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Pythagoras

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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 10 Apr 2016 at 03:51
Question is whether the uncertainty principal is a epistemological limitation, which will eventually be overcome, or a metaphysical limitation which demonstrates that weird stuff happens beyond this point.

I can only get through the first half of his books, but Sir Roger Penrose talks about the brain and its activity on the quantum level (in the second half of his books).

For coins, I think that both interpretations (discovered/invented) have merit.  If one can say that light is both a wave and particle (which one can, but unless one is a physicist, one doesn't really understand it), then maybe both 'discover' and 'invent' can, depending on the scenario, work well in describing "what" happened with the introduction of coinage.  But just as one could not imagine the personal computers of today, plus tablets and smart phones, from looking at the Eniac or the Univac or even the Pascal adding machine, so too one could not imagine where coinage would go from looking at the earliest electrum coins of Lydia and Ionia.

I have a book that i have started to read, and it looks fascinating, but I never have got that far.  It is called; The Shape of Time:  Remarks On the History of Things, by George Kubler.  Genius requires the right temperment, the right character to flourish, but it also requires the right environs.  It is one thing to be at the beginning of a trend, and another to be towards the end.  Perry and McArthur were of the right temperment to interact with Japan.  Johannes Kepler was a mathematician who took over Brahe's data and with the persistence of a mystic deduced his three laws, paving the way for Newton.  Kepler was a "Pythagorean" who was intellectually honest enough to admit that the planets didn't go in circles. Kepler today would probably be lost in astrology, but at the time he was needed for a key transition.
Genius has the potential to make the most of an opportunity when it comes along, again it is one thing to be at the beginning of trend (which will not start unless the right kind of person is there), it is another to be in the middle or at the end of the trend.
Pythagoras was both at the end of a trend, the oral tradition of Epic poetry, the student of Hermodamas, part of a poetic lineage going back to a friend of Homer, and at the beginning of a trend, the introduction of coinage into Magna Graecia and Sicily, preceded only by the initial introduction of coinage, in Ionia and Lydia.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 11 Apr 2016 at 01:51
franciscosan      https://en.wikipedia.org/wiki/History_of_coins  What do you think of editing this page?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 11 Apr 2016 at 04:36
I am pretty much limited in my interest to ancient Greek, with a little bit into Roman.  So there are vast areas that I don't know about for coinage, like Chinese "coinage."  But one thing that is painful about wikipedia, is that they want whatever is status quo in a subject, not anything that is new or possibly "controversial."
One thing you knew about the Encyclopedia Britannica, whomever edited an article was an expert in the field, that means that they might have had an axe to grind, but they were well worth hearing.  The fact that wikipedia tries to not take sides means that by default, they take sides.
But, I will look at it again, and maybe tweak it a little, I have done that before, maybe I should look at this article that you suggest, on the history of coinage.

The theory that Pythagoras is the originator of the incuse coinage of Magna Graecia, is an old theory.  I am just brushing it off.  The usual counterargument is that Pythagoras immigrated to Southern Italy in c. 532 BC (which I accept), but the coinage started before that, in 550 or 540 BC (which I don't accept).  Therefore, the argument goes, Pythagoras could not have been the originator of the coinage which started before he got to Southern Italy.  The problem is that the dating of 550 or 540 BC is made on extremely tenuous grounds.  I mean, there are no dates on coins, nor can they be dated by somebody's reign.  It is all a matter of relative dating, die studies, overstrikes and hoard data.  Relative dating means that you can tell that one coin came before another and so you can get a relative chronology from that.  If you have a worn coin and a brand new coin buried in a hoard, you know that all other things being equal, the worn coin is older than the new coin.  Likewise the obverse and reverse dies usually get replaced at different times, and so there is an overlap of the dies from which one can tell one is earlier than another.  How long was one die used, well, scholars make an educated guess.  Are broken dies just replaced, or are they reworked?  Is the design good for making the dies last, or is it bad (for example high relief)?  Did they stop minting at sometime, and then start up again?  You can see that there are a lot of considerations which are glossed over, when a date found by relative means is achieved.  In some cases, you can find out a lot from relative dating, in others, like this Southern Italian incuse coinage, which is the first coinage in the area, it is a lot more problematic.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 11 Apr 2016 at 05:00
I don't know how to post pictures.  But if you want to look at some of the coins I am talking about,
look at magnagraecia.nl
you should get a map of Sicily and Southern Italy,
click on the region called "Bruttium" in the toe of the boot of Italy.
then click on "Kroton"
At the top it will say something like 
Kroton 550-500 BC 
spread flan
27-30 mm
AR Stater
[picture]

