The scholarship on whether Pythagoras wrote "Beans, Beans, the Musical Fruit" remains inconclusive.

February 22, 2007 9:40 AM

Everything you know about Pythagoras is wrong (except the bit about the beans). Less the golden-thighed Einstein of the Ancient World and more the L. Ron Hubbard of Magna Graecia. [Last link has some rude words]
posted by Kattullus (41 comments total)

Whole number fetishist, in denial of zero.
posted by Burhanistan at 9:43 AM on February 22, 2007 [1 favorite]

LOLNUMEROLOGISTS

Who thought Pythagoras was Einsteinian? I've only ever heard 3 things about him:

1) Got lucky by having a Theorem named after him
2) Harmonic series
3) Killed a man for discovering irrational numbers (oh the irony)

I'll go read the article now to discover which of these warrants golden thighs and is wrong.
posted by DU at 9:56 AM on February 22, 2007

Interesting that, in the Moby Dick line about the Pythagorean maxim, the two winds explicitly mentioned and jokingly implied by the phrase 'wind from astern' move in exactly opposite directions.
posted by matthewr at 10:00 AM on February 22, 2007 [1 favorite]

Parts of this are ridiculous:

Mystic, yes – or at least the leader of a religious cabal which believed in transmigration of the soul and was disciplined enough to take political power in several cities of southern Italy. But mathematician, no. Not at any rate if, with Russell and Penrose, we think of a mathematics based on deductive proof,

The tone there is that Pythagoras was a religious nut and not a scientist. First of all, for Pythagoras to believe in the transmigration of the soul would be to put him ahead of his time, as that particular religious philosophy would not dominate Europe (and the world) for another 1000 years. It may sound silly to the enlightened scientific world now, but it obviously wasn't silly during his time or for quite some time thereafter, even in the most academic circles.
posted by Pastabagel at 10:02 AM on February 22, 2007

I just like the fact that we've run out of A-List historical figures to desconstruct and we're now on to the benchwarmers of history.

"You remember the name Pythagoras vaguely from somewhere in elementary school? Yeah, well he isn't who you think he is!"

Next on the list: Despite being a so-called "Black Fresian", Beaucephalus wasn't actually black!
posted by tkolar at 10:06 AM on February 22, 2007 [1 favorite]

Pastabagel: I tend to agree. It's easy to look back and pick apart people like Pythagoras or Freud and dismiss them as nutty. But the fact is they were pioneers working in previously uncharted territory, so their own first maps are likely to have some human artifacts. How many of us are exploring the unknown?
posted by Burhanistan at 10:09 AM on February 22, 2007

I thought the whole cult aspect was pretty well known.

Hell, in high school we used to joke about prep for math tests including (or more likely consisting of) "abstaining from beans".
posted by dreamsign at 10:09 AM on February 22, 2007

I thought all the old scientists and philosophers were considered pretty crazy by modern standards. From Socrates to Newton. In the future people will talk about how Neils Bohr was a raving loon.
posted by damn dirty ape at 10:13 AM on February 22, 2007

Well, I guess once you see that you can model some aspect of the world with numbers, that it's very tempting to try it every where to see if it fits. You can hardly blame them for not being entirely systematic or logical about it.
posted by empath at 10:26 AM on February 22, 2007

I am btw, a bit confused how the Greeks figured out the 'ratios' of tones.

Did they know about sound waves? Or was this ratio referring to something else?
posted by empath at 10:27 AM on February 22, 2007

The tone there is that Pythagoras was a religious nut and not a scientist etc

Well, whether or not believing in the transmigration of the soul put him ahead of his time, which I doubt, it doesn't really affect the point that he was probably a mystic rather than Mr Geometry.

