Plato's Less-Than Ideal Arithmetic

Philosophy is nothing more than footnotes to this guy, so they say.

Plato rightly deserves his central place in the Western canon.  He founded a school--the Akademia--from which we get both the word and the inspiration for the modern academy.  His insistance on the immorality of the soul so suffused the Greek-speaking world--including the authors of the New Testament--that Nietzsche dismissed Christianity as mere 'Platonism for the masses.'  Plato wrote over thirty dialogues that survive as masterpieces of argument and storytelling--a feat made all the more striking by the fact that back when Plato lived there were no paper mills, no printers, no bookstores, and no pens.  Plato pretty much set the aims, the methods, and the questions of philosophy for the next two thousand years.

But despite his heavyweight resume, Plato seems to have flubbed his math a bit.

Here's Plato calculating the exact amount that the philosopher's life is better than the tyrant's, from Book nine of the Republic.

Or if some person measures the interval by which the king is parted from the tyrant in truth of pleasure, he will find him, when the multiplication is complete, living 729 times more pleasantly, and the tyrant more painfully by this same interval.

What a wonderful calculation! And how enormous is the distance which separates the just from the unjust in regard to pleasure and pain!

Yet a true calculation, and a number which nearly concerns human life, if human beings are concerned with days and nights and months and years.

Plato's math, according to the footnotes in the second edition of the Grube translation of the Republic are "hard to follow."  Here's a try.  The tyrant experiences only two-dimensional pleasures, while the philosopher experiences three dimensional pleasures.  Additionally, the philosopher is nine times away from the tyrant in terms of pleasure, so the philosopher's pleasure is represented by a nine-unit cube, while the tyrant's pleasure is represented by a one-unit square.  But Plato flubbed things getting to the number 729, which was sacred to the Pythagoreans.  He miscounted the number of times removed the tyrant was from the philosopher (it should have been five, not six) and multiplied where he should have merely added.  Sadly, it turns out that the philosopher is only 125 times happier than the tyrant!

But we can't blame Plato for having trouble with his sums.  In Plato's time, before zero, before calculators, before arithmetic notation, math was decidedly hard to do.  Here's another example of Plato doing math, from the Republic, Book 8:

Now that which is of divine birth has a period which is contained in a perfect number, but the period of human birth is comprehended in a number in which first increments by involution and evolution, obtaining three intervals and four terms of like and unlike, waxing and waning numbers, make all the terms commensurable and agreeable to one another. The base of these with a third added when combined with five and raised to the third power furnishes two harmonies; the first a square which is a hundred times as great, and the other a figure having one side equal to the former, but oblong, consisting of a hundred numbers squared upon rational diameters of a square (i. e. omitting fractions), the side of which is five, each of them being less by one or less by two perfect squares of irrational diameters ; and a hundred cubes of three. Now this number represents a geometrical figure which has control over the good and evil of births.

What Plato's trying to say--again according the Grube Edition's footnotes--is that the human number is the product of three, four and five raised to the power of four, or (3*4*5)^4, which comes to 12,960,000.  This can be shown geometrically in two ways.  First, by the area of a square with the sides of 3600 or as a rectangle with sides 4800 and 2700.  Simple enough for us moderns.  But we have the ease of working with arabic numerals.  You can see how Plato--even Plato!--can be forgiven for messing up his math.

And you thought math was hard in high school!  Sacrifice a cock to Asclepius in thanks that you were never a math student in ancient Athens.

Three Things The Ancient Olympics Can Teach The Modern Olympics

The Olympics started in the seventh century before Christ, when young women completed a footrace to see who would become a priestess of Hera.  From these humble beginnings, the Olympics became the foremost of the four pan-Hellenic games, a ceremony so important to the Greek-speaking world that truces were called in order for athletes to arrive at the games safely.

These Olympics were not the familiar biennial show-case of brute physical competition that we know and love.  The race with the Olympic torch--now so engrained in our image of the Olympics that is has become a synecdoche for the festival--was an innovation brought in by Hitler in the 1936 games.  The gold, silver and bronze medallions replaced the traditional reward of an amphora of olive oil and a sprig of olive.  In the translation between ancient celebration and modern spectacle, some important aspects of the competition were lost.

