This article discusses four-dimensional raytracing.
It works like three-dimensional raytracing, except that the rays are drawn from the viewpoint through cells in a 3D cubical grid in 4-space, rather than through cells in a 2D square grid in 3-space.
The resulting raytraced image is a 3D arrangement of coloured ‘voxels’ representing a view of 4D space, just as a regular raytracing is a 2D arrangement of coloured pixels representing a view of 3D space.
Now, I’m looking at the pictures there, and having a hard time putting them together. Yes, the seies of pictures of spheres on the website are a series of 2D renderings of slices of the solid 3D ‘image’ created by the raytracer. I think. But the real rendering is the solid 3D image.
Let’s assume that there are now or will soon be implants for direct brain reception of visual stimuli. Would it be possible to learn to perceive these synthesised solid 3D images, in all their depth, directly?
Yes, it’s possible. I trained myself to visualize in 4D, but it took me about eight years to do so (why, yes, I am obsessed… Why do you ask?). In moments of extreme lucidity, I’ve occasionally been able to glimpse 5 dimensions, but that’s rare.
8 years, I have been able to do that for a while and would actually also say the same about occationally be able to glimps a 5th also. I don’t know how long it took and it was after at least one degree in ME that I could perceive it. I always felt that I perceived somewhat multi-dimentionally anyway, perhaps all I had to do it apply it to what I learned instead of develope it as you most likely had.
People have trouble visualizing 4D space? I find 4D, 5D, and higher levels of n-dimesional space trival to visualize. Non-euclidean space-time isn’t a problem either.
Wait, you people can do it? I can visualize 3-space. I can picture three squares coming together to form the vertex of a cube, sure.
You can picture four cubes coming together and forming the vertex of a hypercube? You can picture five hypercubes coming together to form the vertex of a 5-cube?
Chronos and kanicbird, could you give a little more detail on how you accomplished this. I understand how to model a 4d image in three space but I can’t see how you can visualize four mutually perpendicular straight lines.
Obviously there’s not much point to asking Cthulhu since his (its?) perceptual apparatus are so different from ours.
It’s probaly possible to train yourself to visualize n-dimensional Euclidan space (not something that I can claim to do or to of tried), I imagine spending time looking at four-vectors helps.
No, that would be 5 dimensional. Rougly what I did was train myself to treat time as another spatial dimension. So for visualizing the edges of a hypercube, for instance: That’s a full cube for an instant, then the edges vanish but the vertices persist for a little while, then the full cube re-appears for an instant, then it all disappears.
As for those rare glimpses of five, if I could remember how I did them, they wouldn’t be so rare. I’m pretty sure they involved four spatial and one temporal dimension, though.
Sorry, I forgot to really respond to the quote. I can visualize the four cubes being together, but I can’t picture them coming together, since I’ve already “used up” my time dimension.
A technique that is often used to visualise, multiple dimensions, is imagining the extra dimension to be represented by colour. This makes sense, its an unused attribute that is easy to tack onto shapes. So picture a red cube. Now imagine that that cube is turning blue, moving through purple and all the other exciting shades between. That cube just moved bluewards through the fourth dimension!
But did it move towards you or away from you? It doesn’t matter. Technically three dimensional objects do not move around in our mind either. By convention, when we see a three dimensional object decreasing in size, we say its moving away. For conventions sake, lets say that when a 4D object appears blue to the observer, it has moved away.
This does not have to be done with colour, but you get the idea. It is an easy and acceptable way to visualise four dimensions. Obviously, the reason it is hard is because we have no experience with it. So just add colour, something we are familiar with.
This does not attempt to refute the claims of those who can claim to see four spatial dimensions, just a stepping up point for us muggles.
You know, I’ve got to be honest with you. While that does make sense, that is not at all what I have in mind when I think of “visualizing 4D space”. The same goes for treating time as a spatial dimension. I wanna be able to rotate my mental polychora! Heck, even being able to rotate a polyhedron through 4D space would be impressive to me.
I’m kind of disappointed with any 4D visualiziation that doesn’t let me visualize anything other than a 3-sphere and a static hypercube or pentatope.
In truth, all of those mental images people have mentioned isn’t really visulaising the 4th dimension. It’s merely visulaising a 3d slice of the 4th dimension at a time. Now, if someone could truely put it all in theyre head at the smae time, I would be impressed.
Well, when we visualise 3D space, we’re actually seeing a 2D image. Our eyes have 2D receptors, so we percieve every point simultaneously through the area of the 2D image.
To perceive 4D space analogously to the way we perceive 3D space, a being living in 4D space would see 3D images,. It would see every point simultaneously in the volume of the 3D images projected on the 3D ‘surface’ of the receptors of its eyes.
Granted that we cannot create these receptors in our existing space, if we could somehow synthesise the solid 3D images (as the linked article seems to say), could we feed them directly into our brains and learn to perceive them without needing receptors?
IMHO (which, let’s face it, is all you’re ever going to get in this thread) you cannot visualize in 4D, no matter how much you train yourself.
Your eyes are 3D, your physical universe is 3D, your mental map of that physical universe is 3D, everything you ever experience is 3D (excluding the dimension of time, natch.) You have nothing to equip you for 4D visualisation, not even the start of the beginnings of it. “Training” isn’t going to get yourself there any more than training a snake how to run is going to get it legs.
What you can do, however, is imagine 4 dimensions. But since this is only your imagination, how it is visualised is very much a personal and individual trick and bears very little relationship to what 4D is in reality. An accurate visualisation is something that is beyond us, because no-one knows. All we know of a 4th dimension is essentially just conceptual mathematics.
So by all means imagine. But you can take claims from people that they visualise 4D with a pinch of salt. All they’re doing is a mental trick (like Insecta’s excellent colour example) that helps them with the concept. They are still bound to 3D like everyone else.
Isn’t time essentially a fourth dimension? If that’s the case, your local weatherman is an expert in four-dimensional thinking. Fowl hunters and jet fighter pilots might qualify as well.
Every discussion of 4-D thinking invariably involves someone chiming in with the notion of time as the fourth dimension. I don’t see how it helps, and it certainly doesn’t answer the original question, since we’re obviously concerned with spatial dimensions.
I think most people smart enough to ask the 4-D question are smart enough to realize that time is the fourth dimension in our observable universe. And so the fact that they’re restricting the discussion to spatial dimensions is implicit.
I find 4D, 5D, and higher levels of n-dimesional space trival to visualize. Non-euclidean space-time isn’t a problem either.