It's easy to look back and pick apart people like Pythagoras or Freud etc

Slight telescoping of historical difference there. According to the article, Pythagoras wasn't a pioneer working in uncharted territory, he was a religious figure who got assimmilated into the history of maths by later traditions. Also, not as relevantly, Freud was not exactly 'working in previously uncharted territory' - as he said, psychoanalysis was born middle aged, many poets etc had similar insights before him. (See eg The Unconscious Before Freud.)
posted by Mocata at 10:28 AM on February 22, 2007

Also, not as relevantly, Freud was not exactly 'working in previously uncharted territory' - as he said, psychoanalysis was born middle aged, many poets etc had similar insights before him.

In this analogy then, Pythagoras is the poet that predated Freud, who would be analogous to Aristole, or perhaps Euclid.

Pythagoras was born 50 years before Plato, 100 years before Aristotle, and 150 years before Euclid. And he was saying basically that numbers are everywhere and can define everything. Guess what modern mathematics tells us?
posted by Pastabagel at 10:50 AM on February 22, 2007

First of all, thanks for this, Kattullus. Reading this meant a lot to me, if only to remind of things I really enjoy thinking about. We need more of this around here.

Pastabagel: "The tone there is that Pythagoras was a religious nut and not a scientist. First of all, for Pythagoras to believe in the transmigration of the soul would be to put him ahead of his time, as that particular religious philosophy would not dominate Europe (and the world) for another 1000 years. It may sound silly to the enlightened scientific world now, but it obviously wasn't silly during his time or for quite some time thereafter, even in the most academic circles."

I tend to agree. However, file me in the "we don't know a damned thing about Pythagoras, only that a crew of people claiming him were political agitators" category. I happen to think that the author of this piece on Pythagoras is correct to point out that our contemporary portrait of the man is probably silly, but I also feel as though he's letting certain modern prejudices get in his way. He quotes this passage from Aristotle's Metaphysics at one point:

"Marriage, they said, is five, because it is the union of male and female, and according to them the odd is male and the even female, and five is the first number to be generated from the union of the first even number, two, and the first odd number, three; for the odd is for them (as I said) male and the even female."

I have a feeling that Mr. Burnyeat quoted this section thinking, as people often do, that Aristotle means to ridicule the Pythagoreans by recounting these beliefs. Nothing could be further from the truth. There is a fundamental misunderstanding of Aristotle's tone nowadays-- we tend to think that he is being much more derisive and derogatory than he really is, and we tend to repay him by being dismissive toward him and speaking loudly and at length about his supposedly legion errors and mistakes.

However, it should be noted that, among writers, Aristotle is probably the most open-minded who ever lived. He does tend to speak about what other people think, but he is very careful when he does so to do them justice. In this case, he speaks about the Pythagoreans because he really is concerned about the nature of numbers. He may not agree with them in the end, but it is clear from his work that he would not mention them if he did not think that they had something illuminating to say.

In our era, when Dedekind's silly "number line" has utterly ruined our ability to think about numbers in a realistic way, it's hard for us not to laugh off anyone who speaks of numbers as being different from each other, as having their own characteristics, or as having connections to the world at large as some sort of mystical nutbar. This difficult is not helped by the fact that ancient greece was teeming with mystical nutbars. However, we should try very hard to rise above the historical circumstances we find ourselves in and see that there was a great deal of significance in the fanciful way of speaking about numbers that the Pythagoreans had, and even more meaning in the co-opted version invented by the Platonists.
posted by koeselitz at 11:12 AM on February 22, 2007 [1 favorite]

What did the star sing, and an indeterminate number of "careless" Muses hear? I never understood that part.
posted by goetter at 11:28 AM on February 22, 2007

First of all, thanks for this, Kattullus... We need more of this around here.

Heartily seconded; an excellent post!

Pastabagel: Are you claiming you know more about Pythagoras than Walter Burkert?

I was particularly glad to discover Burkert's preeminence in this field, because I've long been a fan of his Greek Religion. He's one of those writers who leaves me in awe of the depth and thoroughness of his research.

