Can anybody truly visualize a 4th physical dimension?
Lots of physics and math books (including the one I’m reading now) say it’s ‘hard’ to visualize a 4th dimension. Is that there way of weaseling out of saying “it’s impossible,” or is it possible?
In 3 dimensions, it’s easy to draw a 2-dimensional picture that clearly represents 3 dimensions. Maybe it’s only easy to ‘see’ the 3rd dimension in the 2-dimensional image because we’re familiar with the 3rd dimension.
Is it possible, in a 3-d rendering (say, a hologram, or a translucent cube) to ‘draw’ a scene that shows the 4th dimension, going off at a right angle to the other 3?
It just is not possible for us to imagine another right angle off a 3D object (eg: you have a 1D line, 2D is a line at a right angle to that, 3D is another line and a right angle to the first two, 4D is another line at a right angle to the first three…we just cannot envision that).
Your eyes cannot interpret any sort of meaningful fourth-dimensional image, but your brain can manage to imagine simple 4D constructs, like the tesseract.
This is my opinion, but I don’t think it’s possible to literally visualize something that you would be otherwise utterly physically incapable of ever seeing.
People can learn to develop a concept of what 4-space might be like, by extending the analogy you suggest. That is, you can show someone a wire-frame cube, then show how it casts different types of shadows on a plane. Then you can say, “Now imagine that this wire-frame structure [show 3D tesseract model] is the shadow in our 3D world of something in 4D.” You can kind of grasp what’s going on mathematically, and understand and predict what can happen to the 3D projection, but IMHO nobody can ever construct a 4D model in their minds of a tesseract, any more than Flatlanderscan visualize a 3D cube from looking at one sequare inside another with their respective corners connected.
When we look at a picture or drawing we are seeing a 2D representation of a 3D world. With simple images it is often possible to make your brain switch back and forth from seeing the image as flat and as a 3D image.
In principle, I guess, there would be no problem with making a 3D picture or drawing (or 2D) of a 4D world so yes I guess it could be represented. The problem is our brain could likely not interpret the image correctly and would only give it the “flat” 3D interpretation and not be able to switch to a 4D interpretation.
If a 4D “person” were standing in front of you you would see only the part of them that impinges in the 3D world.
Easiest to visualize this ala Flatland and take it down a notch.
Imagine a world of 2D creatures. They live on a plane. They have no concept of “up/down”. There is only backward/forward, right/left.
Now you step on their world. You stand six feet off the surface. What do the Flatlanders see? They see just the bit of you touching the surface of their world and would deem nothing odd there (well they might…the treads on your shoe would touch in numerous places at once so that would be very strange to them).
Thing is you would be magical in their world. You could seemingly disappear (pick your foot up) and reappear in another place (put it back down somewhere else). No prison could hold you (to imprison you they would draw a circle around you which you would just step out of). You could see the internal organs of all the Flatlanders and even perform surgery without “cutting” them open.
The list goes on. A 4D creature would be similarly “magical” in our 3D world.
And the sensor of the retina of a 4-D eye would be voxels in a solid ball, bent around the hypersphere of the being’s eye to be equidistant in fourspace from the lens, just as our retinas are pixels arranged in a disc, bent around the sphere of the eye to be equidistant from the lens.
4-D letters would be little 3-D sculptures, printed by the 3-D end of the type being covered by ink and moving in the 4th direction to hit the 3-D sirface of the paper…
i don’t know if using those tesseract images is the best way to visualize a 4th dimension. in fact, visualization in general isn’t very helpful. i think it’s easier to think of dimensions as distinct characteristics - like excel cells. an object can have a cell dedicated to length, width, and height. it can also have color, density, etc. those can be considered “physical dimensions” too.
this gives rise to dimensional analysis. that’s how we have units for the gravitational constant, gas constant, etc. we worked backwards and made the “dimensions” cancel out.
however, what you mean is positional dimension, which is what the tesseracts try to replicate. instead, try and think of time as the 4th dimension. to describe the position of something like… a jet plane you have to give a x, y, and z coordinate. however if you send a patriot missile up there to take it out, you’ll probably miss because it would have moved. all things exist by occupying a location and this location is specified by x,y,z, and time. this is basically (as in really elementarily) the concept of space-time.
File:Dimension levels.svg - Wikipedia is a better way to “visualize” the 4th dimension. the dot is a jet, and it can move in x, y, z, and forward in time.
I would go even farther with that. Even our eyes are just capturing 2D representations of a 3D world. We use two eyes and some clever processing in the brain to visualize the 3D space.
So the leap to 4D is really quite significant - a mental leap has already been required just to get to 3D. Fundamentally, we’re 2D creatures with a few 3D tweaks.
That said, when I’m trying envision 4D, I don’t think of mathematical constructs - I think of time lapse. Just like you can make a 3D MRI by layering 2D images on top of each other, you can sort of create a 4D image by layering 3D “snapshots in time” over each other.
And under that way of thinking, you could argue that we have a 4D art form already: dance. The dancers’ position in space is just as important as their movement through time.
I wouldn’t go so far as to be absolutely certain we couldn’t see a 4th dimension.
Let’s say for example our eyes do have receptors capable of seeing a 4th dimension but since we don’t ever come across a creature or a structure having four dimensions we don’t see it.
For instance imagine everything in the world is either red or green. Our eyes have receptors for Red, Blue and Green. But if everything was either red or green, we’d never see blue. This doesn’t mean blue doesn’t exist. Our eyes would still have the receptors to see the colour blue, but since nothing in the world was blue, we’d never know.
Now if someone was able to build something blue, or a creature from another world came to visit us and was blue, we’d then see it. But we’d only see it if it was there.
So extending this analogy we could say, perhaps we can see in 4D but unless we can create a 4D structure or a creature from another world who is built in 4D comes to visit us we’d never know.
Let’s say Flatlanders are circles and squares (pick any shape…does not matter).
All their internal organs are inside the circle/square. To each other they can only see the outside line defining their shape. A Flatlander surgeon would need to cut them open to repair stuff same as a surgeon does to us.
Now you come along. You can look down on the Flatlanders (literally down from above) and can see all their insides just fine. If you want to fix something (or mysteriously kill one) just reach down and fiddle with their insides as necessary (e.g. pluck a 2d bullet out of one). No need to cut them open at all. They’d never see you do it but it’d be done just the same. Far from magical this would be normal to you and simplicity itself. To them it’d be magic.
I can visualize four spatial dimensions, but it took me years of practice to be able to do so. On a really good day, I can occasionally manage to get five, but that’s always fleeting.
In four dimensions there are two planes that are perpendicular to each other and intersect in a single point. If you can visualize that, you’re doing pretty well.
Charles Howard Hinton came up with a system of colored cubes in 1888 that were supposed to help you teach yourself to grasp the fourth dimension. The system is outlined in his book “A New Era of Thought”. The 125 cubes have different colored faces, edges, corners, and interiors, and by manipulating the cubes you’re supposed to get a sense of the 3D projection of a 4D cube. I don’t know how many hours you’d have to spend fiddling with cubes and trying to keep ten shades of green separate in your mind, but I remember reading a contemporary reviewer claiming that the effect was disturbing.