you can see how one side is opposite the other.  In Aristotle, there is a list of 10 Pythagorean opposites, and the Krotoniate doctor Alcmaeon gets into opposites as well in his medical theory, (health is a matter of balance).  There are other examples from different dies, this particular one is not that geometric, other dies show more geometry in the design.  The bronze tripod depicted is a sign of Apollo at Delphi, and some said that Pythagoras was Apollo and that he 'spoke [agorein] like the [Pythia(n)] oracle.  Also Kroton is the third mint in the region to mint, although you can't tell that from the website's dating of the coins.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 18 Apr 2016 at 01:32
Pythagoras of Samos is usually described as either a religious reformer and mystic or, a mathematician and a scientist.  Again, Pythagoras' occupation was a celator, or a craftsman specializing in working with precious metals, and gems, sometimes getting into other areas such as bronzework or architecture.  Whether we are referring to Pythagoras as a scientist or a mystic, we are referring to his vocation or calling, not his occupation.  In modern thinking, however, usually Pythagoras is portrayed as one or the other (religious or math/science), but not both.  This dichotomy matches up with Descartes' dualism, where religion and science are separated.  However, in history there are prominent individuals who had both a mystic or religious streak, and were foremost in the world of science.  One of those is Isaac Newton, who in addition to astronomy and calculus, was interested in magic and alchemy.  Or Johannes Kepler, who in addition to astronomy was interested in what in his day was called Pythagoreanism and number mysticism.
My point is that there is not necessarily any contradiction in Pythagoras being thought of as both a religious reformer or mystic and a mathematician or scientist.  We should realize that if we have a problem with a characterization of Pythagoras as both a religious and scientific figure, we should realize that it is our "modern" problem, not theirs. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toyomotor Quote  Post ReplyReply Direct Link To This Post Posted: 18 Apr 2016 at 02:06
Pythagoras, wasn't he the guy who had a theory?  Wink

Sorry guys, I just couldn't help myself.
I often wonder why I try.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 19 Apr 2016 at 01:34
a theorem, not a theory.
A^2+B^2=C^2 with angle AB a right angle.
Of course they worked it out with geometrical shapes.

Other cultures like India or Babylon may have come across
this earlier.  It was Pythagoras and the Pythagoreans who
formulated as a theorem.  Other cultures used mathematics for
practical endeavors, it was the Pythagoreans who came to look at
it as a science, and explored number theory and mathematics as
an end in itself.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toyomotor Quote  Post ReplyReply Direct Link To This Post Posted: 19 Apr 2016 at 01:52
Franciscoan:

"a theorem, not a theory.
A^2+B^2=C^2 with angle AB a right angle.
Of course they worked it out with geometrical shapes."

Sorry mate, it's all Greek to me.
I often wonder why I try.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 20 Apr 2016 at 11:08
Math is a language
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Post Options Post Options   Thanks (1) Thanks(1)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 20 Apr 2016 at 21:42
Yes, Galileo said that.
But I am not sure how to say, "ouch, I stubbed my big toe" in mathematical notation.
Math is a language.  But language is also metaphorical, or maybe in the context of
the previous sentence, language is a metaphor.  I guess what I am saying is that, "math
is a language" is a meaningful statement, but it is not exact in the way that mathematics
is exact.

