I dreamed in anime once after a month long anime binge.
In physics a proposed solution to the black hole information paradox is the idea of a holographic universe. That is that the universe is a 2D construct plastered onto the surface of a black hole or a “brane” and that the third dimension emerges from the scale invariance of the 2D grid in the universe which means that it has the same rules for interaction whether your scale is micro or macro.
Also I’ll also note here the chapter on 2D beings from PD Ouspensky’s book Tertium Organum. It’s a really fascinating chapter that really makes you think about how limited our perception is. His main argument is that 2D being would only see line, and certain types of lines like angels they would perceive as motion. Motion- the ability of objects to change from one state to another- is the basis of our sense of time. Ouspensky argues then that this sense of time is illusory- the square is actually still but because the 2D being can only perceive it as a line and can’t see it from above like we can, they will have no understanding that their idea of motion and time is just and illusion. Ouspensky argues that our perception of time and motion are similar, incorrectly perceiving motionless objects to be moving. Ouspensky says that time is the direction of the dimension we can’t perceive, the 4th dimension for us, the 3rd dimension for the 2D being.
PD Ouspensky’s argument in this book is that realized beings may just be beings who are able to perceive higher dimensions, and this is why they can know the past and the future as well as perform miracles. Because of this Ouspensky sees imagininng 4D objects like hypercubes or hyperspheres to be a kind of spiritual practice.
Let us next consider the two-dimensional world, and the being living on a plane. The universe of this being will be one great plane. Let us imagine beings on this plane having the shape of points, lines, and flat geometrical figures. The objects and “solids” of that world will have the shape of flat geometrical figures too.
In what manner will a being living on such a plane universe cognize his world?
First of all we can affirm that he will not feel the plane upon which he lives. He will not do so because he will feel the objects, i.e., figures which are on this plane. He will feel the lines which limit them, and for this reason he will not feel his plane, for in that case he would not be in a position to discern the lines. The lines will differ from the plane in that they produce sensations; therefore they exist. The plane does not produce sensations; therefore it does not exist. Moving on the plane, the two-dimensional being, feeling no sensations, will declare that nothing now exists. After having encountered some figure, having sensed its lines, he will say that something appeared. But gradually, by a process of reasoning, the two-dimensional being will come to the conclusion that the figures he encounters exist on something, or in something. Thereupon he may name such a plane (he will not know, indeed, that it is a plane) the “ether.” Accordingly he will declare that the “ether” fills all space, but differs in its qualities from “matter.” By “matter” he will mean lines. Having come to this conclusion the two-dimensional being will regard all processes as happening in his “ether,” i.e., in his space.
He will not be in a position to imagine anything outside of this ether, that is, out of his plane. If anything, proceeding out of his plane, comes in contact with his consciousness, then he will either deny it, or regard it as something subjective, the creation of his own imagination; or else he will believe that it is proceeding right on the plane, in the ether, as are all other phenomena.
Sensing lines only, the plane being will not sense them as we do. First of all, he will see no angle. It is extremely easy for us to verify this by experiment. If we will hold before our eyes two matches, inclined one to the other in a horizontal plane, then we shall see one line. To see the angle we shall have to look from above. The two-dimensional being cannot look from above and therefore cannot see the angle. But measuring the distance between the lines of different “solids” of his world, the two-dimensional being will come continually in contact with the angle, and he will regard it as a strange property of the line, which is sometimes manifest and sometimes is not. That is, he will refer the angle to time; he will regard it as a temporary, evanescent phenomenon, a change in the state of a “solid,” or as motion. It is difficult for us to understand this. It is difficult to imagine how the angle can be regarded as motion. But it must be absolutely so, and cannot be otherwise. If we try to represent to ourselves how the plane being studies the square, then certainly we shall find that for the plane being the square will be a moving body. Let us imagine that the plane being is opposite one of the angles of the square. He does not see the angle—before him is a line, but a line possessing very curious properties. Approaching this line, the two-dimensional being observes that a strange thing is happening to the line. One point remains in the same position, and other points are withdrawing back from both sides. We repeat, that the two-dimensional being has no idea of an angle. Apparently the line remains the same as it was, yet something is happening to it, without a doubt. The plane being will say that the line is moving, but so rapidly as to be imperceptible to sight. If the plane being goes away from the angle and follows along a side of the square, then the side will become immobile. When he comes to the angle, he will notice the motion again. After going around the square several times, he will establish the fact of regular, periodical motions of the line. Quite probably in the mind of the plane being the square will assume the form of a body possessing the property of periodical motions, invisible to the eye, but producing definite physical effects (molecular motion)—or it will remain there as a perception of periodical moments of rest and motion in one complex line, and still more probably it will seem to be a rotating body.
