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4D Tesseract: Fourth Dimension Game

fourthdimensiongame.com

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Re: 4D Tesseract: Fourth Dimension Game

#21

Post by Jun8 »

If you think that us 3D people will never be able to wrap their heads around 4D, you have to read Charles Hinton's (http://en.wikipedia.org/wiki/Charles_Howard_Hinton) The Fourth Dimension (https://archive.org/details/fourthdimension00hintarch). This is the guy who coined the terms ana and kata (from Greek) for the two additional 4D directions, analogous to up/down, etc. (he also invented a gunpowder baseball pitching machine that, some say, led to his dismissal from Princeton, due to player injuries).

Now that's interesting on its own, but his sister-in-law, Alicia Boole Scott (http://en.wikipedia.org/wiki/Alicia_Boole_Stott) is also amazing. She was the daughter of the famous Boole, and made big contributions to higher dimensional mathematics, especially 4D, e.g. she proved there are exactly six regular polytopes in 4D. She "made beautiful cardboard models" of 3D cross sections of these. This, while she was working as a secretary in Liverpool (sad reality of early women scientists/mathematicians).

They don't make them like that anymore! It would be interesting to have documentary on 4D based on these interesting people.

EDIT: Also, in catastrophe theory, the Swallowtail catastrophe, which has 3 control and behavioral dimension was named by the French mathematician Bernard Morin (http://en.wikipedia.org/wiki/Bernard_Morin), who is blind since he was 6!

Re: 4D Tesseract: Fourth Dimension Game

#22

Post by pawn »

keammo1 wrote: post #10
CodeCube wrote: post #5

For those trying to wrap their heads around this ... I find this segment by Carl Sagan from the original Cosmos to be pretty well presented on the topic: http://www.youtube.com/watch?v=UnURElCzGc0

His explanation is more or less adapted from "Flatland: A Romance of Many Dimensions" http://www.amazon.com/Flatland-Dover-Thrift-Editions-Abbott/...

I read that book in high school for extra credit in a math class, and really enjoyed it.

Re: 4D Tesseract: Fourth Dimension Game

#24

Post by kybernetikos »

codeflo wrote: post #19
bladedtoys wrote: post #9

Earlier quoted context omitted.

It's tricky because there is just no way to show 4D phenomenon without a lot of sacrifice. I ended up using a combination of "perspective" for size and differing transparency and a fair amount of movement. All of these are artificial of course. The explanation on the page takes another approach: all black and white line drawings and a lot of brevity. But it's really a hell of a lot of fun tying to figure out how to p…

Displaying a 3D image in a 2D space also requires sacrifices. Obviously to a lesser extent, because you only lose one dimension, but the principles are the same. Reconstructing a 3D scene from photographs is an insanely tricky problem, and it only looks simple to us because our brains have specialized circuits for that task.

Makes me wonder what this game would be like on the occulus rift.

Re: 4D Tesseract: Fourth Dimension Game

#28

Post by NAFV_P »

Reminds me of the time that Sting sang "Message in a klein bottle". Of course, as soon as the bottle was thrown into the sea, the water seeped in destroying the message on the paper.

"Bollocks", said Sting. "There goes my proof of the Riemann Hypothesis."

Re: 4D Tesseract: Fourth Dimension Game

#29

Post by T-hawk »

moron4hire wrote: post #12
jsonmez wrote: post #2

I'll just be the first to admit that I am indeed too dumb to grasp this concept. I've stared at it for a long time, but I do not get it.

I think of it this way: if you try to draw a 3D cube on a 2D screen, what you really have is a 2D image. If oriented correctly, and nobody told you anything about that cube, you might mistake it for a 2D hexagon. If instead that cube were rotating, you would see the change in the shape of the hexagon and realize that the image is supposed to be a cube. But the reality is, it's still a 2D image. It's just a representa…

So, when you're dropping from N to N-1 dimensions, you lose something, something that you can sort of get back if you add some motion in.

Adding the motion restores the subtracted dimension as time. That's why that works.

Re: 4D Tesseract: Fourth Dimension Game

#30

Post by finnh »

joshdick wrote: post #6
jsonmez wrote: post #2

I'll just be the first to admit that I am indeed too dumb to grasp this concept. I've stared at it for a long time, but I do not get it.

I had a math professor who put it this way: Just think of a general n-dimensional Euclidian space, and then set n=4.

Counting sheep is easy: just count the legs and divide by four.
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