An interesting quote from the last ("beans") link:

"Beans, black and white, were, according to this interpretation, the means of voting in Magna Græcia, and "Abstain from beans" would, therefore, mean merely "Avoid politics"-a warning which, we know, was warranted by the troubles in which the school was involved on account of the active share which it took during the founder's lifetime in the struggles of the popular with the aristocratic party in Southern Italy."

I have no idea whether that's true, but it's interesting to think about.
posted by languagehat at 11:48 AM on February 22, 2007

Oh, yeah? Well that Cartesian plane guy was much worse!
posted by nofundy at 11:52 AM on February 22, 2007

The tone there is that Pythagoras was a religious nut and not a scientist. First of all, for Pythagoras to believe in the transmigration of the soul would be to put him ahead of his time, as that particular religious philosophy would not dominate Europe (and the world) for another 1000 years. It may sound silly to the enlightened scientific world now, but it obviously wasn't silly during his time or for quite some time thereafter, even in the most academic circles.

You are wrong. Pythagoras definitely believed in the transmigration of the soul, but not into the heavenly realm, but into other objects. Eating no beans refers to their association with this transmigration. Empedocles (Kirk Raven Shofield 2005, fragments 414-419) believed the same thing for the same reasons.

That having been said, it has been well known for a while that Pythagoras wasn't particularly intellectually renowned and much more important as a political figure; we even have fragments to that effect, KRS 256, 257, and 280.

He was regarded as a divine figure (the "Hyperborean Apollo"), who possessed divine attributes, including the golden thigh as well as an ability to speak to snakes and rivers. (KRS 273, 274) The source of his political influence was held to be his divine charisma and ability to convince people, something like the idea expressed in the Pentecost story. (269, 270)
posted by nasreddin at 12:12 PM on February 22, 2007

But you are right, it is anachronistic to impose a worldview like ours on someone who clearly believed his intellectual abilities came from his divinity.
posted by nasreddin at 12:14 PM on February 22, 2007

This is so old that even Voltaire made fun of Pythagoras.
posted by nofundy at 12:30 PM on February 22, 2007

Pastabagel: Are you claiming you know more about Pythagoras than Walter Burkert?

No, but I certainly know more about Burkert than Pythagoras.

Seriously, where did this come from? I wasn't taking issue with Burkert, but rather with the author of the review. And even then I was simply pointing out that to label him a mystic at a time when many intellectuals were also mystics is disingenuous and a bit unfair as it implies something entirely different today than it did then. Furthermore, Pythagoras's role in mathematics was more that of a visionary than a rigorous practioner. The notion that numbers and their relationships to one another somehow permeated all things was revolu. But again, neither of these is a criticism of Burkert, but rather a handful of the reviewer's statements in the review.
posted by Pastabagel at 12:30 PM on February 22, 2007

Man, I wish I was an ancient Greek. Barely anything was invented. You could get in the history books for simple stuff like making a screw or writing a play with more than two characters. These days you have to like, cure cancer.
posted by Durhey at 12:34 PM on February 22, 2007

languagehat beat me to the "abstain from politics" explanation of the beans, which has always been my favorite.
posted by anotherpanacea at 12:48 PM on February 22, 2007

He may have been a freak, but I heard he could play a mean triangle.
posted by Muddler at 1:01 PM on February 22, 2007 [1 favorite]

I was simply pointing out that to label him a mystic at a time when many intellectuals were also mystics is disingenuous and a bit unfair

The point of the review (which is Burkert's point) is not that Pythagoras was a mystic and therefore a know-nothing we can all have a good laugh at, but that he was a mystic and not a mathematician. Attributing mystic properties to numbers was perfectly normal at the time, but it did not make you a mathematician.
posted by languagehat at 1:06 PM on February 22, 2007

In our era, when Dedekind's silly "number line" has utterly ruined our ability to think about numbers in a realistic way, it's hard for us not to laugh off anyone who speaks of numbers as being different from each other, as having their own characteristics, or as having connections to the world at large as some sort of mystical nutbar. This difficult is not helped by the fact that ancient greece was teeming with mystical nutbars. However, we should try very hard to rise above the historical circumstances we find ourselves in and see that there was a great deal of significance in the fanciful way of speaking about numbers that the Pythagoreans had, and even more meaning in the co-opted version invented by the Platonists.