Today we'll look at three aspects of the Ancient Olympics I think should be returned to the modern Olympics.

The first is Athletic Nudity.  The Greeks competed buck naked, slathered in olive oil.  The origins of this practice are murky.  Thucydides said that the Spartans "were the first to bare their bodies and, after stripping openly, to anoint themselves with oil when they engaged in athletic exercise."  Other sources point to the Athenians, whose government, after a guy tripped over his shorts while running, decreed that all sports should be conducted naked.


The explanation for the nakedness, according to John Mouratidis, was to either to "inspire fear or horrify their enemies."  He quotes L Bonafante suggesting that Hellenistic nakedness resulted from the "apotropaic use of the phallos, gestures against the evil eye, etc."  That et cetra is enticing--what other apotropaic uses can the phallos be put to?  But we must move on.

My reason for advocating a naked Olympics is transparent.  No one worries about the evil eye anymore, and there have been no notable short-tripping incidents in any Olympics I can remember.  But I think that athletic nudity would make the games more entertaining, more beautiful, and more exciting.  Especially the pommel horse.

A Pankration competition depicted on a vase.

The second ancient innovation is Pankration, which is Greek for "savage unrelenting beat-down."  Actually it is Greek for "all powers."  Pankration was a mix of boxing and wrestling, whose rules were easy to learn but hard to master.  Two men squared off against each other, trying to inflict so much pain against his opponent that he would submit by holding up his index finger.  The fighters could do anything to inflict this pain--barring biting and the gouging of the eyes, nose and mouth--and while they did not have weapons, in later years, the pankratiasts wrapped their fists with leather and metal.  You heard right, they could do anything.  They could kick the stomach or the testicles, they could inflict chokeholds and armlocks and brutal throws.  Many competitors died.

Pankration produced its heroes.  One man won a match even though he was dead.  Arrachion of Phigalia was in the Pankration finals for the third time running, and after an evenly-fought bout his opponent held him in a neck hold from which he could not escape.  Arrachion's trainer called out "What a fine funeral if you do not submit at Olympia!"  With that, Arrachion twisted his body around, kicking his opponent's foot, breaking it.  His opponent, in unbearable pain, gave up the match.  But Arrachion had broken his own neck and lay there, dead.  His limp head was donned with the laurel leaves of victory, and he became a legend across Greece.

Modern-day Mixed Martial Arts (or MMA) is similar to Pankration.  The sheer undaunted brutality of these competitions should be enough to inspire the "pity and fear" that Aristotle said good tragedy should inspire in us.  So why not let it become an Olympic sport?

The third innovation that the ancient Greeks can give the modern Olympics is not as cool as nakedness and bloodthirsty lawless death-matches.  It's poetry.

The ancient Olympic Games were closed by a competition among poets to see who could best praise the winning athletes.  These poems, called epinicians, were dreadfully popular, and have survived thousands of years.


In the modern Olympics, art competitions were held from 1912 to 1948, for sport-inspired architecture, painting, sculpture, music, and literature.  The competitions were called off because, in the opinion of the Olympic committee, the artists were all professionals.  The 1952 Olympics in Helsinki boasted a non-competitive art show, but without the agony of struggle, victory and defeat, the artistic side of the Olympics sputtered out.

Modern art is moribund, sealed air-tight in an ivory sarcophagus of academic rigor and bloodless cerebral muttering.  Our generation might be one of the first in human history for which poetry has no popular charm--and the fault is the poets, who insist on being daringly arty, when they should work to be beautiful.  A poetry competition celebrating the accessible agony of athletic competition, done in all the languages of the world, would help a little in giving feeling back to poets.

Day Six: Gobekli Tepe To Gaziantep, The Old To The New. The Amazing Awesome Anatolian Road Trip Diary

This is day six of the Amazing Awesome Anatolian Road Trip Diary.

