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Various items about My view of Reality
===========================ø MON.JAN,1995ë1ë2 ø===========================
|15:30| now days , when the conversation gets around to religion , I call my
self a NeoPythagorean ...
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... 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
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
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Under the History of Mathematics TimeLine
sdcc14.ucsd.edu/~fillmore/blurbs/P322.html has the following set of
Pythagorean Triples known by the Babylonians circa -1700 .
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
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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
> A thoughtful article discussing (my take) on creation-evolution issues:
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
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
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
( 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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