From: Brett Paatsch (paatschb@ocean.com.au)
Date: Mon Jan 27 2003 - 20:54:47 MST
Avatar wrote:
>
> The tesseract is a 4-dimensional cube. On this page, you will see it
> projected into 2-dimensional space, but you can dynamically click and
> drag the wireframe model with your mouse and unfold and re-fold it in
> four dimensions. You can see the tesseract from all directions in
> 4-dimensional space:
>
> http://pw1.netcom.com/~hjsmith/WireFrame4/tesseract.html
Interesting stuff! But when you put it in a side view so that all that is
visible are only three rectangles, shouldn't you also be able to stretch
that
shape and thereby lengthen the rectangles? Is the limit in the programming
or the user-perceiver-interface (me)?
I read a book featuring tesseracts recently. Unfortunately the friend that
gave me the book for Xmas has commandeered it to check it out herself so
I haven't got it handy to check the author or title. In the book the
tesseract
was draw as a three dimensional cross. 3 cubes wide, four long, one deep.
To see it as a tesseract you had to imagine the two farthest sides of the
3 cube crossbar being bent around to touch each other, and the same thing
hapening at the same time with the four cube long 'main beam'. This seemed
to raise a problem, though. The visual "bending" could be done in either of
two ways. The three cube and four cube lengths could be bent in the same
direction (the four around the three) or they could be bent in opposite
directions (three "in" and four "out").
I find this whole 4 D space thing really interesting. I can never quite tell
if
I'm being invited to imaging something absurb (like hearing someone say
"picture a square with three equal sides" - which I "picture" as a triangle
by
"any other name"), or whether its just that my perceptions can't do
correctly
what they are being challenged, quite validly, to do.
H G Well's Timemachine made time the fourth dimension. Seeing length,
width, breadth and then duration as all essential to the "existence" of
everyday
objects wasn't too hard.
But the tesseract is, (as I understand it), using four *space* dimensions
each at 90 degrees to the others. So space would be the fifth.
Then I try and imagine something like Hawkings objects with 10 or 11
dimensions and the wheels are way off. Best I can do is imagine three
axis with six or seven very small balloons attached to the origin. These
balloon dimensions would always be there but only kick in and have an
impact when the length of the rays from the x, y and z axis are shortened
way way down.
I enjoyed hearing Carl Sagan describe "Flatland" on his TV series Cosmos
when I was in secondary school in the early 1980's. But I never really *got*
the point either visually or conceptually. I think "the point" was to
extrapolation Flatland (the example) but to see ourselves as 3-space-D
beings incapable of seeing 4-space-D objects but able to see their
3-space-D "image" or "shaddow" as it passed through our
3-space-D universe. I think the shaddow of the 4-space-D cube was the
tesseract but I'm not sure. I was watching in on TV (only 2D) and couldn't
manipulate (as with the link above) and so I think my mind just gave up on
it.
Brett
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