The Definition of Points
in [Math]
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From: SucMucPaProlij on 13 Mar 2007 15:24 "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")
From: SucMucPaProlij on 13 Mar 2007 15:48 > 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 . . . > point is coordinate in (any) space (real or imaginary). For example (x,y,z) is a point where x,y and z are any numbers. line is collection of points and is defined with three functions x = f(t) y = g(t) z = h(t) where t is any real number and f,g and h are any continous functions. Your definition is good for 10 years old boy to understand what is point and what is line. (When I was a child, I thought like a child, I reasoned like a child. When I became a man, I put away childish ways behind me.....)
From: Randy Poe on 13 Mar 2007 15:55 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 . . . > The modern axiomization of geometry due to Hilbert leaves points, lines, and planes undefined. In fact, he famously said about this construction: "One must be able to say at all times-instead of points, lines, and planes---tables, chairs, and beer mugs." In other words, despite whatever intuition and inherent meaning we might ascribe to these things has no effect on the mathematical structure. No doubt Lester will find this approach lacking and assert he has a superior axiomization built up from "infinite epistomological ontologies of finite tautological regression" or something equally meaningless. - Randy
From: Clifford Nelson on 13 Mar 2007 16:14 In article <et6v6r$1ov$1(a)ss408.t-com.hr>, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > > 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 . . . > > > > point is coordinate in (any) space (real or imaginary). > For example (x,y,z) is a point where x,y and z are any numbers. > > line is collection of points and is defined with three functions > x = f(t) > y = g(t) > z = h(t) > > where t is any real number and f,g and h are any continous functions. > > Your definition is good for 10 years old boy to understand what is point and > what is line. (When I was a child, I thought like a child, I reasoned like a > child. When I became a man, I put away childish ways behind me.....) Primary means like prime, first. First things first, second things second, third things third, etc.. 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. See: http://bfi.org/node/574 Cliff Nelson Dry your tears, there's more fun for your ears, "Forward Into The Past" 2 PM to 5 PM, Sundays, California time, http://www.geocities.com/forwardintothepast/ Don't be a square or a blockhead; see: http://bfi.org/node/574 http://library.wolfram.com/infocenter/search/?search_results=1;search_per son_id=607
From: Jesse F. Hughes on 13 Mar 2007 16:16
"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!) -- "All intelligent men are cowards. The Chinese are the world's worst fighters because they are an intelligent race[...] An average Chinese child knows what the European gray-haired statesmen do not know, that by fighting one gets killed or maimed." -- Lin Yutang |