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    Various items about My view of Reality

    Proposed Banner of the NeoPythagoreans -- B A 2005

       
        =========================== MON.JAN,199512 ===========================
      |15:30| now days , when the conversation gets around to religion , I call my
       self a  NeoPythagorean ...
        ============================: TUE.SEP,970909 :============================
                              ... by which I mean that the understanding of our
       reality and existance we can accomplish is that which we can understand in
       mathematical form . I do NOT include the various numerological and mystical
       accoutrements associated with the ancient Pythagoreans .
       Standard religions assert the understanding of our world stopped with one or
       another ancient group of authors . I believe the motivation of all great
       mathematics and hard science is the truest quest for understanding of our
       predicament . This search has continued thru the millenia continuing today
       and it will continue thru the time we learn how to make sand think .
       The masses reject this notion of religion because it implys extremely hard
       mental work which only a small portion of humanity is capable of in any
       generation .
       My own quest is summarized in  CoSy/Views/PsychoPhysics  .
       One of the great souls in the APL community has been  GerardLanglet  who pursued
       the computational commonalities underlying a Theory of Everything .
      
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      COMPUSERVE / GO Encyclopedia  / Search term: pythagoras
      Articles selected: 2 that begin with [ "pythagoras" ]
       2 Pythagoras of Samos          3 Pythagoras, theorem of
      Pythagoras of Samos -------------------------------- ( say'-muhs )
      Pythagoras of Samos, c.560-c.480 BC, was a Greek philosopher and religious
      leader who was responsible for important developments in the history of
      mathematics, astronomy, and the theory of music. He migrated to Croton and
      founded a philosophical and religious school there that attracted many
      followers. Because no reliable contemporary records survive, and because the
      school practiced both secrecy and communalism, the contributions of
      Pythagoras himself and those of his followers cannot be distinguished.
      Pythagoreans believed that all relations could be reduced to number relations
      ("all things are numbers"). This generalization stemmed from certain
      observations in music,mathematics, and astronomy.
      The Pythagoreans noticed that vibrating strings produce harmonious tones when
      the ratios of the lengths of the strings are whole numbers, and that these
      ratios could be extended to other instruments. They knew, as did the
      Egyptians before them, that any triangle whose sides were in the ratio 3:4:5
      was a right-angled triangle. The so-called Pythagorean theorem, that the
      square of the hypotenuse of a right triangle is equal to the sum of the
      squares of the other two sides, may have been known in Babylonia, where
      Pythagoras traveled in his youth; the Pythagoreans, however, are usually
      credited with the first proof of this theorem.
      In astronomy, the Pythagoreans were well aware of the periodic numerical
      relations of heavenly bodies. The CELESTIAL SPHERES of the planets were
      thought to produce a harmony called the music of the spheres. Pythagoreans
      believed that the earth itself was in motion. The most important discovery of
      this school--which upset Greek mathematics, as well as the Pythagoreans' own
      belief that whole numbers and their ratios could account for geometrical
      properties--was the incommensurability of the diagonal of a square with its
      side. This result showed the existence of IRRATIONAL NUMBERS.
      Whereas much of the Pythagorean doctrine that has survived consists of
      numerology and number mysticism, the influence of the idea that the world can
      be understood through mathematics was extremely important to the development
      of science and mathematics.                               Janice A. Henderson
      Bibliography: Gorman, P., Pythagoras: A Life (1978); Guthrie, W.  K.  C.,
      History of Greek Philosophy, 5 vols. (1962-75);  Philip, J.  A., Pythagoras
      and Early Pythagoreanism (1966);  Stanley, Thomas, Pythagoras (1989);  Valens,
      Evans G., The Number of Things:  Pythagoras, Geometry and Humming Strings
      (1964).                                    See also: MATHEMATICS, HISTORY OF.
      Pythagoras, theorem of -------------------------------- ( pi-thag'-uh-ruhs )
      The theorem of Pythagoras is a statement that the square of the hypotenuse of
      a right triangle is equal to the sum of the squares of its other two sides.
      At the time of Pythagoras of Samos (6th century BC), the square of a number n
      was represented by the area of a square with side of length n. Using this
      representation, the Pythagorean theorem may be stated: The area of the square
      on the hypotenuse of a right triangle is equal to the sum of the areas of the
      squares on the legs.
      Pythagoras, or perhaps one of his students, proved that if triangle ABC is a
      right triangle with a right angle at C, then cc = aa + bb. The converse
      [ inverse |BA] theorem (If cc = aa + bb in a triangle ABC, then the angle at
      C is a right angle) appears to have been used much earlier. For example,
      early Egyptian surveyors used knotted ropes to form triangles with sides 3,
      4, and 5 units long. Because 5 X 5 = 3 X 3 + 4 X 4, the angle opposite the
      side of length 5 was assumed to be a right angle. This surveying technique
      was useful for marking off the boundaries of fields after the annual flooding
      of the Nile River.
      In EUCLIDEAN GEOMETRY the theorem of Pythagoras provides a basis for the
      definitions of distance and similar equations hold in spaces of higher
      dimensions.                                            Bruce E. Meserve
      Thank you for using CompuServe!               Off at 15:14 EST 2-Jan-95
      
