s all?" Assistwo asked. 

         "Now turn around and walk backwards," Inventor said. 

         Assistwo understood this as being the negative view which would be a mirror of the normal view and should have supposed this would happen, but Assistwo did not like to walk backwards. 

         "Ok, what did you see," Inventor asked. 

         "You means besides a waste of potential for a really good laser show? Ok, ok. I know what you mean. Following the north/south viewpoint perpendicular to the east/west axis viewpoint the square appeared to get larger but the numbers showing of our positive distance got smaller as we got closer. On the other side of the wall," Assistwo continued, "the numbers changed erratically without any seeming order until exiting the south side where I was told to turn around and walk backwards. A little too interactive in my opinion. Then, instead of getting larger it seemed to be getting smaller. The numbers returned to zero when we exited the square and continued still going backwards from zero even lower into greater and greater negative numbers. Ok, lots of questions. First, why did the numbers stop at zero and start up again at zero as if the north and south walls were the same thing and nothing in-between them existed? Is this a matter of bad programming on your part or am I to believe that the inside of the cube has no measurable properties?" 

         "Instead of measuring the cube, or square since no 3D aspects were involved except the up/down axis viewpoint," Inventor began, "we were measuring how the square sees the Universe, and how the square sees itself. They are two different ways to measure existence and different rules you must apply to either one depending on what you want to measure. The square sees the world the same way as we do but is not as confused about where it starts and ends. The square, without having different parts that keep moving all the time, is much more sure of where it stands so to speak. Space and everything else in space that is not itself begins at its borders and counts away from them." 

         "But why forwards in one way and backward in another?" Assistwo asked. "Isn’t then, everything else just away?" 

         "That is a problem. For our purpose of keeping things clear in the fuzzy logic world of inside matter, it helps to have a clear idea of which way is up, so to speak. You might not get lost literally passing through but sticking to one common point of reference to follow before, during, and after, makes connecting all the dots easier which is why we choose one viewpoint to follow. My keypad kept track of our movements’ time and speed, and the lasers will simulate to us what we would see moving from down to up through our world, and the cube we have built slightly above and below it."

         Inventor motioned for Assistwo to stand around a small point around the middle of where the square had been. "Going up?" he asked with a smile. 

4.3:  Riding the hidden line of sight

         Assistwo could assume everything he was going to see now before he saw it but played along, not just to make Inventor happy, but because he really saw how much thought Inventor had put into the project. He had come a long way from diagonal red and blue lines that were only half lines in two different places. This was much clearer to him it seemed, and though he already knew all of this, he could not see how others could misunderstand it. He then thought, "But Inventor knows by experience, if there is a way to misunderstand even this, others will find it." But then he thought with a grin, "But that just means Inventor will start fresh looking for an even simpler way to explain it." 

         "Which way is positive this time?" Assistwo asked. 

         "Up is. We are almost nearing zero now," Inventor replied. He too was happy not to have to walk backwards this time. This "trip" merely meant standing next to the dot "line" represented the up/down line of sight while the lasers simulated what one would see on a trip upwards. As long as one stood by the laser dot, one would see what a 2D person would see all around him going "up" an elevator with the cube and their whole 2D world or Universe merely a single floor.

         The room was black except for the dot. "What happened to the idea of parallel 2D worlds?" Assistwo quipped. 

         "We are going for simple, remember?" Inventor reminded. 

         In an instant they passed through the bottom wall. Now they were in the cube’s bottom half and the square as they saw it before was all around them. Inventor had not added colors yet so the bottom half looked no different that the north or south halves did. 

         "It did not matter," Assistwo thought, "even the investors should understand it even without colored sections." 

         "What have you done to the real world?" Assistwo asked. 

         Now that the cube was around them, though they were really just standing in an empty room, Inventor knew Assistwo was asking what would be shown to signify the passing through their 2D world. Suddenly the lasers depicted them in the middle of an amusement park. It was nighttime. All the rides were lit up and spinning around, and people were walking about. It all caught Assistwo completely by surprise. After a slightly brighter dot signifying the up/down viewpoint or line of sight, merely turning on the lights of the room signifying the end of the "ride" would have been a shock. He was awestruck. In a flash it was gone and only the cube appeared around them again. 

         "A cube ride through and for amusement parks. The investors are going to love that. Now I know why you did not have time to color in different sections of the cube."

         "We have to pay for all this cool equipment somehow," Inventor said. "We are coming up to positive space now." 

         In another instant the cube was gone and just the blue dot remained with only the numbers on the keypad to show they were still supposed to be moving. 

         "Great ride," Assistwo said, "would have been better if we knew how to look up or down." 

         "I do have one where the north/south viewpoint axis represents our world and you pass through it while walking from west to east, but all you see is blobs of colors while looking at our world sideways. Other than that it looks the same as the first trip we made from the north to the south. I bet a 3D person could understand seeing his world while passing through it sideways but it would probably not be something people would want in amusement parks." Inventor said. 

         Amusement parks are very conservative and mostly boring in Flatland. The lack of a vertical incline means all of the rides just spin you around until you get dizzy which most Flatlanders can (and do) do at home for free. 

         "Your comment about not being able to "look" or "see" or "comprehend" in an up/down direction was very intuitive. The numbers and the turning around and walking backwards shows the square seeming to get smaller in each of its "away" directions. While going or following the up/down line of sight, likewise we would have seen the same thing when approaching the cube and leaving it as we saw from the north and south trip we took. It would seem to get bigger as we got nearer to it and smaller as we moved away from it," Inventor said. 

         "Whoa, I get another picture here. When you said," Assistwo added, "you turned our world sideways in one of your simulations, it too, like the cube, would seem to get bigger as we would get closer to it and smaller if we turned around once we passed through it. If we could have looked in the up or down directions while following your up/down line of sight, we would have been able to "see" our whole world appearing to get smaller and smaller as all of it equally at once was moving in our "away" direction. Have you come up with a name for it yet? The ride I mean." 

         "I am thinking of calling it, The Elevator." 

         "A little grandiose, don’t you think?" Assistwo quipped. 

         "Names are not important. I have already thought of what we would "see" if we could see in the up/down direction while approaching our world and leaving it from the up/down line of sight, if we could see in or combine 2 lines of sight at once. Would you like to see it?" Inventor asked. 

         "Are you kidding?" Assistwo said, "Let’s ride!"

         Inventor again hit some buttons while they stood in the center of the room. This time 2 squares kept getting bigger around them. Because they were made of laser light, they could see both at once. 

         "The inner square is the cube. The outer square represents a section or a bigger area of the amusement park around the cube. It is important to note that the sides of the square we see around us are the outside edges of it, as if it was turned inside out all around us. We won't see the inside edges of it until we pass through its wall. The same goes for the outside area around the square. It's objects too look smaller than they should be and are all around the square seemingly inside out as well, and appearing get bigger and appearing to all move closer to the square and closer to each other as we get closer to entering the cube. Now watch as I now run the program of the people and the rides and remove the cube so we can see them better," Inventor said as he pushed some more buttons. 

         As the inner square vanished, the simulations of the people and the rides could be seen but too small and grossly distorted, though getting bigger and clearer. As they passed through the real world plane, they were back in the amusement park again, but then everything started to get smaller and more distorted again, moving away from them and away from each other in all directions, Just as everything in the park was too small before but getting bigger, now everything was getting smaller as the whole section of the amusement park shrank around them. 

         "So that is how it would look in 3D vision," Inventor speculated. "Similarly if a 3D person were to be able to perceive 3 lines of sight simultaneously but traveled in a 4th perpendicular or at 90 degrees to all other 3, or "away" equally at once to the 3 he could perceive he would "see" if only he were able to look from that line of sight, his whole world seem to shrink when moving away from his world in either direction from that line of sights version of "up" or "down"." 

         "Though it would simply be a matter of perspective," Assistwo agreed. "Things only look bigger and smaller in your relation to your distance from them. If there are 5 dimensional beings who could see or line up 4 lines of sight, following the fifth mentally perpendicular to the four they normally see at once, they could only imagine it as their world seeming to be getting smaller as they moved equally away from all points of it relative to their position at once. So how many dimensions are there?" 

         "Maybe infinite, maybe none. Maybe they only exist in here," Inventor said pushing a button to create the square back around them again, "or in here." 

         He pushed another button and they stood inside a full 2D simulation of a brain. 

4.4:  2 ways of getting small

         Meanwhile, back in the 3D world, Researcher’s assistant was trying to get his own investors to create a ride through simulated 4D space. While he could not imagine how to make the whole 3D world seem to shrink as a 4D person might see it when moving away from it, passing through a 3D world in the "turned" position definitely sounded promising. 

        "So this is why things seem to get smaller and disappear when we rotate them into 4D space", he said to Researcher. "They are moving away relative to us, as our world would seem to get smaller from the line of sight or perspective they are following."

         "Correct, and there are 2 directions to that line of sight of that extra dimension you imagine perpendicular to the ones you normally perceive, 2 ways for either the object to seem to get smaller relative to your world, or for your world to seem to get smaller following that line of sight away from all points in your world equally or at once."

         "Because we have glass elevators," his assistant said, "it is easy to understand moving up and looking down on an amusement park and seeing it seem to get smaller and still make sense of it all." 

         "Right," Researcher said. "We understand 2D and 3D worlds equally as well thanks to gravity. The "ground" of our 3D world is actually a 2D world we are confined to almost every minute of our lives. We are not Superman. We can’t without machines simply go up and over obstacles unless they are very small or we can find a 2D path to follow over it which we can get some traction on. The only thing that is hard to understand of the elevator example is the negative view with the same distortion effect would occur in both directions. In space it is easier to visualize. If the elevator went in both directions through the middle of a space station, looking at it getting closer or further away from either direction up or down would be the same kind of distortion." 

         "Since we know our normal everyday regular cubes have a very small 4th dimensional value in that direction," his assistant concluded, "turning it either way in a fourth dimension would make it seem to get smaller as the part we are tipping "in" is smaller than the part we are tipping "out". From the objects point of view at the part we tip out, our world is getting smaller as our normal perceived 3 dimensions are all moving in the "away" direction at once. So if everything has four or more dimensions, what causes anything to be locked into realities? Why aren’t things rotating all the way into and out of normal 3D space all over the place? Why do we need a machine to "coax" parts of the cube into a 4th way of rotating equally "away" from our other three?" 

         "Because they like it here?" Researcher joked. "I can’t say yet. We have only started entering matter in this story. That will have to wait for a bit while we consolidate the ground we have covered thus far. We know from the objects point of view, its shape does not change relative to what dimensions it happens to be in or looked at and measured from at any given moment. It is only that we think we are "seeing" or "measuring" the entirety of it. Since we know our "walls" of our 4D cube are less than 1 meter in the 4th dimension, it is hollow."

         "Right," the assistant added, "if it was fully 1 meter in each of its 4 dimensions, and we put all 8 in place, it would be a solid 4D cube, what we call a Tesseract." 

         "Yes," Researcher said. "It has to do with the way that we cheat and add to its 4th dimensional value. If we did not stop a 20cm but kept going all the way to 1 meter so that it was 1 meter in all 3 of our dimensions plus 1 meter in the fourth, we would not need 8 cubes. We would then have created a solid 4D cube already, though it would have no function. By making 8 "sides" made up of cubes, and putting them together we have the same 1 by 1 by 1 by 1 meter 4D cube but with a hollowed out center. If we or Inventor kept the enlarging process going all the way to 1 meter in the extra dimension, when we turn it 90 degrees it would seem the same size, though we still are not seeing it from the same side or the same angle because all of its dimensions would be the same from every direction, including the extra one."

         "Yes," the assistant agreed, "without wanting to make it hollow there would be no point in Inventor assembling a cube of square panels if each of the squares was or could make a cube by itself. The thinner we keep the extra dimensions thickness, in our case the 4th dimensional value,  the larger the inside of or 4D cube or Tesseract will be. Instead of 20cm, we could use 5." 

         "Exactly, we don’t know how small yet we can go except that it has to be thicker than zero and that we have to have a square around the middle of the cube to pivot it around. The thinner its 4D’ness, the smaller each cube "side" will appear to get when turned in either direction in an extra dimension directly opposed equally to our other 3. The closer that thickness in that dimension is to zero, the closer it would seem from our points of view to be vanishing. The thicker its 4D’ness, the thicker what remains of it will be seen as existing or remaining in our normal dimensions of space."

         Researcher continued, "If Inventor had used smaller cubes, cube shapes with very little height extending above and below his world, when he did the up/down simulation, he would have had the entering the cube times a shorter period of time before entering the amusement park, and the exiting time closer to that time as well." 

         "So by simulating following a viewpoint through space, he was using time to visualize or represent a dimension he could not "see"," the assistant added. 

         "Yes, time can be used interchangeably with any other dimension you want to visualize or try to understand. If we had his budget and a holodeck, we could illustrate moving through our space on a 4th dimensional line of sight also using time. Though we cannot look "up" or "down" in that direction, like Inventor and Assistwo couldn't look down from their elevator, we would not be able to "see" our world coming closer and seeming to get bigger when approaching it, or look back after passing through it from away from it to see it appearing to get smaller, we can use time to represent the rest of the journey along that line of sight. Like their 3D cube appeared a square to them, if we stood inside a large 4D cube or Tesseract, it would appear as a normal cube to our level of perception. While traveling "up" from some other dimension along a fourth line of sight passing through the middle of our Tesseract, and there are no parallel 3D worlds above or below us in that dimension, we would first see nothing, then a normal cube around us. If we made it see through or glass, for a briefer period of time we would see our 3D world around us again, then just a cube, then empty space. As Assistwo said, we could theoretically add other worlds around us "above" and "below" on that fourth line of sight or axis, each as fully 3D to us, as their elevator could have had not just one floor or real world to get off into, but many floors of full 2D worlds for them to exit into. Time itself can be thought to be that elevator. Every one of those worlds could be thought of as another dimension of ones own world at another moment in time, and every moment one exists one is bumped up to the next "floor"." 

          "Time sure comes in handy. Using it to represent height made Inventor able to envision the cube in the first place. Now he has just gone hi-tech to show others what he "saw" in his mind," the assistant said. "So what’s next?"

4.5:  Pivot Points: Upsetting the happy sponge

         "Pivot points," Researcher began. "Without pivot points all of these ideas would be useless. Inventor was able to secure his square panels from seemingly 2 different directions at once, from the north and south at the same point relative to east and west, halfway between, and at the same point in time. Time will become increasingly important as a dimension so understanding it as a dimension and working it into the conversation as if it were a physical dimension is now crucial as we prepare to go inside matter more and more. We know the north end and the south end are not two different directions with the new way we see objects. The north is the positive side of the north/south viewpoint and the south is the negative side of the same viewpoint or axis. They are mirrors of each other and though each can be thought to be positive or negative, once you decide which is which, you have to keep it that way. Inside of matter is like the Bermuda Triangle which cannot be measured in the same way, and instruments would go haywire. Keeping and sticking with positive and negative viewpoints relative only to the OUTSIDE world is how not to get lost, conceptually speaking."

         "It sounds like it is bigger in there than out here if one can’t go through a 1 meter cube mentally without risking getting lost", his assistant said. 

         "Not bigger, just with as many dimensions as you can imagine. Inventor’s new way of measuring means objects dimensions we must view as scalable since we cannot tell from "out here" how many dimensions there are or may be projecting outwards from "in there".  As long as we stick with dimensions we perceive in our world, we are ignoring for the moment or choosing not to see, and accounting for what we might not be seeing by dealing with it separately later, what other properties objects might have sticking out into other dimensions we cannot measure or see from out here. The Titanic is one example. The iceberg below the surface is what we are not accounting for but we will have to later. Just because we see objects as they tip into our world, we cannot measure from "out here" if they might be bigger "in there". If a boat were 2 dimensional or floated exactly at the surface level, how big the icebergs are below the surface would seem to be irrelevant. If you lived in a 2D world and everything stayed floating evenly like a square sponge on the surface the water of a bathtub, how much 3 dimensionality it had would not matter. The surface area in your world would seem stable and that is all that would ever count or matter to you. What you can measure of the sponge, its diameter, would be all that mattered in your world as long as it floated stably and Inventor never invented machines to mess with that balance. Likewise when I said our cubes like our matter do not normally spin out of our 3D world unless we force them to because they "like it here", I was not being cute. It is stable in this reality evenly even if it protrudes into one or many more additional dimensions as well. It is like a happy sponge of 3 dimensionality or 4 or 5 as seen from our 3D surface measurements or seemingly 3D "outside" looking in. Like the 3D sponge floating in sync with 2D world which is really a 3D ocean, to those who only perceive 2 dimensions and are confined or live only at the water line, its 2 dimensional properties are all that matters as long as it floats evenly. To us, objects 3 dimensionality which we perceive are all that matters as long as our they seem to conform to our 3D expectations because we can see 3 lines of sight, or line up 2 perpendicular to the only real line of sight common to every dimensionality, the "away" one."

           "So even," his assistant speculated, "if we could imagine that fourth line of sight which we can only now envision 3D shadows of as 1/4 lines of sight seemingly in many places at once, if we could bring that fuzzy line to us into focus with the other 3, even that might not be enough to see what’s going on in there." He motioned toward a solid 4D block of matter they built for fun. 

         "Nope, only seeing 4 lines of sight at once," Researcher responded, "seeing the difference between a solid 1 by 1 by 1 by 1 meter solid 4D cube or Tesseract, and a 1 meter cube in our 3 dimensions but only 1 cm thick in the fourth, even with this added line of sight, we might still be seeing only the tip of the iceberg of any piece of matter, if it has more than 4 dimensions. Remember too that there are angles even from 4 dimensional lines of sight "seeing" where our 4D solid cube and our 3D solid cube with limited 4th dimensionalness would look identical."

         "Yes, head on from some of the 8 direct angles, or from positive or negative aspects of the 4 lines of sight at direct "away" points to line up the other 3 equally. It is only by turning the "away" line of sight at an angle that they could see how 4 dimensionally thick it really is, and we can only judge a cube to not be a square if it seems one, without shifting over the "away" plane or line of sight by attempting to move around it or moving it relative to me if I can turn it," the assistant said. 

         "Since we cannot judge the dimensionality from outside an object how many dimensions an object really has, the math is different for the inside, we pick as many lines of sight we can relative to the outside world, give them positive and negative values, though neither is ever actually positive or negative but potentially both, pick one and stick with it. The number of dimensions within is indeterminate."

         "I thought we were doing pivot points," the assistant reminded. 

         "Yes, Inventor had to secure his narrow thin square panels resting happily upon the surface of his 2D world at 2 points to pivot around and still remain partly in his world. To make it as easy as possible, he picked the minimum distance across, 1 meter. Instead of just zapping one end up, he put the pivot point in the middle so he could zap one end up while zapping the other end down. The time had to be the same for all things to occur. Since the distance was the shortest, it conformed to one line of sight perfectly, in this case, the north/south. Both the north and south ends had to be secured at the same time, and in sync with the dual zapping of the east and west ends. If only the north end or south end was held at that time, the square panel would seem to disappear into a dot around that point it was held, and be very hard to pull back into 2D space," Researcher concluded. 

4.6:  Choosing a way to be- a stable little D

         "What if," the assistant said hesitantly, "as you said, the square "liked" 2D space since in 2D space it is at its maximum length and width in relation to it evenly. Maybe it is a 2D world for a reason, because as you said, they have settled or chosen to be on that plane of existence or aligned themselves to it, the same way 3D objects can settle on a 2D plane like the rings of Saturn or orbits of stars or planets settle down to 2D planes." 

         "Yes," Researcher concluded, "if a 2D world existed or a 3D world existed, either way, occupants that perceived it would see it as stable if they saw it at all. We can suppose that mostly 2D squares prefer to be "in-line" with the rest of Flatland, and if left alone and there are no parallel 2D worlds above or below for it to eventually prefer as being closer to realign itself to, not to be "sticking up" or between parallel realities, it would eventually return "in-line" with the rest of Flatland or whatever 2D reality it happens to be closest centered around. If Flatland were the only 2D "ground", we can see it pulling the square back down via some sort of gravity so that the square is back happy and stable as an asteroid in an asteroid belt, which if you are an asteroid is where you prefer to be, like the rings around a planet. A 2D Universe would be that way because of a tendency for things to want to line up that way to be more within them than outside of them, when they appear as stable and can remain static or level to them. Otherwise they would simply appear and vanish, if seen at all, as if "just passing through" and not even stop to see that realities attractions, or even perceive it as someone else’s common reality at all."

         "Reality tourists, popping in and out wherever and whenever they please like they own the place, don’t you hate those types!" the assistant joked. "So why don’t the squares just snap back into place?" 

         "It was decided a long time ago that the amount of Mystericity it would take to jolt or nudge objects into an extra region of space where they prefer to be sticking out into as little as possible, would be too much for us, as mere researchers to be able to afford, if the pull of our 3D world upon 4D objects were too strong. We therefore assume that though eventually a lost square will realign itself with some 2D world, it will take a long time as the pull is very slight or we could not do the things we do even in a story. In this story, that "snap back" to a 2D or 3Dness is so slight once broken free, we are assuming they are stable however which way we turn them once we stop them from moving, even if in many thousands or millions of years they would realign themselves to how they were most happy or stable before we started messing with that stability in relation to our world by zapping parts of them outside of it." 

