3 ms·

I would love to see as many attempts at this as possible, as I am having an incredibly hard time visualizing / understanding more than 3 dimensions.

by calini 3y ago

0xndavd 3y ago
It is an inherently hard/nearly impossible task for us, three dimensional beings. I gave a shot at attempting to give an explanation here: https://github.com/ndavd/ncube/#but-what-am-i-actually-visualizing https://github.com/ndavd/ncube/#but-what-am-i-actually-visua...
- adonovan 3y ago
  It’s worth saying that visualizing 4-cubes is hard but _that’s ok_: it’s not a task our brains had any evolutionary need for, and even if we could visualize 4D, 5 would be harder still, yet it’s easy (relatively) to usefully imagine very high dimensional spaces, even infinite Hilbert spaces, when talking about ML feature space or quantum mechanics or whatever. So don’t get hung up on visualizing more than 3D. After 1D and 2D, you get the idea.
IvyMike 3y ago
"It is very hard to visualize such a dimension directly. Off and on for some fifteen years, I have tried to do so. In all this time I’ve enjoyed a grand total of perhaps fifteen minutes’ worth of direct vision into four-dimensional space." - Rudy Rucker, The Fourth Dimension https://www.rudyrucker.com/thefourthdimension/ https://www.rudyrucker.com/thefourthdimension/
GoblinSlayer 3y ago
There's Pacman4D.
rikroots 3y ago
My attempt at an animated tesseract from a while back: https://codepen.io/kaliedarik/pen/yLbQpKq https://codepen.io/kaliedarik/pen/yLbQpKq I'll be honest: I can't visualise anything beyond 3 dimensions, so I have no idea if my attempt even comes close to being accurate. To me the result looks like a spinning cube which also thinks it's a torus trying to eat itself. I think the cube should be trying to eat itself in (at least) 3 directions as it spins in 4d?
- 0xndavd 3y ago
  Interesting result. Unsure whether it's correct. Doesn't look far off but it's hard to say without examining the code. Feel free to take a look at ncube's code. Some parts are a bit abstract since I had to generalize it to arbitrary dimensions, but let me know and I can provide some assistance.

I would love to see as many attempts at this as possible, as I am having an incredibly hard time visualizing / understanding more than 3 dimensions.

by calini 3y ago

I would love to see as many attempts at this as possible, as I am having an incredibly hard time visualizing / understanding more than 3 dimensions.

0xndavd 3y ago

It is an inherently hard/nearly impossible task for us, three dimensional beings. I gave a shot at attempting to give an explanation here: https://github.com/ndavd/ncube/#but-what-am-i-actually-visualizing https://github.com/ndavd/ncube/#but-what-am-i-actually-visua...

adonovan 3y ago
It’s worth saying that visualizing 4-cubes is hard but _that’s ok_: it’s not a task our brains had any evolutionary need for, and even if we could visualize 4D, 5 would be harder still, yet it’s easy (relatively) to usefully imagine very high dimensional spaces, even infinite Hilbert spaces, when talking about ML feature space or quantum mechanics or whatever. So don’t get hung up on visualizing more than 3D. After 1D and 2D, you get the idea.

IvyMike 3y ago

"It is very hard to visualize such a dimension directly. Off and on for some fifteen years, I have tried to do so. In all this time I’ve enjoyed a grand total of perhaps fifteen minutes’ worth of direct vision into four-dimensional space." - Rudy Rucker, The Fourth Dimension https://www.rudyrucker.com/thefourthdimension/ https://www.rudyrucker.com/thefourthdimension/

GoblinSlayer 3y ago

There's Pacman4D.

rikroots 3y ago

My attempt at an animated tesseract from a while back: https://codepen.io/kaliedarik/pen/yLbQpKq https://codepen.io/kaliedarik/pen/yLbQpKq I'll be honest: I can't visualise anything beyond 3 dimensions, so I have no idea if my attempt even comes close to being accurate. To me the result looks like a spinning cube which also thinks it's a torus trying to eat itself. I think the cube should be trying to eat itself in (at least) 3 directions as it spins in 4d?

0xndavd 3y ago
Interesting result. Unsure whether it's correct. Doesn't look far off but it's hard to say without examining the code. Feel free to take a look at ncube's code. Some parts are a bit abstract since I had to generalize it to arbitrary dimensions, but let me know and I can provide some assistance.