4 ms·

You gotta think outside the hypercube

101 points by surprisetalk 8mo ago

Groxx 8mo ago
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".
telesilla 8mo ago
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 https://youtube.com/shorts/TGuxwgUyu2A?si=knDzBVqTaZ4oqMEj
- rikroots 8mo ago
  I've got a rotating tesseract demo up on CodePen[1]. At least, I think its a rotating tesseract - I have no idea if it's an accurate representation because tesseracts lead me into thinking about quaternions and then my brain shuts down. [1] - https://codepen.io/kaliedarik/pen/yLbQpKq https://codepen.io/kaliedarik/pen/yLbQpKq
  - telesilla 8mo ago
    Thanks! I took your code and modified a bit to remind me of what I had saved years ago. Not quite right but closer. https://codepen.io/tessaracting/pen/yyaMawL https://codepen.io/tessaracting/pen/yyaMawL Careful around complex numbers! BTW poetically enough, codepen has a tesseract for a logo.
Nevermark 8mo ago
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.
layer8 8mo ago
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. ;)
- amenghra 8mo ago
  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 https://en.wikipedia.org/wiki/Flatland
  - layer8 8mo ago
    There’s also The Planiverse, with a different take on what a 2D world would look like. https://en.wikipedia.org/wiki/The_Planiverse https://en.wikipedia.org/wiki/The_Planiverse
- unnah 8mo ago
  It's not so easy any more if you try to rotate the hypercube and have to visualize intersections with arbitrary hyperplanes. Already in 3 dimensions the intersection of a cube and a plane can be a non-regular polygon with 3-6 sides.
cobbzilla 8mo ago
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!
- snovv_crash 8mo ago
  Timecube... Although I'm not sure if that's what you were thinking of.
Mistletoe 8mo ago
“Speaking of ways, pet, by the way, there is such a thing as a tesseract.” -A Wrinkle in Time
vpmadd52huq 8mo ago
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.
- lukan 8mo ago
  "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).
  - mavhc 8mo ago
    Most of our thinking now is about how we made rocks think, gods, and fiction. None of those are created by evolution
    - tenuousemphasis 8mo ago
      Yes, we've managed to make our ancient hardware run more modern software but it's a bit of a kludge and causes compatibility issues.
    - Copyrightest 8mo ago
      [dead]
- LoganDark 8mo ago
  I can think of new colors, but I don't have a way to relate them to stimuli I've experienced, which makes it difficult to make sense of them the same way I can recall seeing existing colors. Still, I and many others have a notion of color that encompasses more than what my eyes can actually see, and I even have some friends that see much, much more in terms of color (such as texture, sensation, etc.)
remipch 8mo ago
On the subject of higher dimension mathematics, I recently discovered this video : "The most beautiful formula not enough people understand" You might find it interesting too. https://www.youtube.com/watch?v=fsLh-NYhOoU https://www.youtube.com/watch?v=fsLh-NYhOoU
deleted 8mo ago
[deleted]
useftmly 8mo ago
[dead]

101 points by surprisetalk 8mo ago

Groxx 8mo ago

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".

telesilla 8mo ago

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 https://youtube.com/shorts/TGuxwgUyu2A?si=knDzBVqTaZ4oqMEj

rikroots 8mo ago
I've got a rotating tesseract demo up on CodePen[1]. At least, I think its a rotating tesseract - I have no idea if it's an accurate representation because tesseracts lead me into thinking about quaternions and then my brain shuts down. [1] - https://codepen.io/kaliedarik/pen/yLbQpKq https://codepen.io/kaliedarik/pen/yLbQpKq
- telesilla 8mo ago
  Thanks! I took your code and modified a bit to remind me of what I had saved years ago. Not quite right but closer. https://codepen.io/tessaracting/pen/yyaMawL https://codepen.io/tessaracting/pen/yyaMawL Careful around complex numbers! BTW poetically enough, codepen has a tesseract for a logo.

Nevermark 8mo ago

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.

layer8 8mo ago

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. ;)

amenghra 8mo ago
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 https://en.wikipedia.org/wiki/Flatland
- layer8 8mo ago
  There’s also The Planiverse, with a different take on what a 2D world would look like. https://en.wikipedia.org/wiki/The_Planiverse https://en.wikipedia.org/wiki/The_Planiverse
unnah 8mo ago
It's not so easy any more if you try to rotate the hypercube and have to visualize intersections with arbitrary hyperplanes. Already in 3 dimensions the intersection of a cube and a plane can be a non-regular polygon with 3-6 sides.

cobbzilla 8mo ago

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!

snovv_crash 8mo ago
Timecube... Although I'm not sure if that's what you were thinking of.

Mistletoe 8mo ago

“Speaking of ways, pet, by the way, there is such a thing as a tesseract.” -A Wrinkle in Time

vpmadd52huq 8mo ago

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.

lukan 8mo ago
"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).
- mavhc 8mo ago
  Most of our thinking now is about how we made rocks think, gods, and fiction. None of those are created by evolution
  - tenuousemphasis 8mo ago
    Yes, we've managed to make our ancient hardware run more modern software but it's a bit of a kludge and causes compatibility issues.
  - Copyrightest 8mo ago
    [dead]
LoganDark 8mo ago
I can think of new colors, but I don't have a way to relate them to stimuli I've experienced, which makes it difficult to make sense of them the same way I can recall seeing existing colors. Still, I and many others have a notion of color that encompasses more than what my eyes can actually see, and I even have some friends that see much, much more in terms of color (such as texture, sensation, etc.)

remipch 8mo ago

On the subject of higher dimension mathematics, I recently discovered this video : "The most beautiful formula not enough people understand" You might find it interesting too. https://www.youtube.com/watch?v=fsLh-NYhOoU https://www.youtube.com/watch?v=fsLh-NYhOoU

deleted 8mo ago

[deleted]

useftmly 8mo ago

[dead]