The Definition of Points
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From: Lester Zick on 13 Mar 2007 18:07 On Tue, 13 Mar 2007 20:24:01 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > >"PD" <TheDraperFamily(a)gmail.com> wrote in message >news:1173810896.000941.35900(a)q40g2000cwq.googlegroups.com... >> On Mar 13, 12:52 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~~ >> >> Interestingly, the dictionary of the English language is also >> circular, where the definitions of each and every single word in the >> dictionary is composed of other words also defined in the dictionary. >> Thus, it is possible to find a circular route from any word defined in >> the dictionary, through words in the definition, back to the original >> word to be defined. >> >> That being said, perhaps it is in your best interest to find a way to >> write a dictionary that eradicates this circularity. That way, when >> you use the words "peculiar" and "definitional", we will have a priori >> definitions of those terms that are noncircular, and from which the >> unambiguous meaning of what you write can be obtained. >> >> PD >> > >hahahahahahaha good point (or "intersections of lines") And it might be an even better point if it weren't used to justify mathematikers' claims that lines are made up of points. ~v~~
From: Lester Zick on 13 Mar 2007 18:11 On Tue, 13 Mar 2007 16:16:52 -0400, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: >"PD" <TheDraperFamily(a)gmail.com> writes: > >> Interestingly, the dictionary of the English language is also >> circular, where the definitions of each and every single word in the >> dictionary is composed of other words also defined in the dictionary. >> Thus, it is possible to find a circular route from any word defined in >> the dictionary, through words in the definition, back to the original >> word to be defined. > >The part following "Thus" is doubtful. It is certainly true for some >words ("is" and "a", for instance). It is almost certainly false >for some other words. I doubt that if we begin with "gregarious" and >check each word in its definition, followed by each word in those >definitions and so on, we will find a definition involving the word >"gregarious". > >Here's the start: > >gregarious > adj 1: tending to form a group with others of the same kind; > "gregarious bird species"; "man is a gregarious > animal" [ant: ungregarious] > 2: seeking and enjoying the company of others; "a gregarious > person who avoids solitude" > >(note that the examples and antonym are not part of the definition!) An interesting point. One might indeed have to go a long way to discern the circularity. However my actual contention is that this variety of circularity is quite often used by mathematikers to conceal an otherwise orphan contention that lines are constituted of points. ~v~~
From: Lester Zick on 13 Mar 2007 18:13 On Tue, 13 Mar 2007 18:43:09 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick 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~~ > > Point > http://mathworld.wolfram.com/Point.html > > A point 0-dimensional mathematical object, which can be specified in > n-dimensional space using n coordinates. Although the notion of a point > is intuitively rather clear, the mathematical machinery used to deal > with points and point-like objects can be surprisingly slippery. This > difficulty was encountered by none other than Euclid himself who, in > his Elements, gave the vague definition of a point as "that which has > no part." Sure, Sam. I understand that there are things we call points which have no exhaustive definition. However my point is the contention of mathematikers that lines are made up of points is untenable if lines are required to define points through their intersection.It's vacuous. ~v~~
From: Lester Zick on 13 Mar 2007 18:17 On 13 Mar 2007 12:08:57 -0700, "Douglas Eagleson" <eaglesondouglas(a)yahoo.com> wrote: >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~~ > >Points are rather importent things to try to get correct. I am still >looking for some references, easy web kind, to allow topology to >express points. > >And if a point was expressable, a function. And so nth topoogy is >possible, but I need a Matlab transform that links a theorm, to the >applied coordinate. And so the basic idea is to allow points where the >size as infinity are expressable. > >This solves a symmetry problem. And resolves the question of sets of >rationals to irrationals as true sized, infinities! > >So the topology of the point is a theorm I need. > >Any ideas? Well if the intersection of lines defines points it indeed occurs to me that points must be spherical since lines can double back on themselves from all different directions. However that suggests as well that if the contention of mathematkers is true then points constituting a line must connect through points on each sphere. ~v~~
From: �u�Mu�PaProlij on 13 Mar 2007 18:18
> Bucky Fuller's kindergarten teacher gave her class semi-dried peas and > toothpicks to build "structures". All of the kids built structures that > had 90 degree angles like squares and cubes except Bucky. He could not > see because he didn't have a pair of glasses yet, and felt that the > triangle and tetrahedron were strong, but the square and cube did not > hold their shape. He got a patent for the structure he made about 60 > years later. He thought like a child for about 60 years and started to > write Synergetics. 15 years later the first volume was published. > it is nice story but nothing more. It is one of the stories that fits in "how to become rich and successful" book, chapter "Change the way you think and all your problems will be solved" |