Quite possibly the plane being will regard the angle as his own subjective perception, and will doubt whether any objective reality corresponds to this subjective perception. Nevertheless he will reflect that if there is action, yielding to measurement, so must there be the cause of it, consisting in the change of the state of the line, i.e., in motion.
The lines visible to the plane being he may call matter, and the angles—motion. That is, he may call the broken line with an angle, moving matter. And truly to him such a line by reason of its properties will be quite analogous to matter in motion.
If a cube were to rest upon the plane upon which the plane being lives, then this cube will not exist for the two-dimensional being, but only the square face of the cube in contact with the plane will exist for him—as a line, with periodical motions. Correspondingly, all other solids lying outside of his plane., in contact with it, or passing through it, will not exist for the plane being. The planes of contact or cross-sections of these bodies will alone be sensed. But if these planes or sections move or change, then the two-dimensional being will think, indeed, that the cause of the change or motion is in the bodies themselves, i.e., right there on his plane.
As has been said, the two-dimensional being will regard the straight lines only as immobile matter; irregular lines and curves will seem to him as moving. So far as really moving lines are concerned, that is, lines limiting the cross-sections or planes of contact passing through or moving along the plane, these will be for the two-dimensional being something inconceivable and incommensurable. It will be as though there were in them the presence of something independent, depending upon itself only, animated. This effect will proceed from two causes: He can measure the immobile angles and curves, the properties of which the two-dimensional being calls motion, for the reason that they are immobile; moving figures, on the contrary, he cannot measure, because the changes in them will be out of his control. These changes will depend upon the properties of the whole body and its motion, and of that whole body the two-dimensional being will know only one side or section. Not perceiving the existence of this body, and contemplating the motion pertaining to the sides and sections he probably will regard them as living beings. He will affirm that there is something in them which differentiates them from other bodies: vital energy, or even soul. That something will be regarded as inconceivable, and really will be inconceivable to the two-dimensional being, because to him it is the result of an incomprehensible motion of inconceivable solids.
If we imagine an immobile circle upon the plane, then for the two-dimensional being it will appear as a moving line with some very strange and to him inconceivable motions.
The two-dimensional being will never see that motion. Perhaps he will call such motion molecular motion, i.e., the movement of minutest invisible particles of “matter.”
Moreover, a circle rotating around an axis passing through its center, for the two-dimensional being will differ in some inconceivable way from the immobile circle. Both will appear to be moving, but moving differently.
For the two-dimensional being a circle or a square, rotating around its centre, on, account of its double motion will be an inexplicable and incommensurable phenomenon, like a phenomenon of life for a modern physicist.
Therefore, for a two-dimensional being, a straight line will be immobile matter; a broken or a curved line—matter in motion; and a moving line—living matter.
The centre of a circle or a square will be inaccessible to the plane being, just as the centre of a sphere or of a cube made of solid matter is inaccessible to us—and for the two-dimensional being even the idea of a centre will be incomprehensible, since he possesses no idea of a centre.
Having no idea of phenomena proceeding outside of the plane—that is, out of his “space”—the plane being will think of all phenomena as proceeding on his plane as has been stated. And all phenomena which he regards as proceeding on his plane, he will consider as being in causal interdependence one with another: that is, he will think that one phenomenon is the effect of another which has happened right there, and the cause of a third which will happen right on the same plane.