         "So if secured by only one end of a line of sight, north or south, the object would seem to disappear into a point when turned as it had only one pivot point," the assistant said. "If both opposing lines of sight are held at once, they seem, if extremely thinner in that dimension outside of their normal "happy" number, they seem to disappear into a line. Why do we use a square?" 

         "We use a square for the same reason and placement that Inventor did, to make it the most easy to turn and to keep the most of it in our world as possible, as he chose the points of the shortest distance half way between each end of the square and held the middle, by zapping one half positively and the other negatively, it was the easiest and most efficient way to keep it in his world and control where it existed out of it. We secure two lines of sight from both directions at once to keep the most of it centered in our world which we can at once, and it seems to collapse into plane, in this case square shaped plane, only as thin as it is thick in the extra dimension, in his case the 3rd, in our case, the 4th. If our means to hold it were only 1mm thick we could, if its if the cube were only 1mm thick evenly a 4th dimensional measurement, we could rotate an entire 1 meter solid cube down to only a 1 meter square only 1mm thick." 

4.7:  The iceberg outside of space

         "And it would only weigh that much too," said the assistant, happy to be the one to finally bring that up and not even in the form of a question either. Perhaps he would get a name one day or at least lose the "the" for a capital "A", just as Researcher was now known with a capital "R" and no "the" in front anymore. 

         "Yes," Researcher added. "we know from our experiments thus far that we are not making the area within our reality more dense, and we have decided that the pull or wantingness to "snap back" into this reality is negligible and any object once turned remains stable until we, not the object itself, bring it back into line with our normal space. With the force of its restabilization factor in relation to our world so close to zero, the only part to have weight is the amount in relation to or with our world." 

         "So much for trying to guess something’s inter- dimensional volume or mass by weight I guess," the assistant said with a shrug. 

         "Yes," Researcher added, "those units of measurement can only apply to parts within the dimensional planes you perceive and exist within every day. Lets go back to the sponge and the bathwater example of Flatland. We will make all others in Flatland soap film floating on the surface. However soap film or Flatlanders made of soap film might understand weight or gravity in relation to size, the sponge would conform because it is essentially suspended in their space evenly so our 3D notions of weight would not affect it or how a 2D person would understand weight in a 2D world. As long as the sponge is able to maintain an even, seemingly weightless co-existence on the surface, the thicker sponge would seem to have many of the same properties as the soap film people themselves. The same kind of 2D laws would seem to match each. In other words, the only parts of the turned cube still existing within our space have to obey the laws of Physics and the way we measure things in our space."

         "So if that is true," his assistant said, "we have no way of telling how many dimensions objects have from outside of them. A 2D person could not tell a 1 inch thick sponge floating on their world from a 5 inch one. A 3D person cannot tell a 1 meter square 1mm thin, from a turned dimensionally 1 meter solid cube by measuring any of its properties from outside of it. But if the measurements of the inside are different than how me measure the outside, what can we do until we get to, in the story, how to measure something inside if we cannot assume the number of dimensions it might have independent from how it may seem or exist outside itself?" 

         "Until then," Researcher said, "we can talk about pivot points."

         "I thought we did," the assistant said. 

         "Not nearly enough," Researcher continued. "So far we and Inventor have been taking the easy way out. Assuming that it is hard to rotate objects outside of the space where they are established, have lots of connections, acquainted with other objects, have settled down into, put roots into, and are perfectly content to remain in, we have gone the easiest route possible to upset that. We zap one end one way, at the same time zap the other end the other way, all while grabbing a firm hold on the middle. Though it would take more energy, we could hold onto one end and try to zap away the other end into another dimension of space. By holding the middle, it seems to be trying to be trying to come and go in both positive and negative lines of sight at the same time. On our cube, the east end and west end appear not only to be passing through the middle, but through each other, before coming out whole but reversed on opposite sides. By looking at Inventor’s version of the same thing, we can visualize the east and west ends passing over each other in the middle before coming down seemingly upside down from the opposite directions. To understand our more puzzling problem of reversed 3D objects, it requires a quantum leap in our understanding of 3Dness to understand how 3D objects are just as reversible as 2D objects regardless of whether 4D space exists to turn them within. Remember, if Inventor is right, space can contain any number of dimensions and the number of dimensions is decided within the objects themselves how many dimensions they exist in, space is omnidimensional."

         To this the assistant remarked, "I thought it was the other way around. I thought that the space we are measuring outside from contains the preset number of dimensions and all objects can be or must be thought of as omnidimensional while inside of them?" 

         "No, omnidimensional means without limits. Space itself is not 2D or 3D or whatever. It is the objects themselves agreeing to exist as 2D, 3D, 4D, etc. An object which finds itself 2D and all other objects around itself seem 2D is going to come to the conclusion that all objects and space itself is two dimensional. We see ourselves as 3D and all other objects seem 3D by means we can measure so we tend to think of space itself as 3D. What Inventor said was that we need to think of the number of dimensions inside an object as indeterminant or scalable, not as omnidimensional or without limits. Objects to some extent determine the number of dimensions they extend outwards into, or how many degrees of Suchness they can maintain at once. If it has 3, it can seem to fall in line or exist to others with 3, 2, or 1. If it has 4, it is real to all other objects of 4, 3, 2, or 1 dimensionality." 

         "Shouldn’t it go the other way?" the assistant asked. 

         "No, definitely not. If an object has only 3 levels of Suchness, or only extends outwards into space upon 3 lines of sight at once, only to other 3D objects and less can it seem to have existence. It can align itself or blend in with a 2D world or 2D rules of existence as the 3D sponge happy to float on a 2D world, or asteroids most happy to never leave a 2D plane around a planet. But if some objects can or do decide on or enable 4 lines of sight, 4 degrees of Suchness, they would be perceived of existing with and relative to only 4D objects and lower. True 3D or 2D objects, though they could perceive 4D objects, by comparison would have a zero value of that 4th dimensionality, and would not seem to exist to THEM, those 4 dimensional objects or beings." 

         The assistant reminded, "We seem to keep getting thrown off of the subject of pivot points." 

         "Maybe," Researcher said, "where we are seemingly getting thrown off, we are creating new pivot points for others. Yes, you are right. Back to pivot points. In the normal "spinning around the center" we have been doing looks confusing because 2 different ends are reaching a second pivot point, not really a pivot point but like one which we call the apex, both at the same time headed in different directions. That is why to normal 2D people, at a certain point after passing the apex, east seems to start becoming west and west starts become east, the same with our blocks. That is where all the points east and west from each worlds point of view become reversed and start returning again from opposite directions. The apex can be thought of like a second pivot point in time when each end or tip is the furthest "away" from our triplane of 3 planes of right angles, and must begin its return trip or orbit back to where it began." 

4.8:  Dancing upon another apex

         Assistwo was very happy. He wowed the investors with Inventor’s demonstration of the 3rd mysterious line of sight which everyone inexplicably was suddenly interested in. They started selling them to amusement parks everywhere. As the only real alternatives to rides which only spun you around (which as I said, Flatlanders had been doing from time immemorial for free) to make you dizzy, the 3rd viewpoint ride was a big success. Inventor now had even more money than before and found there was more than one way to fry a square. This time he put the pivot point not in the middle but at the 2 east corners, northeast and southeast. Instead of using positive and negative Mystericity as before, he packed all of the positive Mystericity his amusement park funded new super generator could provide and zapped it all into the west side corners. 

         "You might want to step back a bit," he said to Assistwo who thought he stood far enough safely to the east. 

         Sure enough and just as Inventor had predicted the square soon rematerialized backward to the east of where it previously was standing. Instead of coming into their world slowly, it seemed to come in almost at once and then go almost at once again. It made several appearances in both spots before getting stuck partway in-between. Inventor had used far more Mystericity than was needed, but he was quite pleased with his new generator. 

         "Now," Inventor said to Assistwo, "we have the second pivot point or apex in our space where we can see it. We can visualize clearly the east half and west half do not pass through each other. East and west ends stay intact and apart from each other in the other dimension we can’t see." 

         "Yes, much simpler to understand except for the popping into and out of existence at two different locations, seemingly in either place depending on what time it is. Apart from that, much easier to understand." Assistwo added sarcastically. 

         "Well the Physicists will think so. Let’s not tell them about it though", Inventor joked. "They already take this probably here, probably there stuff way too seriously already. Well, even if we can’t explain it easily to other 2D people, we know what we are seeing. Because it always must rotate around the pivot point, which is now at the extreme east end, the west will now come into view or our space opposite of east as before, but because east is securely set in place and cannot switch places with west, the entire block must come out over there."

         After lots of practice, Inventor calculated the exact charge to get the square to come to a full stop all by itself backwards. This happened so slowly one could see the west end gradually disappear "up" then slowly coming back into view opposite to where it stood before, seemingly rebuilding itself in another location backwards.

         "Though," Inventor said, "it now takes twice as long to reenter our space as it not only has to go "up" but also across to the east, in a sense the original apex is still an important point but now twice as far away from our world. Before since the pivot point was in the center in our world, east and west ends could both be working on realigning themselves to our world at the same time. Now, everything west must go east of east while east itself barely moves serving as the pivot point. Another apex or pivot point can be thought to exist where the tip of the west end begins passing "over" or "under" the east end. Since that pivot point is now much further away from our world now, the full width of the square instead of half, and like I said, it is now moving through our space as well, why it comes out somewhere else in our world, it is now making a much larger circle."

         "So," Assistwo began, "any movement in any direction is the same kind of movement following the same laws. But how come it is so hard to get things to move in the up/down direction, into and out of existence from our limited points of view, if things are happy or happier always standing still even in the up/down direction, than moving them in any other line of sight?" 

         Inventor replied, "It is not that it is harder to move things in the up/down direction, just harder for us because we lack substance or force to push it in a manner or means of definition in a dimension we lack. If we had more mass in that additional field, we might be able to tip it outside of this reality, the reality we perceive, even accidentally but then if we had more mass in that field, we might not see it as being outside of our dimensions because we could become able to perceive the up/down dimensions that might exist above and below it as well and be able to line up 3 lines of sight simultaneously because we would then be perceiving ourselves through our own mass as 3 dimensional as well."

           "I know," Assistwo said, "That your machine pushes things from a direction we cannot, being so locked into a 2 dimensional plane of existence, through manipulating objects ways they push out or assert themselves into or in relation to that addition dimension we do not perceive. Can’t we do the same thing to move objects through our dimensions of length and width, that is hamper its desire to move outwardly west and east at once by subduing the west tendencies to make it move east?" 

         "It is not that it can’t be done with the machine, it just requires far less energy for us to push it that way using objects we do have mass or definition with in our own dimensions. Manipulating its internal pushes and pulls on itself to move it into and out of our space is a much more complicated and wasteful approach than simply pushing it using something else. Since we cannot leave our "plane" of existence, we need to do that other kind of movement from within the object itself to get it started in that direction. Once we get the movement kick started so to speak, those parts tell all other parts of the object to move in that direction as well, if cohesive and stable enough throughout its mass from where we try to turn it. If too thin there or the rest is too heavy, we would break it instead. When that doesn’t happen and we can get parts of it to move, they tell the other parts of it to move or turn in the same way too if they all want to stick together as the same mass. If they want to stay connected, they have to do what all the parts combined at once do, like Siamese twins. If one wants to go one way, and the other the opposite way, the get nowhere. Most objects that seem to stand still are really in balance from all directions of wanting to move in all directions at once. Since the inverse is equal for all directions around itself, it creates a field all around itself which says that it is whole and has a positive existence, at least at the moment."

 5.1:  The Carryover Principle

         "Why only at the moment?" Assistwo asked. "I thought all matter is inherently stable." 

         "No," Inventor replied, "all matter is inherently unstable and cannot exist the way it does. The Universe as it would stand at any given moment in time is impossible to exist that way at all." 

         "But we perceive it does, so who is lying, we by perceiving it to be existing, or the Universe for tricking us into thinking that it does?" Assistwo said wondering if he really wanted to know the answer. 

         "We both are, ourselves and the Universe. We both agree to cheat in the same manner and way at the same time. Since the Universe as it stands at any given point is impossible, it agrees to carryover that instability somewhere else and resolve it later. It is like a hypothetical government always spending more than it can afford to so it, in a sense,  cheats and says it will resolve the matter sometime in the future to restore the balance." 

         "So by carrying over the instability to be resolved at a later date, the Universe requires that later date to balance itself out. Wouldn’t then it balance out and then be stable?" 

         "Providing it ever does or can reach that balance. If not, like the hypothetical government, when that next moment or year comes, it takes what is still unresolved and again agrees to carry that over and resolve itself or its imbalance in still yet another time, on and on, as long as it takes. As long as the imbalance is manageable, or it never actually ever is paid off completely, or never grows too wide that it can never conceivably ever get paid off, the system’s balance through imbalance to be resolved at a later date, actually seems logical." Inventor said. 

         "Wouldn’t we want it to be in balance or even have a surplus?" Assistwo queried. 

         "With a government deficit, yes, with this Universe of unresolved issues, certainly not! The Universe we perceive is, in a sense, having the opposite problem. It has more than it could ever spend, or a positive imbalance." 

         "I wish I had the Universe’s problems," Assistwo added. 

         "Because we see all matter as having a positive nature or existing with all positive values in the dimensions it asserts itself outward into, it has a negativity problem. It needs something to stand out against in relation to, to balance itself," Inventor added. 

         "But you said it uses time to balance the books, it never needs to offset its positive cash flow problem so long as there is time in the future to resolve the issue," Assistwo asked. 

         "Yes, but what if there is no such thing as time, or no time left?" Inventor asked. 

         "If there is no time, then the Universe and ourselves are delusional since it needs time to pay down the surplus, and we for perceiving time’s existence. If there is no time left, the Universe has a problem if its books must balance. I guess it would just have to find or make the time for it somehow." 

         "And there you go," Inventor said. 

         "I thought I was still here," Assistwo quipped. 

         "To exist, matter must have space outside itself, and if that cannot balance, it must have time to sort out how to balance itself if space is not the answer. Since we as scientists perceive space and time as the same thing or interrelated, this is what matter needs and creates to offset its abundance of positivity inherent within its own existence." 

         "So it doesn’t use time to figure out or resolve the imbalance, time itself coupled with space IS the answer it comes up with to resolve its existence’s paradox or imbalance." 

         "Correct. Because our existences are in relation to that solution, we must, to exist within the Universe, buy into equally its two tenants, that we have mass and that we have time and space to offset that mass or exist within. So long as we buy into both the positive and negative aspects equally, we are existing within the same framework and moving along in step with whatever else adheres to or uses the same framework to define itself by." 

         "Well," said Assistwo, "I still don’t see the negative. If having mass means I must have time and space to exist within to balance it, and time and space I like, and mass I like having too, where is the downside?"

         "Downside, good or bad, these are matters of perspective. Nothing inherent within this imbalance says you have to like or dislike it, or it needs to be enjoyable or unpleasant. Only that if you have some, you need to take equal amounts of the other (mass and space/time that is, not good times and bad times). It is a package deal," Inventor concluded. 

5.2:  The Energy Problem

         "I thought," began Assistwo, "that energy was the carryover principle, that whatever cannot be solved by understanding mass and space and time alone is resolved by the concept of energy. That energy makes everything balance or seem to work."

         "But that is to view energy as a term outside of mass. We can if we so wish, see energy as a property of mass. To see an object we seemingly put in motion in regards to another mass, we can also view that energy or acceleration as changing or increasing or being channeled into that mass itself. By doing that, we can view or see that nothing really moves." 

         "I thought everything moves," Assistwo said. 

         "Everything moves relative to other things," Inventor said smiling. "Nothing does or can move relative to itself, twisting and turning of ourselves and contortionists notwithstanding, and falling 3D cats I have dreamt might exist since our 2D cats keep twisting around all the time. Though these things are living and can move some parts relative to other parts, we cannot significantly shift the position of our whole physical perimeter without something to push away against or pull ourselves towards, or have something else moving to push or pull against our locations." 

         "So everything’s momentum can be thought of as a property of inherent within or contributing to its mass. What about gravity?" Assistwo asked. "That can cause things to move and cannot be answered by this example thus far." 

         "Putting aside for the moment that gravity does not cause objects to move so much as bends the space around them, gravity as we know," Inventor said, "has to do with or is inherent within the mass itself. Instead of viewing gravity as motion relative or in relation to other objects, we can see gravity as a motion relative to each object themselves." 

         "If every object has a positive surplus of existence," Inventor continued, "it balances with a negative creation of time and space surrounding it, pushing outwards from the borders of its mass, gravity can be thought of as the return flow of that wave, or the undertow or backwash of that space/time it emanates outwards’ negative counterpart, but since then we are viewing space/time as the negative "existence" to matters positive "existence", the negative motion of space/time outwards from an object, its counterforce, or gravity, we see as a positive force of motion towards the object." 

         "But," Assistwo said eagerly hoping to catch Inventor off-guard, "you just described space/time in two different ways in the same sentence. You said space/time is the creation in opposition to matter as if it were an equal inverted "substance" yet you described it as a force emanating outwards in relation or in opposition to gravity’s pull inwards. How can space/time be thought to be like a substance and a force or energy at the same time?" 

         "How," Inventor countered, "can light be a substance and a force or energy at the same time?" 

         "Matter, the power of the Dark Side!" Assistwo said while breathing like Darth Vader. 

         "Space/time doubles up or trips over itself while seeking to exit or leave away from matter defined by the number of dimensions the matter exists within. If an object pushes its existence outward into two dimensions, that has a counterpart imagined both in relation to both directions away for each dimension or line of sight, and how those two directions or lines of sight correspond or interact with each other as they leave the object or the area directly around the object. Likewise, for 3 dimensions, they double over, triple over more precisely, each other in 3 different ways it pushes outwards. In 4 dimensions, then quadrupling over each other 4 different ways, as so on and so on. This creates space/time statically locally around the object but it moves outward like light in all directions. You could ascribe this negative force as a different name, but it is part of the same aspect of space/time being generated locally around the object to provide the countermeasure to matters over abundance of positive values in each of its dimensions."

         "This is getting complicated. It seems the only way to figure all of this out is from within the matter itself, if matter is starting all these other wheels in motion by trying to exist," Assistwo said. 

         "Yes," Inventor agreed. "If matter did not try to exist, it would not need space and time to try to balance itself through or in. Or we could blame space/time for wanting to exist and creating matter as its negative counterweight to balance it. If we see the potential of space/time as the positive force, matter becomes the dried up shell or waste products space/time must leave behind after the party is over. In this interpretation we or actual things are not the positives but the negatives that can no longer exist as many things at once, but are the leftovers of what had to occur for time and space to be able to move ahead to the next set of possible circumstances. Our actuality to space/time might seem a necessary inconvenience or base jumping off point for its multiple states of reality. In space/times reality only zero and infinity are real numbers and all others are imaginary constructs need to bookend them by giving space to separate them. To the other way of seeing matter as the positive, zero and infinity become the imaginary numbers and the ones in-between become the real numbers. Both can be seen to be either, as it is only your point of view or choice about which to set or see as which." 

         "But once you decide, you must stick with it," Assistwo joked. 

         "Yes, it is much the same as the orientation of yourself in regards to matter as we have used repeatedly. Speaking of which, we need to go back into matter resolve all of this since, as you pointed out, we see matter and existence as the positives, and generally in a good/bad sense, we see or experience the upsides. Since we decide actual existence is real and potential only the means to achieve that reality, instead of vice versa which is an equally valid point of view, the whole paradox begins in here, he said pointing to his cube, and as we will see from this trip inside, because it is a paradox, it also ends in there as well. From an even wider perspective," Inventor said with a smile, "it never even leaves there."

 5.3: Perspective, cheap sunglasses, triplanes and time

         Researcher walked into the room where his assistant was working wearing dark sunglasses with a horizontal line across the middle. 

         "A bit flashy for you, don’t you think," his assistant quipped. 

         "Oh yes, they are all the latest rage. I like my sunglasses to say "Hey look at me, I am so cool!" No, these are my new 2D glasses. They help me see in 2D. I bought them off of an ad in an old comic book," Researcher said. 

         "So what’s the point in seeing in 2D? You think that is what makes Inventor so smart?" 

         "You think that is a joke but yes, I probably do think the ability to bounce back and forth from 2D to 3D thinking gives Inventor his insights into more dimensions. Being equally proficient in understanding both gives him a ground or backdrop for exploring more. The point of these glasses is that with them, we will try to see "down" to 2 dimensionality to see how we or others that might have 4 dimensionality might see "down" to our level of perceiving only 3."

         "I hate my level being described as down compared to another’s but I get your point," the assistant said. "Can I borrow them after you are done, they do look kind of cool." 

         "To review briefly, we know 2D people have 2 lines of sight and can line up only 1 when the other line of sight is used as marking points "away" or perpendicular to the first one. We know in 3 dimensional perception, one can line up a second line of sight with another crossing the away one at a specific distance to create a combined "plane" of sight when equal points on it are equally away from the other remaining "away" line of sight. Note that the whole 2D world now is the "plane" of reference, not a line of sight like in the 2D world. The 2D person’s cross reference intersecting the away line of sight was another "line" of sight, or a 1 dimensional way of seeing. Our 3D equivalent to the cross section perpendicular to the away line of sight for us is a 2 dimensional plane." 

