Re: [zzdev] :zz: Ranks (was: Re: STILL NOT WORKING

[Mark-Jason Dominus <mjd@xxxxxxxxxx>]

> "Rank" is the generalized term for "row" and "column",

There should be a word for a collection of connected cells in the same
rank.  Example:


        A--B--C--D              P--Q--R
                 |              |
                 N1-N2-N3-N4-N5-N6

Unless I misundestand youm all seven cells ABCD PQR are in the same
rank, but ABCD are in one blurfl and PQR are in a separate blurfl.

This is the thing I have been calling `pier', but I don't like that.
My vote is for `beam' unless you already have a name for it.

> However, a rank may be a loop....  Already a number of scientists
> have shaken their heads and mumbled nervously about this.  We don't
> know any formal description that fits in known mathematics.

Oh, it's no trouble.  Mathematicians call it a `product space', and
they are quite happy to take products of circles.  If you take the
product of two line segments, you get a plane segment.  If you take
the product of a segment and a circle, you get a cylinder.  If you
take the product of two circles, you get a torus.

If you have a ZZ object in three dimensions all of which are
ringranks, there are a lot of mathematicians who will come along and
say, ``Ah, yes, S1-cubed.''  (S1 is topological jargon for the
circle.)

Hmm, I'm suddenly inspired to make a ZZ object that is shaped like a
Klein bottle.  It shouldn't take long.