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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
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