"THE FOURTH dimension" "The solid matter around us has length, width and depth." "We say it has three dimensions." "But we can imagine things and beings with a different number of dimensions." "A thread so thin that its width and depth are neglectible has only length, or one dimension." "We can determine a point on it with a single number- the distance X from the end of the thread." "An infinitely thin sheet of paper, without depth, has just two dimensions,- length and width." "We need two coordinates to find a point on it, such as X the distance from the left edge, and Y the distance from the bottom." "Similarly, in a room with three dimensions - length, width, and height- we need three numbers to find one point," "X, the distance to a wall Y, to a perpendicular wall, and Z, the distance from the floor." "In the same way, infinitely thin sticks placed end to end represent one-dimensional entities." "LENGTH - 1 dimension" "Rectangles from a sheet of paper are two-dimensional." "LENGTH AND WIDTH - 2 dimensions" "Bricks stacked side by side are three-dimensional." "LENGTH, WIDTH AND HEIGHT - 3 dimensions" "By analogy, we can imagine the existence of a fourth dimension." "Let us suppose infinitely flat beings living in a two-dimensional space." "They recognize the other flat animals around them but cannot imagine anything outside their universe, neither above nor below the plane they inhabit." "Objects crossing their space are perceived only as flat planes." "So if we stick the tip of a pencil into their universe they'll witness a miracle." "Unable to conceive of its source they'll think it just magically appeared." "If they hid a treasure in a two-dimensional box we could plunge a hand into their world" "and, being three-dimensional, make off with the treasure leaving their detectives without a clue." "Similarly, if there were a fourth dimension a being could manifest in our world in some mysterious, puzzling way, perhaps pulling on our ears, and we'd see nothing more than its fingertips." "It could materialize in our world like a genie in a fairy tale." "Our tiny flat creatures could only see the outer contour of their peers on their plane." "But we, living outside their space, could see their insides." "in the same way, a four-dimensional being could see all our organs at once." "It could amuse itself by extracting a bone from our skeleton without breaking the skin, though separating it from the flesh would be a challenge." "Suppose we turn one of these flat creatures over." "Its new position would be symmetrical but irreversible, this symmetry can be demonstrated by turning over a G." "Similarly, if a four-dimensional giant flipped us around, our heart would be on the right." "With our right hand now where our left was, we'd write backwards and a three-dimensional being would need a mirror to read our new handwriting." "Now let's consider time as one of the three dimensions, two-dimensional beings live in the plane of the present, while the past falls away below, and the future falls from above." "Let us imagine an orange passing through their world, they first see a small spot, which gradually grows larger and larger," "then the center of the orange appears, the spot briefly stabilizes, then shrinks and finally disappears." "To them the phenomenon of an orange was merely a disk changing over time." "Now let us look at the example of a match." "In the time dimension it is solid matter with a shape that delineates past and future." "MATCH" " PRESENT, PAST, FUTURE" "Let us light the match." "In the time dimension a thinning of the match indicates the moment it's lit." "When it has burned halfway, let us put it out." "A four-dimensional solid when reduced becomes rectilinear again." "On an atomic scale, the particles we see moving in this plane could be infinitely long, thin threads, the present plane moves along this skein, and at any moment, a cross-section would give the atoms' current position." "But since the threads are tangled, as the present plane moves, it looks like the atoms are moving." "According to this hypothesis, the only movement is a displacement of the present plane through the dimension of time." "On a human scale if we could perceive four-dimensional matter past and future would be visible." "We would see a solid hand touch a solid object before the act occurred." "Living beings, who seem to be born grow up, and then die, would instead be immutable beings merely passing through the present." "We can see images of the same person at different ages as three-dimensional cross-sections of a four-dimensional being who himself remains static and unchanging." "There are tiny books called "flip-books"" "that create the illusion of animation as their pages are flipped." "The universe could be like such a book." "The present is the page in view, the past has already been seen, while the future has not yet been revealed." "PRESENT" "PAST" "FUTURE" "Do these hypotheses actually describe reality?" "At this point we have no way of knowing." "These suggestions are only meant to stimulate reflection, and also show how mathematical analysis can expand the limits of what we consider possible."