I've always wondered why humans seem to be unable to visualize four-dimensional objects in their heads.
When discussing this with others, the arguments often revolve around the fact that as we experience our reality in 3D, there should be no reason for us to be able to visualize anything in a higher dimension.
This argument seems like an arbitrary limitation of the human mind, which I don't think holds up. It is sometimes associated with our inability to think of new colors, but I think this is a completely different problem.
I have a beautiful animation of a tesseract on an old drive somewhere I kept, back in the animated gif days, I'd look at it now and then in wonder. Reminds me of the same extraordinary feelings about the beauty of the universe with this clip: https://youtube.com/shorts/TGuxwgUyu2A?si=knDzBVqTaZ4oqMEj
There was some 90s shareware DOS visualizer for various 4D shapes. I think it might have been called Hypercube, and thought this article might have been about it. It wasn’t, but was quite informative nonetheless!
The simplest hypercube visualization is taking the fourth dimension as time. Then it’s just a regular cube that appears at once, and a unit of time later again vanishes instantly. ;)
Flatland is an interesting way to think about dimensions. If we were living in a 2D world, anything living in the 3D world would blow our minds and do things we would think should be impossible.
Pretty immediately my new favorite hypercube-displaying-exploration article. That's a great, very clear step through the problems and common methods, and I really like the end results.
I suspect every attempt will be unsatisfying, but it does a good job of showing "there's more happening here than it looks like at first".
I've always wondered why humans seem to be unable to visualize four-dimensional objects in their heads.
When discussing this with others, the arguments often revolve around the fact that as we experience our reality in 3D, there should be no reason for us to be able to visualize anything in a higher dimension.
This argument seems like an arbitrary limitation of the human mind, which I don't think holds up. It is sometimes associated with our inability to think of new colors, but I think this is a completely different problem.
"This argument seems like an arbitrary limitation of the human mind, which I don't think holds up. "
And why not?
Evolution did not reward us for thinking about spaced out concepts, but for coming up with new ways to get food, outsmart the prey, build tools.
That thinking in 4D is helpful for building tools is a new thing so we evolution did not optmized for it (yet).
I have a beautiful animation of a tesseract on an old drive somewhere I kept, back in the animated gif days, I'd look at it now and then in wonder. Reminds me of the same extraordinary feelings about the beauty of the universe with this clip: https://youtube.com/shorts/TGuxwgUyu2A?si=knDzBVqTaZ4oqMEj
I was glad to see the cube defined symmetrically around the axis, i.e. abs(x) <= a.
Like a circle, radially, vector length <= a.
I get anxious when encountering the inconsistency between origin centered Hyperspheres and 0-1 bound Hypercubes.
There was some 90s shareware DOS visualizer for various 4D shapes. I think it might have been called Hypercube, and thought this article might have been about it. It wasn’t, but was quite informative nonetheless!
The simplest hypercube visualization is taking the fourth dimension as time. Then it’s just a regular cube that appears at once, and a unit of time later again vanishes instantly. ;)
Flatland is an interesting way to think about dimensions. If we were living in a 2D world, anything living in the 3D world would blow our minds and do things we would think should be impossible.
https://en.wikipedia.org/wiki/Flatland
There’s also The Planiverse, with a different take on what a 2D world would look like.
https://en.wikipedia.org/wiki/The_Planiverse
Pretty immediately my new favorite hypercube-displaying-exploration article. That's a great, very clear step through the problems and common methods, and I really like the end results.
I suspect every attempt will be unsatisfying, but it does a good job of showing "there's more happening here than it looks like at first".
“Speaking of ways, pet, by the way, there is such a thing as a tesseract.” -A Wrinkle in Time