         "So like multiple 1D Universes moving away from the observer can seem to mark points of the away direction to a 2D person, multiple 2D "planes" or 2D worlds can be seen as marking or making points along the away line of sight to a 3D perspective. This means multiple successive 3D worlds would be the frame of reference of the "away" line of sight from a fourth dimensional perspective," the assistant concluded. 

         "Yes, for the lack of a better word other than 3D worlds or Universes, I call them triplanes of sight. Away in 2D is marked as an away "line" of sight perpendicular to the away direction. In 3D it is a 2D "plane" of sight perpendicular to the away direction. In 4D, it is a 3D plane of sight, or "triplane" of sight. Each extra dimension provides an "over" view of a 1 dimensional less "world" of another. If we stacked Flatland Universes vertically and move through them horizontally, they way we normally move, we would seem to be passing through many 2D Universes with each step we take. That is how a 2D person could or would perceive our extra dimension, as an infinite number of stacked 2D worlds. Likewise, multiple 3D worlds would be stacked together marking distances "away" in a 4th. Saying go 3 meters that way, it would mean from our point of view, an x many number of 3D Universes "away" in that direction, and depending on their perspective or which way they were facing, they could see that "world" to us, from this one, if they had a facility for understanding 3 lines of sight at once." 

         "Don’t you mean 4 lines of sight at once," his assistant corrected. "We, after all see 3 lines of sight." 

         "No, we see 2 lines of sight at once, but we understand 3. These glasses will show that 2D people would only see 1 line of sight but understand 2. From a 4th dimensional perspective, they could if they had perception of 3, use that as we and 2D people can easily imagine one more than we can actually see at one time. It is the ones we combine or see at once which we directly perceive. For the extra one we cheat," Researcher said. 

         "I take it time is involved here," his assistant guessed. "I remember it being said that it will come up more and more now. Didn’t Einstein say that time was a 4th dimension in that we move through successive 3D worlds stacked together as you just described?" 

         "Yes, time is the wildcard everyone uses to give them that extra ace of perception they cannot directly perceive, but think they do. No matter how many physical dimensions we can directly perceive, we can always cheat and use time to imagine one higher. Inventor did it with 1D worlds to illustrate his own 2 dimensionality, and to describe a 3D world as multiple 2 dimensional worlds over time. Einstein used time to describe multiple 3D worlds strung together. But we are talking about 4 physical dimensions plus time. Physical dimensions we can move through freely in either direction without causality problems. Time as we perceive it runs in only 1 direction. Riding time is like riding the blast wave of a star going supernova. It spreads out in all directions but can only be perceived as traveling in 1 direction, away. To be in time is to be forever locked within the edge of the blast moving outward as the rest of the blast/event zone and thus in that direction or place, it never seems to move but you cannot step outside of it and must travel in lock step with it. Time is a different animal than a special direction but can be used interchangeably as a wildcard substitute for a spacial direction for understanding 1 dimension higher, but cannot actually take the place of one fully for it is of a different nature." Researcher said. 

         "Ok, I take it time is more complicated than your cool sunglasses. I take it we use time to imagine a higher physical dimension because time, like that extra physical dimension, can be thought to string together multiple dimensional realities you normally experience so you can "see" or imagine you see what it would be like to step "through" multiple dimensional Universes of your own reality. How else is time important?" 

5.4:  To everything turn, turn, turn

         "Stick spinning," Researcher said. 

         "I think you are trying to see from Inventor’s perspective a little too much," his assistant joked. "You are even beginning to relate everything to that." 

         "Would turning sound better?" Researcher responded. "Now I get to play with and thereby write off as an official expense the cost of these $10 sunglasses. I can’t help but see in 2D. We as 3D capable beings can line up 2 lines of sight at once. Inventor built a cube but from his point of view, though he knows differently, all he or anyone else in his world can perceive it as is 4 lines, 2 of which can only be seen at a time from a single position. We built a Tesseract but all we can perceive of it is its 3 dimensional angles where it intersects with our world. Using these horizontal shades, and getting down in line with a tabletop we can imagine seeing that sample cube on the table as just lines. Even if we align ourselves with a 2D world, we would still see all sides of the square sticking up below it or over it at once. We need to conceptually block our ability to see the full square sitting on it, to see only the lines of it as Inventor sees it." 

         "I think I am coming up to speed now," his assistant said. "Because "away" is always taking 1 dimension less than the one you exist in or normally perceive, everything is always flattened out like a pancake unless we turn it. When we turn it, our brains compare its old shape to its new shape and keeps track of where the parts we no longer can see directly now, where they have gone off to. A small child turning a block or rock over and over to see it from all sides is remembering all its possible perspectives or angles it can be seen from and puts together a mental image of the whole object."

         "Right," Researcher said. "By remembering and recording the parts we can no longer see moving in the "away" direction, by turning objects around in every direction possible to us, we comprehend the whole object we can never see all at once. Using these special sunglasses, we can see only the edges of a square as it would appear to a 2D person. A 2D person who knows squares or works with them never has, can, or every will see a square directly all at once like we can see it from above. They can see one or two lines of it at a time, 1 line if directly facing it, or 2 equal lines moving "away" at equal angles when viewing it directly at a corner. By turning it or walking around it, a 2D person can conceive of what a square could look like though he never actually "sees" more than 2 lines at a time." 

         "Ok, I am fully up to speed and am moving with you now. Likewise we cannot fully see cubes because we cannot line up 3 lines of sight at once, but we can line up 2 so we can see square at once without needing to turn it. Because "away" always takes up 1 line of sight, we understand cubes or 3 dimensional objects by turning them and using our brains' processing to remember where the sides are that have moved away out of our sight. We can only see half of it at a time, or 3 sides," the assistant said proudly. 

         "Yes, and if someone or something could line up 3 lines of sight at once, they would see all sides of our cubes at once naturally. They would need silly glasses like these to try to figure out why we cannot see the other side of a cube or dice at the same time as we see it from this side. They naturally would see all sides of the cube, even if trying to get fully "in line" with our world just as my getting in line with a 2D tabletop world. Without special glasses, I would still be able to see above and below it. A 4 dimensional perceptional being would be able to line up his sight which is only 4D when turning or moving, to imagine how a 3D person might perceive a world as easily as we can comprehend a 2D world but would not be able without extra work, not be able to see through things in it." 

         To this the assistant added, "How do you mean see through things? I do understand that we can see a square all at once from looking at it from above, and I can buy that from a 3 lines of sight at once perspective, one could see all six sides of a cube at once as easily as we can see all sides of a square at once, but we see the whole square from outside of it, not through a wire frame model." 

         "The thing is," Researcher concluded, "is that we cannot conceive of how seeing through something is not really seeing through it. To us it is seeming to look "through" it but it is also analogous to what you said as well. You have to remember, no matter how many dimensions you add, "away" is always different, like time is always different, just in another way. From a 4th dimensional viewpoint or higher, if the object exists outside of themselves, it is always some distance away, whether you can comprehend it as a line of sight away like a 2D person could, a plane of sight away as a 3D person could, or a triplane of sight or a world or 3D Universe away as a 4D person could see it. To see all six sides of a dice directly in front of them, all in positive lines of sight for each of the 3 directions they can line up at once, to us it cannot help but seem to be looking through the object instead of seeing it from the opposite direction simultaneously. As we will see later, it is also why a 4D person could not tell a Tesseract from an ordinary cube without turning it. Yet ironically, they are not seeing through it in the ordinary sense either. To see the other side of a cube as we see it when we turn it, the outside view, seems to require using the negative lines of sight, which a 4D perceivable being cannot do any more than we can. A 4D person viewing an object clearly away from it cannot be on both sides of it at once by using positive and negative lines of sight. To use or combine any positive and negative lines of sight would require being on both sides of the object simultaneously. Seeing the other 3 sides of the dice "through" the other sides is more analogous but not more accurate. 4D beings could not see through solid matter, though in a lot of ways, it does look that way." 

         "Ok, now I am getting confused," the assistant said. 

         "As well you should be at this point," Researcher surmised. 

         "Why is that? Being confused is good?"

         "Being confused is reaching the point where you know the rules that have applied or worked before are braking down and you must begin to look at the problem or situation from a perspective new to you or one you have not needed to consider seriously before. In this case neither explanation by itself will stand on its own. Though it is never optimal or desirable, one must accept the seeming inconsistency temporarily, not making dogma out of it as some are wont to do, but for the moment concluding that neither perspective applies in total, both are descriptive of the situation somewhat, neither are accurate but by combining two different perspectives or ways of seeing it, you can continue on for awhile until you can find a third which will account for the seeming inconsistencies in the two you cannot for the moment, reconcile."

         "And those being? I forgot," the assistant said warily. 

         "That from a truly 3D perspective, not the fake 3D one we build from 2D perception and memory, but a true lining up of 3 lines of sight at once, one is both seeing all of the "outsides" of a dice at once without seeing through it, yet also is seeing through it because they do not need to go around it by use of one or more negative lines of sight either," Researcher reminded. 

         "I think you are right that we better not get too comfortable with that seeming inconsistency as it does not really seem to be self-consistent at all." 

         "Yes, but unfortunately both seem to describe the situation in part, though they also seem to cancel each other out if you try to put them both together." Researcher said. 

         "Well send it all to the Physicists, they love these kind of inconsistencies. Where they don’t exist, they like to invent them just to make the numbers add up," the assistant joked. 

         "What supports the see-through explanation is the 4 lines of sight, 8 if you count the positive and negative, where a Tesseract and an ordinary cube look the same head-on away from you at any of the 8 side cubes you look at it directly away from," Researcher added. 

         "Yes, I remember the analogy," the assistant said. "When a 2D person sees a square head-on from directly away from 4 directions, he sees an ordinary line and cannot know it is a square until he rotates it. When a 3D person sees a cube head-on directly from 3 lines of sight or 6 directions counting positive and negative lines of sight, it looks like an ordinary square unless you turn it." 

         "Yes, and this applied to 4 dimensionality both offers the proof of the "see-through" explanation on one hand, and goes against it also in a way. Inventor knows 4 ways to view his cube, that 2 others are from a direction beyond his perception, and that the four sides he sees meet up and attach with each other in a linear way that seems bent from his direct perception," Researcher said. 

         "Right. North, south, east, and west walls edges when completely in his world cannot conceivably stay in contact with each other from a 2D viewpoint, he could imagine them "bending" to show the relationship of their contact in 2D, though he knew their shape did not change, but to illustrate it to others or imagine it himself he could imagine 3D space as a warped version of 2D space or mostly 2D objects being "bent" in 3D space," the assistant said.  See bottom image

         "Correct, just as we have to "bend" 6 blocks to make them all seem to fit neatly together to illustrate concept of a Tesseract. Though we know they still have a block shape somewhere, and a solid Tesseract would have block shapes in every dimension, to us to imagine how they fit so snugly together with all six sides of all 8 cubes staying in constant contact flush with each other, we have to show them as bending in 3D the way Inventor would show them bent in a non-perspective 2D drawing of how his cube sides stay in contact in another dimension," Researcher concluded. 

         "So Inventor could never see the top or bottom square but knew them to be the size and shape of the square "sides" in his world. In seeing each square’s side as a line, he knew it was still a square from another angle and that he was only seeing part of it at once. We can never see the top or bottom cubes of our Tesseract yet we know they are the size and shape of the six turned "side" cubes we can see, and in the same location "above" and "below" from another direction we can’t see," the assistant said. "So where does all of this lead us?"

5.5:  Silly 3D glasses

         "To 4D people with silly 3D glasses, I hope," Researcher continued. "Though we cannot view a Tesseract as anything but an ordinary cube, though we know step by step from building it that it is one, and Inventor will never "see" his cube as more than 1 or 2 lines at once, just the square portion remaining in his world looking pretty much like an ordinary square, we have here in this seemingly ordinary cube to us, something that both would, and would not, look like a Tesseract in six directions which we can conceive and two in which we cannot. It is the six that we can know that count. Inventor too has 4 clues with his lines he could know we would see as full squares, and 2 ways or angles of seeing it completely beyond him."

         "But," the assistant interrupted, "we are lost for explaining definitively how a 4D person or 3 lines of sight at once plus away seeing person could see all of each of the 4th dimensionally turned 6 cube "sides" we can see, how they could see all 6 sides of each of them at once, impossible from our perspective, and also despite the fact they are pressed against each other from our view internally, yet still would see all 6 sides of each all plainly by their outsides, just as Inventor could probably not conceive of how we can view a whole square at once, something he never has nor ever will see." 

         "Nor will we see all of a cube at once, though we do have ways of understanding bits and pieces of how it is done. We can start by forgetting the "bottom" and "top" cap cubes of a Tesseract which are completely out of our dimension. A 4D person who can mentally picture our 1 triplane only perception, the way I did looking across a conceptual 2D world of the table top, to him the completely out of our dimension "cap" cubes would not be visible anyway. What that does leave is how the 6 turned sides in the shape of a cube appear thicker without silly 3D glasses than an ordinary cube of minimal 4 dimensionality. If he had silly glasses that prevented seeing around or through things, they might look the same, if he had sunglasses as silly as mine. Without the sunglasses, he would notice a pretender Tesseract from a real one at the same point we would notice if a flat square is really a cube or not." 

         "When the next side should come into view," the assistant declared. 

         "Yes, for us that is the point when turning a cube on a single axis that we see the next of its six sides. By viewing and remembering the altered position of the first face or side, and seeing another one coming up the same, we can see it as another side similar to the first. While still looking mostly head on, from a true 3D viewpoint or 3 lines of sight at once, they would not know until they start to see the other side whether they are looking at a "full" Tesseract (when we are seeing a fully cube instead of a flat square) or whether they are seeing a "flat" cube." 

         "So how does this figure?" the assistant asked. 

         "Seeing through the object both helps and hurts understanding why this is the case. To know when the next "side cube" comes into view, its dimensionality must be seen separately than the first’s means to some extent, it is seeming to see through each one separately. Once the second cube comes into view, it becomes apparent immediately this is different "cube side" as to us, seeing the next side of a cube we know it to be a different face. If it was just a thin square, once tilted beyond a certain angle we could expect to begin seeing the other side. If we do not, we know whatever shape it might have beyond that, we know it is definitely not a cube. Beyond that point it would seem either cube-like, or bends at a narrower angle, or is a completely narrow square. The more we turn it, the more realize what its true shape is. With a Tesseract, turning on a single axis, that point is the same, once the next "side" comes into view it becomes apparent whether it is truly another separate cube form "side". To immediately be able to tell whether a full 4D shaped Tesseract from a mostly 3D shaped cube at the same points and ways we would know 3D objects from mostly 2D ones implies the ability to see through to the other side of each object shown. Yet at the same time, if one could see through 3D objects, how could one obscure another one behind it? The same math applies that the most "sides" of our 8 cube sided 4D Tesseract which can be seen from 3 lines of sight at once is 4 cube "sides" at once. We can only see 3 sides of a dice at once out of six possible. Every time a new one comes into view, another must pass out of view at the same time. The same with Inventor’s cube squares. Once you see the third side of a square with only 1 line of sight plus away, the first side disappears. If it was a matter of seeing through 3D objects, one could not obscure another behind it. It is not so much seeing through it but seeing all of it at once from every possible outside perspective but all in positive lines of sight at once ahead of you and not seeing beyond it." 

5.6:  2D Einstein’s grand slam to clear the bases: X-ray vision, not!

         Assistwo walked into the lab where Inventor was working. He was wearing a dark monocle, all black with a pinhole through the middle of it. "Look", he said, "I have this cool monocle with a pinhole through it so I can see in 1D." 

         Though Inventor knew this to be Assistwo’s warped sense of humor, he was obviously annoyed at the joke, and was not used to not being able to make all the good points in a long while. 

         "May I remind you of the motto outside my door?" Inventor said pointing toward the door. 

         "You mean "Abandon all hope of understanding ye who enter?""

         "No, the other one."

         "Medis Ageometretos Eisito?" 

         "No, the one on the other side." 

         "All things original in this story originate here?" 

         "That is the one. Remember we are supposed to be at the top of the ideas food chain," Inventor said. 

         Assistwo corrected, "I don’t think you get outside enough to grasp the concept of a food chain. Being at the top means you eat everything else. The bottom is the first to be eaten." 

         "Whatever. We are not doing the 1D monocle thing. It is bad enough we have been reduced to batting cleanup for other’s messes again. Go ahead and ask." 

         "How did you know I was going to ask a question?" Assistwo said flashing his trademarked and patented grin. "Ok then, time to dust off the 2D Einstein, what didn’t they know, or in the form of a question not mentioning the less original others making all the good points lately, could 4D beings or someone with 3D lines of sight plus away see through 3D matter as one method describes or around the edges to see it from the other sides?" 

         "Seeing through matter is absurd!" Inventor said glad to be getting something off of his chest he was unable to find a way to say earlier. "Only someone who cannot understand 1 dimension higher would make such an assumption which is so obviously WRONG!" 

         Assistwo stood back 2 steps. He knew Inventor was going to attack this matter full steam and wanted to make sure he was as inconspicuous as possible. Inventor was not getting angry but tended to talk rather animatedly when he had a lot to say which he had not been able to say for awhile. 

         "If something could see through matter of any dimensions it would not be matter, transparencies, wet T-shirts, and sexy nightgowns excluded. Depending on the material and thinness, matter can seem transparent but even thin metals are not see through. If 3D matter were only 3D it would be invisible, not see through, from a 4D capable 3D line of sight plus away perspective. If it were slightly 4D, depending of course on the thinness and material, that would not be what makes it seem see through, or more specifically, why one could see all 6 sides of a cube at once. The idea that some super-D being could look through a block and see how many dimensions were "within" it is just plain ridiculous."

         "But so is seeing from a negative line of sight," Assistwo said quietly. 

         "Yes, that is equally absurd but putting 2 absurd notions together does not make them less absurd, it is only admitting you don’t know, which is good and a start, but throwing them both out usually makes more sense. Yes, if something is away from you in the away line of sight, you cannot jump around it to see it from the other side, but the warping view of extra dimensionality can make it seem so. I am not used to having to refer to someone else referring to my work but this is important. Yes, I know that 4 bent diagonally squares around a center square to illustrate our 4 up/down side walls of a cube makes the most sense from a purely 2D drawing, and that a Tesseract or 4D cube would make the most sense to a 3D mind by seeing at least six of the cubes bending so they can all touch where they are supposed to touch, but the first rule about understanding one or more dimension higher is that it is not supposed to conform to the ideas of how things work and the way you understood things before. You must expand your mind and the way you see things completely being open to new ideas and knowing it is not supposed to make sense the way you thought about it previously." 

         "Take this square that we really know is a cube," Inventor continued. "If someone was going to use this as an example, and thankfully in this way they did not, they might have thought we might have thought the same thing about how a 3D individual with 2 lines of sight plus away could see all 4 corners and sides of each square at once. Thankfully no one brought my name into it saying I would have thought the same thing, but lets go with that using someone else 2 dimensional. Someone 2 dimensional, yes even me a long time ago, might have thought that because we need to walk around a square or turn it to see more than 2 sides at a time, and knew that someone who could line up 2 lines of sight at once could see all 4 sides and all four corners of a square at once, our first thought would be to think of them either being able to see "through" it, or to see it from both sides or both directions at once. Obviously you and I have proven that we understand it only can be done from a point of view we do not normally possess, but 3D people theoretically should know their situation would look the same to us, either as their being able to see through matter or seeming to be on both sides of it at once, though they would know neither is the case. They would need to include the fact that their perceptions of matter are not completely accurate, as we must do daily in our working on the cube project." 

         Assistwo could sense Inventor did not like being dragged into discussing people in the story he preferred not to seem aware of, yet he did not like the ambiguity that seemed to be settling in on the issue and was determined to make all of this go away as quickly as possible to start in on a fresh new topic or perspective. Inventor was not, in his own mind, a cleanup hitter. 

         "The point not made so obvious is that only from an EXTRA perspective and from an EXTRA DIMENSION can all sides of a square be seen at once, 2 lines of sight plus away and in 3 dimensions, not 2. Only from 3 lines of sight plus away and from a 4th dimensional viewpoint can all six sides of a cube be seen at once. Our ways of viewing objects do not apply nor include, nor even describe a 2 line of sight plus away way of thinking. A 3 line of sight plus away lining up view would seem equally just as incomprehensible to any reasoning of those who could only line up 2 lines of sight plus away at once, unless they made the connection that it cannot be done from their point of view so it requires, no pun intended, another point of view, or stepping back or our of their 3D space, and then it makes sense. For a 2 lines of sight plus away view being able to see all four corners and all four sides of an ordinary Flatland square at once, he or she would have to leave Flatland and peek at it from up or down in another dimension, not bending the object but bending the 2D rules of Physics which were only thought to apply. We would think it can’t be done because in a 2D world, it CAN’T be done! Likewise, no one or nothing could see six sides of a cube from within a 3D world because likewise they would have to cheat and peek "over" or "under" at it from a slightly 4D angle and a 3 lines of sight plus away view from outside of its 3D world, to see the other 3 sides one cannot see normally at the same time as the other 3, but seeing through matter, argh, don’t get me started on that one!"

            "So that leaves us with being on both sides at once and seeing only the outsides. I must say," said Assistwo, "I like the sound of people not being able to see through solid matter better, but being in two places at once does not sound right either."

