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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

#11

Post by zokier »

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 dimensional graphics to be able to say if you would be able to do projection directly from 4D->2D (as our displays still are 2D), or if it is better to go 4D->3D->2D.

Bit disappointing that the video spends a lot discussing general 4D stuff and less about the dynamics part which is the actual subject.

Here is video of one of the other visualization systems referred in the paper which if I interpret it correctly does projection with depth of field https://www.youtube.com/watch?v=dT5YCs84jJU

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

#12

Post by zokier »

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…

Just for reference, I found this 2017 about 4D animation suite "Fourveo", the thesis discusses the different ways to visualize (cross-section, projection via 3d and directly) 4D scenes. Unfortunately the software itself doesn't seem to be available anywhere, and there is scant other information about it.

https://scholarsarchive.byu.edu/etd/6968/

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

#13

Post by terramex »

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?

Obligatory "I'm not a physycist, but...".

String theories require extra spatial dimensions (to total of 10, 11 or 26), but those dimension are so small and/or looping so that we cannot detect them.

Other approach is to treat our 3D space as slice of higher dimensional space.

https://en.wikipedia.org/wiki/String_theory#Extra_dimensions

String theories have a lot of problems (biggest ones is that they are currently unverifiable using experiments and they do not give any meaningful predictions about our 3D view of universe), but many theoretical physicists are working on them.

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

#14

Post by evanb »

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?

I am a physicist.

It is perfectly possible to formulate theories of physics in higher spatial dimensions. In fact, many high-energy theories like string theory require many spatial dimensions for mathematical consistency. It is something we actively look for signatures of in experiments.

What we have found is that our observations are incompatible with 'extended' additional dimensions. Extended here means that you can go a sizeable distance. It's not that the other dimensions would just stop, but they'd be more like Pac Man---these dimensions might have periodic boundary conditions, making them circles. If the circle's radius (or circumference, equivalently) becomes very large, such a 'compactified' dimension starts to have a lot of space in it, much like the familiar 3 dimensions. So, we can put an upper bound.

My most recent recollection. We may yet have missed dimensions as large as 1mm in [diameter, circumference, I forget]. The most sensitive probes with the fewest assumptions about the structure + particle content of the universe tend to be gravitational, and gravity is very hard to measure precisely on very short length scales.

edit to add: the latest summary of extra dimensional searches from the Particle Data Group http://pdg.lbl.gov/2019/listings/rpp2019-list-extra-dimensio...

even better, here's the PDG's review, rather than their technical summary: http://pdg.lbl.gov/2019/reviews/rpp2018-rev-extra-dimensions...

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

#15

Post by pujjad »

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 attracted by a heavy one would either escape to infinity or get sucked into collision.

For n = 3 we get stable elliptic orbits or non-bound parabolic and hyperbolic orbits.

Collision only occurs when the lighter body heads directly towards the heavy body within 2R (R being the heavier body's radius), ie. the impact parameter is zero [2]

[1] https://doi.org/10.1002/andp.19203660503

[2] https://en.wikipedia.org/wiki/Impact_parameter

edit: grammar

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

#16

Post by jawns »

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?

Keep in mind that on Earth-scale, movement through the fourth dimension would be pretty easy to notice. There's a lot of stuff on Earth, so seeing objects bounce in and out of view would be a pretty big deal.

But our universe as a whole is almost entirely empty space, with visible objects appearing to make up only about 5 percent of the universe's total volume. Noticing 4D things flit in and out of our 3D universe might be difficult at that scale.

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

#18

Post by gridlockd »

echelon wrote: post #17

This would make for a really fun video game. Think about a 4D shooter in the vein of Portal. I imagine that after awhile the human brain would learn to recognize patterns in 4D spatial reasoning.

The author is also developing a videogame (Miegakure) that has 4D mechanics. It's a puzzle game though, not a shooter.

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

#19

Post by throwaway_pdp09 »

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 I missed it, any films actually done that?

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

#20

Post by limomium »

jawns wrote: post #16
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?

Keep in mind that on Earth-scale, movement through the fourth dimension would be pretty easy to notice. There's a lot of stuff on Earth, so seeing objects bounce in and out of view would be a pretty big deal. But our universe as a whole is almost entirely empty space, with visible objects appearing to make up only about 5 percent of the universe's total volume. Noticing 4D things flit in and out of our 3D universe mi…

So what about subatomic particle scale? Would it look like particles spontaneously appearing and disappearing? Quantum tunneling through obstacles? (they actually went around in another dimension)
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