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How much of Pythagoras was scientist, how much was mystic

  1. Dec 15, 2003 #1


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    Pythagoras has a bad name for being a mystic
    he is known to have founded some kind of religious community
    in southern Italy where they reverenced the proportions of the universe or something
    (if you know more factual detail please fill in some)

    Also I have seen the opinion stated that he was not, after all, the first person to realize the thing about the square of the hypoteneuse---or to discover a geometrical proof of it

    but he undoubtably existed (some time in 600-500 BC?) and seems
    to have done EMPIRICAL SCIENCE at least once in his life!
    I say this because he is said to have found the relation between musical pitches and the lengths of a set of strings under equal tension. If this is true it would have involved some kind of experiment (or the equivalent observation).

    the Greek thinkers of classical and hellenistic times are generally considered to have been reluctant to get their hands dirty with experiment---they thought they could find out the truth about nature by pure thought and mathematics. Real empirical physics or---as it used to be called---"Experimental Philosophy" didnt get started until much later, say roughly Galileo's time, he called it the "New" Science.

    What I find intriguing are the occasional hints that Empiricism was there already as an undercurrent.
    There is documentary evidence, I am told, that Ptolemy knew the amount lightrays are refracted in water (has a table of angles of refraction in one of his writings). How would he if no one had ever made experimental measurements of refraction?
    Maybe they did experiments but mostly kept quiet about it and gave the impression that the findings all came by pure abstract thought.

    also there is a pythagorean streak in modern theoretical physics
    (the business of believing that there are simple beautiful proportions deep in nature, and symmetries and so on-----and sometimes letting aesthetic considerations guide investigation:
    it is not so far from Pythagoras with his "all is number" doctrine or from Kepler with his 5 Platonic solids ruling the planets, something easily as crazy as the standard model, if not more so)
  2. jcsd
  3. Dec 15, 2003 #2


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    seven essential vitamins for a healthy spirit

    just heard the call of a red-shouldered hawk
    clear morning
    a propos of philosophy I was thinking about the human spirit and its need for art----and by Art I mean specifically the Seven Liberal Arts defined in classical times

    the spirit (or personality or self or whatever you call it) needs other things MORE perhaps like love and virtue and the society of others and courage and above all patience----but these are like food and water and sleep, they are not like VITAMINS

    the seven liberal arts are like seven essential vitamins which, if you dont get enough your spiritual bones grow crooked, but you may not notice for a long time-----it is not like going without food or water or sleep or fellowship of lovedones, it is a need that is more subtle and more difficult to discover: like for the B-complex vitamins where you eventually get berri-berri or pelegra if you lack them (not sure about what it is, but it is something better avoided)

    the idea of the seven liberal arts (listed by a Roman philosopher circa 50 BC but already traditional) is that you DO them.
    You, dammit, do not just APPRECIATE them. The root idea of art is "skill" (german: die Kunst) and the seven liberal arts are the seven liberal SKILLS which the generally educated person was expected to be able to practice---not just listen to or look at or judge or know about, but do.

    there was something akin to this expectation in confucian chinese education. a gentleman was supposed to be able to play the guitar, or something resembling a guitar. and in classical mandarin society the CIVIL SERVICE exam (and the emperor had a very large class of civil servants who basically ran china for centuries) involved writing something more or less like a SONNET so help me you had to write a poem and maybe even several to be advanced in the civil service! They didnt have the sonnet form but they had rhyming and somekind of formal structure that counted syllables

    so when I see someone CONTRAST art with physics, it occurs to me that what we are seeing is a kind of
    vitamin-deficiency that is widespread, apparently, in this day and age

    of course this is merely personal opinion on my part and not really well thought out either!
    but I am thinking that our culture must be missing some cogs
    we all share the Book of Genesis but
    how many can respect the universe it
    talks about
  4. Dec 15, 2003 #3


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    the seven liberal arts (basic general ed curriculum in classical world which persisted on thru medieval times into renaissance universities) essentially formed European consciousness over the course of a number of centuries (fifteen centuries give or take?)

    the seven liberal arts

    rational argument ("dialectic", logical reasoning, debate)


    As you see there were 3 essentially VERBAL skills and 4 skills having primarily to do with proportion, spatial relation, ratio, harmony---NON-verbal in effect
    ("right brained" stuff, the last 4 might be called, something you need visual imagination for, and to develop an ear for musical intervals, another kind of proportion)

    The interesting thing was that these 7 skills were considered the accomplishments of a gentleman---they were not practical preparation for a job. There were specialized job-skill preparations for various kinds of crafts and professions but those were different.

    my suspicion is that if they had had physics they would have
    expanded the definition of one of the arts to be general physics (including astronomy but not limited to it)

    it just happens that for them, at that time, theoretical physics was mostly the model of the cosmos you got in astronomy---a kind of geometric picture of the universe with spheres and stuff. if they had HAD newton and kepler laws they would have included that in the curriculum of the arts. but they didnt so they just made that one astronomy.
  5. Dec 15, 2003 #4


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    A very nice set of posts. I agree with almost all of it.