         "Nor should it, that view is equally invalid, though its result is at least the correct one. One is seeing the OUTSIDE of all six edges of the cube at once from outside of its 3D environment and from a 3 lines of sight plus away perspective, not 1 millimeter into it, not one molecule below the surface." 

         "I get the point," said Assistwo. Inventor it seemed really did not like the idea of someone being able to see through matter. It must be left mysterious and flexible beneath the surface to Inventor or he would not find it as interesting, Assistwo thought. 

         "So how can one see all sides at once without using a negative line of sight?" he asked. 

         "Simple," said Inventor seemingly glad to be able to now put all of this behind him. "Since it cannot be done from a 3D 2 line of sight plus away point of view, it needs to be done from a 4D 3 line of sight plus away point of view. No 4D person could do it from in line with a 3D world, you must step back out of it a bit to bring the other side, in this case the other 3 sides, not normally seen at once into view, the same as tipping above or below a 2D world to glimpse the top and bottom sides of a square to see all 4 sides at once. Since it has been referred to as a "plane" of sight, encompassing our whole 2D way of seeing, if you move away from our plane of sight, you see things not possible to see through, and you still don’t, you see around them. Moving completely away from our plane of existence, one can see the whole square at once we could never imagine, with all four corners being equally distant and away at the same time, where one could spin a stick on that plane and never have it appear to get larger or smaller, oh the possibilities! But I digress. In a 2D reality, that view is not possible, we can never get an equal distance from all 4 four sides and 4 corners to see it that way. In a 3D reality, they could never get equally "away" from all 8 corners and all 6 sides of a cube to see it that point of view as equally distant, away, or flat in front of them. By cheating and seeing over the fence of a 4D reality, they could get equally away from their 8 corner cube as easily as someone in a 3D reality could be equally away from a mostly 2D squares four corners."

5.7:  New ground

         "So," began Assistwo, "it would be similar to your mapping of the areas of your sphere project. One could only accurately map a sphere on another sphere. Seeing all six sides of a cube at once, from a 3D 2 lines of sight plus away perspective would be like trying to map a 3D sphere on a 2D drawing. One must necessarily bend and alter its perceptions to describe the effect with one less dimension."

         "Precisely!" said Inventor back to his old usual self once given new ground to cover. 

         "Just like you have to crack open a sphere," he continued, "to lay it flat on a 2D surface, and even then you get a warped picture, to understand seeing all sides of a cube at once 4 dimensionally you have to think of it as cracking open the cube and laying all six sides before you as flat in front of you. That is how, without the warping and distortion, they appear from a 4 dimensional perspective. It can seem like seeing all around it at once but only from a perspective no normal 3D person with a 2 line of sight plus away perspective could imagine or understand. From the extra dimension, it makes sense since all points in the 3 dimensional space can be equally away from its outside triplane of existence at once. One steps back away from it not in any of the normal 3 dimensions to view all sides at once, that would be as silly as our walking backwards from our square and hoping to glimpse all 4 corners, but by going outside of our 2 dimensions moving our whole world including the square equally "away" one can be directly "over" all 4 corners equally, not possible in a 2D world. In a 4th dimension, one could simply step back from all points on a triplane of existence to equally be "over" all 8 corners and all six sides of a cube to view them all at once without being in 2 places at once, nor needing to see through it. But if it makes people happy, they can view 4D space as warped or bent 3D space as we could consider 3D space 2D space bent in another direction. That is trying to keep the old rules and change them to fit a new problem, but once they are ready, they should be brave and consider using a whole new set of rules when their minds can handle it." 

         "So that explains why one can’t see through to objects behind it, but can see all sides around it? I hate to admit it but being new to 3D, I am having the same problems as they have with 4D," Assistwo said. 

         "It is a little bit harder but like making the jump to 3D as you have already done, it just means going a little further, maybe a lot further, but down the same road. The most ridiculous thing about the last section was that an ordinary cube could be mistaken for a Tesseract by a 3 line of sight plus away person while totally within a 3D environment or triplane of sight. Ok, maybe with some silly glasses limiting their sight to 2 lines of sight plus away, but that would be neither remarkable nor to the point. A 2 line of sight at once person trying to get level with a 2D world would never confuse a square in a 2D world for a cube. As long as it was inline with a 2D reality, from any distance it would look 2D. Our cube on the other hand, could look like a possible cube or tilted square from in line with our world precisely because it is not inline with the rest of our world. Without being opposed to our world with all four corners equally away to look like any thing but a line, no normal square would look like anything but a line from in line with our world, even with 2 line of sight convergence. Likewise no ordinary cube could be mistaken for a 4D Tesseract when viewed totally "in line" with the rest of a 3D world. To a 3 line of sight plus away way of seeing, unless it stuck out from the rest of the mostly 3D world as our cube would seem to rise above our mostly 2D world, it would look as flat from that viewpoint as every other mostly 3D object would, which as we have already mentioned looks pretty darned flat from a 4D perspective. Now the Tesseract they built, that is another story. Since it had cubes fitted at right angles "away" from their world, a simulated 4Dness would be apparent, just like one of our square panels sticking up out of our 2D world might either mean a cube or a square way out of alignment with our world. A square panel turned away from a mostly 2D world viewed from in line with a 2D world by more lines of sight than we have, could either be a square or a cube. It could be mostly 2D or very thin, or as thick or thicker than a square in another direction. The extra lines of sight always would run into "above" and "below" into the other dimensional lines, planes, or triplanes, or how many other dimensional "worlds" exist not normally perceived. Unless it stuck up out of it either below it or above it, no way our squares could be mistake for cubes while viewing them directly away from them in line with our 2D world, no matter how many lines of sight you add." 

         "But there are 2 views that a square looks like a cube," said Assistwo wonderingly. 

         "Yes, there you go. Though a cube can look like a square six ways, a square can only pass for a possible cube 2 ways head on above or head on below. The whole idea of a 3D person trying to get their view "in line" with a 2D world, no ordinary square would ever be pointed in manner to look like a possible cube. Likewise, there are 8 ways for a Tesseract to look like an ordinary cube, but there are only 2 views for an ordinary mostly 3D cube to look like a Tesseract. As long as those mostly 3D cubes are viewed "in line" with a mostly particular 3D world, they could never pass for a Tesseract. However, a turned cube like one of our turned squares, could be at the right angle to pass for a Tesseract." 

         "And that angle would be," Assistwo said proudly finally catching wind of the logic of the argument, "with all 8 corners and all 6 sides an equal distance away."

         "Correct," said Inventor. "When "in line" completely with one single particular 3D world, to a 3 line of sight plus away perspective, everything would look as flat as Flatland to a 2 line of sight person, but a turned cube at an angle with all 8 corners an equal distance away would appear to be at the right angle and have the right depth the other objects would not seem to possess. It would appear to be at one of the 8 angles it could be mistaken for a Tesseract because all of its turned 3 dimensional depth all would be facing toward it, one would need to go around it to see its 4th dimensional value, to see if it was really as flat as everything else, just turned toward it, or how "thick" in that extra dimension it really was. Because all 3 of its 3 largest dimensional values would be directly facing it, it would be both hiding its 4th dimensional value and be obscuring what was behind it." 

         "But that sounds like a rare thing," Assistwo said. 

         "Only when going one step up or down the dimensional ladder. If there are 3 dimensional worlds or multiple 2 dimensional worlds, it would be a rare possibility that a 2 line of sight plus away 3 dimensional being would be exactly in line with ours. It would most likely be at some angle opposed. 3 dimensional beings could exist in and move through 2 dimensional Universes without perceiving them as such. 4 dimensional beings could pass through 3 dimensional Universes and not perceive of their existences either, just it being a part of their space they normally pass through. The idea of trying to be "in line" with a particular lower 2D or 3D world would seem absurd unless they saw objects all lining up that way for a particular reason and wondered why. To turn objects into another dimension, as we have seen already, they must already exist or have a value of that dimension already. Unless that dimension is relatively insignificant or unused, it may be unimportant to have awareness of that aspect of space, like bacteria living only at the surface of a still pond. More likely, it would seem objects, at least living objects, would become aware of most or all of the dimensions they exist within that were necessary for their survival. Beings of lesser dimensionality or so thin to be close to a wisp of existence might go unnoticed. Things of equal size possessing equal stable number of dimensions would register on each other’s radar, and they would define that space, possibly within countless other dimensional regions of space, ways of interacting with other similar sized dimensional objects, though that seeming Universe might exist within and through others of more or less dimensions not registering to each other, but some parts possibly overlapping existences and spaces in others as well." 

         "As you said, a 4D being or objects could have existence in a 3D, 2D, or 1D Universe but not the other way around. A 2D person or 3D person or object would have no existence in a 4D world without possessing the necessary non- zero dimensional values. Isn’t this weird possible overlapping of different dimensional Universes at bit much?" Assistwo said rolling his eyes. 

         "Just because it could be or be seen that way doesn’t mean it has to be or be seen that way. And if it were true, it is only slightly less weird as multiple 2D Universes or multiple 3D Universes. That objects can exist in more dimensions than they perceive or that Universes can exist around them which they cannot perceive is nowhere near the top of the Universe’s weirdness scale. With an object big as a sun, who could measure how many dimensions it might possibly exist within? Even this 1 meter square cube is an enigma of how many dimensions it can contain. Even with a slight unintentional 4th dimensional thickness, it could even be mistake for a full 4D Tesseract from 2 views. Looking at it from outside it and thinking we know how many dimensions it currently exists within is impossible without a new math, map, or understanding of its internal structure or order." 

         "So it’s back to inside matter again?" Assistwo asked. 

         "Isn’t it always?" Inventor asked back, "By the way have you seen the new motto for my door?"

         "Another one?" Assistwo shrugged emphatically. 

         "Yes, two on each side now, it needed balance," Inventor joked. 

         Assistwo went outside the door and read, "There are no objects, there is only matter as a whole. There are no dimensions, there is only space as a whole. There are no minds, there is only consciousness as a whole." 

         "It seems like we have a long way to go still yet," Assistwo said when entering the room again to Inventor who seemed to be getting ready to leave. 

         "If not us," Inventor said, "then those who will come after us. The horizon to how far we are permitted to go at this time is approaching faster now. We must stop for awhile or risk sailing of the edge of our 2D world." 

         "I don’t like the sound of that," Assistwo said grimacing. "If possibly not us, then at least tell me what’s over that horizon in case we don’t get there ourselves."

         "That the same perspective or space at different times is exactly the same and completely interchangeable with different perspectives and points in space at the same time," Inventor said moving toward the door. 

         "Heavy," Assistwo quipped. "I hope we are the ones who get to try and explain that one. I don’t like the sound of falling off of or moving out of phase or sync with the 2D world." 

         "No," Inventor agreed, "that does not seem desirable from any possible perspective from within it. From an outside perspective, who knows?"

         "Certainly not me!" Assistwo said flashing his almost omnipresent impish grin. "What about you Inventor? Inventor..?" he said while turning around not realizing Inventor had quit for the day and already was headed home. 

6.1:  Burying the wire frame model: Beginning the end

         "Where now from here?" the assistant asked Researcher more than a little worried Inventor might not be around anymore. 

         "The most perfect and perennial question," Researcher replied. 

         "Huh?" the assistant said. 

         ""Where now from here" is the most basic question. It can either be thought to be a location or state of future order to travel in time to reach. "Here" implies that you have existence in time and space, "Where" implies both another location or state of being, and "now from" means you have time or the means to travel to that other location or time where things might seem different." 

         "Slow down, I haven’t had my coffee yet. How about "What’s next?"" the assistant said. 

         "Now we have to sweep away the most popular ways of looking at tesseracts, the wire frame mode and inner to outer conceptualizations. Since we have already stated, and know by experience, that the 2D equivalent representation of a cube drawn non-perspectively isn’t even close to representing what a cube really is like, we must see the wire frame Tesseract model as equally useless," Researcher concluded. 

         "2D...non-perspective...wire frame model?" the assistant stammered while sipping his coffee. 

         "Yes," Researcher continued, "the idea of representing a cube in 2D imagining a smaller "inner" square, 4 diagonally bent sides, and an "outer" square. A wire frame Tesseract is just as bogus. The only way to begin to sort out the mistakes, the same mistakes, is both to imagine parallel 2D and 3D worlds of either different dimension of 2D and 3D worlds, or the same world at different times, it makes no difference."

         "I thought," said the assistant both warming up to the discussion, and with his coffee at the same time, "that there is a big difference between time and another physical dimension in that time runs only in one way and in a physical dimension you can travel in either direction freely. It seems you are approaching the horizon Inventor was worried about, getting out of sync with his world. Don’t you take that warning seriously?"

         "Only too well, but we must begin to test the deeper waters sometime. Getting a little bit ahead of the rest in deeper waters might be possible as long as we don’t lose track of the shore or try to outdistance too much those around us. We will be using time and another set of physical dimensions interchangeably as if they were the same thing for building a better representational model of a Tesseract the only way you can, by stretching it into another dimension. Since we don’t have any other dimensions handily understandable for us to use, we will use time as if it were a physical dimension one could travel through, though that may not be the case, but it makes it easier to describe it that way. Time, Inventor used to illustrate his cube the best way possible, and time we must fully exploit now to kill off the wire frame model of a Tesseract completely. Time as we said earlier is the best tool for both understanding other dimensions or other dimensional worlds of the same number of dimensions as yours co-existing together side by side, and for understanding the full dimensionality mentally of your own reality you only partially perceive at a time and must move around in, or turn it in relation to you, to get the fullest picture possible of that extra "awayness" dimension which flattens everything out in all directions or all dimensions around you, no matter how many you perceive. "Away" always takes away one of those dimensions and only time coupled with movement can bring it back or make it seem real, even though it is partially an illusion spread out over a dimension existing mostly in perception spread out over space AND time."

           "Too deep for me," the assistant said worriedly. 

         "Yes, turning back now to the wire frame model," Researcher said with a smile. "Its biggest fault is it tries to bring into focus things which cannot exist in the same dimension at once. In both the cube 2D minus perspective wire frame model, both the inner and outer top and bottom of the cube are in the same location relative to the 2D world in different directions the same distance away. They are both the inner square by that representation. The outer one which appears inside out is not representational of any reality whatsoever, and the same goes for the 3D model of the Tesseract. Both the "top cap" cube and the "bottom cap" cube fully in another dimension would both have to be understood as the center cube in the representation. If in both wire frames you view the inner square or cube, depending on which you chose, as representing both tops and bottoms at once, and the sides not warped in one directions toward the middle but in both directions at once toward the middle in 2 different directions at the same time, then you have the only minorly useful use for the wire frame model. However, if you use multiple drawings of the same object in different successive Universes, or 2D or 3D worlds either in another dimension or another time, it becomes simpler to see the relationship. Draw two 2D worlds above and below the 2D world with 2 full squares, then a warped bubble for the sides. Straighten the sides to what from any of the 2D planes or worlds in between points of view would vanish into a line between the 2 squares and you have a perspective drawing more accurate." 

         "We already have perspective drawings of cubes," the assistant joked. 

         "Don’t get sarcastic," Researcher warned. "Yes we have an understanding of 3D perspective drawings but from a 2D point of view, the equivalent drawing would be a side bent around so much it would be vanish into a straight line at the edge of the square that would be representing both squares at once, and the sides would become invisible, that would be an accurate non- warped view." 

         "Without meaning to be sarcastic, but by extension, that would mean the only way to draw or sculpt a Tesseract would be as an ordinary cube, call it 2 cubes at once, and that six other cubes exist only as imaginary square planes at the surface connecting them, but disappearing into an event horizon around the surface of it?" the assistant asked. 

         "Fasten your safety belts because here is where we have to begin bumping back and forth between multiple 3D worlds you can either think of as parallel 3D worlds in your own timeframe or different times of your own 3D reality. Whichever way you want to look at it you can, but now we have to go to multiple realities or multiple timeframes of the same one, and deal with them both as one and the same thing," Researcher said. 

         "Why to I get the feeling," said the assistant, "that Inventor was proving how much smarter he is by not wanting to go this far?" 

         "Yes, there be dragons ahead. Should I continue?" Researcher asked. 

         "What the heck, I don’t care, just thought the point of no return ought to be commemorated somehow," the assistant responded. 

         "Ever the optimist," Researcher remarked. "Since one can use multiple dimensional or parallel Universes existing indifferent regions of space at the same time or the same Universe at different time periods, I will use them interchangeably, first as one then the other. If you are uncomfortable with the idea of parallel dimensional 3D worlds existing within or around your own, you can just imagine being able to move slightly back and forth in time into another time frame, then back again. To set the stage, let’s imagine that the Universe starting with one big bang. Though that is a very poor analogy, it is one many people are comfortable with for some reason. Boom, a big something explodes sending a shockwave in multiple dimensions of space in all directions away from that point (argh). Within that blast zone or shock wave is the Universe you perceive. Riding time is like being locked within that wave. You could surf it forever because you and it are moving at the same rate and in the same directions so technically from your point of view it both never moves and always moves, and at the same time. Perception causes you to bounce back and forth from perceiving its movement through movements of yourself in relation to other things, or moving other things in relation to yourself. Yet both you and everything else are the same object moving outwards in sync with each other, a static wave of debris of the same object shattered into both space and time, or into a fracture of space and time itself."

         "Even though that would take years to explain," Researcher concluded, "time is short so let’s just keep moving along. Behind that wave is another wave, an aftershock so to speak. Since time is fractured as well as space, let’s imagine that second wave following is the same as the first wave. Second verse, same as the first. Each of these waves spreading outwards successively is the same wave at different points in space and time, at the same time and in the same space. This is the framework we will use for the time aspect of describing 4 dimensional objects. We will imagine the same object appearing at the same place at the same time in multiple space and time periods, but since we can’t use either of those terms anymore because we are attempting to collapse or view them in the same line of sight simultaneously, space and time fractured together, we will use the terms blast zones or waves, where they exist in the same spot relative to the ahead and behind zones. If you are not comfortable with the idea of fractured time, ignore the time references and concentrate or relate it all to fractured space, or multiple dimensional 3D worlds because, though I will bounce back and forth from describing it in both ways, the time references are just to make it easier to understand (as long as you are willing to throw out notions of causality that is)." 

         "Since this will be both relating to a physical dimension as well as time, I will now change the numbers a bit. We must now ascribe our 3D world a numerical 4D value. We will say all objects we perceive have a common 4th dimensional "width" of 10cm. For convenience we will say our 8 cube "walls" of a Tesseract are no longer 20cm but 10cm along with everything else in our world, unless we widen them. The spheres (remember them?) really need no top or bottom cap to be confined, if we really have confined them at all. Since they seem to want to or only be able to leave our triplane of existence for a few moments at a time, and exist mostly here as far as we can tell, we can think of their movements through multiple Universes or blast zones as limited. When we widen or increase the 4th dimensional value of our cubes beyond the 10cm of our normal existence we are building a higher wall into or through other dimensions or other times making it harder for them to go over. Without a top or bottom capped, if all six turned cube sides were wide enough, it would be like higher prison walls, requiring them to stay out of phase with this world for as long a time away as the walls are high. Think of the spheres as birds with clipped wings or too young to be able to fly directly away or straight away from our triplane of existence to go over the walls even without needing a top and bottom cap. Since the walls can be infinitely high if we can increase the 4th dimensional mass somehow, the only limits are if we knew how to do it, and how much matter we could find to channel into it." 

         "Instead of keeping it," Researcher continued, "exactly the same from every direction, lets make a rectangular Tesseract. Let’s take a 1 meter cube only 1cm of 4th dimensional volume and throw it only 2 dimensional blast zones ahead, and another one 2 blast zones or alternate realities behind our Universe’s movements through time. Now that we have the top and bottom caps in place fully ahead and behind in time and space at a given and perpendicular location and distance in time or space, 20cm or two blast zone worlds ahead, and 20cm or 2 blast zone worlds behind but in the same location in space or in time depending on which way you want to look at it. If viewing it as alternate physical dimensions, they exist in each relative to this one at the same time and moving through time at the same rate relative to us. By increasing the 4th dimensional  "mass" or "time" of six more cubes to 30cm and keep them evenly above and below our 3D triplane or Universe, and moved them into six spots adjacent to where the other cubes exist in different timeframes or alternate dimensions, we would have an airtight 4 dimensional barrier on all sides of 4 dimensions." 

         "So in the time example," the assistant said, "you have increased it to an extra time or blast zone reality forward and backward in time from our own. That coupled with the 2 blocks also 2 time zones ahead and behind means in all directions in space and time around it there is a block moving through time with it at an equal speed. Problem is of course.." 

         "Yes, causality. When looking at it from a strictly time perspective, throwing things perpetually ahead of your timeframe is never a problem so long as it always moves ahead of you at the same rate so you never have to deal with the effects of the paradox. However, throwing something back 2 timeframes behind requires altering the past which from our point of view has already occurred. As long as the block is not moved, it is irrelevant too. Since its 4th dimensional mass has no weight in our Universe in the physical sense of extra dimensionality, and time one would think has no weight either, we could throw it backwards into however many timeframes it stood in the same spot over and over again indefinitely increasing its 4th dimensional volume exponentially and never encounter a paradox so long as it and our world move at the same rate together."

         "What about throwing it back further than it was at the time?"

         "That would be bad, and an inexplicable paradox would develop," Researcher concluded. 

         "What about moving it into the future, wouldn’t that be affected?"

