negative (multi)dimensionality

[thigle]

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 ?

[wendy]

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.

[thigle]

wow.

"...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...
Negative Dimensionality and General Schemas Theory: http://holonomic.net/gs03a04.pdf

[jinydu]

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.

[wendy]

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.