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4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

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Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#41

Post by anigbrowl »

pujjad wrote: post #15
jayd16 wrote: post #9

I'll ask any physicists out there. A 4th spatial dimension probably doesn't exist, right? Even if we couldn't perceive shapes across a 4th dimension, we would still perceive things moving through the 4th dimension like we see in 4D toys. In reality we don't ever see anything like this (spatially anyway). Is that correct?

If there were 4 spatial dimensions + 1 time dimension we would end up in an unstable universe. Ehrenfest (1917/1920) studied the hydrogen in n dimensions and concluded for n> 3 that neither classical atoms nor planetary orbits can be stable, because the inverse square law of electrostatic and gravity becomes an inverse cube law. When n > 3 there are no stable orbits to the two body problem: an incoming light body att…

A beautifully clear explanation.

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#42

Post by phinnaeus »

throwaway_pdp09 wrote: post #19

I am genuinely surprised for a long time that I've not seen 4D monsters in films. It has been so obvious to me there's potential there. It would of course be a flat 2D projection of a 3D slice through a 4D creature, so it would look like a smoothly morphing between different creatures, and in and out of existence so we've sort of had morphing for a long while (since Willow, C. 1985) but... there's potential. In case…

Maybe there will be an adaptation of the Three Body Problem novels.

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#43

Post by EL_Loco »

Why do these n-dimension demos always have the little 2d man seeing the world as if he could fly away from his 2d plane and see it from above? In that example where narrator says the 2d man would be intrigued about the circle floating, he would actually only see a line moving up and down. The ball crossing the plane would be just a line stretching and shrinking. If he lived in a 2d world, what he could actually see would be /pretty/ limited.

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#44

Post by jblow »

EL_Loco wrote: post #43

Why do these n-dimension demos always have the little 2d man seeing the world as if he could fly away from his 2d plane and see it from above? In that example where narrator says the 2d man would be intrigued about the circle floating, he would actually only see a line moving up and down. The ball crossing the plane would be just a line stretching and shrinking. If he lived in a 2d world, what he could actually see w…

He would be able to see a circle the same way you can see a sphere. Do you feel like you can only see discs, not spheres?

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#45

Post by FPGAhacker »

jblow wrote: post #44
EL_Loco wrote: post #43

Why do these n-dimension demos always have the little 2d man seeing the world as if he could fly away from his 2d plane and see it from above? In that example where narrator says the 2d man would be intrigued about the circle floating, he would actually only see a line moving up and down. The ball crossing the plane would be just a line stretching and shrinking. If he lived in a 2d world, what he could actually see w…

He would be able to see a circle the same way you can see a sphere. Do you feel like you can only see discs, not spheres?

How different would a 2d square look projected onto a 1d view, vs a circle?

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#46

Post by javajosh »

FPGAhacker wrote: post #45
jblow wrote: post #44

Earlier quoted context omitted.

He would be able to see a circle the same way you can see a sphere. Do you feel like you can only see discs, not spheres?

How different would a 2d square look projected onto a 1d view, vs a circle?

If you rotate a square, then the length will oscillate. A circle will remain fixed (but presumably would have surface detail to clue you in that it's rotating.)

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#47

Post by chadmeister »

dang wrote: post #30
AlbertoGP wrote: post #2

Wow, the title does not make it justice: I only went to look at it in an idle moment after lunch. Much better to transcribe the beginning of the video: 4D Toys is a toy box filled with 4-dimensional toys. By 4-dimensional I mean that they exist in a world with 4 dimensions of space and 1 dimension of time, instead of 3 dimensions of space and 1 dimension of time. It turns out that the rules of how objects bounce, sli…

Ok, let's take the title from the video instead. Thanks for pointing this out! Sometimes the best work hides behind dry or modest language. It's easy enough, albeit annoying, to brush away the inflated mediocre. It's so much harder to locate the unseen gems. Edit: ah, I see - the video is from 2017, and there was a thread back then too: https://news.ycombinator.com/item?id=14471931 . I guess we'll make an ugly hybrid…

Thank you this is still much better than the useless original title

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#48

Post by avhon1 »

zokier wrote: post #11

It would be interesting to see how it would look with the 4D scenes properly projected instead of cross-sectioned. I mean that is how we get 3D scenes on our puny 2D displays; we don't generally do the sort of cross-sections for 3D like they show in the flat-land example except in some specialized applications. Of course cross-section is still valid method of visualization. I don't know enough about higher dimensiona…

You could display 3D projections of 4D objects on a 2D screen with anaglyph graphics. (Think red- and blue-filtered glasses.)

https://en.wikipedia.org/wiki/Anaglyph_3D

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#49

Post by serf »

throwaway_pdp09 wrote: post #19

I am genuinely surprised for a long time that I've not seen 4D monsters in films. It has been so obvious to me there's potential there. It would of course be a flat 2D projection of a 3D slice through a 4D creature, so it would look like a smoothly morphing between different creatures, and in and out of existence so we've sort of had morphing for a long while (since Willow, C. 1985) but... there's potential. In case…

if you're into anime, check out Seikaisuru Kado.[0]

The antagonist is a being from another dimension who routinely shows off dominion over N dimensions, with the effect looking something similar to what is demonstrated in the siggraph video.

The story and ending are rather weak, but the physics questions posed are interesting. I like any franchise that discusses the teletransportation paradox.

[0]: https://myanimelist.net/anime/32032/Seikaisuru_Kado

Re: 4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020

#50

Post by elil17 »

If you find this interesting, you'll really love the short book "Flatland: A Romance of Many Dimensions." It's a deep dive into what a dimension really is, intuitively, and also satirical commentary about Victorian society.

https://www.gutenberg.org/files/201/201-h/201-h.htm

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