    Just a few comments though.

    The common view that Greek thinkers didn't like to get their hands dirty came mostly from Plato, who was an aristocrat, and wrote like one. He dissed the Sicilian philosopher Archytas for making a toy airplane that flew. But that just shows that people like Archytas existed. Archimedes, another Sicilian, was a physicist who did experiments. So were Straton, Eratospthenes, and other investigators.

    But just as today there are many fewer hard science sites on the web than there are sites about political opinions, so social philosophy tended to overwhelm nature study in terms of output.
  6. Dec 15, 2003 #5


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    that just shows what an edge guy you are :wink:
    i try to make it as extreme as i sincerely can to allow
    for some controversy and a wholesome ruffling of the feathers
    so I do not count on agreement (and only hope for a little interest!)

    but I am glad you do!

    I didnt know the story of the toy airplane or Sicilian experimental tendencies

    the king of sicily Frederick II (roughly 1200-1250) had a
    menagerie--was a close observer of birds (feeding, migration, mating, all kinds of behavior) and speculated about reasons and wrote a multivolume book in latin that reads almost like 19th century naturalist observations---but the book had a practical purpose since some parts specifically relate to falconry----Frederick also had aristotle translated (some science books that happened not to be available in Latin at the time)
    he was also a patron of mathematics and Fibonacci performed in a mathematical tournament at Frederick's court
    he was also a patron of poetry and was honored by the greatest poet of the German middleages Walther v. der Vogelweide, to whom Frederick gave a fiefdom.

    So this king also had empirical science tendencies and supported Art
    (at that time Fibonacci was the foremost algebraist of Europe and introduced Europeans to the decimal notation---he won the tournament, it goes without saying, by quickly solving the problems posed by Giovanni da Palermo) and Frederick's court people (no doubt with his encouragement) invented the sonnet form and wrote the first poetry in Italian.

    this impresses me as very cool for circa 1230
    I should mention that Frederick later became the emperor of the HRE and I believe at one time was also king of Jerusalem. Britannica says he thought the Crusades were a bad idea and advocated a negotiated settlement (which would have been a rather odd position circa 1230 I should think!) He didnt get along very well with the pope.

    Carla motivated me to start using LaTex so I will take this opportunity to practice.
    We were talking about the number 13 quintillion that (like 1/137) is so important to living things
    and I called it N, in a nearby thread,
    and gave examples including speed of sound in gas at temperature T (expressed as kT in natural energy units) and molecular wt 29---basically thinking biatomic gas air.


    Today around here the temp is 2E-30
    and since N is 13E18 that makes NT 26E-12
    the (7/5) is because its biatomic and multiplying by
    that and dividing by the mol. wt. 29 gives about 1.2 trillionth.
    So the sqrt is about 1.1 millionth (of the speed of light) which
    is indeed the speed of sound around here at the moment.
    It's cold, about Fahrenheit 50
    Last edited: Dec 15, 2003
  7. Dec 15, 2003 #6


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    In reason's ear they all rejoice---Joe Addison 1712

    The Spacious Firmament on high,
    With all the blue Etherial Sky,
    And spangled Heav’ns, a Shining Frame,
    Their great Original proclaim:
    Th’ unwearied Sun, from Day to Day,
    Does his Creator’s Power display,
    And publishes to every Land
    The Work of an Almighty Hand.

    Soon as the Evening Shades prevail,
    The Moon takes up the Wondrous Tale,
    And nightly to the list’ning Earth
    Repeats the Story of her Birth:
    Whilst all the Stars that round her burn,
    And all the Planets, in their turn,
    Confirm the Tidings as they rowl,
    And spread the Truth from Pole to Pole.

    What though, in solemn Silence, all
    Move round the dark terrestrial Ball?
    What tho’ nor real Voice nor Sound
    Amid their radiant Orbs be found?
    In Reason’s Ear they all rejoice,
    And utter forth a glorious Voice,
    For ever singing, as they shine,
    ‘The Hand that made us is Divine.’

    (after Psalm 19:1-6)

    I reckon this is a pythagorean vision
    Kepler's book Harmonice Mundi was published in 1618
    Kepler thought that in the 5 platonic solids he had
    found the harmony of the universe----and threw in the
    three laws for extra (his third law was discovered that year)

    this ode of Addison about Listening with Reason's Ear
    (fundamentally what physics is) came less than
    100 years after Harmonice Mundi. Addison published it in his
    popular journal "The Spectator". It was 1712 and Benjamin Franklin
    (who invented and constructed the first rotating electric motor) was six years old

    pythagoreanism and empiricism epitomized by Kepler and Galileo
    are core European spiritual values

    Initially Addison wanted to write a different ending on the first stanza:

    "...And publishes to every Land
    The Work of an Almighty Tentacle."

    but he found that tentacle didnt rhyme with Land, so
    he changed it to an Almighty Hand.
    This is called poetic license, sometimes you have to change things
    just to make it fit the meter or rhyme pattern. Since we all know She has tentacles, no harm is done.

