negative (multi)dimensionality

If you don't know where to post something, put it here and an administrator or moderator will move it to the right place.

negative (multi)dimensionality

Postby thigle » Sun Aug 07, 2005 6:11 pm

i came few times across a concept of 'negative dimensionality'. i don't get it. how does it function ? what is a -1 dimensionality ? or -3, -4 dimensionality ? &, is there such a similar counter-common.intuitive step across -3d and -4d as is across 3d & 4d ?

any suggestions ? :roll:
thigle
Tetronian
 
Posts: 390
Joined: Fri Jul 29, 2005 5:00 pm

Postby wendy » Sun Aug 07, 2005 11:33 pm

Negative dimensions don't really exist per se.

The lowest dimension normally asscribed to a polytope is -1 (nulloid), although the lowest actually seen is -2 (in the dyadic representation of the desarge configuration).

In the main, they need to be calculated, and are there largely to stabilise products like the tegum and pyramid products.
The dream you dream alone is only a dream
the dream we dream together is reality.

\ ( \(\LaTeX\ \) \ ) [no spaces] at https://greasyfork.org/en/users/188714-wendy-krieger
User avatar
wendy
Pentonian
 
Posts: 2014
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Postby thigle » Fri Aug 12, 2005 9:56 am

wow. :shock:

"...the lowest actually seen is -2..."

can you ex.plain a bit, or give some reference where i could dive into this a bit more, please ?

also, i consider these (from http://holonomic.net) to be interesting, but leaves me hungry... :cry:
Negative Dimensionality and General Schemas Theory: http://holonomic.net/gs03a04.pdf
thigle
Tetronian
 
Posts: 390
Joined: Fri Jul 29, 2005 5:00 pm

Postby jinydu » Fri Aug 12, 2005 10:23 am

A quick search of "negative dimensions" on Google turns up:

http://www.math.yale.edu/mandelbrot/web ... b_neg.html

It comes from the Yale Mathematics department website, so it should be credible. However, I don't understand it.
jinydu
Tetronian
 
Posts: 721
Joined: Thu Jun 10, 2004 5:31 am

Postby wendy » Fri Aug 12, 2005 10:49 am

I really do not have a reference for dimension -2.

The thing came out when i was having one of my "discussions" with Norman Johnson over the nature of the nulloid (what he calls the nullitope). He identifies this with the set-theory empty set, but i disagreed with him over this, and mentioned that pondered polytopes typically have a lowest surtope of -2 dimensions, quoting the Desarge Configuration as an example (it's a pondered simplex).

Later on we discovered things like pondered cubes, etc.
The dream you dream alone is only a dream
the dream we dream together is reality.

\ ( \(\LaTeX\ \) \ ) [no spaces] at https://greasyfork.org/en/users/188714-wendy-krieger
User avatar
wendy
Pentonian
 
Posts: 2014
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia


Return to Where Should I Post This?

Who is online

Users browsing this forum: No registered users and 7 guests

cron