4D toys • Hacker News Board

Re: 4D toys

#41

Post by dan_mctree » Sat, Aug 04, 2018, 12:24 PM UTC

rzwitserloot wrote: post #12

Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…

I think you can't. The problem is that we don't actually see 3D, we basically see 2D twice. This gives our senses enough info to reconstruct a 3D mental image, but the information we gain isn't truly 3D.

Actual 3D-sight might include us seeing the inside of objects, what's behind them, etc.

We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax. In projections on images, it's easy to just use color and get rid of parallax, and still get sort of close.

Suppose we tried to make a 3D projection of a 4D world, we don't actually get any significant new tools. We're still going to be limited by having to use parallax and color. This doesn't allow us to add enough information to add that 4D projection into 3D as neatly as the 3D into 2D works. At best you could try to distribute the information somehow. For example by giving information about the third dimension through brightness and the fourth dimension through hue. It certainly wouldn't work nearly as well though.

Re: 4D toys

#42

Post by ianai » Sat, Aug 04, 2018, 12:27 PM UTC

scrollaway wrote: post #28

simias wrote: post #27

Earlier quoted context omitted.

The problem is that while everything you see on your (2D) monitor is effectively 2D our brain is good at taking 3D cues (shadows, perspective, parallax etc...) to reconstitute 3D "data" from it. For instance look at 3D rotating cube on your monitor: https://www.youtube.com/watch?v=5E10zYKln3g Even though there's no shading, a bad resolution and zero context anchoring it in a familiar setting you immediately see it as…

> Could we teach our brain to "think in 4D" and interpret these cues differently? To a certain extent probably, maybe if you spent hours and hours and hours in a VR simulation with 4D objects you'd starting getting a feel for it. I doubt you'd ever get as good as with 3D objects since we've been exposed to these literally every waking moment since we're born.* Good lord! Has anyone tried? This reminds me of the backw…

Yes mathematicians have tried to visualize 4d for quite some time. I remember hearing about one who famously spent much time to developing a notion of 4d.

It’s possible to represent n+1-d scenes into n-d scenes.

Re: 4D toys

#43

Post by ianai » Sat, Aug 04, 2018, 12:29 PM UTC

anotheryou wrote: post #37

dm319 wrote: post #36

Earlier quoted context omitted.

Yes, and I think this just shows how a 3d representation on 2d gives our brain the _illusion_ of 3d. This doesn't work for 4d, because our brain doesn't have an internal understanding of 4d objects.

I think once we have it interactively our brain will adapt.

It’s t least worth a shot.

Re: 4D toys

#44

Post by arketyp » Sat, Aug 04, 2018, 12:33 PM UTC

matte_black wrote: post #33

arketyp wrote: post #18

Earlier quoted context omitted.

What would be the benefits of the 3D VR? There will always be a 2D bottleneck on your eyes' retina. The most important perspective clue I would say is temporal sampling. For dynamical systems, Takens theorem says that a high dimensional topology can be restituted by the sequential sampling of a single variable alone. It seems likely to me that our perception generally works by this principle. That being said, I think…

What would a 3D eye even be like? Is it something like having independent depth perception per eye?

Photons travel in 3D space and may only be occluded by 2D surfaces. There is no getting around that fundamental aspect of reality. In this universe.

Re: 4D toys

#45

Post by throwawaymath » Sat, Aug 04, 2018, 12:41 PM UTC

This is an old video [1], but it remains the clearest visual explanation of multiple dimensions that I've ever seen. I really can't recommend it highly enough. I think anyone trying to visualize a 4D object will get something out of watching it.

I played with the 4D toys app after it showed up on /r/math a while ago. I like it and I think it's useful. My only complaint would be that it's a little too open ended. While it's nice to provide a simulated tactile experience of four dimensions, I think the app should provide a bit more visual intuition. That's one of the things I like about this video. ________________

1. https://www.youtube.com/watch?v=90olwwLdEYg

Re: 4D toys

#46

Post by bunderbunder » Sat, Aug 04, 2018, 12:49 PM UTC

dan_mctree wrote: post #41

rzwitserloot wrote: post #12

Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…

I think you can't. The problem is that we don't actually see 3D, we basically see 2D twice. This gives our senses enough info to reconstruct a 3D mental image, but the information we gain isn't truly 3D. Actual 3D-sight might include us seeing the inside of objects, what's behind them, etc. We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax. In projections on images,…

> The problem is that we don't actually see 3D, we basically see 2D twice.

Most of us do. But people who only have sight in one eye have no difficulty perceiving three dimensions. And some fairly large percentage of people with binocular vision are stereoblind, typically without even realizing it.

If anything, I'd say it's not that

> We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax.

so much as that we're aided in converting our 2D sight into 3D mental models through the use of stuff like color and parallax through the use of stereopsis.

Re: 4D toys

#47

Post by machiavelli1024 » Sat, Aug 04, 2018, 12:53 PM UTC

rzwitserloot wrote: post #12

Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…

You can’t reconstruct a 3D scene from a 2D projection unless you take educated guesses.

E.g. When you look at a picture with something that looks like a chair, you assume that it’s indeed a chair, and then you can estimate its size/pose/etc. But there are infinitely many non-chair shapes that would produce the exact same projection. It’s just that you won’t encounter them in real life, except maybe in trickshots like this: https://youtu.be/SKpOKXAVjGo

Re: 4D toys

#48

Post by rekshaw » Sat, Aug 04, 2018, 1:08 PM UTC

The video ends saying that trying to fit a 4D cube in a 4D hole is like a child playing with toy blocks. Hypothetically, if a child was raised with regular VR simulations that allowed the child to manipulate 4D objects, would their brain "learn" it and in a way unlock the 4th dimension?

Re: 4D toys

#49

Post by eerikkivistik » Sat, Aug 04, 2018, 1:12 PM UTC

MrEldritch wrote: post #8

eerikkivistik wrote: post #3

What tools were used to build this I wonder?

Part of it is that the developer's spent the last decade building a game engine and toolchain for 4D content while developing his 4D puzzle game Miegakure ( http://miegakure.com/ )

That looks incredible. Do you know if the developer has published any papers or code on the subject?

Re: 4D toys

#50

Post by jonbarker » Sat, Aug 04, 2018, 1:25 PM UTC

Sharlin wrote: post #32

anotheryou wrote: post #24

Earlier quoted context omitted.

I'd say we have two eyes and compile to something 3D, which is mostly possible because of that and nothing is hardwired, just takes a lot of responsive feedback to rewire itself.

We see a 2D projection and infer some 3D information from stereo parallax and other depth cues. But it’s still a 2D projection in the end. A real 3D ”vision” would not have a ”viewpoint”, no perspective, no foreshortening. It’s difficult to even imagine what it would be like to perceive that.

Stereo parallax, great term. In other words how cross-eyed we are.