Re: HyperCube (Diamond Explained)

Whoa!  Hold on!  Let me address each point (and I promise a new ascii 
drawing at the end of this post, so we can pretend we're still in this 
newsgroup *grin*)

FRM writes:

>  Well, to continue this thread (and, yes, I know this ain't alt.physics),
>time IS the fourth dimension, not "can be." The trick is that the
separation of Time and Space is an artificial distinction -- physics 
tells
>us that Time and Space are two manifestations of the same thing, no
different from width, depth or height. And yes, the fourth dimension is 
90
>degrees off from the other three... If you've followed all that, you should
>have a headache by now.

You may call time the fourth dimension if you wish, but it is no more 
the "official" fourth dimension than, say, width is the offical second 
dimension.  In fact, if you've ever drawn a distance vs. time graph like 
we all probably have in physics class, then you've designated time as 
either the first or second dimension.  It's all what you want to call 
it.  As for time being 90 degrees from length, width, and depth, well... 
that's like saying that red is 90 degrees away from blue.  If you drew 
it that way on a color wheel, then fine, but make sure we have some kind 
of frame of reference or the statement is meaningless.


>   The problem with this discussion, despite Michael's valiant attempt, is
that hypercubes are almost impossible to draw on paper/computer screens.
Michael's was a good start, but it takes a 3-D model to best show what
we're talking about.
>
>That's why the hypercube is only a theory -- it SHOULD be possible, but in
>realistic, practical terms it doesn't exist. Outside of advanced math
classes, the best use of the hypercube is as an example of where logic 
ends
>and common sense begins.


Hypercubes are not impossible to draw on paper or computer or a 
blackboard... we've just seen several examples.  Unless you mean that 
cubes and other 3-D objects are impossible to draw in two dimensions as 
well, which you could argue.

The hypercube is not where "logic ends", it is a very logical extension 
of the concept of dimension.  It exists as surely as any mathematical 
object.  In "realistic, practical terms", even something as simple as a 
square does not exist.  A square is an abstraction, even the most 
precise tools or computers can create a "real" square.

Fun discussion, Reverand!

Here's my new hypercube (thanks Veronica!)


                  (
 AAAAAaaaaaaaa!
              (   ()   )
    ) ________    //  )
 ()  |\       \  //
( \\__ \ ______\//
   \__) |       |
     |  |       |
      \ |       |
       \|_______|
       //    \\
      ((     ||
       \\    ||
     ( ()    ||
      (      () ) )
       
             
      Hyper-Cube




-- 
 ----       __  __ () _ _ __    __  _  _ __ __   ___ ___       o      
| \_|_\    |  \/  |--| '(| =|  |  \| |/o \ " /|_/ O | O )        ()  o
|_|_| |    |_\__/_|__|_|_|__|  |_|\__|_/\_|_|___|__/|_\_\     o_/||\/ 
 \|__\|  Michael Naylor, mna...@math.fsu.edu, (904) 644-8433   _/\_

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