===========================ø MON.JAN,1995ë1ë2 ø===========================
|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 :++++++++++++++++++++++++++++

       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

       ( 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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