"It's all Greek to me," comes from when everybody studied Latin, but the advanced students would get to study Greek if they wanted to do so.  Now that fewer people study latin, you could probably say, "it is all Greek to me" about studying Latin.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 20 Apr 2016 at 23:15
Originally posted by franciscosan franciscosan wrote:

Yes, Galileo said that.
But I am not sure how to say, "ouch, I stubbed my big toe" in mathematical notation.
Math is a language.  But language is also metaphorical, or maybe in the context of
the previous sentence, language is a metaphor.  I guess what I am saying is that, "math
is a language" is a meaningful statement, but it is not exact in the way that mathematics
is exact.

"It's all Greek to me," comes from when everybody studied Latin, but the advanced students would get to study Greek if they wanted to do so.  Now that fewer people study latin, you could probably say, "it is all Greek to me" about studying Latin.

All abstractions tend to be exact in the way our senses our not.

What I find delusional is the mind vs matter dialogue.  Information has been shown to have physical properties and that pretty well destroys the duality issue.


The relationship between math and science is one that philosophers have wasted a lot of time on.  Math may be a more exact language than native languages but in some ways that is only because the definitions are fixed.  Like all languages however math is not so exact when it tries to describe physical reality which is why science approximates reality.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 23 Apr 2016 at 07:03
Platonism believed that mathematical objects had a reality separate from sensate objects, Godel was a Platonist and his Platonism basically allowed him to come up with the incompleteness theorem, contra Russell and Whitehead and Carnap and others, showing that (from my understanding) a comprehensive, coherent theory of mathematics is not logically possible.  Penrose also believes in the independence of mathematical objects.
mind body dualism is just a model that has some usefulness in certain areas.  Any half decent philosopher know that it is very problematic.  But what is more problematic is a materialism that pretends to be the end all and be all, by ignoring intentionality and other mental phenomena.  People seem to want to wrap things up in a nice mechanistic model, but there are things that go beyond those things, Penrose tiles and irrational numbers show that there is world beyond rational prediction/description.

You should understand that philosophers are not asking for your permission to "waste time" on math and science.  But if you mean that science has become professionalized in the last two hundred years and is often intolerant of anybody who imposes on their territory, yes that is probably true.  Scientists want research money, and anyone else asking about what they are doing, are annoyances to that goal.  Of course some the best of them engage in philosophy themselves, I don't suppose you would have told Heisenberg that philosophy was a waste of time when he wrote "Physics and Philosophy"?  Postmodernism, on the other hand, plays rather loosely with scientific terminology.  I still get a big kick out of the Sokal affair.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 23 Apr 2016 at 13:16
Perhaps I should have been more clear because I was not implying that philosophy was not useful to science although I could come up with a long list of imminent scientists who believe that is true.  

What I was saying is that math is abstract and absolute while science is observational with all the limitations that implies in terms of "accuracy".  This is self evident by definition and should not be a point of contention.  

Nobody need deny that there is a world beyond rational prediction/description to argue that that world is not the world of science and I would argue that in some ways philosophy is best when it is grounded in science.  I would also argue that the scientific method is self evident and the philosophy of science should only nibble around the edges not question this self evident and trivial fact.

