About time this ancient Greek had an airing here. Expelled by mainland Greeks for heretical notions, famed for framing ideas for O level maths, admired by his disciples, mocked by modernists intriguing to mind over matter and ethereal day dreamers? What of him, Res Historians? Is the world any richer for his influence?
Answers on a thread please and not yards of yellow look-it- up- yourself site addresses, mmm?

For a start, well before Pythagoras's time "his" famous theorem was known by Babylonian, Indian and Chinese mathematicians - and probably, even earlier still by the 'very' ancient Egyptians too, who certainly knew about the 3:4:5 right-angled triangle. But then any 'advanced' civillisation that was routinely involved in construction works and land surveying etc. probably would discover the rule for practical use, rather sooner than later. It is often claimed that Pythagoras came up with the first proof of the theorem, but I rather doubt that the Babylonians, Indians and Chinese, who already well understood its application, hadn't themselves proved it for all cases well before Pythagoras ... frankly it does take only a bit of playing around with triangles on a sand board before the proof becomes fairly demonstrably evident ... literally QED. But anyway the first mention of Pythagoras in association with the theorem is in Roman writings - four centuries after Mr P's death.

Meles meles wrote:

For a start, well before Pythagoras's time "his" famous theorem was known by Babylonian, Indian and Chinese mathematicians - and probably, even earlier still by the 'very' ancient Egyptians too, who certainly knew about the 3:4:5 right-angled triangle. But then any 'advanced' civillisation that was routinely involved in construction works and land surveying etc. probably would discover the rule for practical use, rather sooner than later. It is often claimed that Pythagoras came up with the first proof of the theorem, but I rather doubt that the Babylonians, Indians and Chinese, who already well understood its application, hadn't themselves proved it for all cases well before Pythagoras ... frankly it does take only a bit of playing around with triangles on a sand board before the proof becomes fairly demonstrably evident ... literally QED. But anyway the first mention of Pythagoras in association with the theorem is in Roman writings - four centuries after Mr P's death.

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These bloody Greeks. Their influence seems to dominate all intellectual activity: philosophy, mathematics, the natural sciences, literature, religion. Everything great, good or original can be traced back to them. The great thinkers of other cultures - Persian, Jewish, Indian, Chinese, Egyptian - are somehow seen as, if not exactly inferior, as somehow just rather exotic: admittedly quite interesting in their own way (sometimes), but really not terribly intellectual. Just the nibbles before the important Athenian main courses. How come?

And did the Greeks actually pinch an awful lot of "their" ideas from more ancient cultures? This was briefly suggested, I think, on the old Plato thread, when Priscilla mentioned Zoroaster. We got a bit of an El Nord snort* and no more was said. But I wonder - clever people are often very, very good at "borrowing" - and then passing things off as original. I'm reminded of something James McNeill Whistler once said to Oscar Wilde:


Oscar Wilde: I wish I had said that.
Whistler: You will, Oscar; you will.

I wonder if some Egyptian, discussing all these jolly interesting "pricks and lines" with the young traveller from Samos, ever observed the same thing to Pythagoras?

*Friendly (honestly) joke, not sarcasm - nordmann does snort a lot.

(sniff)

Blow your nose.

(snort!!!!!!!!!!!!!!!!!)

Thanks - that did the trick.

Py "Golden Thighs" Thagarus was hardly a nutter, Priscilla. Well, not by the - admittedly loose - standards in operation in his neck of the woods at the time. Whether he had an original thought in his head or not regarding maths or religion etc he definitely was regarded by those around him and his successors as having at least defined the academic principles by which education could best be conducted. His notions of "schools" and their interaction with society are still pretty much the basis of modern education. Skill training certainly, but within a social context preparing the student for more than just the succesful execution of a task or two.

Regarding "the Greeks" being perceived as "at the bottom" of all subsequent intellectual and theological disciplines etc. They were the first great "assemblers" of diverse academic data from a wide variety of other sources, and this did seem to enable them to make quantum jumps in academic applications that the others couldn't match at the time. But I am sure that they did not see themselves necessarily as cleverer than their non-Greek peers, at least not as a default attitude. There are so many examples of individual Greeks purposefully setting out to acquire ever more data from these sources, indicating a tacit but definite acknowledgement that innovation and philosophy were developmentally ongoing in the non-hellenic world too. Our warped view of their role might have been encouraged in no small way by the guys themselves - the rise of Roman dominance saw a reciprocal rise in "Greek" nationalism which included reminding everyone of their prowess in these matters - but that was a later development. Up to then they seemed to have been the world's first great "information foragers", and for that we are definitely indebted to them.

many thought Pythagoras a nutter because of his fear of eating beans, for instance...... too embryotic, I assume. he wore odd clothes and probably consorted with Druids. Men of the oak were well known in Magna Graecia. That his family an many disciples were murdered - Croton? I forget, must read my own book on that bit - and intense secrecy of his cult followers everywhere suggests more widespread antipathy than merely his founding schools of learning.

Later his music in the spheres notion was subject for much debate. But he had other interesting ideas about mind over matter too. I have used that in a tale or two, hence some indepth research at the time I was writing. He was, of course a believe in oracles - especially Delphi and had belief in Apollo and his several areas of governance but not of any of the others of the Olympian myths. A unique chappie with many interesting facets; Pythagoras a kind of intellectual Salvador Dali is how I sense him.
Snort on that lot, nord, do.  Good to know that you are still around, raising a tired eyelid from your apparent head on paws slumber hereabouts these days.

