Hypercubes and the Fourth Dimension!

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I'm obsessed with hypercubes, and other polychora, and the general concept of 4+-dimensional spaces to date. I want to understand them intuitively, and mess around in a virtual 4-space for fun. I shudder at the thought that I might have to write a 4D physics engine to do so though.

You can see a fully animated hypercube here in full 3D. You can change the stereo mode if you don't have the 3D glasses (like me) under the option name "stereo mode". You can pick stereoscopic cross-eyed, parallel-eyed, or just change it to a single image 2D view if you like as well as the 3D glasses-using anaglyph mode.

You can read about them on Wikipedia here.

Does anyone else think this is as cool as I do? What are your thoughts?

Sadly, the script won't load for me. I got the older version to work, but it was rather disappointing.

Our math club built a model of a hypercube out of Zome tools last semester. Great fun. Nothing like n-space geometry to really put a boost in your day!

Aww, sorry Apera. I dunno what to tell you. You can still click the "stereo" button to switch display modes though, although there's only one manual stereoscopic one, and I'm still not sure whether it's cross-eyed or parallel.

Yay math club! ... I dunno what Zome tools are though. .__. But hellz yes! ^^

This tip may not work for everyone, heck it may not work for anyone... but it's how i can see 4d+ shapes quite clearly in my head.

first, use the time axis... we'll go with a sphere here, it starts as a point, and grows quadratically until it's a full size sphere, and then it starts to shrink again, in a reverse rate to how it grew.
do that a few times. as many as you need, that is...
Eventually after doing it a while, you'll be able to see it all at once.

This is much easier with a closed surface, such as a tesseract (hyper cube).
It gets very difficult when you move into open shapes, like a hyperbolic hyper-plane.

To do the hypercube, you have to tilt it, otherwise it's a cube out of nowhere then it's gone again.

Once you can immediately see a 4d shape... you can add more dimensions the same way... at least so long as you don't suffer what JustMax likes calling "brainkerplosion"

Zome tools are like tinker toys for mathematicians. They're rods of varying lengths and balls with different shaped openings, designed to make various shapes. One day the club president and I (I was vice-president at the time) used several Zome kits put together to build a giant buckyball so big we could sit inside it!

zome tools:
http://www.zometool.com/

some models of hypercubes made with them (not ours. I don't know where the photos of ours got to):
http://www.borderschess.org/KThypercube.htm

One cool thing about hypercubes is how "capturing" them in 3D can look so different, depending on which angle one is viewing. It is just like being in the novel Flatland!

Wow. I knew I kept my old 3D glasses for a reason.

I've been enchanted by tesseracts since watching Cube 2: Hypercube , which is my least favourite of the Cube movies, but it introduced me to tesseracts. The 3D glasses really make the shapes on that site look amazing. I could stare at them all day. And I like that you can control it, that's pretty awesome.

I completely don't understand how they work, but I sure would like to find out. Watching this picture I feel like I almost understand, but watching the ones on that site you linked erases anything I thought I understood.

This is helpful for understanding the notion of a hypercube a little better. It helped me a lot.


@Sparrowrose: I should get Zome tools now. I wants dem. >.>

@Exclavius: That is really cool. I always had trouble figuring out the notion of a hypersphere in my head. Thanks.

I'd go as far as to say that's impossible, but I'd be very happy if you could prove me wrong

The theory of relativity is a 4D physics engine.

ruveyn

Actually, the universe without relativity would be a 4d engine.

With relativity and we have a 5d engine.

If you're referring to general relativity, then not really. Geometries arising out of the warping of space-time can of course be embedded in a 5D euclidean space. However, it's still 4D in a non-euclidean space. The fifth dimension is just a tool we use to picture the non-euclidean geometries when we construct embedding diagrams. It has no physical significance.

That's still beside the point, because what I'm doing still adds another dimension to any sort of physics engine yet developed to my knowledge, which renders the example and arguments moot. I suppose it may actually be impossible, though such a thing strikes me as quite silly. Ridiculously difficult, certainly, but impossible? I highly doubt it.

Still though, I'm pretty lazy and disorganized. I may never actually do this, but I like to think that someone will, in time. >.>

Has anyone heard of Miegakure?

All the equations of relativity and electrodynamics can be done with tensors of order 4. Where did you get 5d from ?

ruveyn

It's easier to envision it in 5d than to contort it into a 4d space.

Physics (the universe) usually does things the "easy" way.
You can use ugly tensors to describe the universe, or you can use elegant and easy 5-space.

You apparently know little or nothing about physics.

I seriously doubt that you even know what a tensor is.

ruveyn