If a multi-colored cube passes through the plane, the plane being will perceive the entire cube and its motion as a change in color of lines lying in the plane. Thus, if a blue line replaces a red one, then the plane being will regard the red line as a past event. He will not be in a position to realize the idea that the red line is still existing somewhere. He will say that the line is single, but that it becomes blue as a consequence of certain causes of a physical character. If the cube moves backward so that the red line appears again after the blue one, then for the two-dimensional being this will constitute a new phenomenon. He will say that the line became red again.
For the being living on a plane, everything above and below (if the plane be horizontal), and on the right or left (if the plane be vertical) will be existing in time, in the past and in the future: that which in reality is located outside of the plane will be regarded as non-existent, either as that which is already past, i.e., as something which has disappeared, ceased to be, will never return; or as in the future, i.e., as not existent, not manifested, as a thing in potentiality.
Let us imagine that a wheel with the spokes painted different colors is rotating through the plane upon which the plane being lives. To such a being all the motion of the wheel will appear as a variation of the color of the line of intersection of the wheel and the plane. The plane being will call this variation of the color of the line a phenomenon, and observing these phenomena he will notice in them a certain succession. He will know that the black line is followed by the white one, the white by the blue, the blue by the red, and so on. If simultaneously with the appearance of the white line some other phenomenon occurs—say the ringing of a bell—the two-dimensional being will say that the white line is the cause of that ringing. The change of the color of the lines, in the opinion of the two-dimensional being, will depend on causes lying right in his plane. Any pre-supposition of the possibility of the existence of causes lying outside of the plane he will characterize as fantastic and entirely unscientific. It will seem so to him because he will never be in a position to represent the wheel to himself, i.e., the parts of the wheel on both sides of the plane. After a rough study of the color of the lines, and knowing the order of their sequence, the plane being, perceiving one of them, say the blue one, will think that the black and the white ones have already passed, i.e., disappeared, ceased to exist, gone into the past; and that those lines which have not as yet appeared—the yellow, the green, and so on, and the new white and black ones still to come—do not yet exist, but lie in the future.
Therefore, though not conceiving the form of his universe, and regarding it as infinite in all directions, the plane being will nevertheless involuntarily think of the past as situated somewhere at one side of all, and of the future as somewhere at the other side of this totality. In such manner will the plane being conceive of the idea of time. We see that this idea arises because the two-dimensional being senses only two out of three dimensions of space; the third dimension he senses only after its effects become manifest upon the plane, and therefore he regards it as something different from the first two dimensions of space, calling it time.
Now let us imagine that through the plane upon which the two-dimensional being lives, two wheels with multi-colored spokes are rotating and are rotating in opposite directions. The spokes of one wheel come from above and go below; the spokes of the other come from below and go above.
The plane being will never notice it.
He will never notice that where for one line (which he sees) there lies the past, for another line there lies the future. This thought will never even come into his head, because he will conceive of the past and the future very confusedly, regarding them as concepts, not as actual facts. But at the same time he will be firmly convinced that the past goes in one direction, and the future in another. Therefore it will seem to him a wild absurdity that on one side something past and something future can lie together, and on another side—and also beside these two—something future and something past. To the plane being the idea that some phenomena come whence others go, and vice versa, will seem equally absurd. He will tenaciously think that the future is that wherefrom everything comes, and the past is that whereto everything goes and wherefrom nothing returns. He will be totally unable to understand that events may arise from the past just as they do from the future.
Thus we see that the plane being will regard the changes of color of the lines lying on the plane very naively. The appearance of different spokes he will regard as the change of color of one and the same line, and the repeated appearance of the same colored spoke he will regard every time as a new appearance of a given color.
But nevertheless, having noticed periodicity in the change of the color of the lines upon the surface, having remembered the order of their appearance, and having learned to define the “time” of the appearance of certain spokes in relation to some other more constant phenomenon, the plane being will be in a position to foretell the change of the line from one color to another. Thereupon he will say that he has studied this phenomenon, that he can apply to it “the mathematical method”—can “calculate” it.