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Re: D=5



You have to read carefully what Robert Cohen said - "If I never experienced a
3-dimensional object" - which I take to mean as someone who has zero depth
perception and sees everything as on a flat sheet of paper.

The problem with this is that people change the rules of the game as they add
dimensions and pretend they are doing the same thing. Gamow did this in "1-2-3
Infinity" and it annoyed the heck out of me. You can't get his final figure
following his rules exactly as he defines them.

If you follow the rules as stated you will get exactly what Cohen sees - which are
two 2-D squares with their corners connected. If you go to the next level (4-D)
what you should see if you follow the rules - which no one does - is a box kite!

I know I'm going to get flak on this from the cognoscenti, but I insist they only
get their pretty structures by breaking their own rules. There - that should bring
some replies :-)

Bob at PC

"John S. Denker" wrote:

Robert Cohen wrote:

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| / | /
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If I never experienced a 3-dimensional object, I would see the drawing above
as two 2-D squares with their corners connected.

Please look again.

1) You should be able to see that there are _three
different ways_ in which it can be decomposed into
squares with their corners connected.

2) You can also imagine how the various squares slide
relative to each other when the viewpoint of the
projection is changed.

3) You can arbitrarily label various pairs of squares as
the XY, YZ, and ZX faces.

=========

The same goes for hypercubes.
http://www.monmouth.com/~jsd/physics/gif48/tesseract.gif

1) There are four different ways the hypercube can be
decomposed into pairs of cubes.
http://www.monmouth.com/~jsd/physics/gif48/tesseract-chop.gif

2) You can imagine how the cubes slide relative to each
other when the viewpoint of the projection is changed.

3) You can arbitrarily label certain pairs of cubes as the
XYZ, YZT, ZTX, and TXY hyperfaces.

===============

I think it's amusing. My neices thought it was amusing.

If you expect it to be clear at first glance, you're
expecting too much. You have to stare at it for a good
long while.