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udderdude

Magic120Cell

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Hot damn

Maybe if I just move this green piece to- *Head 'Asplode*

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Explain to me how it is Four Dimensional. It can't change over time because that would make it unsolvable.

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I think in this case, the 4th dimension is a physical/mathematical one. It's almost impossible to represent n+ dimensions in any sane way with our standard 3 physical ones, so it's more of a novelty.

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AirRaid said:

Explain to me how it is Four Dimensional. It can't change over time because that would make it unsolvable.

It's a 2D projection of the 4D equivalent of a dodecahedron's definition. Its sides were coloured and subdivided by some amount and scrambled just like a Rubik.

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well this is ridiculously adrenaline-pumped psychobitch insane.

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Exactly.

Zaldron said:

It's a 2D projection of the 4D equivalent of a dodecahedron's definition. Its sides were coloured and subdivided by some amount and scrambled just like a Rubik.


A dodecahedron is still just a 3D shape though.

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Mathematically, the fourth dimension can be whatever the hell you want it to be.

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GreyGhost said:

It's part of a broader conspiracy to get .NET installed on our computers!


Curses, foiled again!

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exp(x) said:

Mathematically, the fourth dimension can be whatever the hell you want it to be.


Fair enough, but what is it here? The only thing I can think of is colour.

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yeah, I can't really wrap my head around this concept. I told my wife about it, and she was like "but there's only 3 dimensions, where is the 4th?". I tried to explain what I understand, but with an inferior understanding, it only lead to more confusion.

I can't even solve a 3d Rubik's cube.

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Didn't Danarchy once claim that he saw in 4 dimensions after smoking copious amounts of weed, therefor somehow proving the existence of the supernatural? Perhaps he can come and explain it.

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AirRaid said:

Fair enough, but what is it here? The only thing I can think of is colour.

My guess is that the program projects four dimensions onto three. My linear algebra is a bit rusty, though.

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AirRaid said:

Exactly.
A dodecahedron is still just a 3D shape though.

Which is why I said "definition". In four dimensions, you can build a regular solid with 720 regular pentagons instead of just 12. What you see here is a projection to 2D space, or just a surface, your monitor's surface. A projection consists of sacrificing length and angle fidelity in a given geometric object in order to visualize it in a inferior number of dimensions. In a 3D cube with all sides length equal to 1, a orthogonal projection to screen will, depending on the view's rotation, sacrifice all or some of the 90 degree angles, and change the lengths of sides to less than 1 for some or all.

Note that with clever rotation, you can maintain a large portion of a cube's definition intact, if for example your projection is aligned so that the cube looks like a square, for one of its sides is facing directly to the observer/projection surface, you get 8 of the 12 sides at length 1 and many angles correctly at 90 degrees. The caveat is that 4 sides have been reduced to 0, not to mention the angles conformed disappear completely. Knocking down a further dimension, projecting a 2D projection of a cube into a line by scaling it vertically or horizontally to 0% makes it even less obvious. At this point it looks like it could be anything really.

This is what you're seeing, the 720 pentagons, subdivided into some triangles, odd shapes and such as done in a Megamynx (a dodecahedron's version of the Rubik cube, a special subdivision that allows you to twist the pieces unencumbered), with their side lengths and real angles modified to fit in a 2D projection.

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The 4th dimension is what comes after the three we can see. You have height, width, breadth (i guess), then something else. Basically, think of it this way. In one dimension, you have a line. In 2 dimensions you take four lines, fold them together and you have a square. In 3 dimensions, you take six squares and fold them together to get a cube. In 4 dimensions you take 7 cubes and fold them together and get a tesseract. Like so:



A lot of theories basically consider the universe to be in a 4-dimensional shape.

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The tricky thing with representing 4-dimensions in 3 is that it looks as though you are just taking two squares, as seen in Dan's post, and connecting them with lines. However, those "lines" are actually the boundary of other cubes connected to the two colored ones, and their shape is not actually being changed. Rather, their appearance is, as they are distorted due to perspective. All cubes in a tesseract have the same area and size.

The best way I can imagine 4-dimensions is thinking of all the cubes in a tesseract occupying the same space, but being "folded" into each other. They are all connected, but in order to move from one to the other, you have to move along 4D space. As 3D creatures, we can only see and understand one 3D part of a tesseract, where as a 4D creature could see and comprehend all of them at the same time.

What I'm trying to say is...this shit is crazy.

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The book Flatland deals with the problems of a 2D being interacting with 1D and 3D space. It was written to be a satire of Victorian culture, but it's also very good for explaining the issues with dimensional perception.

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Anyone seen Cube 2: Hypercube? (Shown every once in awhile on Sci-Fi channel).

Didnt that take place in a 4D realm?

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scorpion said:

pikshur


The key here is that the object in question is actually rotating, not scretching/warping in any way. It's just rotating on the 4th plane (the W plane) rather than the X, Y, or Z planes. We're just not used to seeing this kind of behavior and therefore not used to understanding it.

People really need to study the concept of the 4th spacial dimension because it seems that most people just muddle the issue with "time" which really has nothing to do with anything here.

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Snarboo said:

The tricky thing with representing 4-dimensions in 3 is that it looks as though you are just taking two squares, as seen in Dan's post, and connecting them with lines. However, those "lines" are actually the boundary of other cubes connected to the two colored ones, and their shape is not actually being changed. Rather, their appearance is, as they are distorted due to perspective. All cubes in a tesseract have the same area and size.

The best way I can imagine 4-dimensions is thinking of all the cubes in a tesseract occupying the same space, but being "folded" into each other. They are all connected, but in order to move from one to the other, you have to move along 4D space. As 3D creatures, we can only see and understand one 3D part of a tesseract, where as a 4D creature could see and comprehend all of them at the same time.

What I'm trying to say is...this shit is crazy.

That's actually pretty well said. Another book on this subject, in addition to flatland, was this book our teacher read us in 6th grade. I think it was called The Boy Who Walked Through Walls, which deals with how 3-dimensional beings perceive the 4th dimension. I think it was intended for younger readers, but it was still kind of interesting.

There was also some website that had a rotatable tesseract that you could mess around with. It gave you a pretty good idea of how they're shaped. At least, as good as you could get.

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