Reading this comment, I couldn't help but think of synaesthesic savants who describe their experiences with numbers in similar terms, like Daniel Tammet, and wonder if Pythagoras' mathematical abilities result from a similar neurological affect.
posted by Blazecock Pileon at 1:09 PM on February 22, 2007

"What were the beliefs and practices of the historical Pythagoras? This apparently simple question has become the daunting Pythagorean question for several reasons. First, Pythagoras himself wrote nothing, so our knowledge of Pythagoras' views is entirely derived from the reports of others. Second, there was no extensive or authoritative contemporary account of Pythagoras. No one did for Pythagoras what Plato and Xenophon did for Socrates. Third, only fragments of the first detailed accounts of Pythagoras, written about 150 years after his death, have survived. Fourth, it is clear that these accounts disagreed with one another on significant points."

Way back when I was taught in my history of Math course that he was not widely believed to have been a real person in said community. That Nichomacus in early accounts was speaking more to the myth of the cult of Pythagoreans before being exterminated. Funny then seeing all this talk about who the real Pythagoras was...
posted by kigpig at 1:12 PM on February 22, 2007

Which is to say I have doubts that being a mystic necessarily excludes one from being a mathematician per se. The Golden Ratio, for example, has long held appeal to religious mathematicians, due to its ubiquity in nature.
posted by Blazecock Pileon at 1:13 PM on February 22, 2007

Interesting that in all the palaver about the Pythagorean abjuration of beans, no one bothers to point out that, aside from meats, beans are the canned food most likely to give you botulism, which probably implies you could get botulism from cooked (and perhaps uncooked) beans sitting around more easily than from other vegetable matter-- which would seem not to be beyond the experience or powers of observation of the Pythagoreans, if true.
posted by jamjam at 1:46 PM on February 22, 2007

Not from uncooked, and only from cooked if they're stored in a low-acidity, low-oxygen environment, such as is present in home canning, or under oil with garlic in your refrigerator.

I don't think that the Greeks in the 5th century B.C. did much home canning. If somehow they did, adding honey or lemon would prevent spoilage.
posted by goetter at 2:29 PM on February 22, 2007

languagehat: "The point of the review (which is Burkert's point) is not that Pythagoras was a mystic and therefore a know-nothing we can all have a good laugh at, but that he was a mystic and not a mathematician. Attributing mystic properties to numbers was perfectly normal at the time, but it did not make you a mathematician."

And that point is well taken. But my own (probably small) disagreement with the article stems from this: I don't believe there is such an isolated field as "mathematics." The chief lesson Plato seems to have borrowed under the name of 'Pythagoreanism' was that mathematics is part and parcel with understanding the fundamental nature of the universe; one recalls, for example, his Socrates' admonishment to Meno that he didn't understand virtue because he didn't know enough geometry. I'm inclined to agree; I have a feeling, as bold as it may sound, that a true mathematician has to be either a mystic or a philosopher of some kind.

At least Heidegger remembered this, but hardly anyone else does. The number one refers to the fundamental experience by which human beings know the world: we separate a thing out, we know it as one before we name it, before we even experience it as such. The number two is a word for another such experience which has an interesting but different tenor to it; it adds something to the world we experience, and it is a fundamental feature of our spiritual landscape, because it introduces the fact to us that one thing can be not-another thing. The number three is yet another; it has a very particular quality, because it is the moment at which we realize the aspect of many that is beyond dual.

Because numbers are part of the way we see the world, and the contents of mathematics are some of the only things most of us take part in daily without deduction or sensual perception of them, I think that a little mysticism is warranted. Certainly more mysticism than is granted them now; we hardly know whether we should treat numbers today as anything more than markers on an imaginary line. They are assuredly more.

