See 4-D Space With 3-D Glasses

purpleant writes: "A hyperplane is a 3-dimensional space that slices through the 4-dimensional space, the same way a 2-dimensional plane can slice through our 3-dimensional space. The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope. The HyperStar applet displays those finite chunks, one shell at a time. The inner shells are complete -- each shell completely encases the previous shell. The outermost shells have holes in them."

Comments

Re:Purdy...

[AaronBaker2000]

... too bad I don't really have a clue what it means. *sigh* I guess this is why I'm not majoring in Math ;-)


You should read Flatland. It's a fun beginners guide to other deminsions. It's a great story too.

It is difficult, but...

[tanveer1979]

the thing about opening our minds is right.
We have always lived in three dimensions, so visualizing 4 dimensions Per Se is almost impossible coz our nuerons have been hardwired for 3 dimensions. So we can observe 4 dimensions in transit. For example if youwere a 2 dimensional being(thats not possible coz 3 is the minumum number of dimensions to sustain life) and a 3D sphere passed through your space, you will see a point, growing into a circle and then again into a point.
So if a 4D object came it would look like a morphing 3D object.
If mankind were able to create and use 4D's travel would be a whole new frontier. Esp since space-time is curved, Just imagine traveling a million miles instantaniosly
Confused! Go through stephen hawkings works! you will be even more so :-)

Re:Reminds me of a story...

[invid]

According to the Theory of Relativity, mass curves space. The question is, in what direction is it curved? In the direction of a higher physical, non-time producing dimension, perhaps? You've seen all those pictures that show a representation of a black hole curving a two-dimensional space to a singularity. You've heard the theories about wormholes providing short-cuts through the universe. These theories take it for granted that our space is curved within a higher physical dimension. Instead of being the 4th dimension, time could be the 5th dimension.

Extrapolation for 4d/5d sound

[metlin]

There was something similar done by a guy called Luke Dahl, only it was for audio.

It was a Markhov chain extrapolation of the 3d sound as perceived by a 3d being and using a series of normalizations and transforms.

It was called Frobenius Norm, and was a composition of how a 4-d sound would sound to a 5-d being, I think. I just remember it being "spiffy" and very addictive! :-)

It was also featured in Woodstockhausen 2000.

Re:God

[xscottyx]

IF there is a god, I imagine that he would have to be 5D or 6D. I say that because I think that we ourselves are 4D beings, since we experience time. I imagine that God would be 5D, since I don't think that he would be limited to any particular time like us. I think that God could also be 6D, since I can't see God as being limited to one universe, but that depends on whether or not there is a multiverse. Is that weird?

Tic tac toe

[tuxedo-steve]

A fun four-dimensional exercise is 4d tic-tac-toe. It's easiest if you build yourself up to it:

1. Start with your typical 3x3 tic-tac-toe, on a piece of paper.
2. Now add two more grids. Visualise each grid on top of the one before. It's not difficult to see how this is played. You can get three in a row on a single grid, just like normal. Or you can get three in a row by getting the middle square of each grid (3 in a row, vertically). And so on. This is basically tic-tac-toe in 3D. 3 sets of 3x3 grids. 3x3x3.
3. Now, add another two sets of three grids. So now you've got 3x3 3x3 grids (still with me?). You can still win just like in the 3x3x3 version. But you've got another 3x3 ways in which to do it. The tricky part is, to visualise each possible `3 in a row', you've got to mentally `rotate in' any one (and only one) 3x3x3 cubic plane.

Sorry if that's difficult to follow. If you work it through on paper, you'll see what I mean. This is what being bored in math class will lead you to think of, when plain old tic-tac-toe just doesn't seem challenging anymore. :)