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Hyperspace Star Polytope Slicer

04/01/2008 8:25 PM

This interesting Java applet creates rotating animated slices of 4-dimensional polytopes (polytopes are higher-dimensional analogs of ordinary 3-dimensional solid polygons).

I don't know if this "polytope slicer" has any practical applications, but its strange beauty provides enough reason to have a look at it. While there, be sure to experiment with the various applet parameters for some mind-blowing visual mutations.

This applet makes me wonder if human brains -- having evolved in environments with only three spatial dimensions -- generally have the natural ability to perceive real meaning in projections of hyper-dimensional objects. I like to think that I enjoy these hyper-dimensional visual stimuli because they awaken new mental abilities in my powerful and flexible brain. But I also fear that maybe these images merely supply eye-candy for neurotic naked apes like me. Or maybe they do a bit of both. What about you -- do you find any appeal in these images, or is it just me?

Hyperspace Star Polytope Slicer

http://dogfeathers.com/java/hyperstar.html

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#1

Re: Hyperspace Star Polytope Slicer

04/02/2008 11:12 PM

I guess I have to admit I'm in the "ape" category

I've been an avid SciFi reader for long time (don't laugh ... there are often a lot of good 'possibilities' to consider, and some good cases of SciFi becoming Sci-Fact).

Although, sometimes I can get a brief glimpse of that which is greater than my current time-dimensional surroundings, it is never more than a glimpse.

My best-case tool is analogy (for instance, referencing the effects of being 2-dimensional [which is also difficult, but a little easier to comprehend], moving into 3-dimensions) to try to understand the ramifications of moving outside our own realm.

Sometimes, we can embrace the 'fact' of other time-dimensional realms, but, for me, I'm not sure how I can grasp it.

BUT, surely a tool like this could help (same as 3-D modeling helps some to see an object when they can't visualize it) ... AND, it IS pretty .

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#6
In reply to #1

Re: Hyperspace Star Polytope Slicer

04/04/2008 2:20 PM

My best-case tool is analogy (for instance, referencing the effects of being 2-dimensional [which is also difficult, but a little easier to comprehend], moving into 3-dimensions) to try to understand the ramifications of moving outside our own realm.

With regards to a 3-D person trying to comprehend 4-D objects, yes, the most useful analogy seems to be that of a 2-D person interacting with 3-D objects. Edwin Abbott wrote "Flatland", a fictional book how 2-D beings might experience their world and also the encounters with higher dimensions. In one scene, a 3-D sphere passes through the 2-D world of Flatland. The residents there are baffled by what they see -- a point suddenly appears from nowhere, smoothly grows into a circle, then smoothly shrinks back into a point which suddenly disappears. Only by struggling with the difficult concept of "Spaceland" (3-D space), do the residents of Flatland begin to overcome their confusion about the mysterious visitor.

Now who has the more challenging task, Flatlanders trying to understand Spaceland, or us Spacelanders trying to understand Hyperspace? I think we have the tougher task (look at the Polytope Slicer to see what I mean), but fortunately we have nice bulbous brains instead of the thin pancake of neurons that passes as a brain in Flatland!

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#2

Re: Hyperspace Star Polytope Slicer

04/03/2008 1:32 AM

If you like this sort of thing, as do I, check out this site:

http://demonstrations.wolfram.com/

Orpheuse

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#3
In reply to #2

Re: Hyperspace Star Polytope Slicer

04/03/2008 4:32 AM

Very cool ...

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#4

Re: Hyperspace Star Polytope Slicer

04/03/2008 9:44 PM

Neat.

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#5

Re: Hyperspace Star Polytope Slicer

04/04/2008 2:33 AM

Get out of my mind!!!

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#7
In reply to #5

Re: Hyperspace Star Polytope Slicer

04/04/2008 2:28 PM

Cool image! I like the way the inside surfaces of the inner cube become the outside surface of the outer cube (and vice versa). The thing constantly turns itself inside-out and outside-in. This reminds me of the warning that ordinary 3-D safes do not offer any security against 4-D beings -- hyperbeings can easily reach into a closed 3-D safe by exploiting the 4th dimension! And I imagine that 4-D surgeons would not need to split open the rib cage of a 3-D person when performing heart surgery.

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#8
In reply to #7

Re: Hyperspace Star Polytope Slicer

04/09/2008 12:12 AM

That doesn't mean they won't do it, just for kicks. And they may even be sadistic enough to go 'old school' and cut ya in 2d.

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