Blazecock Pileon: "...I couldn't help but think of synaesthesic savants who describe their experiences with numbers in similar terms, like Daniel Tammet, and wonder if Pythagoras' mathematical abilities result from a similar neurological affect... Which is to say I have doubts that being a mystic necessarily excludes one from being a mathematician per se. The Golden Ratio, for example, has long held appeal to religious mathematicians, due to its ubiquity in nature."

That's a very good point. Once again, I too have a feeling that there might be something in mathematics that lends itself to the mystically-inclined.
posted by koeselitz at 3:13 PM on February 22, 2007 [2 favorites]

Burkert notwithstanding, my own take on the beans issue has to do with beans creating gas, and pneuma meaning both spirit and breath (and, yes, flatulence), and so it becomes a plea against cannibalism. So to speak. Transmigration of souls fits in there somehow as well.

I've never been able to sell this idea - the low lifes tend to snigger, the high brows to sneer - but what the hell, I've never heard anyone else put it forward. (Which is not to say they haven't, I've just never heard of it.)
posted by IndigoJones at 3:30 PM on February 22, 2007

So you're saying in a couple of millennia L.Ron Hubbard will be remembered fondly and have theories named after him?
posted by dances_with_sneetches at 4:07 PM on February 22, 2007

/throws down the "hermes trismegistus" gauntlet./
posted by oigocosas at 4:37 PM on February 22, 2007

Pythagoras is thought by some to be the founder of the movement that spawned the Essenes, a movement which would have added the Jewish element to the Orphic mysteries. Essene scholar, Martin A. Larson, believes that the Essenes were basically Jewish Pythagoreans who incorporated the resurrected soter of the ancient world into the messiah concept, which gave us Christianity, by way of the founding Teacher of Righteousness, who was crucified, and whom Jesus was emulating.
posted by Brian B. at 4:43 PM on February 22, 2007

Medical historians have suggested that the beans prohibition referred especially to broad or fava beans. In Mediterranean populations (or people of Mediterranean descent) a sex-linked genetic disorder called G6PD deficiency causes the eater of fava beans to have an attack of fever (a hemolytic crisis, as with malaria).

There is an entire website on modern favism. It doesn't kill you, so it hasn't bred out.

In antiquity, beans were poor people's main protein source; the Pythagoreans either were poor or adopted a philosophically austere lifestyle. They might consider eating beans.
posted by bad grammar at 5:23 PM on February 22, 2007

I don't think that the Greeks in the 5th century B.C. did much home canning. If somehow they did, adding honey or lemon would prevent spoilage.
posted by goetter at 2:29 PM PST on February 22

You might want to consider signing up for a refresher course in food safety, goetter-- and a little more food history might not be amiss, either.

If the Greeks had added honey to their cooked beans they could well have been creating a problem where none existed previously. According to the Mayo Clinic:

Infants younger than 12 months are at risk of infant botulism from eating honey. Infant botulism is a rare but serious form of food poisoning.

Honey is a known source of bacterial spores that produce Clostridium botulinum bacteria. These bacteria are typically harmless to older children and adults. But when ingested by an infant, these bacteria make a toxin that can cause infant botulism. It's unclear why this occurs in infants and not in older children or adults.

Lemons, on the other hand, evidently "only reached the Mediterranean toward the end of the 1st century AD, when the Romans discovered a direct sea route from the southern end of the Red Sea to India." (From The Oxford Companion to Food, p.449.)

I mentioned botulism from canned beans to indicate a surprising relationship between botulism and beans. As I assume you must know, botulinum spores can survive boiling for some time, and contaminated food must be raised to a temperature of 250F for at least 3 minutes to be sure of killing them, a far higher temperature than the Greeks would have been able to reach by simple boiling. The fact that they are the second most likely source of botulism from canned food implies they could often be contaminated with the spores in an uncooked state.
posted by jamjam at 5:27 PM on February 22, 2007

I am btw, a bit confused how the Greeks figured out the 'ratios' of tones.

