CS  Response to John Conway
Subject: RE: Coordinate systems
Author: Jesse Yoder jesse@flowresearch.com 
Date: Sun, 8 Feb 1998 13:16:20 -0500
John Conway wrote -
> Thanks for your thanks. I think it's not really in "measuring
> circular pipes" so much as in considering (say) fluid flow around
> such pipes, that a special coordinate-system would be used.
RESPONSE - You're welcome. I guess I was speaking carelessly -- I didn't
mean measurement of circular pipes so much as measuring fluid flow
within such pipes (I don't know where you would measure flow around
pipes, unless you're talking about orifice plate measurement or open
channel flow measurement, where you use weirs or flumes).
Then you wrote:
> I think that what you call "selecting a Point size to suit a
> particular measurement" is obviously very sensible, but that it's
> silly to use "Point" and "point" with different meanings. Have you
> any strong reason for doing this rather than using the same language 
> as everyone else - for instance saying something like "working to
> within a tolerance of 1/100 of an inch"? I thought you had, namely
> that you felt Euclid's "points" didn't exist, but perhaps some
> absolute "Points" did. 
RESPONSE: I'm glad you finally agree that selecting a Point size to suit
a particular measurement is obviously very sensible. As to the idea that
it's silly to use "Point" and "point" with different meanings, I have
two comments:
a) This whole idea of using the terms in Circular Geometry with
different notation arose as a result of your repeated objections to what
you said was my conflating the terms used in a Euclidean sense vs. a
Circular Geometry sense when discussing Circular Geometry, as I note in
a footnote to the article I recently posted. It sounded like a good idea
at the time.
b) I believe that the meaning of a term is defined by its rules of use.
Obviously the rules for the use of the term 'Point' are different from
those for 'point', since Points have area, while points do not. So they
do have somewhat of a different meaning or connotation. Also, as I
mention in a footnote, it is possible to create a circular geometry that
is somewhat parallel to the one I am proposing by taking the terms
'point', 'line', 'circle', etc. in their Euclidean senses. In fact, I
more or less credit you in the footnote for suggesting this idea
(perhaps this is an incorrect attribution, but I believe in giving
credit where credit is due). So capitalizing these terms does call
attention to the differences in these two possible circular geometries.
If my language of Points can be replaced by something like "measuring to
within the tolerances of 1/100th. of an inch" (I claim that there is
some implicit limit in any measurement, even though the measurer may not
think about his assumptions in each case), then that's fine with me. In
that case, the language of Points could be reserved for times when you
are explaining the complete foundations of measurement, which is, after
all, something of a philosophical question.
You then continue:
> I'm surprised that you regard changing a coordinate-system as
> "extreme": to me it seems a rather trivial and practical matter.
> I have a suggestion to make. If it's really the case that
> your distinguishing between "points" and "Points" is practical
> rather than theoretical, why not just drop it and use a more
> traditional language in the interests of better communication 
> even if (like many other people) you'd really prefer it if language 
> hadn't developed in the way it has? I say this because talking
> about the use of words is much less valuable than talking about
> the things they represent, and your present terminology has made
> it very difficult (at least for me) to understand what you're
> really trying to say.
RESPONSE: If dropping the use of "Points" will help you understand
better what I am saying, then I am certainly willing to do this. But at
the same time, I find your comments that you "find it very difficult to
understand what [I'm] really trying to say" somewhat frustrating at this
I realize that what I am saying may be difficult to understand when it
is viewed in isolation, rather than as a complete system. Up to this
point, then, I have been fully in sympathy with your comments that you
"do not understand" whay I am trying to say," even to the point of being
willing to alter my terminology so that you would be better able to
comprehend my remarks. In fact, I viewed your repeated claims not to
understand what I am saying as a reason to further elaborate and attempt
to explain myself. You also said that I don't define my terms and also
don't understand what I mean or even adequately think through what I am
saying before I say it.
So to meet your objections, I have done the following four things:
1. Provided a discussion of the basis for my proposal (namely, what I
claim are flaws in the foundations of Euclidean and Cartesian geometry).
2. Provided a list of the axioms of Circular Geometry that defines the
fundamental concepts of 'Point', 'Line', and 'Circle' that I am using
and gives rules for their use. What's more, this list of axioms does not
rely overly much on Euclidean axioms or definitions, as you said my last
effort to axiomatize my system did.
3. Provided three practical consequences of the use of Circular Geometry
to the measurement of fluid flow in closed pipes.
4. Provided a graphic that depicts the Coordinate System I am talking
about, together with the Point that can be used to generate this system.
Please note that I have done all the above in the space of seven pages,
that I have done so in plain English and have not relied on the
introduction or the use of words that people of common sense can't
understand (with the possible exception of the discussion of fluid flow
measurement, which might presuppose some technical understanding), and
that I have not surreptitiously taken your ideas and smuggled them in,
claiming them as my own but rather have given credit where credit is
due, including not only to you, but to other members of the geometry
forum from whose comments I have benefited.
If after all this, you still say to me: "I don't understand what you are
talking about," then I would say to you: "What is it that you don't
understand?" And where specifically do I make a statement that you
disagree with or find hard to grasp?
Jesse Yoder






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