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*To*: zzdev@xxxxxxxxxx*Subject*: Re: [zzdev] :zz: Ranks (was: Re: STILL NOT WORKING*From*: Mark-Jason Dominus <mjd@xxxxxxxxxx>*Date*: Wed, 28 Oct 1998 19:41:49 -0500*In-reply-to*: Your message of "Wed, 28 Oct 1998 17:02:40 +0900." <3.0.3.32.19981028170240.00f8f2e0@xxxxxxxxxxxxxxxxxxx>*Reply-to*: zzdev@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.

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

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

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

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