4D toys • Hacker News Board

Re: 4D toys

#11

Post by anotheryou » Sat, Aug 04, 2018, 10:05 AM UTC

Can someone help me out here?:

I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view?

I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too.

edit: found this: https://youtu.be/S-yRYmdsnGs?t=252

even better: https://youtu.be/dy_MUfBuq2I (turn on subtitles)

Re: 4D toys

#12

Post by rzwitserloot » Sat, Aug 04, 2018, 10:06 AM UTC

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 located, in _ALL_ 3 dimensions?

This raises the question:

Can you render a 4D scene onto a 3D viewport such that us humans are pretty good at understanding where every object in the scene is, in all 4 dimensions?

I assume the answer is 'yeah, you can do that'. I wonder what that would look like.

It's complicated of course; our eyeballs are involved and they kinda work in 2D and not 3D; where we humans can casually glance at a 2D viewport rendering a 3D scene for a second and know what's happening, we'd have to walk around the 3D screen rendering a 4D scene in order to even see everything.

Re: 4D toys

#13

Post by abhiminator » Sat, Aug 04, 2018, 10:06 AM UTC

This is incredibly cool. I feel this would be super useful for teaching children (like my nephew who's 11-years-old) to think about the fourth dimension as a component of the fabric of space instead of time as it's usually understood.

Re: 4D toys

#14

Post by chiasmic » Sat, Aug 04, 2018, 10:10 AM UTC

anotheryou wrote: post #11

Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/…

I am by no means an expert, but I have thought about trying to visualise the fourth dimension. The issue is that we don’t really see 3D. While in 2D we can view every pixel simultaneously, when we view in 3D we have the issue of aspect and concealed voxels. You can’t visualise simultaneously all voxels of a cube, as most are under others or otherwise obscured. This therefore limits how much we can use 3D to mimic 4D. Perhaps if we were to spend more time with semitransparent objects our brains could learn to visualise 3D better and then maybe 4D.

Re: 4D toys

#15

Post by anotheryou » Sat, Aug 04, 2018, 10:13 AM 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 asked the same question a few seconds before you :) found this: https://youtu.be/S-yRYmdsnGs?t=252

and even better, this: https://youtu.be/dy_MUfBuq2I

Re: 4D toys

#16

Post by joshumax » Sat, Aug 04, 2018, 10:15 AM 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…

Unfortunately, it's not as simple as that (although I wish it were). While you could generate a 3D perspective on each 2D "slice" of a 3D viewport, it wouldn't be that much more different than what's going on in here. The main issue arises from trying to render a 4-polytope in a universe where we ourselves can only sense 3 dimensions "natively."

Re: 4D toys

#17

Post by Udik » Sat, Aug 04, 2018, 10:18 AM UTC

anotheryou wrote: post #11

Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/…

Of course you can, and it would be different from the cross-sections seen in this video. I doubt it would ever become intuitive though, I suspect our brains are hard-wired for a 3d world.

Here's a video of a rotating 4d hypercube in a 3d perspective:

https://www.youtube.com/watch?v=t-WyreE9ZkI

It's called a tesseract, and as each face of a 3d cube is a 2d cube (a square), each face of a 4d cube is a normal 3d cube, that we see skewed by the perspective.

Re: 4D toys

#18

Post by arketyp » Sat, Aug 04, 2018, 10:21 AM UTC

anotheryou wrote: post #11

Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/…

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 we are quite heavily hardwired to 3D perception. I suspect these circuits cannot be wholly overridden.

Re: 4D toys

#19

Post by bhouston » Sat, Aug 04, 2018, 10:22 AM UTC

I would have through the he would have done a projection from 4d space to 2d space similar to how 3d graphics does a projection from 3d to 2d. Similar to http://christopheremoore.net/4d-renderer/ It I guess in that case it would be difficult to interact with it in VR.

I guess this slicing technique works but it would be a bit weird.

Re: 4D toys

#20

Post by sarreph » Sat, Aug 04, 2018, 10:23 AM UTC

chiasmic wrote: post #14

anotheryou wrote: post #11

Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/…

I am by no means an expert, but I have thought about trying to visualise the fourth dimension. The issue is that we don’t really see 3D. While in 2D we can view every pixel simultaneously, when we view in 3D we have the issue of aspect and concealed voxels. You can’t visualise simultaneously all voxels of a cube, as most are under others or otherwise obscured. This therefore limits how much we can use 3D to mimic 4D.…

What an interesting idea! Have you ever produced anything for a representation of 4D with translucent 3D? I'd be very interested to see it...