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*To*: zzdev@xxxxxxxxxx*Subject*: :zz: Mathematicians and Ranks (was: Ranks (was: Re: STILL NOT WORKING*From*: Ted Nelson <ted@xxxxxxxxxx>*Date*: Thu, 29 Oct 1998 21:33:30 +0900*Cc*: ted@xxxxxxxxxxxxxx*In-reply-to*: <19981029004149.17351.qmail@xxxxxxxxxx>*References*: <Your message of "Wed, 28 Oct 1998 17:02:40 +0900." <3.0.3.32.19981028170240.00f8f2e0@xxxxxxxxxxxxxxxxxxx>*Reply-to*: zzdev@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. N1 .. N6 are also a rank. D-N1 is a rank. P-N6 is a rank. (If the connections as I see them are correct). >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. Before we go further let's make sure we agree on this !-) >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? >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 ... ChrzT At 07:41 PM 10/28/98 -0500, you wrote: > >> "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. > > > > ____________________________________________________ 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."

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

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

**Re: [zzdev] :zz: Ranks (was: Re: STILL NOT WORKING***From:*Mark-Jason Dominus

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