         "No," Researcher speculated, "Since all futures of the moment will record the objects movements in the past as well, all future time states likewise would move in sync as well. So long as it does not get thrown back further in the same location than where it already was, no real paradox could conceivably occur."

         "What about in the spacial sense of alternate dimensions moving in sync with our time?" the assistant asked. 

         "There one at least does not have to deal with causality problems. You would simply be increasing the mass of the 6 side cubes into one extra dimension parallel world from our point of view in each direction away from this one. The conceivable problems with that are that that space not be occupied by another object, that it be moving not just necessarily in time sync with us, but spacially as well. If there are no alternate realities, that would seem easier than worrying about hitting something, but then if it were only empty space, this could cause things to drift off away from our mostly 3D reality which is moving through space and time at a set rate," Researcher responded. 

         "For the record," said the assistant, "we have been treating extra dimensions thus far as empty unoccupied space with no objects, forces, or pulls."

         "Yes, but we cannot know that," Researcher replied. "If objects could exist in parallel triplane dimensions with their own movements, forces, energies, and so on, we could not predict anything about location or state of objects turned into them, except that for the moment they are still attached, what happens to them later we cannot see. With all of the seeming inconsistencies of using the time model, at least we can visualize and predict what was and will be where and when." 

6.2:  Ahead to the past: Sensible time distortions: Missing them two too

         "If we consider the beginning of time as an event spreading outwards in all dimensions in space at once moving at the speed of light, moving in line with that event would mean it would always be occurring at once. It would always be its own birthday. It would also be like a tree falling in the woods without even God to hear it. It is only an event when it hits or affects something," Researcher said. 

         "What if it hits something but does not affect it?" the assistant speculated. 

         "Without affecting it, who is to say it really happened?" Researcher answered. "It might be akin to a minor fender bender neither person wants to make a big deal over or acknowledge. It can also be compared with an unstoppable force hitting an immovable object. They both might call it a draw. Consider the moment the Universe began with all its aftershocks, time distortions of the same event waves hitting an object in space which refuses completely to yield or acknowledge its mighty blast like powers whatsoever. As the Universe event passes around it, it remains steadfast throughout every possible echo realties. Since it is in the same location in every subsequent time event which may come later, it remains motionless and outside of time. There the Universe passed by in an instant at light speed and may as well never have happened at all since it had no effect. From moving completely in step with the birth of the Universe, which is also outside of time as we perceive it in a different way, always being the same time, the object was moving by it at light speed but did not affect it like a sealed straw through a bubble."

         "Once the birth of the Universe hits something that is affected, perception begins. The moment of conception so to speak keeps moving on but now it started dragging this other thing along with it. The other thing just sitting there as empty space or perception waiting to happen was just sitting around in nothingness, and wham, gets hit by the birth of the Universe like getting hit by a freight train or a large truck. Things from its point of view and the Universe’s point of view get very weird. Suddenly from the Universe’s point of view, a fracture develops. Unlike the immovable object which stayed identical through all the subsequent identical echoes, this new problem is appearing differently in each subsequent blast zone or echo. Ignoring this to the insurance company is not an option. Everything in each subsequent echo or blast zone is changed by this whatever it is which did not have the decency to remain immovable, and thereby would have been utterly forgettable." 

         "From the object or space’s point of view affected by this collision," Researcher continued, "it is equally troublesome. Suddenly sitting in the middle of nowhere doing nothing is not an option. Time echoes are suddenly everywhere passing around it and sweeping itself along with it. It is now moving or seeming to be moving along with the rest of the Universe but not quite as fast. It is being bounced from one echo into another, trying to hold its ground while a time storm echoes all around it, like trying to hold onto a flagpole in a hurricane, making some progress at not being totally swept away, but constantly losing ground as well." 

         "By that example," the assistant interjected, "wouldn’t the wake of the collision be traveling in the wrong direction? The object would be affecting or disturbing the time moving away from it where the past times had already passed by it." 

         "Yes," the researcher replied, "from the point of view thus far, moving forward in time now in the same direction as the original event, in this case the birth of the Universe, by not keeping up to speed with it, it seems to be disrupting the time behind it creating a wake of its existence backwards in time. The original event is still moving on ever outward but the shadow of the object not keeping up with it is being cast outward now as well. As if things weren’t bad enough for both, the event and the object or space itself, it now gets even worse. It loses its cohesion and begins to break apart, into smaller and smaller pieces.  From the object or spaces point of view, the accident was fatal. With each new piece that breaks off, a new event occurs, each new event creating its own smaller wake around it seemingly moving backward in time as each piece is still hurled forwards by the original blast but now at slower and slower speeds as it begins to break apart more and more. Ironically as it slows down from the speed of the original event and the original accident’s speed, it actually begins moving faster and faster through time now." 

         "Because," said the assistant trying to stay in the conversation, "it is not keeping up with the original event. It is passing through more and more aftershocks as the original event gets further and further away ahead of it, and as each remaining section slows, the beginning, which is still moving at the same speed, seems to get more and more distant." 

         "Correct," agreed Researcher. "Since that time has already moved on past our ever smaller remnants of that collision, even if they could regain the speed of either previous original events, they could never catch up with them so causality is preserved. As each piece moves slower and slower, time speeds up more and more, though because they are still moving pretty quickly still in the direction of the original event, all times does not seem to fly by in an instant as it would for the immovable object, nor stand still like it does moving completely in step with the birth of the Universe either. It has found a happy middle ground." 

         "Yet it is still getting bounced from echo to echo or blast zone to blast zone, but at a predictable or seemingly even rate now I take it?" the assistant asked. 

         "Yes, the time distortions even make sense now. The wake is moving away from it backwards in time, but also ahead of it in space, where the birth of the Universe has already moved on ahead of it, this time distortion ahead of itself into the past actually becomes its identity. The blast zones or echoes hitting it now tend to hit you in the face without warning, but turning around to see the trail you are leaving behind ahead into the past gives you bearings on a location in time and space. By neither keeping up with the birth of the Universe nor holding ground completely letting it all pass you by without affecting you, you are partially dragged along with it and partially holding ground passing through echo after echo remaining as intact as you can for as long as you can." 

         "But I take it this is all perceptual?" the assistant asked. 

         "Probably," Researcher guessed. "Since the only set points in this are the beginning moving outwards at an infinite rate and existence, and whatever can remain steadfast or at zero throughout, each successive moment in time is both always occurring when viewed in step with the original event, never occurring to anything that can hold its ground, and at varying rates for everything moving at various speeds in-between, or being dragged along with it, more accurately."

         "So we have plenty of company," his assistant said trying his best to sound like Assistwo. 

         "Yes, whatever else that broke apart moving nearby whether actually all the same object or space hit by the collision or debris from other collisions create the local space and local time around objects."

         "Whoa, whoa, whoa. Once I think I understand where you are going, you slip in a curve. I thought time was the blast zones or echoes from the beginning of the Universe hitting us in the face. Now you are saying time is created locally between objects, which is it?" the assistant asked. 

         "Either, both, I can’t say for sure. After the last section’s "corrections" by Inventor, this time I am not going out on a limb anymore. If I was going to guess, I would say the blast zones or echoes are caused by the original event, but are also concentrated around matter which is collapsing them ahead into the past. This creates local time and space fields around and between objects, and the rate we move through these creates our local perception of time in conjunction with, and by relation to, the other matter around us," Researcher answered. 

         "I sense you being a bit more careful with your words since Inventor pretty much tore into everything you said last time. Do you think they are coming back?" the assistant asked meekly. 

         Though Researcher did not like anything about what that question implied, he let go any impulse to take exception to the honest question which he had been wondering himself. 

         "I don’t know," he replied. "I wouldn’t mind being completely embarrassed by having all of this thrown out the window like he did last time if it meant seeing something I have not considered or overlooked. I have to admit, I hope they attempt what he thought now is not the time for. If not, I will miss his constantly showing me up." 

         "And Assistwo too," his assistant reminded. 

         "And Assistwo too," Researcher agreed. 

6.3:  Multiphasers on stupify

         "So it seems," the assistant began, "we are talking about, for lack of a better term for it, multiphasic realities. Parallel dimensional realities in which objects can extend through more than one reality at a time." 

         "Yes," said the researcher, "just as one extra dimension seems like an infinite number of parallel numbers of ones perceived previously, 3 dimensionality as stacked 2D worlds, 4 dimensionality would be to us like stacked 3D worlds across time or parallel 3D worlds in or at the same time. Either could be thought to be the case depending on how you look at it. Either way, traveling through or moving out of one would be done by seemingly moving into or through another. From a 3 triplane of sight plus away point of view, similar to how sight in line with a 2D world would be able to glimpse other parallel 2D worlds nearby, that extra line of sight, when only in line with ours, would not be perceiving around objects as Inventor rightly pointed out in correcting me, but would be aimed at perceiving realities nearby to our own in nearby times ahead and past in the time sense, or alternate dimensional 3D worlds in the spacial sense." 

         "And those can be thought of as being equal, similar, or even inter-changeable depending on how you look at it? I don’t know if we are over our heads yet but we sure have left the shallow end of the pool," the assistant speculated. 

         "We have to bear in mind as Inventor said, that it is not normal for any 3D 2 plane of sight plus away viewing to be completely locked in line with a 2D world, or for a 4D 3 triplane of sight plus away point of view to be completely in step with a 3D world. From any other point of view, a more common mixture of partially multi-spacial views of objects from angles we don’t normally see them from, or partly multi- temporal views of objects near times, depending on how you look at it."

         "Depending how?" the assistant asked. 

         "If there are no extra physical dimensions, the time sense would apply. If there are 4 physical dimensions to the objects, then the spacial view could apply also. Since we don’t know absolutely which would apply, thinking in both terms covers the bases better," Researcher answered.

         "So in the previous example of a mostly 3D cube with a slight 4th dimensionality, if when turned can be thought of as being a cube in each of its realities, how come it looks like a cube in none of them?" the assistant asked. 

         "That answer is fairly obvious," Researcher replied. "Because, as we have given for the purpose of argument all mostly 3D objects a common 4D value of 10 cm, remember if they were completely 3D only they could not be turned, it would only look like a 1 meter cube only from completely within that reality we and it exist in equally together. From any other angle it would look flat. When we "rotated" it out to cover more multiphasic realities at once, we spread it thinner over each separate reality. It is still a full cube, though still fairly flat in a 4th dimensional sense, but now you need to see it, from our limited points of view, from more than one reality at once. It is like a turned mostly 2D square from out above and beyond a 2D world, partly in many 2D worlds at once, at least that is how a 2D person would see it. Part of it would exist within each "parallel" 2D world above and beyond their perceptual plane of sight. Since we would not perceive 3 dimensionality as separate 2D world’s stacked together, we see it as normal a direction to be pointed in as any other." 

         "So from a 4D perspective or 3 triplanes of sight plus away, a 3D world view would be uncommon?" 

         "It depends," Researcher said as be began considering the question. "If completely only 3D, a 3D world would not exist to them. We can perceive and understand a mostly 2D world because of gravity. Until fairly recently, much of our existence could only be dealt with on 2D terms. Going over something was limited to catapults, flying and landing safely with machines or balloons was only a dream. We still live in a mostly 2D world but we are building taller buildings, flying more often above our world, tunneling more below, but mostly, gravity still locks us into a 2D mode most of the time. Similarly from a 4D perspective, gravity might limit one of their methods of movement so they might be able to conceptualize our more limited 3D sight or way of viewing things as we can conceptualize a 2D way of thinking and viewing things." 

         "No 4D Superman?" the assistant joked. 

         "If planet and gravity bound, no, no 4D Superman, but maybe 4D superbirds."

         "Not with the price of gasoline today. On my salary, even my 3D Superbird costs too much to feed!" the assistant said rather enjoying the chance to mention his beloved Mopar.

         "So with gravity," Researcher continued, "the 4th dimensional movement would be confined to either alternate nearby, what would seem only from our limited view, as either nearby 3D worlds or nearby time "zones" we cannot travel through. When we turn our mostly 3D slightly 4D objects "outward" away from our 3D space, they appear thinner because they are trying to cover the same space at more times, or more multi-dimensional "spaces" at the same time, but only from our points of view. To them, its just a region of space or an alignment unusual for them, or impossible without the necessary non-zero 4th dimensional value to make that possible."

         "Yes, and if the cube was fully 4 dimensional, it would look like a full cube when viewed from completely in line with each one of the alternate 3D realities we would see it as existing within," added the assistant. 

         "And from a view outside of what seems to us a to be 3D world, looking in, it would be apparent from any angle not directly  perpendicular to that 3D world, that that object had an extra dimensionality to it, and that it "stuck out" of it in a way that most other objects did not," he continued. "What if all objects in our perceived 3D world had varying degrees of 4th dimensionality?" 

         "Then our way of perception would probably go unnoticed to those with more ways of perception. If a lot of mostly 3D but slightly 4D objects seemed to line up, that might be of interest from even a 4D perspective, as we might wonder why 3D objects in space prefer to line up in 2D planes of movement. If there was no seeming order to our random values of 4Dness, our perceived world would not be readily apparent from other perspectives. Though they might perceive of a 3D way or 2 plane of sight plus way of looking at things, without an order or pattern to go on visible from their perspectives, they would not know where our perceptions of the Universe begin and end." 

         "So how do perceptual orders form?" the assistant dared. 

         "I am not going out on a limb on that one in case Inventor comes back. It is however safe to say, I think, that objects moving together at the same speed or in the same blast zone with each other would be apparent to each other. If they moved in tandem with each other at that moment, and in similarly repeatable subsequent times and similar distances, they would be real to each other, all riding the same wave or on the same wavelength. Similar sizes helps too." 

         "You said with each other at that moment and in similarly repeatable moments," the assistant asked. "What did you mean by that?"

         "What you termed a multiphasic way of viewing things, objects stretched over multiple time periods in the same space being seen as the whole object, or equally possibly existing in different regions of space, to us different Universes, all at the same time, means we cannot view it as ever existing in only one way or the other. Since time itself is one of its components, it must seemingly exist in the same space and time repeatedly and at once to seem to exist. Since both views apply, we cannot see either the time nor the space of its existence as absolute. It has no existence in any particular moment in time, it only exists through time into space or through space into time," Researcher concluded. 

6.4:  Mapping 4D objects on spinning spheres

         When Inventor walked into the lab, he thought he knew the kind of greeting he would get from Assistwo, but as always, Assistwo surprised him yet again. 

         "Hey Inventor, I’m not dead!" Assistwo said. 

         "I thought you going to say "Hey Inventor, I thought you were dead!" That has been the reaction I have been getting everywhere I go today. But you are right, from your point of view, your own continued existence is more important or noteworthy to you. Either that or you are smart enough not to remind me that I am still here, but it is nice to see you too," Inventor said while settling back into work mode. 

         "I thought we were done, or done for," Assistwo said. 

         "Nothing lasts forever, not even time," Inventor began, "all I really said was now is not the time to be discussing too heavily the ramifications of space and time being completely interchangeable, and I still believe that to be the case. It is still not time to go there yet. However, my favorite topic has come around again, and I couldn’t sit this one out." 

         "Oh no," Assistwo said bracing himself, "not again! Please don’t tell me." 

         "Yes, that is right, ball spinning!" Inventor said smiling. "What, you thought I was going to say something else?" 

         "I am not touching that one," Assistwo said, "too easy and too many ways to go, I will let you continue without comments for awhile." 

         "Ok, I will take the ball from here now, so to speak," Inventor began. "Stick spinning, and my new favorite, ball spinning, illustrates spinning on one, two, and three axises. You can spin a stick on two axises but it is not as fun as spinning it in only one direction, plus you can’t paint spots on it." 

         Assistwo was beginning to turn purple from restraining himself from making a comment on this. It was still just too easy to say something smart, but he stayed true to his word and remained silent. 

         "Ball spinning," Inventor continued, "will represent curved 3D space, which as we have already mentioned can be analogous to 4D space. We also said 3D space can be thought to us 2D people as being similar to 2D space curving around back into itself, and 4D space can be thought of as 3D space curving around itself as well. But that will come later, for now we will first deal with the spinning."

         Enough time had passed for Assistwo to control himself from making a smart, wise-ass, and possibly very rude joke. It was not easy for Assistwo to let it go, but he simply said, "Paint spots on it?" 

         "Yes, with a ball or sphere we can paint spots on it relative to the positions of the sides of our cube. Since the ball is curved outwards, we can see the spot at the top and the spot at the bottom at the same time, something not even a 3D person could not see in regular 3D space which is not curved, or two opposite sides of a cube at once. Since from a 4D or 3 lines of sight plus away perspective this is possible, it appears from a 3D 2 lines of sight plus away perspective that 3D space can be curved, which as we already said repeatedly only appears to be the case, and only from a limited 3D perspective." 

         "Right," said Assistwo, "before getting all cryptic and mysterious about space and time being interchangeable, we did, ok, you did, a pretty good job of explaining all points of a mostly 3D cube appearing as flat from 2 directions perpendicularly and equally "away" from its 8 corners at once. From those two angles outside of normal 3D perceived space, a mostly 3D cube would be indistinguishable from a fully 4D cube or Tesseract until it gets turned or you try to move around it. Are the 8 corners of the cube analogous to the 8 cube sides of a Tesseract?" 

         "I said we will first deal with the spinning before getting into curved space or 4D," Inventor reminded. "Ok, since stick spinning is my forte, I get to explain stick spinning in 3D terms, only now we are using balls because of the spots we can paint on them. Each of the six spots, best represented by different colors, represent 3 sticks, or lines of sight, all moving through the center of the ball or sphere at 90 degree right angles to each other. Spinning on one axis only can be viewed in more than one way. We in the 2D world can only view spinning on one axis one way, what we will call edgewise. In stick terms, it would seem to be getting thinner and wider as it moved with one end further and one end closer, then both equal distance, then the other end closer and its opposite end further away. There is no top down view of a spinning stick from our perspective, alas, what a sight that would be, as the spinning requires both of our 2 dimensions to occur. As it has already been pointed out, from a 3D 2 line of sight plus away point of view, spinning on 2 lines of sight perpendicular to each other and the away line of sight would be similar to each other, and to the way we view a spinning stick but the 3rd way where all points of a plane or 2D world are equal points away, that is quite different." 

         "Yes," said Assistwo, "where the tips go around each other but never get closer or further away to the observer, where the spinning axis is completely in line with the away line of sight." 

         "Exactly Assistwo," said Inventor. "With our ball with spots on it, the equivalent of that event would be having one spot always in the center and four other spots chasing each other around the edge. That is one way to view spinning on one axis. The other way to view it is 90 degrees away from that point where both axises spin points are equally in the "away" direction and both spots at the "poles" around which it spins are visible at once. The you have a very different view of the same spin. Now instead of making a circular motion around the visible edge, we see stick spinning the way we see it in the 2D world, as the spots representing the axises or sticks come closer to the viewer and then move away. When both poles around which it spins are equal distance away, the other 2 axises move in a straight line across the middle in-between them."

         "Don’t they always run in a straight line between them?" Assistwo asked. 

         "Yes, but it does not always look that way. Depending upon the position of the observer, each spot can seem to travel around the edge, stay right in front of you, or seem to continually move in a straight line in one direction across, or a combination of these depending on the angle of your "away" position relative to the angle of the spin. If we spin it on 2 axises at once, it gets even more complicated."

         "So if both of the "non-away" axises are both at 90 degree angles to the away line of sight, they automatically line up with each other and follow each other in a straight line from the away line of sight or away from whichever other axis is turning’s perspective. The old "Once an away direction is determined, all other points of the other axises are on a plane away from it." What about triplanes?" Assistwo asked. 

         "Not yet Assistwo, you keep running ahead of me," Inventor admonished. "Yes, whichever one of the 3 axises of a sphere is turning, it serves the same principle as an away line of sight, it makes the other two seem to line up in a particular way, relative to that motion. In this case they seem to follow each other in a line like a big letter X spinning when viewed from above. That is something we can see clearly when the line of sight is directly over one of the poles around which it spins. When both poles are visible or equal distance away, both parts of the X converge into what we know of as 2 line of sight convergence." 

         "And spinning on two axises at once", Assistwo quipped. 

         "That would seem way if you were directly over one of the poles of spin, the other pole of spin, were it to be spinning on a 90 degree angle to the first, that extra point of spin would be around one of the spots moving around the edge. This means that if you were directly over the first spinning axis and turned exactly in sync at the same speed with it, it would appear normally to you as if spinning on only one axis," Inventor said. 

         "Double spinning, I don't think I like where this is potentially going," Assistwo said wondering if he should have had eaten first on the way to work. 

         "Right you are, to the game room, Assistwo."

6.5: The Centrifuge and the Omoglatron

         Ever since the success of the 3D amusement park ride, Inventor's experiments were privately funded by the proceeds from them, leaving Inventor free to invent all kinds of weird things with seemingly no purpose. Many of these could also double for new amusement park rides since, as I said, pretty much were lacking and basically consisted of spinning you around since they have no vertical axis in their 2D world. One of the older rides already invented was called the Centrifuge, which Inventor bought anyway since he was now rich, rides were the reason they had all the funding, and said it was necessary for his research. He also thought it was fun. 