As to dualism you can split the world up into as many component parts for analysis as you want but all the components of necessity are part of the same reality.  Whether or not science can capture a picture of that reality is in many ways an unanswerable question.  In any case saying math is not logical implies that reality is not logical but that, if true, is as likely a flaw of logic as it explanation of anything.  I think this line of reason results from a kind of conceit that exaggerates the human potential to "understand".  That conceit in my mind comes from the habit of thinking in terms of kind not degrees.  All understanding is an approximation even if it is expressed in absolute terms.  The mind is as real as home runs and money but is a social construct and social constructs are just as real as atoms.  We only make the assumption that social constructions are some how without physical existence because honestly we don't know what it means to be physical. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 23 Apr 2016 at 13:18
Philosophers if they are employed by public institutions do need to ask my permission to get payed :-)  I'm not sure why you bring this up all the time but I'm just as concerned about philosophers wasting my tax dollars as physicists.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 24 Apr 2016 at 00:41
If observational limitations are implicit, then it is not a matter of self-evident definition.  It took a long time to realize that observation was important, especially since people tend to see what they want to see.  To us it is obvious that the motion of Mars is in an ellipse, but it took a long time before Kepler actually took Brahe's data and analyzed it with I "fine toothed comb," figuring out a circular orbit (+epicycles, etc.) did not fully account for things.  But yes, you are right, there is a difference between the phenomena being studied and "static" that is confusing the issue.  Part of modern science is realizing something that was previously "static" (or unexplained, such as the orbit of Mercury), is actually part of the phenomena for which there is an ordered explanation (explained by relativity).
Kepler was a Copernican, which at that time were also considered to be Pythagorean (since in antiquity some 'scientists' such as Aristarchus were heliocentric).  Kepler really wanted the heavens to move in perfect circles, but we owe it to his intellectual honesty that he came with his 3(?) laws.

Oh, I think that science can definitely capture _a_ picture of reality, but that picture is limited, and some scientists know that, and other scientists don't.  I didn't say that mathematics was illogical, but I guess that is a fair assumption, Russell and Whitehead tried to reduce all mathematics to logic and failed.  Godel came up and showed that it logically could not be done.  There are stories of professors who had spent their entire careers trying to reduce mathematics to logic breaking down and crying when they heard of Godel's achievement.  But what I was saying was there are irrational numbers and non-repetitive geometric shapes that are used by Penrose to show that there are sequences that cannot be predicted by any computer, including theoretical unlimited Turing machines.  I mean, look at Pi, or the square root of 2, here are numbers that are at the very core of basic mathematics, and yet we cannot 'define' them.  There are stories that the Pythagoreans suppressed the knowledge of irrational numbers, they were familiar with proportions in music, for example where the length of a string should be held to get an octave, and so irrational numbers were scandalous, something frightening and disturbing to the limited order for which the Pythagoreans were looking.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 24 Apr 2016 at 01:07
Oh, as far as philosophers or scientists being paid, the traditional division implied by Plato is that philosophers do it for the love (of wisdom), whereas sophists do it for the money.  Plato could do that,
because he was an aristocrat and probably independently wealthy.  Sophists may have been a little mercenary in their teachings, but one should remember that most of our teachings about them come from their critic, Plato.  As far as what I do, I don't need the (pitiful) money, the headache of teaching what is required instead of what I want, or the politics of the University.  What other people do, is their business.  As far as I am concerned the university teaches only indirectly about what philosophy really should be, the pursuit of the truth and living the good life (I don't mean frat parties.).  Scientists tend to get grants and thus at least pay for themselves.  but instead of looking for the truth, they too have a myopic agenda, pursuing their interests, even if it means suppressing others.  A scientist may wax poetic about the pursuit of science and following the truth, but still, the fighting is fiercest on the smallest territory, and when some steps on their toes, they will scream bloody murder.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote wolfhnd Quote  Post ReplyReply Direct Link To This Post Posted: 24 Apr 2016 at 02:24
You know sometimes I forget what we are talking about ;-)
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 25 Apr 2016 at 05:56
In ancient Greek, the word for Truth is aletheia, which means "not forgetting."  In Greek mythology there is the river of forgetfulness, "Lethe," so aletheia is the "a"- prefix privative plus "lethe."

