[indspenceable]

Often when I see something about 4d it uses this same analogy: a 2d being seeing a crosssection of a 3d world, in 2d. However, the video is in 2d, and it's able to show 3d in a much better/more clear way, clearly, cause when it's showing that example it's got a cutout of the "3d" view (which is still 2d!).

Why can't we do the same thing with 4d? Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?

[squeaky-clean]

I remember playing a flash or java game years ago that did exactly this. It was a 4d maze, rendered in stereoscopic 3d. It displayed the images side by side and you crossed your eyes to get the 3d effect.

It was really disorienting (the 4d, but also the eye-crossing), and like the post author says, just bundles of lines rather than solid shapes. Still very cool.

Ooh, I found it!

http://www.urticator.net/maze/

[fao_]

Thank you so much! I've wanted something like this for ages. Now to figure out how to cross my eyes consistently with astigmatisms...

[jerf]

"Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?"

Yes, you can. This program just doesn't.

[jacobolus]

There’s a big problem with that, which is that we don’t actually see in 3 dimensions. Our eyes only get 2-dimensional projections of a 3-dimensional world.

[hoprocker]

The 2D->3D analogy made sense to me -- only being able to see the cross-section that is visible in a current dimensionality -- but I got to wondering if you couldn't use some of techniques from information visualization techniques to show a representation of that extra dimension in the current dimensional landscape (ie fading the object as it gets farther away from the current dimension).

[js8]

Maybe they could do something like a fog? That is, if the object was farther away in the 4th dimension, it would appear less distinct or more fuzzy/blurry, like being in the fog.

[hcs]

Miegakure did something similar where it showed a shadow of the 3D space immediately adjacent to the currently visible slice. I think he since removed that, so I expect he must have experimented with something similar in 4D Toys and decided against it.

[ucarion]

That's a neat idea! But I think it might be a bit overwhelming and confusing. It would help with getting the bigger picture.

Every 4d object would end up being a clear 3d cross-section where it intersects with our 3d world, plus a cloud of superimposed and increasingly hazier 3d cross-sections above and below us along the 4d ("w") axis, projected down onto w=0 3d-space.

[mabbo]

Watch the part about the slicing of 2d world looking at the 3d objects. That slice is infinitely large in both dimensions, yet it can't see the 3D objects when they aren't in the same plane.

Now apply the same analogy to our world: our 3D world is just an infinitely large 3D plane in a 4D world. When the objects aren't in our 'plane', we can't see them.

[pbhjpbhj]

See also Flatland (http://amzn.to/2qKFrOh, aff. link) which is a short novel in part about 2D shapes discovering the third dimension.

Edit: Didn't notice it was mentioned at the end of the comments, https://news.ycombinator.com/item?id=14472395, there's a free version linked from archive.org.

[ShrubberyKnight]

Purely theoretical, but the presence of a 3D object can be detected by a 2D creature, by it's shadow, depending on relative positioning of object, 2D surface, and light source. What would a 3D shadow look like, with no need for a wall or flat surface onto which the shadow would be cast? For that matter, what would 4D light look like, if it even differs. Maybe the light we see is only a shadow of something from the 4th Dimension, or maybe a portal or doorway we have not yet learned to use to it's potential.

[amelius]

Yes, I would also expect a projection rather than a crosssection. One reason could be: perhaps it would make the game too confusing and difficult?

But I'd still like to see the difference.

[collinmanderson]

I would like to see _four_ simultaneous 3d projections of the 4d space, each ignoring (or flattening) one of the 3 dimensions.

[mirekrusin]

Exactly, you could do it with transparency/mesh lines/color gradient - it would be interesting to see.