Did they know about sound waves? Or was this ratio referring to something else?

They're referring to ratios of string lengths.

If you sound an unstopped string, and then sound it stopped at its halfway point (i.e. a 2:1 length ratio), you'll hear notes an octave apart. If you sound an unstopped string, and then sound it stopped 1/3 of the way up (i.e. a 3:2 length ratio), you'll hear a perfect fifth. 5:4 is a major third, 9:8 is IIRC a major second.

It turns out that a 2:1 string length ratio also produces a 2:1 frequency ratio — it's a side effect of the physics of strings — but they didn't know about that part yet.
posted by nebulawindphone at 6:03 PM on February 22, 2007

Infant botulism from the spores in honey is a separate problem. Infants shouldn't consume honey for that reason. Food preserved in honey is otherwise safe, because the bacteria won't reproduce in strong sugar solutions. The Greeks preserved raw quince in just this way.

C. botulinum spores are everywhere. It's a common soil bacillus. Adults can safely ingest the spores. Happens every time I venture into the garden for a snack, I'm sure.

I didn't know that about lemons. Thanks.

My point was that sealed, anaerobic cans of beans - the locus of C. botulinum reproduction that makes botulism the hazard that you cite, and that makes the "botulism cook" time/temperature necessary - most likely didn't exist in 500 BC, so I doubt that the Pythagoreans associated them with either dead babies or dead mathemagicians.
posted by goetter at 6:22 PM on February 22, 2007

1. The L. Ron Hubbard analogy was mainly to indicate two things: 1) That Pythagoras was a cult leader & 2) That Pythagoras seized temporal power through his command of his cult. Who knows, maybe L. Ron Hubbard will end up being revered as the greatest man of our times. Can't say I find it particularly likely, but things sometimes have a funny way of turning out. I used Einstein as the modern archetype of the scientific genius. I used this analogy to summarize the main thrust of the article .

2. Oh, and DU, guess what, everything you knew about Pythagoras turned out to be wrong! :) (except the bit about his luck, which is a value judgment and therefore debatable... I mean, a fat load of good it did him while he was alive).

3. The "except" link is a debunking of the "abstain from beans" - favism link.

4. As to mysticism and numbers... well, I'm irreligious, so mysticism mostly has value to me on an aesthetic level. For instance, I found this passage by koeselitz laden with meaning:

"The number one refers to the fundamental experience by which human beings know the world: we separate a thing out, we know it as one before we name it, before we even experience it as such. The number two is a word for another such experience which has an interesting but different tenor to it; it adds something to the world we experience, and it is a fundamental feature of our spiritual landscape, because it introduces the fact to us that one thing can be not-another thing. The number three is yet another; it has a very particular quality, because it is the moment at which we realize the aspect of many that is beyond dual."

While 'males are odd numbers and females even numbers' is trite and meaningless to me.

Apophenia (pattern recognition) is a subject of endless fascination for me. The way people can construct, say, the picture of a goat out of the random scattering of stars. I have a vague conjecture that good art activates apophenic impulses in the brain. Stendhal syndrome would then be an overloading of the parts of the brain that involve the recognition of patterns. I believe sacred geometry is a function of the same neural wiring. I find the Chartres labyrinth immensely beautiful and I intend to trace it in the proscribed manner one of these days, even though I wouldn't be doing it out of a spiritual impulse.
posted by Kattullus at 6:43 PM on February 22, 2007

My point was that sealed, anaerobic cans of beans - the locus of C. botulinum reproduction that makes botulism the hazard that you cite, and that makes the "botulism cook" time/temperature necessary - most likely didn't exist in 500 BC

I would be highly interested to read any source you may care to c/site which claims that the bottom of a pot full of cooked beans is too aerobic for Clostridia to grow there.
posted by jamjam at 7:07 PM on February 22, 2007

If beans were as dangerous as all that back in the day, then presumably lots of people would abstain. Why single out Pythagoras?
posted by IndigoJones at 12:40 PM on February 23, 2007