zz: Mathematicians and Ranks (was: Ranks (was: Re: STILL NOT WORKING

[Ted Nelson <ted@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
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