         The Centrifuge was basically a big spinning circle with walls. If you stood in the center and opened the doors you would see the room outside of it spinning around like most other Flatland rides. However, if you moved away from the center spot, you would spin more erratically and faster and eventually if you moved further away or could not hold a point further away from the center, you would get thrown up against the wall. Inventor speculated this force seemed similar to one he called gravity, which of course no one took seriously as their is no gravity in Flatland or their Universe would seem 1D more than 2D if they did have such a force. (The lack of gravity also would make the Centrifuge not work, but never mind that for now, that will come later.) 

         On Inventor's instructions, he and Assistwo got into the Centrifuge ride. In the middle he set up a video camera. He instructed Assistwo to hold on to one wall while he stood on the opposite side and turned the ride up to full speed for 5 minutes. Assistwo was right, it was not a good idea to have had lunch first on the way to work.

         After they were done, Inventor showed the videotape. 

         "You don't look so well, Assistwo," he noticed. 

         "Was it really necessary for us to be in the videotape? Couldn't you have used dummies or poles or anything else?" Assistwo wondered aloud. 

         "Yes, but then it wouldn't have been as fun. You really should try to enjoy your work more, Assistwo," Inventor added. 

         "I just had lunch," Assistwo said. 

         "Well, you should have said something. As we can see on the tape, though we are clearly spinning around the camera, it looks identical to this tape we made yesterday where we stood in the same spots and spun the camera around, except for the part where you throw up. Next time, say something," he added. 

            "So the question becomes," he continued, "how can we tell if something is spinning relative to its environment or if its environment is spinning around it?"

            "For you maybe, for me the question is when is it a safe time to eat lunch," Assistwo quipped. "At least it wasn't the Omoglatron.... Oh no, don't tell me."

            "Yes, its time we did the Omoglatron thing. As we know, the example we just did describes spinning in a non-curved spacial environment. To really understand spinning from the inside out, whether relative to other things in your Universe or spinning outside of your Universe and back into it as the squares spin, it is best to look at it from an Omoglatronic perspective."

            "Omoglatronic?" Assistwo remarked. "It is bad enough for you to invent new words like the "Omoglatron", at least you had a concept to back it up, but do we really need to invent new adjectives as well?"

            "Stop being so Assistwoish."

            "Ok, that was too easy, sorry I mentioned it. Can't we just use other objects in our environment to tell what is moving and what is not? We do have air to hit to tell us if it is we that are moving."

            "But what if our entire environment is moving with or underneath us?" Inventor replied.

            "But we don't have gravity yet and we are not doing gravity yet," Assistwo remarked. "We still have to do the Omoglatron bit."

            "I know, I just wanted to give the answer to Universe Inc.'s Paradoxes and Probability Waves question at the end. It seemed like a good place to put that in."

            Assistwo shrugged. "I know you have been given a lot of latitude in this story, being the smartest and all, but isn't giving the answer to questions in parallel stories you are not even in a little much even for you. We do need to maintain some semblance of readability you know," Assistwo preached.

            "Maybe, but it seemed relevant and I figured I would give you another minute for your stomach to settle before getting into the Omoglatron."

            "Ok, I did not consider that angle. Anything else possibly not relevant to the story you wish to talk about? I am all ears," Assistwo said eagerly.

            "Sorry, that was it, let's get Omoglatroning."

            "Now verbs too?" Assistwo joked, "but can you use it as a preposition?"

            The Omoglatron was Inventor's latest creation. It simulated how things might appear in distance, shape, and movement in a curved 2D Universe curved into a 3rd dimension into the shape of a ball. Thus whatever direction you move relative to everything else in Flatland, if the 2D Universe were curved, you would eventually return to the same spot but coming from the opposite direction! This was really a radical idea for 2D-only thinking people, but most had gotten used to not understanding what Inventor's rides were really supposed to represent, as long as they looked really cool and psychedelic. In this respect, the Omoglatron did not disappoint. 

            The symbol on the Omoglatron stood for its concept, a % sign. The idea was that any object moving in a straight line across a curved Universe would also be seen to be circling two points at different ends of the Universe. 3D people would understand that if the world were flattened out and you could see around the curvature, from a 2D perspective, a plane traveling in a straight line along the equator would seem to be circling the North Pole from someone watching it from there with the curvature flattened, and someone else on the opposite end of the curved Universe, in this case the South Pole,  would see it circling around them from the opposite direction. The Omoglatron used mathematics and computers to "flatten out" the curvature of a curved Universe so you could see "around" or "through" the curvature to things you could not normally see because they would be beyond the curvature's "horizon". This made things weird enough, but spinning around at the same time really made things get weird!

            Since Inventor was a natural born 3D thinker, he realized the Omoglatron concept would work the same for a 3D Universe curved into a 4th dimension or a hypersphere. If he could fly a rocket directly away from the top of his cube or any sides, if going in a straight line long enough, and if the curvature was perfectly round and symmetric, he would eventually approach the cube from the direction of the side opposite it. Thus the % symbol's logic would still be there in 3D, only it would best be represented by a flat plane with 2 balls, one above it and one below it. As with the line also being or representing both circles at the same time in the 2D example, the flat plane and both balls would be representations of the same flat plane, seen from within it, and how it would appear at two other parts of the Universe completely away from each other (at the maximum distance possible and the plane running in-between.

            He also realized that the flat plane would seem to bend in two directions at once if one imagined a flat plane between any two objects anywhere in the Universe, no matter how far apart the were and no matter how pronounced the curvature of the Universe was, or how long it was before you came back to the same spot. The bigger the Universe was or the closer the objects in question are to each other, the seeming bending of a plane between them stretching out in all directions halfway between two objects in 3D space in a curved 3D Universe further away from a direct line between two objects, the less that plane would seem to bend. The smaller the Universe was or gets, or the further the two objects get from each other, the more pronouncedly different objects on that plane would be in how to measure its distance to each object because it would seem to bend toward each at the same time, becoming greatest half the distance of the Universe away where that straight non-curving plane would in fact also be a sphere where all points on that plane are the same distance away, like all points on the equator are the same distance (if the Earth was perfectly round) from the North and South Poles, yet it also is a straight line.

6.6: Omoglatroning and stick spinning in reverse

            "Assistwo, please get me my 1 meter by 20 cm stick I use for demonstrating things, and withhold the comments please."

            "Why would I say anything? Why suggest I would yet again suggest you demonstrate something for once without dragging that thing back out. Why would..."

            "Those are the kind of comments I meant to withhold, please."

            "Yes, my Master. I shall speak no more against you. You are my God."

            "You are not irreplaceable, you know," Inventor suggested.

            "Maybe, but I *AM* irrepressible, that is what makes me me, and why I am still around. Here is your stick. I won't tell you what you can do with it."

            "Ugh. Ok, here is where this justifies that. I will stay here and you place the stick in-between us so that both tips are the same distance apart from each of us in the middle of the room," Inventor said.

            "Oh good, are you finally going to show how the tips curve toward me and toward you at the same time if the middle of the stick is in a direct line between us both?"

            "No, but thanks for pointing out what I am NOT ready to do yet. Every time you get ahead of me, it distracts away from how impressive what I do say is."

            "Maybe it makes it look more simple in comparison? Ok, wacha gonna do with da stick 'dis time?" Assistwo asked genuinely curious.

            "Nothing. This time the stick is just going to sit there. You and I are going to do all the work."

            "Ok, I get bonus points for withholding comments on that line," Assistwo remarked disappointedly. 

            "Duly noted. Now if your stomach is settled, spin to your right. I will stay here and spin to the left."

            "Ok, sounds like square dancing. Now what's the point?"

            "What do you see?" Inventor asked.

            "I see the room spinning around and once every rotation I see the stick. I don't know if you are spinning or not."

            "Ok, bad example. I will move the stick a little to the side in-between us. I forgot that in 2D, the stick would block your view of me. I have been spending too much time thinking in 3D. Now what do you see?"

            "How could you forget..., ok, now I see you spinning on the other side of the room once every rotation."

            "Now you keep spinning at that speed, and I will spin the opposite way at the same speed and our eyes should line up almost with the stick. Now back up a bit directly away from me and the stick."

            "How far away?" Assistwo asked.

            "Half the distance of the Universe should do. I will go the other half away from the stick myself too."

            "No problemo," Assistwo said, "Do I get paid for travel time?"

            "Quit being a smart-ass and get in the machine," Inventor remarked.

            Assistwo climbed into the Omoglatron and punched in the numbers representing the location he was going to, the speed and direction of his spin, the location of the stick, and Inventor did the same in another module. As Assistwo's simulator neared the mark, Inventor's seeming spin began to slow, his face enlarged until it completely surrounded Assistwo not spinning at all.

            "You know I was only kidding about you being my God. I hate it when you do this God-mode thing," Assistwo remarked.

            "How do you think I feel every which way I turn, I have to look at your sorry puss?" Inventor replied.

            "As we know," Inventor added, "if each of us is at the opposite end of a curved Universe, every direction we look, with proper automatic amplification and compensating for the curvature every direction away from wherever each object is, there is another single spot opposite it at the Universe's maximum distance away if the curvature is symmetric in all directions. Therefore if something is round like a circle, your or my head for instance, we see that curve reversed from this spot like it surrounds our entire universe in all directions."

            "Yes, and in a 3D Universe curved into a 4th dimension, all spheres would not only seem to curve away from you if you were next to one outside of it, but at the opposite end of the Universe, its shape would be reversed relative to your position, and curve toward you from all directions," Assistwo deduced, "So what is the point?"

            "For now, movement and spin," Inventor said. "Though from the readout on the Omoglatron we know it accounts for my spinning in one direction at a given speed and your spinning in the opposite direction at the same speed, which is why I see you not spinning. What if we did not have that information, how could we tell if we were spinning slow, fast, or not at all?"

            "By using something else for reference, of course. Though the Omoglatron is set in this instance to remove all other objects except your stick which we both see as orbiting around us, and we know it is not moving at all, we would know we are spinning and at what speed," Assistwo reasoned.

            "But what if we did not know that the stick was not moving, what if it indeed was moving in a straight line in-between us as it seems to be doing? The again we could be spinning fast, slow, or not at all. We could no longer use it to determine our spins."

            "True," Assistwo added, "but then we could use other objects. Surely we can conceive of a Universe with more than 3 objects, you, me, and your stupid stick. Just punch in more objects into the Omoglatron data and we could tell if we are spinning or if the stick is moving."

            "But what if they are all moving in the same direction along with it? What if not only are we at opposite ends of the Universe, what if we are at different apexes at which all the rest of the matter in the Universe was orbiting around?" Inventor asked.

            "Well the odds of that being the case would be extremely slim I would think," Assistwo answered. "Of all the places in the Universe for us two to be, what are the odds that one of us would be in one of those two spots, and the other would be in the others spot, and from only in that case could it appear that way? I think it is safer to deduce that it is we that would be moving relative to them. Maybe I am just not so willing as you to assume the entire Universe revolves around me. Sorry, but that was just too easy a setup."

            "No, I would have said that too.  It was easy, but sometimes easy shots are still good to go for. The thing is, as we understand spinning, yes if the Universe was slowly revolving around a central point, there would be only two "poles" or two spots where it would appear to be moving in unison from to appear to be not moving at all if you were viewing it while spinning along with it at the same speed, but this is due to our limited understanding of the concept of "spinning". I think that if we knew that space folded around itself, in ways possible in a curved Universe not possible in a flat Universe, there could be many such spots or even potentially any spot could be one of those spots with enough dimensions to spin in."

            "Then again, our limited ideas of spin is perfectly logical since we are only 2 dimensional," Assistwo reasoned, "and it could be also reasonable that you could be way off the mark thinking that spinning could explain things in higher dimensional movement simply because of that limited experience with higher dimensional states. It could just be spinning is just spinning to them. To us, it uses all of our dimensions, but it could be just inconsequential sideways movement in higher dimensions."

            Inventor began, "While I agree my understanding of spinning seems more relevant to everything because of our two-dimensionality,  no movement which cannot be understood because it occurs in tandem with other movements ought to be ignored. Just because it is not visibly moving or visibly spinning does not mean it is not the case. The more perceptions you have of other dimensional types of awareness, the more ways there are to "line things up", but the more you assume what you can line up at once itself may not be moving altogether in directions you can't possibly imagine yet, the more ways you have to be wrong as well."

            "For example," he added, "how far away am I from you? If we are both spinning, you will be going in circles without knowing it if you try to come to cover the space between where you are and where I am. If indeed the stick is not moving, you would be better to match your spin with it before starting off, and you would cover the same distance much more quickly. If you did not have the numbers to tell you that you are spinning, you might have assumed neither you nor I am spinning and the stick was moving, but from sticks point of view, you would be traveling in circles, not in a straight line, on your way to get to me, taking very much a longer route."

            "But," Assistwo countered, "if I knew the size of the Universe, and your location opposite me, when I leave this spot, I would no longer see you as spinning, only from this spot do our equal spins in opposite directions seem to cancel each other out. Once I begin moving, I should be able to notice I am spinning and correct myself to take a straighter path to reach you from the point of view of the stick, if it were really not moving."

            "That is assuming the size of the universe is constant or that I did not suddenly start spinning on my own, or we both (or the entire Universe through another dimension) were not moving at the same speed across space ourselves in tandem. In that were the case, you might reach me more quickly by simply figuring out how to stop moving and let me come to you, or by figuring out which direction we are both circling the Universe in, and reverse that so you are coming toward me while I would be moving toward you."

           "But isn't that the same thing?" Assistwo added. "If we were indeed both moving circling around the Universe at opposite ends in tandem, would not decelerating or slowing that movement to move in the opposite direction from where we both are heading in a curved Universe be the same as accelerating toward you faster?"

            "To you or I, it would look no different whether you change direction to slow down and let me come to you or simply speed up more in the direction we both are moving in simultaneously now, it is both at the same time, but objects in between us in the Universe, if moving in different directions relative to our movements, it would look completely different from each of their speeds and points of view."

            "This seems the whole "speed collapses space in a curved environment" thing. It does not matter if it is ahead or behind you because from someone else's point of view it can be seen as either or both from their points of view. I guess spin can make that much more complicated," Assistwo concluded.

            "Yes, in a curved environment, with many things moving relative to other things, my "speed" toward you is also affected potentially to others perceptions as our movements relative to them and other objects. From this point opposite you in the Universe, any direction I choose to go toward you in a straight line, regardless of what direction we may be spinning or together moving synchronously across space in another direction, to anything else in the Universe in-between us, to some it would look like I am reversing to go in the direction you are going in to meet you halfway, to others I am chasing the direction you are going in but now in at a faster speed. And of course, in a curved environment, I am doing both at the same time, even from the point of view of where I started from after I left (if something at or marking that point was still moving somehow relative to you and things there remained rotating in the same direction I was after I left). Whatever you are moving toward and shortening the distance to, you are moving away from as well from the opposite point of view, especially clear from where we are now and both those directions are the same distance. Whether I start moving toward you faster or slow down or stop and let you come to me, is ultimately just a point of view."

           "Not if I am the one having to pay for the gasoline," Assistwo joked. "But I get what you are saying, if we both are moving sychronously in a curved Universe equal distances apart in all directions,  it would take the same amount of energy to slow down and let you come to me as to increase my speed faster in a direction we both are heading in, and from opposite points of view, I would be doing both at the same time. You are lucky this ride looks sufficiently cool and mind-bending because I doubt many will understand the logic it represents. Do you have others planned?"

6.7: The Gravity Flyswatter Ride

           "The Gravity Flyswatter Ride," Inventor said. "Is there an echo in here? As we have already mentioned, there is no such thing as gravity in our 2D Universe or everything would seem one dimensional and we never would have been able to make just about every point we have made relative to a 3D universe. Gravity takes away a dimension by pulling everything toward everything else. Since we more or less float around, we can move in both dimensions, north/south, east/west, freely and make the examples necessary to make. If we had gravity, we would be stuck to a "ground" and only be able to move alongside it and jump up and down over things. Other than jumping and jumping while moving, by being able to move mostly only left and right, we would seem more or less one dimensional."

           "Gravity is stupid," Assistwo added.

           "Pretty much, but not having it not only has made our world relevant to the 3D examples, we get to discover it and by doing so, give a better perspective upon it," Inventor reasoned.

           "So if we think gravity is a bad idea, taking away one of our only 2 dimensions, why would you want to make a ride out of it? That sounds mostly for educational purposes only and that is not as profitable. We do have to always think of the bottom line when inventing new rides," Assistwo said haughtily. "Making ever greater profits is after all, the sole point of existence you know."

           "Quite the capitalist you are becoming off of my ideas," Inventor joked. Assuming Assistwo was joking too, he continued, "I think it will be fun depending on how it is done."

           "Why call it The Gravity Flyswatter Ride?" Assistwo asked.

           "Because of how we squish bugs. Since technically all our bugs are "flies" since we don't have a ground, our flyswatters push the bugs at a greater speed with them stuck to it until we splatter them against a wall or other object."

           "I don't think we could afford the insurance premiums for a ride like that," Assistwo added.

           "Basically it follows the same principles as the centrifuge, only reversed. If you hold on to the wall of the centrifuge, you get stuck to it because you are constantly pushed up against its wall. With The Gravity Flyswatter Ride that is reversed, so instead of being on the inside of a circle with "up" being toward the center, you would be stuck to the outside of a circle and away from the center would be the "up" direction," Inventor explained.

           "Sounds like fun but I would hate to be stuck to the outside of a circle for the rest of my life. I had a bad dream about that once," Assistwo said.

           "Gravity is limiting but does have certain advantages. We in a weightless environment have to constantly push off of things to get anywhere. All that bouncing around from one thing to another, if you think about it, gets to be a drag after awhile. I can't count all the times I woke up in the middle of my bedroom having to twist around more than a 2D cat to get myself back to the wall rings to get around again. Gravity is like constantly being pressed against a wall so you will always have something to get traction against to move around on and by."

           "OK, I'm game. Despite having a bad feeling about the idea of being stuck to a wall, I have thought the bugs must have a pretty good time before the wall hits them, kind of like driving really fast until you hit the tree. Being stuck to the outside of a circle instead of the inside of one would be an interesting perspective. When do we get started on it?"

7.1: And now for something REALLY completely different: Assistwo's Evil Perpendicular Universe Dream

           Assistwo woke up in the evil parallel 2D, ok, the evil perpendicular 2D world, the one with gravity. He was correct, gravity was stupid. In this Universe, called Scrolling World because he could only move left and right and jump over things, he was no longer the wealthy assistant to the even wealthier Inventor. In this reality, he was a cook at a chain restaurant called McFrugals.  Though he was, as in the real 2D world, still a brilliant scientist, in this evil 2D Universe, scientists were only valued and employed if willing to make weapons of mass destruction, devise new ways to manipulate people psychologically through subliminal advertising, coming up with new ways to rig peoples own computers, security cameras, and webcams to spy on them to help the secret police, or for devising new justifications and models for cheating poorer peoples out of their lands, money, and resources to make them all servants of The Corporations or die.

           Because Evil Assistwo grew up in this backward Universe, he saw nothing wrong with any of that and would have been quite willing to do any of the above, he just never caught any of the breaks like the real Assistwo did. In this evil Universe, his government was willing to hire all foreign scientists to make all their weapons of mass destruction because they did not have to pay them as much, could deport, torture, or shoot them without trials because they were foreigners (which made them more likely to show up for work on time), and above all, in hopes they would steal some of those ideas to build similar weapons in their own countries so Assistwo's country would have a good excuse for either invading them and taking all their stuff, or just simply killing them so they could use up their weapons and need to make more to keep up their weapons industry, the largest and most profitable industry on the planet, giving it even greater profits.

           Unlike the good 2D Universe without gravity, the disappearing circles in the perpendicular Universe simply passed through it horizontally appearing as lines smart enough not to hang around that Universe as most of their mass was outside of it and they would not have been happy sponges there. (a reference to  4.5: Pivot points: Upsetting the happy sponge) Besides that, they were hunted and killed by those in this Universe and turned into the hamburgers Assistwo cooked at McFrugals.

           Because people in this violent perpendicular Universe never thought to study these circles, just killed them and ate them as a free if inexplicable food source, Inventor never got his funding to study them, so Assistwo never got his lucky break as Inventor's assistant. Yet even in this evil universe, Assistwo's brilliance, tempered now with ruthless cunning, eventually paid off and he worked himself up to the envious position as an assistant manager at a new McFrugals opening up soon.

           Because this was a dream, it all seemed both strange and familiar to him at the same time. What was most strange was the body he had to get around with in this gravity enabled world. His body was not as soft, not designed for constantly bumping into things bouncing off on one object to another. Walls were smooth now too, no ring hooks to grab onto. Though "stairs" were like ring hooks, they were only needed when trying to go "up" and "over" things, most of the time impossible without jumping because there was no way to walk around supporting columns in a 2D plus gravity world, and lifting a door was liable to bring the roof down.

           Now one of his "arm" pairs was usually in contact with the surface at all times, except when moving which was basically leaning forward and falling, and catching himself with another of the "arm pairs" as much as it was pushing himself along. Because this body was not constantly bouncing off of things, hitting things or getting hit by them at greater speeds tended to cause injuries and pain. Pain was pretty much a defining aspect of this evil Universe, and not doing it to others was usually a good source of revenue if you were stronger or had more or better weapons.

           One of the perks of his new position of power was that he got to decide who to hire, give employment to, and thereby prevent from starving to death because many had no jobs and the government forbid people not to have jobs, but would not give them any either, so not having one was a leading cause of death.