        ++++++++++++++++++++++++++++: SUN.JUN,970608 :++++++++++++++++++++++++++++
      
      Under the History of Mathematics TimeLine sdcc14.ucsd.edu/~fillmore/timeline.html sdcc14.ucsd.edu/~fillmore/blurbs/P322.html has the following set of Pythagorean Triples known by the Babylonians circa -1700 .
             Triples
                120     119     169
               3456    3367    4825
               4800    4601    6649
              13500   12709   18541
                 72      65      97
                360     319     481
               2700    2291    3541
                960     799    1249
                600     481     769
               6480    4961    8161
                 60      45      75
               2400    1679    2929
                240     161     289
               2700    1771    3229
                 90      56     106
      
      Here`s a little classic APL demonstrating that the sum of squares of each of the rows of the first 2 columns equals the corresponding item of the third .
             ( Triples [ ; 0 1 ] +.* 2 ) = Triples [ ; 2 ] * 2
      1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
      

      Here's the rule generating all Pythagorean Triples : Generating Pythagorean Triples ============================: TUE.SEP,990907 :============================ Brett A. Bradley wrote: > Well, the original Pythagoreans were vegetarian, in fact Pythagorean was > the term for vegetarianism before "vegetarian" was coined. It only seemed > logical that a Neopythagorean would be vegetarian. ` Learn something new everyday , especially on the Web . I did find a reference to the the abstinance from meat eating thru Yahoo at www.aros.net/~eriugena/essyht~1 . ============================: WED.DEC,991201 :============================ Subject: Re: Darwin v God(s) Date: Wed, 01 Dec 1999 04:33:07 -0500 From: BobArmstrong To: LPQC@aol.com LPQC@aol.com wrote: > A thoughtful article discussing (my take) on creation-evolution issues: > http://www.leaderu.com/orgs/arn/orpages/or151/151johngould.htm Searching for "religion" , FreeFind mechanism on my website appropriately comes up with http://cosy.com/views/Pythag.htm . http:/cosy.com/views/index.htm#Misc will show there`s a related bit at http://cosy.com/views/armstrng.htm . The only exception I would take with Phillip E. Johnson`s conclusion that : " Darwinism is tied to naturalistic philosophy and opposed to any meaningful theism. " is that to me , the incredible intricate reality and meta-reality revealed by pursuit of mathematical/scientific understanding of , as my friend Raj used to ask : "? What is Happening ?" , may reasonably be labeled a variety of Pantheism . ( Maybe this is why I like the Hindu relating of characteristic Gods to various aspects of existence ( and they hang a Bell kids love by the door ) . ) With respect to evolutionary discontinuities , do a search for Rene Thom , whose Catastrophe Theory has been a major influence on mathematical biology over the last quarter century . ( I never met Thom , but he had a ride from the airport in my `69 Corolla wagon . ) It`s still not clear to me how closed membranes or sexual reproduction emerge . Looking up Thom , I clicked http://views.vcu.edu/~mikuleck/rosrev.html , Review of: "Essays on Life Itself" by Robert Rosen who apparently died in `98 . He was one of the great seekers of reality back when . On the other hand , my institutionalized brother Jack Armstrong , is becoming something of a guru for his elemental Christianity . His art is generating a certain amount of fame . See http://cosy.com/art/JackA/JackA.htm . The brilliant innovation of the Separation of Church and State in our BoR is a core reason why I feel so strongly that any forced subsidies of education , if there are to be any , should go to the parents as vouchers for their choice of education for the children , short circuiting the Government establishment of the "The Religion of Immoralism" in Max Eastman`s phrase ( see TUE.SEP,990907 in http://cosy.com/cal99/cur~9909.htm ) . On this issue , the ACLU is mired in Statist merde . I look forward to discussing these issues with some of the respected Rebbis in the NY8 Hassidic community . I`m going to copy this to http://cosy.com/views/Pythag.htm to add to the explication of my world view . Incidentally , my thoughts are similar to those of the Apollo Moon Landers . ( See TUE.JUL,990720 in http://cosy.com/cal99/cur~9907.htm , ) -- --- BobArmstrong -- http://CoSy.com -- 212-285-1864 --- ++ NoteComputing Environment ++ Libertarian candidate , (NY-8) in 2000 : http://boba-in-y2k.org Join : http://www.egroups.com/group/boba-in-y2k/ "The moral defense of a free-market system must rest ultimately on the legitimacy of voluntary transactions and the illegitimacy of force . " Tom Bethell , The Noblest Triumph : Property and Prosperity thru the Ages , p164 . 1998 . ISBN:0-312-21083-3 See http://cosy.com/home.htm#Today for recent commentary and events . |#| == |#| == |#| == |#| == |#| == |#| == |#| == |#| == |#| == |#| == |#|

       
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