The Definition of Points
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From: ken.quirici on 16 Mar 2007 13:48 On Mar 13, 1:52 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > The Definition of Points > ~v~~ > > In the swansong of modern math lines are composed of points. But then > we must ask how points are defined? However I seem to recollect > intersections of lines determine points. But if so then we are left to > consider the rather peculiar proposition that lines are composed of > the intersection of lines. Now I don't claim the foregoing definitions > are circular. Only that the ratio of definitional logic to conclusions > is a transcendental somewhere in the neighborhood of 3.14159 . . . > > ~v~~ My impression is that Euclid defined a line, not in terms of points, and never claimed a line was made up of points, but defined a line as a geometrical object that has only the property of extensibility (length, where length can be infinite). He uses points in his proofs specifically as intersections of lines, if I remember correctly, and makes no attempt at describing or explaining their density in a line. (You gotta lot of 'splainin to do, Euclid!).
From: Tony Lance on 16 Mar 2007 13:53 Big Bertha Thing gyro Cosmic Ray Series Possible Real World System Constructs http://web.onetel.com/~tonylance/gyro.html Access page JPG 12K Image Astrophysics net ring Access site Newsgroup Reviews including alt.war.nuclear Drawing of an ordinary gyroscope. Caption:- Fig. XVI Extract from the Introductory Chapter:- But the most interesting top of all is undoubtedly the ordinary gyroscope. That depicted in Fig. XVI........ although merely sold as a toy, is nevertheless capable of illustrating the gyroscopic phenomena which have been so much made use of in modern mechanical invention. From the book An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic Motion. By Harold Crabtree M.A. Formerly Scholar of Pembroke College, Cambridge Assistant Master at Charterhouse Longmans, Green and Co. 1923 First Edition 1909 Second Edition 1914 New Impression 1923 (C) Copyright Tony Lance 1998 Distribute complete and free of charge to comply. Big Bertha Thing rita Educating Rita This film portrays a dominant spouse and a long-suffering student, to the extent upto and including divorce, book-burning and forced pregnancy. There was zero privacy. Any attempt to re-register or change the password would not work, because the secret could not be kept. Every posting by the spouse is a violation of OU rules and the students education, causing real pain. Vetting by one moderator or by several using a non-public Rita conf. would not work, because the spouse would use the students name, with all the further alienation that would cause. A new policy needs to be adopted. The last resort punishment measure, needs to be the first resort measure on compassionate grounds; that of making the student read-only on FC. The student would thank you for it, but not publically. It would need to be agreed between ACS and OUSA, which is what they are there for. Tony Lance judemarie(a)bigberthathing.co.uk From: Tony Lance <judemarie(a)bigberthathing.co.uk> Newsgroups: swnet.sci.astro,sci.chem Subject: Re: Big Bertha Thing strategic Date: Sun, 11 Feb 2007 13:58:31 +0000 Tuesday, November 18, 1997 10:04:23 PM Message From: Tony Lance Subject: Big Bertha Thing 1 To: FC Mods Discussion From Bibliography of Pastures.(Optional) The preface from An Elementary Treatment of Gyroscopes and Similar Spinning Tops by Crabtree 1909 Classic Cartoon and animated cartoon of Animal Farm by George Orwell NB (2006) Stateside, all investment funding for super-colliders is at ground zero; past, present and future. Politics makes poor science.