           Evil Assistwo loved his new power of life and death over those even more unfortunate than himself as much as his superiors enjoyed weilding it over him. By coincidence, one of those looking for a job was a familiar name to him somehow, maybe from a dream he once had of a freer world without gravity, rampant corruption, price tags on everyone's lives and self-respect, and one with hope.

           "I see it says here your name is "Inventor". That is a really strange name."

           "No more strange than Assistwo," he said daring the slightest hint of a smile.

           "Hey!!! You must show respect for my authoritaaaay!!!" Assistwo yelled while knocking over a table for effect. Having gravity was nice because it just laid there instead of bouncing around the room incessantly after that. The dramatic pause and silence was nicer than it bouncing around during the whole interview or having to stop it. That would have looked silly.

           "My apologies my liege. I will speak no more against you, to me you are like a God, and I but your lowly humble servant," Inventor said showing the full proper humility and deference to Assistwo's superior socio-economic status required by law.

           "That's more like it! Its good to be the king!!! I mean the assistant manager, of course," Assistwo said momentarily not wanting to use the word "assistant" in this lowly jobless person's presence for some reason.

           "So it says here your intelligence marks are off the charts. You must consider yourself a real brainiac. What's a genius like you doing in a burger joint like this if you are so smart?"

       "I don't want to make weapons or work for a government that is oppressive. In our state, that puts me on the shit list," Inventor replied.

            "Well I don't believe you are that smart! No one smart would say something so stupid, even in my dream. The government is always right. You deserve to be poor. I myself would kill for the chance to make weapons of mass destruction like you could.  You may kiss my feet now to show you agree with me."

            Inventor hesitated imperceptibly and then complied.

            "You hesitated!!!" Assistwo screamed, "Why should I hire you now?"

            "It said imperceptibly", Inventor said in defense.

            "Yes but this is my dream and that makes me the narrator too this time. Whatever intelligence you have, it certainly isn't showing. Actually that is why I haven't dismissed you yet, it makes me feel superior. No one wants employees who make them feel inadequate. But how do I know you are not just playing dumb? How do I know once I hire you, you won't in the back of your mind think I am foolish or even wrong on occasion! In short, why would I ever hire someone smarter than myself? You might poison me and try to take my job!" Assistwo said trying his best to inspire both fear and dread simultaneously.

            "Because I have proven I have no ambition. If I am not willing to be obscenely wealthy profiting from making horrible weapons to further enrich a despotic regime, why would I kill someone to become an assistant manager at McFrugals?"

            "I am not quite sure if you dissed my job or showed disrespect for my authority again enough for me to throw things again, it is cool they just stop by themselves, but I must admit, you have a point there," Assistwo conceded. "But why should I risk having someone around who might secretly occasionally think he is smarter than me, huh,  answer that one smart boy!!"

            "Because it shows your greater power more acutely by being able to force smarter people than you to have to grovel before you daily just to survive another day?" Inventor said as humbly as he could manage.

            "My God," Assistwo exclaimed, "you are a smart one aren't you? OK, you have proven your worthiness to have an extended conversation with someone as powerful as I am. Now what is with this gravity shit? I have been trying to figure things out, I was trained as a scientist too, and maybe it is just because it is a dream but this gravity thing is really freaking me out and it is nice to have someone to bounce ideas off of."

7.2: Bouncing off of Evil Inventor

            Evil Inventor maybe able to be called Evil Inventor because he is the version of Inventor in Assistwo's Evil Perpendicular 2D Universe, but he was not AN evil inventor because he consciously and conscientiously, a strange word in this Universe, chose NOT to be forced to invent things for helping his evil republic's overlords. Because of this choice, to survive in this evil alternate Universe, he had been reduced to begging for a menial burger cooking job or be starved out of existence because his evil republic's overlords demanded he have one to obtain food, yet would not give him one, and interfered on occasion with is getting a decent one. Still, he showed his cleverness for being able to survive this strange set of circumstances long enough to be able to beg for that job, and he saw a weakness in power-crazed Evil Assistwo's lack of understanding of the Universe and decided to exploit that weakness to his own advantage.

            He was not cunning like Evil Assistwo, who fit in a little too well in this alternate Universe he thought, but he had shown his genius at being able to survive without turning as bad as those around him. He would not use Assistwo's lack of knowledge to kill him, take his job, take money from him, or make him humiliated or degraded as most would do in this Universe in his position, but he would use that weakness to try to gain a little respect.

            "Since you know of my intellect's reputation, I would be most eager to debate with you the potential ramifications of living in a Universe with an extra and possibly superfluous law called gravity which has a habit of messing up our equations as well as limiting our movements to one dimension less, but I ask a heavy price in return," Inventor explained.

            "Ah! I see you are a worthy adversary for me to clean my teeth on!" Evil Assistwo said, "Let the games begin! OK, they are not really games. Lets get out the Lawyers! Let the negotiations commence!"

            While lawyers need to be consulted on practically every matter when two people wanted to agree on any issue in this evil Universe, Inventor, being jobless, was not able to afford a civil attorney for such matters and had to act as his own counsel.

            While waiting for Assistwo's attorney to arrive, Inventor tried to make small talk. "How good an attorney for potential hiring conversation negotiations does McFrugals help one of its assistant managers to pay for?" Inventor asked.

            "A better one than I ever got as a cook, I'll tell you. Man, was that guy dense. If the evil republic did not legally require us to need lawyers for practically every aspect of our daily lives, I swear this guy would not have been able to feed himself if you put his food in a locked combination box lunchbox with the combination written on the top. But that is what happened when the lawyers took over the government. They just made themselves more and more necessary until you need to have them with you on dates to make sure you are not making any promises or suggestions you might not be able to deliver on later. This guy's not too bad, though I have to pay most of my wages to him of course. McFrugals doesn't cover much. He used to be one of a team of music instruction class lawyers for one of our republic's overlords when he was in the third grade. He helped him get out of having to memorize by heart three patriotic propaganda songs, at least the way he tells it anyway," Assistwo said.

            "Wow. Sounds impressive. Though I doubt those being groomed for leadership roles as children of the overlords, they really have to follow those rules as much as we do anyway," Inventor suggested.

            "Just be glad my lawyer wasn't here to hear you say that. You'd be having to defend that statement in court for the rest of your life. You are lucky I won't blackmail you with that. I have suspected the same thing myself despite what the song, "Overlords Are Super Special People But Also People Like You" says."

            After the lawyer arrived, Assistwo and Inventor were able to come to terms on the ground rules for their conversation about gravity in the context of Inventor's application for an entry cook's position at below minimum training wage at McFrugals. No special consideration was to be given for any points he made in the conversation to his job application, nor would any statements, corrections of Assistwo, or opposing ideas be held against his getting the job. Assistwo was required to refrain from making comments such as "You may kiss my feet now to show you agree with me," and temporarily refrain from making any requests to doing anything extremely humiliating and distasteful to retain consideration for employment for the duration of the gravity conversation only. Assistwo was particularly insistent upon an early sunset clause for that limitation. He remained however, free to berate Inventor's poverty and lower socio-economic position, and the right to throw objects weighing less than 5 kilograms at Inventor whenever he disliked what he was hearing from him.

            "You are going to have to go first," Inventor said, "You are the one who has problems with this world with gravity and, as you said, it is your dream."

            "Of course it is my dream. Why would it be your dream? I am the one with all the power here now!" Assistwo bellowed.

            "But even with all of your so-called "power"", Inventor replied, "You are still dependent upon people like me to tell you things you can't figure out on your own. Score 3 points for the homeless person."

           "You never said you were homeless! Why would you tell me that? You know I am legally forbidden from hiring you. Homeless people are non-persons who have been sentenced to starve to death slowly because they are guilty of the heinous crime of poverty,"Assistwo said in disbelief.

            "True, but I mentioned it to make the point you just made. You are right, and to show how screwed up our world is. You are not allowed to get a job if you have no home and you cannot pay for a home without a job. I said it because I *AM* a non-person sentenced to starve slowly to death, and because our agreement forbids you from considering it as a factor now because you found that out in the course of this conversation," Inventor said triumphantly.

           "Damn lawyers!!! Stupid ****in' homeless person!! If you weren't so thin, malnourished, and diseased, I ought to grind you into burgers and serve you up for dinner to us who work for a living, at least then you would be contributing something to society for a change!" Assistwo screamed as venomently as he could manage.

            "That was a little over the top, don't you think?" Inventor corrected.

            "Yes, but I am supposed to be evil, but all I am allowed to do now is berate your poverty and throw things at you, but I could not find anything under 5 kilos. Wait a minute, I did not see that toaster."

            Whap!

            "Feel better now?" Inventor asked.

            "I don't know, did it hurt?" Assistwo asked.

            "Yes."

            "Ok then, I feel a little better. What I don't understand about this gravity world is practically everything but you can start on my body."

            "Remember our contract," Inventor warned.

            "No, I mean I don't understand it. Why are these four arm thingies so stiff and only bend in a few places?"

            "You may not realize it because your body has grown in this environment, but it takes a lot of work to keep upright and from sinking into a big blob of mush on the ground. Your stiffer frame minimizes the amount of work needed to keep your body upright off the ground," Inventor explained.

            "Ok, what about that?" Assistwo asked. "Why is my head always so far away from the ground. What if I fall over?"

            "I don't know why you want to keep your head so far away from the ground. Why not go into the alley where I have to sleep at night and put your face closer to the ground? You might find out," Inventor suggested.

            "Why is my butt so big? It seems there is a lot of unnecessary fat there which serves no purpose whatsoever. It isn't even aesthetically pleasing and serves no function," Assistwo asked inquiringly.

            "I don't know, you could try going on a diet. Be thankful you don't have a desk job," Inventor joked.

            Assistwo searched frantically for something under 5 kilos. "Where did that toaster go?" he asked.  "What about my eyes?" he added when he could not find anything to throw.

7.3: Eyes on the horizontal prize

            "What about your eyes?" Inventor responded.

            "I have two but they are both on the same side of my head so I have to bend my neck all the way backwards to see what is behind me. I miss being able to turn around. Wouldn't it make more sense to have one on each side so I can see what is behind me when I wish to back up?" Assistwo asked.

            "That is a good question, but not applicable to gravity. Even in your "normal" 2D world, you could not see what was behind you, which from what you say about the size of your ass, may be a good thing after all. It would make understanding when you are moving toward something, you have to be moving away from something or somewhere else easier. Clearer insight into that would have been helpful when contemplating curved spacial environments," Inventor answered.

            "Ok, here is another eye question for you," Assistwo began. "While theoretically I can position my neck at any angle, most of the time it is always pointing ahead at that point where the ground touches the sky. I understand the need for this when moving because it is halfway between looking down to avoid falling into lava or a hole by jumping forward, and looking up to find vines to swing over things avoiding possible pitfalls, and to see if anything is falling down at me from the sky I might need to move or jump to avoid. Damn Scrolling World!!! Every time you want to go to the store, it is like playing an antique video game!! Why do I always look at things this way when not moving, deciding which way something should be pointed "up" and always choosing to view things and people at such an angle?"

            "That is a natural side effect from being raised in a world with gravity," Inventor replied. "Unless something is falling at you from the sky, before we had bombs, missiles, and laser weapon satellites, people actually never had to worry about bad things raining down on them from above besides rain and occasionally lightning or hail. Thus most of the things you would have to be concerned about would start to come at you seemingly very small near the horizon getting bigger as they got closer to you. We still naturally keep our attention at that point, a line for 3D people, not just a point for us, and that is a good reason to keep our heads up as high as possible, so we can see over as many things as possible and see things further away seeming to come at us out of that point. Because we are usually looking at things at the same angle with our heads held high, we tend to view how we see things at that angle as the right or correct way of seeing them if they are usually in the same position relative to gravity. As you mentioned, it is nice sometimes that gravity tends to hold things in place and stop them from moving if the ground is level, so things except wheels are built to be stable in that position held to the ground by gravity. Other animals or other people tend to move across the ground in the same manner so we think they have a "topside" and a "bottom-side", a correct way to look at them while they are suck "upright" to a ground by gravity."

            "Ok," Assistwo answered, "Its a whole environment at once thing. You look across because that is where you may eventually be or will be, and what might be moving toward you will be coming from, and how things seem to "stand" while stuck to the ground by gravity, Now why is it so hard to get around? I loved being able to go around things. I think the reason people are so angry all the time in this reality, trying to control everything and everyone, is because we are always getting in each other's way. You being so malnourished and all, it is easy for me to get by you by jumping over you, you are as thin as a post, but some of these people are so fat it is really hard to clear them. And then they hit you for landing on them when you were only trying to get by them. I know from my limited research on 3D, in such an environment you could actually still go around people even with gravity. Maybe they might be nicer to each other, but gravity sure makes it hard to get past large groups of people in 2D Scrolling World. All that jumping is ridiculous!"

             "Maybe it would be easier for people to stay out of each other's way in 3D," Inventor surmised. "It certainly from our point of view would seem like the best of both worlds, have the constant traction for pushing off against a "ground" that gravity provides along with the ability to also go around people too. Just because they CAN get out of each others way doesn't mean they would, or would be able to if there was too many of them in all directions. Things grow to become a factor in defining their own environment. People in this evil 2D world can be so bothered by what other people are doing whom they never will or never would see, they would travel around to the opposite ends of our 2D world we call a "planet" just to stop them from doing something they don't like. With too many people or people wanting everyone to behave as they say, it can become impossible to get out of each other's way when someone targets your existence as something they wish to eliminate, or have conform to their expectations."

           "For someone who is not choosing to profit from this evil perpendicular 2D Universe, you sure seem to have a handle on it so much I wouldn't mind killing you myself. You really are not trying to enjoy this place enough!" Evil Assistwo replied. "It is fun trying to make everyone do what you say, grovel and beg for another day's existence, fear you and be willing to degrade themselves for your pleasure. You really ought to try to lighten up"

            "I will take that as a compliment. So I take it I am not getting the job then?" Inventor asked.

            "Not a chance in hell. Its not that I would not like to have you around to advise me and generally control your life like a puppet and all, but this chick that came in before you, Hoshi, she was really hot and eager to do literally anything to get the job."

            "She will probably try to kill you and take your job if she was THAT ambitious.  Your butt *IS* very big, after all," Inventor said feeling freer to talk knowing he had no chance for employment.

            "True, she probably would, but the fun I might have in the meantime!" Assistwo said. "Its probably worth it."

            "Well, you stayed within the limits of the contract," Inventor conceded. "Any last questions about gravity?"

            "Yes as a matter of fact, I almost forgot the most important question I had about gravity, What the **** is it?"

            "That's the easiest one. It is..., what is that noise?" Inventor asked.

            "Nothing, please go on, it is...." Assistwo said losing his patience which in this Universe is even shorter than in the real one.

            "I definitely hear a buzzing and its getting louder... It is your alarm clock!" Inventor deduced.

            "I said it is nothing! Ignore it! Explain to me what gravity is or I will have you executed for lying on a job application! I am the one in control here!!!" Assistwo said struggling to maintain his fierceness as the buzz began to drain all his power away.

            "In your dreams maybe," Inventor said looking suddenly not in the least malnourished. "Now hurry up or you will be late for work again, or I will figure out a way to let the real Inventor know he has at least one free shot at you with a toaster."

            "Damn!" Assistwo said rubbing his eyes, "If I only set the alarm 5 minutes later I would rule this World!" Now more awake he pondered whether that was just his weird sense of humor or if he had been doing an uncanny Evil Assistwo imitation. "Nah," he surmised, "who'd want all that responsibility?" before turning off the snooze alarm and going back to sleep.

7.4: Reasearcher's full blue plate special #42: Roller coaster plotlines
 

             In the semi-normal only slightly evil 3D universe, Researcher was late for work again. His assistant was not happy.

             "Have you seen all the crap in our inbox?" he asked seemingly quite perturbed.

            "What, is our spam filter broken again?" Researcher asked yawning. Even though he had been on vacation for 2 years, he was still not getting enough sleep and wished like Assistwo he could ignore his alarm clock again. 

           "Not our email inbox, all the stuff piled up over the last 2 years we have to address. Inventor never did get around to explaining what tri-spinning meant, now we have to deal with curved space-time Universes as well as flat ones, we have to explain 3D and 4D centrifuges, and "Omoglatron" thing which maps a curved 3D universe into a 4th dimension, how weightless environments are analogous to movement through multiple 3D universes with gravity in a 4th dimensional sense, not to mention relating all of it and multidimensional spinning to the Many Worlds Theory without the comedy of evil parallel universes, all while remaining within our lesser page quotas compared with the 2D Universe! Welcome back from your vacation. Feel free to quit at any time."

            "Hmm. It does sound like a good time to quit or even retire. Remember what the most important lesson from The Hitchhiker's Guide to the Galaxy¹ teaches us and you will be fine," Researcher responded.

            "Ok, the answer to it all is 42! We can go home now. That was easy. Why didn't I think of that?" his assistant asked sarcastically.

             "Man, you have gotten more stressed out over the last 2 years I have been gone," Researcher answered. "I used to be the uptight one in this Universe's storyline. Now I need to get some other defining character traits to set us apart now. I meant of course "Step one: Don't Panic"². Have you seen the movie version yet?"

             "Oh, that's a great way to start off. All this to cover in only a few pages and you want to waste words talking about this summer's movies. For the record, no, I have not seen the movie nor even read the book. I did however see the BBC series," his assistant said beginning to loosen up. "Why have you?"

            "No, I haven't seen it either, I was just wondering if it was any good.  The good thing about all you said is if you know what it is you have to do, you have your work cut out for you. It is trying to figure out what you need or ought to do in life that is most of the work," Researcher said with a smile.

            "My, your short only 2 year vacation seems to have done wonders for your attitude. You should take a 2 year vacation every year. I would settle for a 1 year vacation every year. Can mine start now?" the assistant asked.

             "If what you say is true and we have all that on our plate, I think not. Still, it is good to be back. How are our little disappearing spheres doing?"

            "They died out of lack of interest. This storyline has gotten way to unpredictable. I am thinking of a way to write a letter to complain within the context of the story to a fictional Union of Unnamed Minor Characters, the literary equivalent of walk-on extras in cinema and television (Bar patron #3), but I doubt anyone would care about it any more than the spheres we started off with," the assistant remarked.

            "Well, you can't say I didn't see it coming. I felt they were becoming unimportant to what passes for a storyline here way back in the beginning of section 2.5. We are up to 7.4 now and over a hundred pages. Just be glad we have other things now that need doing."

             "Other things we certainly have," the assistant replied, "other things we need or we wouldn't still be here, I just wish there were fewer things needing to be done! You're right. I think I do need a vacation or at least to step back and get away for awhile. Hawaii would be nice I suppose. Ok, any idea where to start?"

             "Well I think amusement park rides sound like fun so I vote for the Centrifuge. That would still have been a viable ride even in the 2D world plus gravity. Spin the wheel fast enough and it seems like you are creating an extra gravity which can seem counteract or supercede your regular gravity. 3D World examples of this would be amusement park rides similar to the Centrifuge. I remember one called the Roundup which you stood beside the wall and got stuck to it like the 2D without gravity version, then it got tilted at an angle so you would spin up and down against the gravity with a greater force so you would not fall down once upside down," Researcher noted.

            "Cool. Like when a rollercoaster goes into a loop. Even without the safety bars, you get held to your seat by the spinning which momentarily supercedes gravity though you still feel gravity too, which gives a different sensation at the tops and bottoms of the loops."

             "Correct," Researcher said. "See this can be fun. Now we have rollercoasters too. Though the spin is great enough to keep you in your seat at the top of the circle, the downward pull is still there because of gravity, but it is lessened and you feel half the force as you do at the bottom of the loop when the outward pressure is combined with gravity to seem to increase or double the pressure which leads to a weird sensation of varying degrees of gravity every few seconds. And if you suddenly stop the ride while in the upside down position when you are against the gravity the most?"

            "Then regular gravity takes over and you better hope those safety harnesses are as strong as they look," the assistant answered.

            "In our space administration's "rides" for potential astronauts," Researcher continued, "to get them used to increased gravity on takeoffs, they are similarly but thankfully for them, statically pressing them against a wall in a circle level with our gravity. It still is a shock to your system, but not as bad as it would be if not level to gravity, because the point is to gradually increase the effect of increased gravity or G's, not to purposely make them feel as sick as possible, which doing the same thing with vertical looping would do."

            "Yes, that is like how I get pinned to the back of my seat when I floor the gas pedal in my Superbird," the assistant said with a big smile.

            "See, you even got to work in another reference to your gas guzzling car again. Strange that Superbirds and cars like them are becoming extinct like the dinosaurs because of high oil prices, when the bodies of the dinosaurs and super "birds" helped create the oil in the first place."

            "In each case," the assistant reasoned, "the motion forward is mixed with gravity in a different way. If a rocket sled, a super car like my own, or an amusement park ride which only accelerates you forward, they increase artificial gravity alongside the normal gravity perpendicularly. I wonder if I will get to dream of an evil perpendicular world too. I am the underrated lesser character in this Universe. I will petition for that in my letter to my Unnamed Character's Union."

            "Complaining about strange plot twists into alternate Universes, and at the same time asking to star in one. Sounds like the inconsistencies you were complaining about. I think it just might work. Go for it," Researcher advised.

7.5: The Evil Omoglatron and 2D Heavens and Hells

             "I got my answer to the letter to my fictional Unnamed Character's Union," the assistant said.

