` `
`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`
`point. `
` `
`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`

http://forum.swarthmore.edu/epigone/geometry-research/sarswimpbli/8E85093A9F04D11180BC00A0C92ABEAC189187@arcmail.arcweb.com