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*To*: zzdev@xxxxxxxxxx*Subject*: Re: Mark-Jason's excellent clarif. (was: Re: Mathematicians and Ranks*From*: Ted Nelson <ted@xxxxxxxxxx>*Date*: Sun, 01 Nov 1998 18:11:39 +0900*Cc*: ted@xxxxxxxxxxxxxx*In-reply-to*: <19981029154512.20895.qmail@xxxxxxxxxx>*References*: <Your message of "Thu, 29 Oct 1998 21:33:30 +0900." <3.0.3.32.19981029213330.01000440@xxxxxxxxxxxxxxxxxxx>*Reply-to*: zzdev@xxxxxxxxxx

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 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. > > ____________________________________________________ Theodor Holm Nelson, Visiting Professor of Environmental Information Keio University, Shonan Fujisawa Campus, Fujisawa, Japan Home Fax from USA: 011-81-466-46-7368 (If in Japan, 0466-46-7368) Professorial home page http://www.sfc.keio.ac.jp/~ted/ _____________________________________________________ Permanent: Project Xanadu, 3020 Bridgeway #295, Sausalito CA 94965 Tel. 415/ 331-4422, fax 415/332-0136 http://www.xanadu.net PERMANENT E-MAIL: ted@xxxxxxxxxx _____________________________________________________ Quotation of the day, 98.10.29: Last words of Oscar Wilde: "Either that wallpaper goes, or I do."

**References**:**:zz: Mathematicians and Ranks (was: Ranks (was: Re: STILL NOT WORKING***From:*Ted Nelson

**Re: Mathematicians and Ranks***From:*Mark-Jason Dominus

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