            "That was fast, I did not even know you had already even written one," Researcher replied.

             "I used email while you went to the bathroom, and they are a very decisive group."

            "What did they say?"

           "They said I had a point about wanting a better plot but that I shouldn't complain about it while the story is ongoing because it could be an intentional plot twist or setting up something which will happen later, and eventually make sense when I see the larger picture at the end. I think they only pretend to represent me and are really suck ups to The Man," he answered.

             "The Man?" Researcher replied.

             "You know, the establishment. Didn't you read 1960's literature or television? That was their term for that controlling group of society that tries to run our lives and keep us down. In this case though, that would be the Author."

            "What about a reversed 3D Universe dream?"

            "That idea was nixed. It said trying to reverse our world might actually improve it too much. Societies would be run by the kindest generous smart people and the most ruthless greedy and stupid mean people would be the least powerful, and corporations would have to do what the governments tell them instead of the other way around. The corporations also would not get to decide who the people could vote for in a general election."

             "That would be too strange. As a consolation, we do get to go back in our discussion to the evil 2D perpendicular universe for gravity examples though,"Researcher said.

            "But I wanted to be  a "STAR". I wanted everyone to know my name, or at least want to know it since I don't actually have one," the assistant said with a sigh.

            "Gravity, Assistwo said, was stupid. I liked that. Although one could also say that gravity makes people stupid," Researcher suggested.

            "So THAT is the reason! I am so relieved. I always wondered about that. So will we conquer stupidity if we learn to conquer gravity?" the assistant wondered.

            "If you count willful ignorance in with stupidity, then no, stupidity is a far stronger force than gravity to overcome."

            "Ok, I'll bite, why does gravity make us stupid. I mean other people. To misquote the lyrics of that famous 2D hit propaganda song, ("Overlords Are Super Special People But Also People Like You"), "Scientists are super special people and *NOT* people just like you,"" the assistant asked.

            "You had to mention that stupid song. Now that tune will be in my head all day! Gravity alters our perception of space because it is specific to the environment we were raised in. If we spent all our life on the ground and never learned how to make objects fly at us to need to avoid, we could blissfully think the world was flat, which where I live and from my point of view, it is, which makes it good for riding my bicycle," Researcher mused.

            "If you think the Universe doesn't revolve around you," he continued, "you might consider all that weird lighting up in the sky beyond the clouds and begin to think they are more important than they really are. To begin to think in those terms, then you really have to eventually give up the notion of a ground, and things having a topside and a bottom-side, and really begin to think in terms of 3 dimensions all the time in ways you don't have to here on Earth with a zero coordinate called sea-level, and with gravity constantly seemingly pulling everything down uniformly in a single direction away from wherever you stand."

             "Can I ask a question?" his assistant asked.

            "Yes, go ahead."

            "That was it. I was just feeling left out because it is sounding like you are going to be going on and on for a bit. Thanks for saying yes, though. The Union suggested I try to assert my existence more if I wish to make, or get, a name for myself," he explained.

             Barely back an hour and Researcher remembered why he needed to get away for so long. "If you are done, I will continue. Thank you. Though we know the Earth is curved, unless we travel great distances or leave the ground or send things great distances, that curvature would rarely affect our lives and we would not think about it and didn't for thousands of years. Now that we think we are ready to leave the nest, we have to start thinking in terms of 3D environments where all 3 axises directions away from us on perpendicular lines or planes of sight are completely interchangeable instead of gravity making a horizontal plane seem special because it is what we are all stuck to most of the time and orient our perceptions around it."

            "If we consider the people in Assistwo's Scrolling World dream were unaware that if they traveled all the way around his planet looking for different cultures to wipe out and make them all behave the same as them, before they got that developed, they might reasonably think the ground is flat in all directions. One could go forward or backward, but going up or down would be totally different. Down would be into the ground, be dirty and if like our 3D planet, it would be very hot with lava and extremely unpleasant and confining. Going up, if you did not have to worry about falling and all the unpleasantness that might come after you hit the ground, would be rather nice, free to move about in more directions freely, with a point of view like upon a big mountain, and finally get to use your ability to look down to see things besides the ground, having it bring more of your world into focus, seeing people smaller going about their business unaware of you looking down on them unless they looked up to the sky."

            "Sounds like 2D heavens and hells," the assistant remarked.

            "Without an understanding of their environments, one could not understand up and down as being the same as backwards and forwards. It would be somewhat easier to go down than up, just dig a hole, but hard to get back up out of, and if they had volcanoes or really deep caves, they might realize it is best not to go down too far. Up might seem nice, lots of lights in the sky and other things up there that one could imagine what they might see if they had eyes and could look down upon everyone all at once (without realizing you could only see half the world at a time) as if up on a really big hill," Researcher surmised. "Yes, it would be much like our early notions of heaven and hell when we thought good people's souls would go up into the clouds and be able to look down on us below, and bad ones would go into the ground with the lava or dark scary creepy places."

            "The relevant point is," he continued, "without knowing how their world could curve all the way around itself and then also having to think gravity pulls in all directions at once around the circle, and that down was really up from the other side of the planet of where you are now, they would not understand the Omoglatron at all. At best, if they tried to build one or even conceived of the notion, it would be how to see across the curved space of their planet, how that could be unfolded like to us trying to flatten out a globe to a 2D map. They might not understand how going up or up at any angle, or down at any angle, not just forwards or backwards, would always also lead back to the same spot. The sky is the sky, the ground is the ground, both completely different worlds than your own, going into one could never be thought to lead you to the other. They just don't and can't ever be mixed or confused. They are 2 separate things. Implying otherwise would be sacrilege."

            "But because," the assistant added, "the real Inventor and Assistwo had no gravity, they could travel freely in a 360 degree circle. They understood more easily how every direction is exactly the same, that the curvature would be in all directions they could move in, or in more directions, because they could move in more directions."

            "Yes. Also in the 2D gravity world, the curvature would be in all directions they could move in easily and they could understand that, plus because that movement was more limited than in the 2D without gravity world, they had a dimension they could not move in to explain to them the curvature or how it could be curved. Less understanding of possible movements = better understanding of where it curves to, but more possible movements says "in what possible direction or space can this bring us back to the same spot," what dimension or way is there for all of these ways to get us back to the same spot!"

            "But is that really applicable to us?" his assistant wondered. "Though we have decided for some time now the world is not flat, and see ourselves stuck to the outside of a bubble or marble in space, we do understand being able to travel in any direction in 3D "outer" space, so is our view limited any longer by gravity since we no longer see the world as flat and realize all of the 3 dimensions we perceive are the same?"

            "They are NOT the same, not with gravity, but now is not the time to go there yet. We have only begun to factor in all that it means,"  Researcher suggested. "In regards to heaven and hell, we still have the same ideas or imagery roughly as when we thought the world was flat. Because we had the up/down direction we never used much in our thinking, we were able to decide how the Earth could curve back upon around upon itself, but a curvature of all 3 dimensions back upon itself, that even other researchers as ourselves are only in our infancy of beginning to understand "curving into what" as those who first thought the world was not flat had to figure out a way to explain gravity, or that how people at the opposite end of the planet as you would not fall off. Because we now have more freedom of movement in space, we can understand up/down, left/right, forward/backward, they are all completely the same there unlike on Earth where up/down is nowheres near the same. But with more understanding of more possible movements, now how to curve all of those back again without having another limited one, that becomes the next problems to solve."

            "Isn't time a limited movement dimension?" the assistant queried. "You have used time before as an analogy."

            "Yes, but movement through a dimension in this example requires time to use to move through it with. What we need is another dimension we can move through and still be moving forward through time at a level that we can continue to have new experiences at the same rate and build new memories with in a way that makes sense to us, with that we would then have a way to describe "curving into what" or curving how."

7.6: Fun smashing into walls (and setting up 4D)
 

            "Ready to have some fun?" Researcher asked his assistant.

             "That depends. Remember how much we have to do and our page quota? I am all for having fun if we don't waste words in the process. We have already wasted words with suspect political comments. That is not technically illegal yet, but still extremely unwise," the assistant reminded. "Unlike Assistwo, we just can't one day wake up and everything will magically be better."

             "Have no worry, this fun is not off the topic nor politically suspect. It involves collisions, smashing into things, and gravity."

             "Sounds like it might pass the censors and Firemen. Go for it."

            "In the 2D plus gravity world, it would be easy to stop from moving because of gravity which, in addition to giving you traction to help you get moving, you could use that traction or friction to slow down or stop. In the 2D without gravity world, depending on your self-twisting skills, it would be difficult to stop to avoid hitting something with nothing to brake against."

            "What about simply changing direction? If you just want to avoid hitting something and you can't stop in time, move perpendicular to it or its path and you can avoid it more easily," the assistant suggested.

            "Yes, that requires less energy or distance to avoid a collision than completely reversing your forward momentum to stop, but every dimensional level has its own preset number of ways to avoid hitting things and gravity also factors into that. Say Inventor decided not to just stand there and take it when Assistwo threw the toaster at him. Because he could not move to the side and dodge it being Scrolling World and all, and did not think to jump over it, he would have had to outrun it, run far enough fast enough before it hit him until gravity pulled it to the ground. Now lets imagine he was so concerned with his neck twisted all the way backwards to see the toaster, by the time he looked forward again he saw he was running full speed towards a wall with little or no time to stop."

             The assistant shrugged at the obvious dialogue, "I hate to have to say it, and hope I never have to again, but I think I would rather get hit with a toaster."

            "That can be arranged," Researcher responded. "So this would leave him two choices in 2D gravity world, try to use the friction of the floor to stop or slow down at least before hitting the wall, or try to redirect and use that forward momentum to try to jump over the wall."

            "Jump over the wall? It sounds more like a fence to me."

            "Ok, a fence. Whatever you want to call it. Since there are no roofs in Scrolling world besides ledges, we will call it the wall with the door above it always open. Stopping would be the first and best option. You know where you are, your environment, you know you have already outrun the toaster and nothing else at the moment is coming toward you from behind. If you can't stop in time, that leave two choices; try to go up and over the fence/wall, or slow down and not hurt yourself as much. If you knew what was on the other side and knew you could clear over it with no damage, you might wish to use that forward momentum to carry you up and over if you timed the change in direction or jump correctly. If there was a highway outside the wall or a possible lava pit, whatever the damage, or if you did not think you could clear it, you might just as well try to slow down as much as possible before slamming into the wall."

             "What is this YOU stuff? I thought we were talking about Inventor. Even though this is just allegorical, I liked it better when it sounded like someone else would be slamming into the wall," the assistant protested. "This is not my idea of fun!"

             "So much for making a name for yourself. You can't even take indirect metaphorical examples which might involve discomfort," Researcher answered. "Now lets go up to 3D, not an indirect example anymore, and it really IS you. Lets say I have had enough of your stupid remarks like that one and you were outrunning a toaster I threw at you, and turned around to find you were about to run into something."

             "If you make it a beautiful super-model, it will be fun again," the assistant suggested.

            "Now in 3D, you have more choices, you can break to your left or right, whichever makes more sense, if you can't stop or move around it by going over it."

            "Why would I want to go over it? That involves going up. Even if I can't go around it by going left or right, I still think I would rather slide into it than go up," the assistant mused.

            "Well that is a personal choice," the researcher suggested. "If you were headed straight for a wall equally in front of your left and right and could not go over it, though it would be difficult to do, you could try to jump backwards just before hitting the wall."

             "That does sound hard to do. We may not know what Inventor's knees are like but mine are not exactly designed for jumping backwards, especially trying to do so while sliding forwards moving in the opposite direction!"

            "But there are examples even you with your fear of heights and constant interruptions might understand," Researcher noted beginning to get a little annoyed again. "Imagine you were running on a highly polished floor with only your socks on, no real way to get any traction, therefore jumping would be using the gravity to slow you down by transferring some of your forward momentum upwards before hitting the wall."

            "Ok, I'll buy that. Actually, I do that all the time at home anyway," the assistant said. "Makes perfect sense to me now."

            "Good, because I have a bad feeling, this, you won't.  Now lets go up another dimensional level to 4D. Before our floating 4D spheres died, they would have made good examples. Lets temporarily resurrect one and have it making the same mistake by heading for a wall. While for them the wall would have to be completely surrounding them 3 dimensionally, for simplicity sake, lets say it does in the dimensions we can't see. Also because our world seemed to hold them here longer than they were not here, lets say a sort of gravity held them in line with our particular 3D Universe as their ground."

             "Wouldn't it make more sense to use our gravity as their gravity to explain it better?" the assistant asked. "I liked Scrolling World better than the weightless 2D world for examples."

             "Each has their uses. Most of the 2D examples were only applicable in terms of relating to our Earth's "surface" 2D world to their Universe. That could not have been done with a gravity 2D world. The gravity-enabled 2D world is more relatable to ours in other ways such as traction, jumping, and planets, but less like ours (than the normal 2D World) without being able to turn around, go around anything, or having columns to hold up roofs you could not walk around. Similarly our world being used as in 4D world examples has similar limitations depending upon which way you wish to "point" the gravity relative to our world. To imagine its gravity relative to our own, you would have to imagine a 4D researcher or inventor being able to walk around within our world, jump within our world, but also be able to step out of it at any time in either of two possible directions we can't see or imagine."

            "If we do get a 4D researcher in the story," the assistant interrupted again, "he better not get a name before me. At least you and Inventor had to wait awhile for names. It seems like I have been waiting forever. However, I vote for Refrigerator for a name. For a 4D person, not for me."

            "If you keep interrupting me, I will vote for Exterminator because we would seem like bugs crawling around on a 3D universe "ground" to them, and since you keep interrupting, it would be good to have an easy way to write you out. My guess is it would be an occupational name. Researcher, Inventor, see a pattern? Refrigerator indeed! Upholsterer would even make more sense!"

            "Now getting back to what I was saying," he continued, "if the gravity was "in line" with ours, it would make more sense in some ways but they would be able to move in 6 directions across our ground and we would only be able to understand 4 directions, left/right and forward/backward or north/sound and east/west, and of course combinations on those lines. By instead using the "ground" and gravity opposed to our world, it makes it clearer in some ways and more confusing in others. At least the 6 all equally opposed directions it could move about freely in would all be within our field of vision and our limited imaginations, plus we already have the example of the jumping spheres we began the story with which could move around seemingly weightlessly and could momentarily "jump" out of line or sync with our 3D universe."

            "But the problem with that is "where is the ground?" If our world is their ground, how can we move? That would make our Universe solid and we could not move around in it," the assistant suggested.

             "Yes," Researcher added with a sigh, "and Inventor or other 2D persons could not easily understand how our world could be like their normal 2D world without gravity, being able to move 360 degrees across a ground, or 2 opposed lines, North/South or East/West at the same time, and also be like Scrolling World, being held to another opposed ground world at the same time. It is the exact same example. So we will decide in the same spirit of that example that the "ground" the spheres are stuck to is just below just below our world in a 4D sense, and they are sticking out through or into our world while always staying in contact with that "ground" completely solid 3D universe we cannot see, imagine, nor move about it, as it would be a solid 3D universe. In the 2D example of Inventor's world existing like the surface of a lake, imagine it only an inch deep and his disappearing circles were balls on the bottom of the lake, and protruding through his universe at the same time, likewise our spheres floating around were actually hyperspheres always in contact with a solid ground 3D universe."

            "Ok, I get it now," the assistant said impatiently. "This is getting too wordy to be fun anymore. Now I even miss metaphorically being smashed into things."

             "Fine, lets get on with it then. Say we set up a restaurant inside our much bigger case for the 4D spheres. One of them was applying for a below minimum training wage job when the other threw a 4D toaster at him. While running across our 4D hypercube cage, which looks like a glass cube to us and seemingly floating across the middle, while running along a 3D ground, a solid 3D universe completely out of our sight but just below our normal 3D universe, he turned around too late to realize he was running into a wall which curved around him 3 dimensionally which we only see part of that wall, though able to move in 4 directions on 2 axises we can see from the middle of the cube's side, all while still on the "ground" we can't see, but without enough time to slide to a stop on that invisible to us "ground" so he had to try jumping over the wall we could only see part of by jumping in direction completely out of and away from our Universe! There, are you happy now? Trying to put all of that at once into a single paragraph quickly, damn word limit, never mind the fact that it is some of the strangest concepts yet strung together ever, all to quickly get back to smashing into walls."

             "I just didn't want to be the last one to metaphorically be smashed into a wall. I have to admit, it did sound a bit strange put that quickly, but nowhere near as weird as it is about to get," the assistant accurately predicted.
 

8.0: Infinity Zero Realm: After an eternity of bad jokes, we finally start in 4th gear

             As Upholsterer was coming back from the store in the 4D universe, he was eager to patch the hole in the couch where a 4 dimensional cigarette burned a hole through it. Not only was the hole in the couch the equivalent to us as a completely self-enclosed 3 dimensional universe, it was also only the width of a 4 dimensional (insert product placement brand name here) cigarette, which are not very wide but even more lethal than a 3D one (ok, forget the product placement commission). The strip of cloth he got, that was extremely thin in a 4th dimensional sense, which made it nice and flexible and easier to sew through, was also the equivalent of a 3D universe to us, only it was a solid leather universe which would not have been very comfortable to try to move around in it but would not have stopped rock musicians and fashion-crazed idiots from wanting to own one to make 4D pants out of.

             He stopped and raised a hypersphere shaped knocker on one of the double doors, also coincidentally shaped as what Einstein believed the Universe was made out of, only his was not brass like these balls were.

             The solid brass hypersphere knocker came down on the 4D door causing such a nasty noise that its occupant, Big Ass, had to cover his ears while walking to the door. There was definitely gravity in this Universe, as well as hangovers.

            "Are you Big Ass?" Upholsterer asked.

             "You've heard of me?" Big Ass inquired back.

            "No, it says so on this invoice. I am here to repair the damage on one of your bosses expensive leather couches from your party last week at this office without permission."

            "It says all of that on the invoice?" Big Ass asked while shielding his eyes from the light of the hyperspheric sun.

            "No, but me and your boss talked a little while ago and I was told to ask for "Big Ass." I am guessing there is not many who would like to be called that. Actually, I was told to bill it to a Mr. Assistant Morefour. I assume that is you, Big Ass."

             "Ok, you can quit with the "Big Ass" now. Only my friends get to call me that. To my boss and most people, they call me Asisfour. That was my boss's idea of a joke. Come on in."

             As Upholsterer set to work on repairing the couch, Asisfour's boss arrived at the office. Each time Upholsterer cut the cloth, it was like a solid leather 3D universe getting smaller and smaller until it was the right size to repair the hole. All the extra leather 3D universes leftover from the cutting he threw away in a nearby 4D trash can.

             His boss seemed in a pretty good mood. Asisfour figured his crashing at the office overnight might go unnoticed.

             "I ought to start having you pay the office rent," his boss suggested to Asisfour.

            "I was drunk and you know what they say about drinking and hyper-driving. Besides, when I crash here I am never late for work in the morning."

            "True, but it takes you just as long to be useful when you are here and hung over as when you are half-asleep at home just thinking about when to show up," his boss admonished.

             "My thoughts exactly, so you won't mind if I go grab a bite to eat to help me over my hangover so I can be of better use to you?"

             "Not at all," his boss replied. "I assumed you would ask as much."

            "You must be psychic then?" Asisfour replied.

             "Right, and this then would be the first time we had this conversation or the first time you wrecked one of my expensive leather couches. You are lucky I am a very forgiving woman," his boss replied. 

            "And a sexy one at that," Asisfour said. "Do you want me to bring you back anything?"

             "No, I made myself something to eat at home."

            "Well, I guess they don't call you Creator for nothing," Asisfour joked while leaving just in time to dodge the hyperspheric Universe shaped tennis-ball from her desk he knew she would throw when he joked yet again about her name.
 
 

Note: I wanted to take Inventor and Assistwo up to the 4D level somehow, but I think this is just as good or better. Their spirits live on through others, similar yet different. It really bothered me that none of the characters were female, but now the time seemed right, the name seemed right, and it seems the 2D duo will be retired once again as the focus now moves logically to bouncing back and forth between the 3D universe and the 4D universe, as before between the 2D and 3D ones, since I feel now confident enough with most aspects of 4D universes to think I can do it correctly, slowly that is, and if I screw it up, Inventor's batting average remains safe and I can blame all the mistakes on Creator. Researcher is now doing better mistake-wise since the blunders of section 5.5 (unlike the unsalvageable section 1.7 (1.7 was mostly gutted and parts were merged with another). Researcher's "mistakes" in section 5.5 did not go off-track too far, and the errors were useful in explaining "accepted" misconceptions about 4D perspectives), which to be fair it seems most others in this 3D world seemed to had made the same wrong conclusions about 4D perspectives anyway. And since a 3D universe will be easier to figure out and explain without making as many mistakes than with the 4D one will be, (though far easier for others to show and  prove the mistakes made in respect to our 3D (physical dimensions) Universe too, though with General Relativity's continued acceptance, maybe not. Even scientists still find ways to believe what suits them, now the same as always.) Researcher just might end up looking like the smartest character in the story from now on. The new major character's name I did not think of until I got to the last few lines, but I have a gut feeling she will prove more than a match for the similarly named 2D super-genius. Book Two may tell. Time too, if there is such a thing. Inventor suggested not, but what does he know? Replaced by a woman. Sheesh. :-)                -The Man.