Pindar Olympian Ode 10, (part)

"The son of Archestratos, winner at Olympia:
read out his name.
tell me where it's written
in my heart's ledger.
I forgot, and I owe him 
a honeyed song.
O Muse and Zeus' daughter,
Alatheia, look to the oversight:
redeem me from the charge
that I'm a liar, a hedger with my friends!"
translation by Frank J. Nisetich

I'm not calling you a liar;) but for the ancient Greeks forgetfulness was a kind of (unintentional??) deceit.  It was a very different world from ours.  How that relates to Pythagoras, I am not sure....:)
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 19 May 2017 at 22:40
We think that if we forgot something, we forgot something, such forgetting is unintentional, and it ought to be excused.  In Pindar Ol. 10, Pindar equates forgetfulness with lying, or hedging "with my friends."  It is a much more severe view of forgetfulness than we have.  To my amateur analysis, it seems like forgetting is intentional.  Overlooking, and either choosing to overlook and ignore, or at least a wanting to overlook, leading to it 'slipping one's mind.'  Again that is me, not Pindar.

Pindar was considered by the Church Father Clement of Alexandria (a Christian Neoplatonist), to be a Pythagorean.  Whether and to what extent that is true, I have no idea, Clement paints with a broad brush, and so it is probably safer to assume that that is not accurate, but it is probably accurate that Pythagoras of Samos looked upon truth in the very Greek way of aletheia or un-forgetting, and not as a factual correspondence between ideas and objects/things.  Besides Homer, Pindar is probably the earliest Greek author that we have complete works of.  So whereas we shouldn't think of him as a Pythagorean, coming so shortly after Pythagoras, and in what became a Pythagorean center (Thebes), he is a good example of what literature and literary figure was in those days, and he probably had an educated layman's understanding of Pythagoreanism at the time. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toyomotor Quote  Post ReplyReply Direct Link To This Post Posted: 20 May 2017 at 01:52
Originally posted by wolfhnd wolfhnd wrote:

You know sometimes I forget what we are talking about ;-)

Yes wolfhnd, and certain members make that very easy. Wink
I often wonder why I try.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 20 May 2017 at 22:21
Everything is related to everything else.  If you can just find the right string you might be able to untangle the knot.  
The ancients used the knot metaphor, the Gordion knot for which whomever untied it would be king, Alexander of Macedon cut it (and therefore, is not so great).  The thread of Ariadne used by Theseus for venturing into the labyrinth.  And the golden thread/chain by which Zeus held up the rest of gods in a tug-a-war from mount Olympus.

The Sufis are influenced by Pythagoreanism through Empedocles (Suhawardi) and by mystic tales of the golden thread which is used for their stories of succession, so and so was the teacher of so and so, and thus making a 'link' in the chain of discipleship.

These are typical mythic stories which have mystic significance, and would have been used by the Orphics and the Pythagoreans in their stories.  For example, Zopyrus of Heraclea, a Pythagorean from Heraclea Lucania, wrote an Orphic work called the "Net" of which we know the title.  Another work he wrote is the 
"Crater" (being probably both the vessel krater and the geological feature, crater), which is probably behind some passages of Plato's Phaedo.

My point is that we can deal with just surface phenomena, or we can recognize certain things as the tip of an iceberg, that they have an affinity to Pythagoreanism or Orphicism (mysticism) and that down below the surface they probably match up with Pythagoreanism, culturally influencing it, and being culturally influenced by it.  So even if we sometimes wander off into ancient Greek culture, we should still realize that we are working in the basis of Greek culture and thus the ground for Pythagoreanism.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote franciscosan Quote  Post ReplyReply Direct Link To This Post Posted: 19 Jun 2017 at 02:55
The Pythagorean Y

"The Pythagoric Letter two ways spread,
Shows the two paths in which Man's life is led.
The right hand track to sacred Virtue tends,
Though steep and rough at first, in rest it ends;
The other broad and smooth, but from its Crown
On rocks the Traveler is tumbled down.
He who to Virtue by harsh toils aspires,
Subduing pains, worth and renown acquires:
But who seeks slothful luxury, and flies,
The labor of great acts, dishonor'd dies."
-Maximinus


Edited by franciscosan - 19 Jun 2017 at 02:56
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