From: Lester Zick on 16 Mar 2007 14:27 On Fri, 16 Mar 2007 16:18:53 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >"Lester Zick" <dontbother(a)nowhere.net> wrote in message >news:1ukbv2hq1fo7ucv8971u9qo37b48bj6a5h(a)4ax.com... >> >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> ~v~~ > >Can you prove that non-circular definition of existence exists? Well that depends on what you and others mean by "existence exists". On the face of it the phrase "existence exists" is itself circular and no more demonstrable than a phrase like "pointing points". It's just a phrase taken as a root axiomatic assumption of truth by Ayn Rand in my own personal experience whether others have used it or not I don't know. On the other hand if you're asking whether anything exists and is capable of being unambiguously defined the answer is yes. I've done exactly that on more than one occasion first in the root post to the thread "Epistemology 201: The Science of Science" of two years ago and more recently in the root post to the thread "Epistemology 401: Tautological Mechanics" from a month ago. The technique of unambiguous definition and the definition of truth is simply to show that all possible alternative are false. Empirics and mathematikers generally prefer to base their definitions on undemonstrable axiomatic assumptions of truth whereas I prefer to base definitions of truth on finite mechanical tautological reduction to self contradictory alternatives. The former technique is a practice in mystical insight while the latter entails exhaustive analysis and reduction in purely mechanical terms. ~v~~
From: Lester Zick on 16 Mar 2007 14:34 On Fri, 16 Mar 2007 15:52:51 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> Please look up the difference between "define" and "determine". >> >> In a theory that deals with "points" and "lines" (these are typically >> theories about geometry), it is usual to leave these terms themselves >> undefined >> and to investigate an incidence relation "P on L" (for points P and >> lines L) >> with certain properties >> >> Then the intersection of two lines /determines/ a point in the sense >> that >> IF we have two lines L1 and L2 >> AND there exists a point P such that both P on L1 and P on L2 >> THEN this point is unique. >> This is usually stated as an axiom. >> And it does not define points nor lines. >> > > >Here is one problem that is much biger that definition of point. Spelling? >How do you define "definition"? Well actually this is at least several years old. I don't claim my own question in that regard was necessarily original but I did raise this issue at least several years ago and have routinely continued to raise it. Quite possibly the silliest definition of definition I noted was David Marcus's comment that a definition is only an abbreviation. >If you have a definition of "definition" you can't prove that it is a really >stuff becouse you don't know what definition is before you defined it. >I can as well say that "definition" is a big red apple and it is true by >definition. You can't prove that "definition" is not a big red apple becouse you >don't have definition of "definition" other then this. Since I defined >"definition" first, from now on "definition" is big red apple :)))) Well you might just as well stop congratulating yourself quite so heartily and learn to spell instead. You don't need to know what definition is before you define it. All you need to show is that the definition for definition fulfills its own definition. ~v~~
From: Lester Zick on 16 Mar 2007 14:51
On 16 Mar 2007 07:00:02 -0700, "hagman" <google(a)von-eitzen.de> wrote: >On 13 Mrz., 18:52, Lester Zick <dontbot...(a)nowhere.net> wrote: >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> ~v~~ > >Please look up the difference between "define" and "determine". Well I considered this problem when I began the root post above. However I couldn't come up with any significant distinction between the two. As far as I could tell any "definition" "determines" a thing and any "determination" for a thing "defines" it as well. There may be subtle distinctions but for practical purposes I take them to be pretty much interchangeable. >In a theory that deals with "points" and "lines" (these are typically >theories about geometry), it is usual to leave these terms themselves >undefined I understand this in theory but this isn't what happens in practice. The moment one says "lines are composed of points" one has defined each in terms of the other. And likewise when one observes that the "intersection of lines defines or determines points". The association of predicates is what definitions and determinations are all about. And to then say that points and lines remain undefined is nonsense. >and to investigate an incidence relation "P on L" (for points P and >lines L) >with certain properties Okay. >Then the intersection of two lines /determines/ a point in the sense >that >IF we have two lines L1 and L2 >AND there exists a point P such that both P on L1 and P on L2 >THEN this point is unique. Well this last claim is totally irrelevant to your primary syllogistic truism. "If A and B" above doesn't support your conclusion at all. You might just as well start off by saying "Unique points are defined by thus and such" and let it go at that. There is no need to pretend that "thus and such" justifies the conclusion that "such points are unique". That's just an arbitrary axiomatic assumption of truth. >This is usually stated as an axiom. >And it does not define points nor lines. Of course it's usually stated as an axiom because the rationalization itself doesn't support the conclusion and in fact has nothing to do with the conclusion. You might just as well say that "this point is unique because the sun is round". But you're wrong if you think this doesn't define "this point" because it's the association of predicates that matters whether the association is axiomatic assumption or not. ~v~~ |