Re: Mark-Jason's excellent clarif. CORRECTED (was: Re: Mathematicians and Ranks

[Ted Nelson <ted@xxxxxxxxxx>]

[Prev. error flagged with asterisk below]
Ha!

Mark-Jason has provided an excellent insight into
 a likely misunderstanding.  Since I did not realize
 this was a likely misunderstanding, I have till now
 done nothing to thwart it.  

Sez he:
><<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.

*Just so.  A new cell [prev. said: "space"] can be created anywhere with only
 the local effects (connex) you want.

ChrzT


At 10:45 AM 10/29/98 -0500, you wrote:
>
>> >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.
>
>
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