Re: Mathematicians and Ranks

[Mark-Jason Dominus <mjd@xxxxxxxxxx>]

> >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.
> 
> ABCD are in one rank and PQR are in another rank.
>  They are in the same dimension.

Oh, that's fine then. 

<<Light goes on>>

I just realized that I keep imainging that zigzagspace is a lattice or
an array, where each position on the lattice might or might not
contain a cell.  But that's totally, totally wrong.  I have to stop
thinking that; it keeps confusing me.


> >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.
> 
> I don't think so ... a rank is a bunch of ordered elements,
>  but the ordering can be in a loop.  That's all.

Sure.  Not every zigzag space is a product space.  I only mentioned it
to point out that mathematicians to understand that things can be
circular and that things that are circular in one direction and flat
in another direction do not bother them.

> >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.)
> 
> This is possible with even just one cell.  But is this the correct
> terminology for sets of elements,
>  as well as continuous objects?

Probably.  I think that topologically they have too much in common for
someone to bother inventing new terminology.  But I don't really know.

> >Hmm, I'm suddenly inspired to make a ZZ object that is shaped like a
> >Klein bottle.  It shouldn't take long.
> 
> Looking forward... uh, inward...
>  better consult the Navel Observatory ...

That project is turning into a ZZ tutorial on algebraic topology.

I'll put it on my FTP site when it is ready.