Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: D=5



-----Original Message-----
From: Ludwik Kowalski [mailto:kowalskiL@MAIL.MONTCLAIR.EDU]
Sent: Wednesday, September 18, 2002 9:55 PM
_______
/| /|
/ / |
| | | |
| |____|_ |
| / | /
|_______|/

Now keep going. Duplicate that, and connect corresponding
corners. I'm not going to draw it using ASCII art, but
it's not very hard to draw it using pencil and paper.
If you can project a D=3 cube onto D=2 paper, you can
perfectly well do the same for a D=4 hypercube.

What is drawn above (sorry I was not able to preserve JohnD's
ASCII picture of the cube, even after switching to Courier font)
is a projection of a D=3 cube onto D=2 screen. How does it
help me to figure out the D=4 structure? My ability to visualize,
or to represent with sticks, etc. ends at D=3. Am I the only one
to suffer from this limitation in this company?

No. I'm with you.

If I never experienced a 3-dimensional object, I would see the drawing above
as two 2-D squares with their corners connected. Since I know what a cube
looks like, I can visualize what the 3-D image "looks like" (in 3-D) that
has the 2-D projection drawn above.

If I draw two 2-D cubes (like that above) side by side and connect their
corners, I see two 2-D representations of cubes with their corners
connected. I acknowledge that it is represents the 2-D projection of a 4-D
image but I can't visualize what the 4-D image "looks like" (in 4-D).

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301