Ah, but "nutterism" was also interpreted as proof of genius by many of his contemporaries too, Priscilla. After all, look at the leeway they afforded the dog man Diogenes of Sinope. Even today the freemasons regard Pythagoras as having had, first and foremost, a "disciplined mind" which in some of their literature they aspire to emulate. Don't ask me how I know this as I will simply deny everything and do a funny handshake (snort!).

Didn't "abstain from beans" mean "don't meddle in politics"? That sounds quite sensible. I know nothing about Pythagoras, but I read about abstaining from beans in a book about Elizabeth I (Elizabeth,  Captive Princess by Margaret Irwin actually).

It's amazing what you can pick up from historical novels.

PS Was it really Pythagoras who came up with the idea of the music of the spheres? I think it's a lovely concept: I first came across it when reading 16th century literature - love of divine harmony and all that -  did not know it originated with the Greeks and mathematics.

So he did. Found this rather nice site:

http://www.musicofthespheres.org/Whatismots.htm

He also believed in reincarnation; said to have admonished someone lobbing a stone at a dog lest it was a close friend. He said its barks were familiar. So he may also have had a witty side but I found no other evidence of it. There have been many claims about where he acquired his several iconic  notions: Egypt, India Druids and so on. For all of that he was a one off with a large albeit clandestine  widespread following. I had never however read of him being the founding father of education - though I have actually used the concept.

His reincarnation theory seems also to have been essentially mathematical. Believing that the universe contained a finite number of souls divided amongst a fluctuating number of "hosts" the idea was to then deduce the logic of humanity's relationship with that universe by trying to understand and even enumerate the pattern of allocation of these souls. Pythagoras (or at least the natural philosophical school attributed to him) is all about patterns. It was a way of thinking that was later abandoned by his successors as it abhorred anomaly and sought to treat this as simply a pattern yet to be deduced. However too many such anomalies then calls the basic presumption into question (existentialism is a recent term for a very ancient concept) which in turn raises the danger of soundly adduced natural philosophical concepts being distrusted or even abandoned as valid fact.

In a nutshell Pythagorean philosophy contains within it the antithesis of philosophical debate and when Milo (and probably others too) began to organise Pythagorean schools into what appear to have been the equivalent of modern "secret societies" which employed vigorous recruitment, indoctrination and membership policies it eventually led to a political stand-off and then actual violence directed against them. Their schools were effectively outlawed and destroyed. However it is obvious that the disciplined nature of their organisation - once the actual religious philosophical content had been excised - held great appeal even to their opponents and in fact became a model of how such schools were founded and organised in Greece for centuries to come. "Pythagorean" became more a term for such organisational principles rather than for any particular philosophical principles the man himself might have advocated - which is probably why so many diverse strands of philosophy (mathematics, natural history etc) are linked nominally back to him, sometimes even as their originator, though evidential support for such a claim is practically non-existent.

His immediate legacy was not so much any innovation within philosophical theory but in how such theory can be developed within a firm educational structure (something that itself may have been a policy he had learnt in his travels to Egypt and the quasi-independent cell-structured educational and religious communities with their own geographical and political bases he would have found there). However having said that this legacy might more accurately be attributed to Milo, who definitely established such an elitist "academy" in Croton in Pythogaras's name.

Later theory which was known to have been produced from within this kind of intensive think-tank system seems to have been called "Pythagorean" by default. A misattribution or later inaccuracy might be why we have now associated one particular mathematical theory with Pythagoras the man. An ironic one too since we have no reason at all to believe that actual Pythagorean philosophy even encouraged the study of geometry except possibly as a tool for divining celestial and universal patterns. Unless the will of the gods could be deduced through trigonometry the theory we now call "Pythagoras's" would have probably been of absolutely no interest to the actual man whatsoever.

nordmann wrote:

Later theory which was known to have been produced from within this kind of intensive think-tank system seems to have been called "Pythagorean" by default. A misattribution or later inaccuracy might be why we have now associated one particular mathematical theory with Pythagoras the man. An ironic one too since we have no reason at all to believe that actual Pythagorean philosophy even encouraged the study of geometry except possibly as a tool for divining celestial and universal patterns. Unless the will of the gods could be deduced through trigonometry the theory we now call "Pythagoras's" would have probably been of absolutely no interest to the actual man whatsoever.

The adjective 'Pythagorean' is to mathematics what the word 'Shakespearean' is to English literature. Just by claiming that an anonymously authored poem or play reads like it could be by William Shakespeare, then attributing a mathematical theory to Pythagoras of Samos immediately adds kudos to that theory. And being a supposed polymath, neither is Pythagoras’ famous name associated only with philosophy or mathematics. Hence in music there is the Pythagorean scale. And there is also the Pythagorean lute. This, however, is not a musical instrument or even a piece of music. The lute of Pythagoras is a geometric pattern based on the isosceles triangle which in turn is used to form pentagrams.



(A Spanish-made patchwork quilt called El laúd de Pitágoras.)

Although it may sound like an ancient concept, the term 'the lute of Pythagoras' is in fact barely 30 years old.