    As for the RHYTHM with which the planets go around, Kepler discovered that any planet's PERIOD (if you raise it to the 2/3 power) will tell you its average distance from the sun and Newton figured out why. So Addison had a clear idea of how the silent motions of the planets could sing praise of the laws of Nature into Reason's ear.
  8. Feb 1, 2004 #7
    science vs. mysticism


    Forgive me for countering the thread title with another question.

    What is the ratio of scientist to mystic of God? Zero, for at level of omniscience, they are the same. Pythagoras was probably around 30/70? Science has elements of faith, and Religion has elements of science.

    Practising the seven liberal arts tends to promote a balanced perspective, and heightens ones' ability to recognise patterns in all things. Pattern recognition is fundamental to all seven "arts", and is the foundation for learning. We learn primarily through duplication of perceived patterns. These patterns all start as thoughts, and end in sound. A gentleman should play guitar (or something), and a scientist should be a gentleman. Someone who has not a clue as to how a chord is made can never fully understand any fundamental vibration interval.

    Contemplation of numbers, and their relations, is a Yoga. It has been said that meditation on natural numerical events is a divine conversation with God.

    Pythagoras contemplations led him to revere "triangular" numbers. By using pebbles or beads, etc. to represent (symbol) numbers, and creating ever larger triangles in the series 1,3,6,10... . He did more than that of course (mathematically), but for every point of value he may have passed on with science, he countered with a 3 points of the ridiculous. ie.- never stir a fire with an iron poker, don't eat from a whole loaf of bread, pick things up that you drop, etc, etc.

  9. Feb 1, 2004 #8


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    Re: science vs. mysticism

    I hear that he got quite daffy.
    Newton was not the most sensible sort either.
    Did you ever read Arthur Koestler's book about
    Kepler called "The Watershed"

    it is taken out of a larger book called the sleepwalkers

    which however I have not read

    I only read the part about Kepler which was taken out and
    made into a separate book---I like it a lot.
  10. Feb 1, 2004 #9

    No, I havn't read read "The Watershed". It is on my list, and perhaps now I will bump it up a few places.

    Examining the personal lives of the great contributors to our history will, with great regularity, show that the right brain functions you mentioned earlier dominate the germination of said contributions.

    This disturbs me in that, in our current system, it is only given a fraction of the credit, and not encouraged in school. We have such an imbalanced left brain society!


    PS- Pythagoras sang and played (guitar) to his students.
    Last edited: Feb 1, 2004
  11. Feb 2, 2004 #10


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    I never thought of that. he probably did

    sometimes a novelist can reveal a truth about the past which an historian cannot

    I believe on the basis of evidence that Albert Einstein played the violin (and liked playing chamber music, duets, quartets etc) and that Richard Feynmann played bongos and some other percussion instruments at times---and would play for his students.

    And if we can trust an episode in the Analects of Confucius, that sage would play a kind of chinese banjo----or else it was the ch'in which is a plucked-string instrument unlike a banjo---in the hearing of his students and one day he was asked why he did that instead of discussing philosophy with them and his answer was dutifully written down---if we can trust the Analects.

    But where in all get-out did you come across all this information about Pythagoras including this detail that he would play the guitar to his students.

    I heard at one time he was driven out of town. perhaps for being cantankerous. Didnt he live in southern Italy? So-called Magna Graecia? Was the town called Crotona? So then he would have become cantankerous in Crotona and been sent into exile.
  12. Feb 2, 2004 #11


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    suppose I wanted to celebrate May 15 how should this be done.
    this is a question for you.

    Kepler recorded in his diary of year 1618 that on May 15 he
    at last saw that the orbit's distance out was the threehalves power of its period

    by May 27 he had finished the book containing that discovery "Harmonice Mundi"

    in our family we have, for some years, celebrated July 4 by reading the Declaration of Independence
    should May 15 be enlivened by readings from J. Kepler?
    He was something of a stylist. and had occasionally surprising
    turns or fits of phrase
  13. Feb 2, 2004 #12

    If you really want to celebrate Kepler, perhaps "The Twelve days of Harmony", where you can not only read from his book on each day, but can also do something that re-creates experimentations and models to verify his predictions.??

    Reference for Pythagoras - "The Pythagorean Sourcebook and Library", by K. Guthrie. Aslo, I read Clifford A. Pickover's "The Loom of God: Mathematical Tapestries at the Edge of Time" around Christmas time, and is quite informative.

    Like any popular figure in history, the stories have grown so that one can not always teel what is truthful. My favorite "likely not to be true story" is how he met his death by refusing to cross a field of beans to safety, and was killed by a left brained mob.

    He was born on the island of Samos (c580BC), and move to Croton to establish his "secret society".

    Certainly, if celebrating Kepler, you could include his two treasures of geometry - Pythagoras' Theorum, and Phi.

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