The Definition of Points
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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: Sam Wormley on 13 Mar 2007 21:23 Tom Potter wrote: > Euclid's Elements > > Definition 1. > A point is that which has no part. > > Definition 2. > A line is breadthless length. > > Definition 3. > The ends of a line are points. > > Definition 4. > A straight line is a line which lies evenly with the points on > itself. > > Definition 5. > A surface is that which has length and breadth only. > Hey Potter--That was a useful posting for a change!
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.
From: OG on 13 Mar 2007 22:22
"Lester Zick" <dontbother(a)nowhere.net> wrote in message news:758ev21t8r8ch5sjuoasdim467bfjvk06q(a)4ax.com... > 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. > What you call 'orphan' is in fact 'abstract', as points necessarily are. |