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Comment by zokier | Hacker News Reader

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

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Well, we get 3D scenes/projections on a 2D screen by being in a 3D world/context and looking at a 2D screen. With that I mean to say that I think (not sure) a 2D image of a 3D projection can only feel 3D if you're in a 3D world.

This also means such a thing should be possible for living in a 2D space and then projecting a 2D world on a 1D screen.

If you're going to play with 3D projections of 4D objects, then in order for it to really feel 4D we need to live in a 4D world. In that sense, this is quite similar to living in a 2D world while seeing a 3D projection. That's way more trippy.

To recap:

Feel 3D: 3D context -> 3D projection -> 2D screen

Feel 2D: 2D context -> 2D projection -> 1D screen

Feel 4D: 4D context -> 4D projection -> 3D screen

What we can do for 4D: 3D context -> 4D projection -> 3D screen

Compare issue with 3D: 2D context -> 3D projection -> 2D screen

I hope this makes sense (and I hope I have it right).

Man, this is tough to write about. I'm not sure if I fully understood all the nuances of your comment.

Makes me wonder if the human brain if born into a 4D world would be able to function, or if fundamentally it is impossible for the brain to process a 4D word.

The thing is, 3D to 2D projections work well because that's how our eyes work in the first place, so we can intuitively understand a projected image on the screen.

When projecting 4D to 2D, weird things start happening. Instead of a ray, each pixel now represents a plane in 4D space. So even while it can be done mathematically, the brain is just overwhelmed by what happens when you e.g. rotate the projection

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/

I believe this is the author's GitHub: https://github.com/neverhood311 (I followed a YouTube link from the paper, and the YouTube profile pic matches this one's.)

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

You can also see the projections as 3d objects in VR.

I suppose you could also compromise by drawing a 4-D wireframe overlaid over a traditional render of a 3-D cross section.

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