The Definition of Points
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From: Clifford Nelson on 13 Mar 2007 19:46 In article <et77vp$prt$1(a)ss408.t-com.hr>, "�u�Mu�PaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > > 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" You missed the point in a discussion about points. The point is that some things are primary, first, simple. The beginning geometry text books say that the tetrahedron is advanced "solid" geometry. Bucky Fuller discovered it when he was four years old because he could not see. Geometry is taught in a way that psychiatrists would call an example of, in layman's terms, a "thought disorder". Ditto for geometry's "points". If RBF had spelled out the obvious conclusions between the lines, sections, and chapters in Synergetics, I'll bet he wouldn't have been able to get his books published at all. 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: Eric Gisse on 13 Mar 2007 20:18 On Mar 13, 9:52 am, 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, lines, etc aren't defined. Only their relations to eachother.
From: �u�Mu�PaProlij on 13 Mar 2007 20:37 > You missed the point in a discussion about points. The point is that > some things are primary, first, simple. The beginning geometry text > books say that the tetrahedron is advanced "solid" geometry. Bucky > Fuller discovered it when he was four years old because he could not > see. Geometry is taught in a way that psychiatrists would call an > example of, in layman's terms, a "thought disorder". Ditto for > geometry's "points". > > If RBF had spelled out the obvious conclusions between the lines, > sections, and chapters in Synergetics, I'll bet he wouldn't have been > able to get his books published at all. > And I am still missing the point. You can't learn all at once. If someone tells you that line is made of points and point is intersection of two lines you can accept it if you don't know anything better. We know better that this and we don't have to accept this definition of point and line.
From: Clifford Nelson on 13 Mar 2007 20:57 In article <et7g4b$cdh$1(a)ss408.t-com.hr>, "�u�Mu�PaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > > You missed the point in a discussion about points. The point is that > > some things are primary, first, simple. The beginning geometry text > > books say that the tetrahedron is advanced "solid" geometry. Bucky > > Fuller discovered it when he was four years old because he could not > > see. Geometry is taught in a way that psychiatrists would call an > > example of, in layman's terms, a "thought disorder". Ditto for > > geometry's "points". > > > > If RBF had spelled out the obvious conclusions between the lines, > > sections, and chapters in Synergetics, I'll bet he wouldn't have been > > able to get his books published at all. > > > > And I am still missing the point. You can't learn all at once. If someone > tells > you that line is made of points and point is intersection of two lines you > can > accept it if you don't know anything better. > > We know better that this and we don't have to accept this definition of point > and line. Bucky Fuller quoted an author who said: science is an attempt to put the facts of�experience in order. Does the tetrahedron create 4 vertexes, 6 edges, and 4 faces, or is it created by them? The axiomatic method of classical Greek geometry begins with the point. Bucky rejected the axiomatic method. He said you can't begin with less than the tetrahedron. �Cliff Nelson On Feb 19, 2007, at 6:57 AM, David Chako wrote: "I agree that the axiomatic method is insufficient in and of itself. It must be informed by experience. Having said that, it is possible to devise rather generic and abstract mathematics which can be shown to work in harmony with most, if not all, relevant experience. As an example, the notion of vector space is one such abstraction. It is in harmony with Fuller, too. Now, axiomatic geometry is a whole other matter vis a vis harmony with Fuller." - David --End Quote-- Examples of vector spaces use the Cartesian coordinate idea of 90 degrees between the axes and Bucky Fuller wrote that that 90-degree-ness has put humanity in a "lethal bind" of scientific illiteracy. http://mathworld.wolfram.com/VectorSpace.html Rational coordinate geometry with Synergetics coordinates was part of his solution. BuckyNumbers are fields over the rational numbers and a field is a stronger notion than a vector space. �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: �u�Mu�PaProlij on 13 Mar 2007 21:20
> Bucky Fuller quoted an author who said: science is an attempt to put the > facts of experience in order. And I agree with this. >Does the tetrahedron create 4 vertexes, 6 > edges, and 4 faces, or is it created by them? The axiomatic method of > classical Greek geometry begins with the point. Bucky rejected the > axiomatic method. He said you can't begin with less than the tetrahedron. > I really don't know if you can't begin with less than the tetrahedron but I know that you must begin somewhere. Beginning is just one point of your journey and after you choose from where to begin you can go in any direction. You can start from the point and create tetrahedron or you can analyze tetrahedron and get to point. At the end you will have both tetrahedron and point. |