We turned off the Urfa highway and suddenly the modern parade of gas stations and stores fell away, revealing a landscape of mud-brick huts, lavender-scarfed peasants, green irrigated farmland, with the hard dry roll of unimproved hills in the background.  The asphalt quickly turned to dirt and rocks.  Barefoot children played in the fields while their mothers worked in the heat.

This could have been almost anywhere in the plains surrounding Urfa.  And in some ways it felt like it could have been any time, too.  Peasant children had probably been playing in these fields for thousands of years, ignoring the tides of kings and princes who had claimed the Urfa plain.

The car clattered up hills, and soon the village shrunk in the background.  Our poor over-worked compact car, stuffed with five full-grown humans and their baggage, struggled.  Soon the winding hill leveled out, and the road bulged into a parking lot.

We stepped out onto a high, wind-blown hill.  Here was Gobekli Tepe—the oldest temple on earth, built over 11,000 years old.

We were met with a middle aged man named Veyal Yildiz, whose family has farmed Gobekli Tepe for generations.  Our Turkish friend spoke with him a while, and we were worried that we would not be allowed inside—Gobekli Tepe is no museum, but a working archeological site where the ruins of dead civilization are day by day being pulled from the earth.  After five minutes of greetings, where are you froms, and what is your names, Yildiz gave a nod and led us to the excavations.

Twenty circle-shaped structures have been discovered under Gobekli Tepe’s dry soil, and four have been excavated.  Large sculpted limestone monoliths three meters high poke from the dry ground, most of them shaped like a pot-bellied T.  They are arranged in circles, with two pillars standing in the center of the circles.  Many of the pillars are decorated with carvings eked out of the rock with flint tools. 

A stone circle, older than bread.  Photo by Jenna Staff.

This site is older than Babylon, older than Stonehenge, older perhaps than agriculture itself.  The people who made it were probably hunter-gatherers who had not yet resigned themselves to settled life and government.  Somehow they dragged the eight-ton slabs of rock up from the quarry a hundred meters away, and then shaped the rock, with only hand-made flint tools.

A path ringed its way around the four open excavations.  Veydal pointed out the interesting carvings.  Here are lizards, foxes, sheep, donkeys, snakes, and boars; nets, pelts of animals, and birds.  On a number of the T-shaped rocks, hands clasped around the front of the spines, and at the sides, you could make out the crooks of bent arms.

At first the rocks just looked like rocks.  But slowly the monoliths took on human characteristics.  The tops of the Ts become the nods of massive heads.  The hands clasping the spines of the T seemed to be resting on bellies, the foxes around the base were pelts covering the privates.  Here, Veyal pointed to two monoliths standing next to each other.  “They think that this one is a man, and this one is a woman.”

We walked to the very top of Gobekli Tepe and sat down to rest in the heat.  A wish tree hung with scraps of plastic bags shaded us from the heavy sun, and four graves piled with loose stones shared the shade with us.  We looked out across the dry landscape, and I thought about the people who built this mound.  No one knows who they were.  No one knows what language they spoke.  No one knows why they spent so much time dragging stones up a mountain.

Only five percent of the whole 22-acre site has been excavated.  Klaus Schmidt, the site’s devoted archeologist, thinks that even after fifty years of work we will still only know the vaguest outlines of this huge temple.

We were the only people there.  We saw no cars.  No tour buses.  Veydal said that about five people a day come here, to Gobekli Tepe, the oldest sacred place on earth.

-&-

A new black-asphalt three-lane toll road took us from Urfa to Gaziantep, the third largest city in Turkey.  As we dove into the city we encountered the worst traffic we’ve seen since Istanbul.  Every one of the million citizens of Gaziantep seemed to push their way through Istasyon Caddesi, Gaziantep’s pulsing artery of traffic and trouble, the cars merging and honking and swerving before suddenly stopping to let pedestrians hurry across the road.

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Our GPS told us to take a left down a road clogged with construction.  We circled around, looking for another route, but this too was blocked with earth moving machines and torn-up cobblestones.  We parked the car at a random parking lot and lugged our bags through the busy streets, reluctantly taking a room at the first hotel that we saw.  Our room was decorated in the style of a 1970s-era Turkish pimp, and the air heavy with the stale smell of cigarettes.

There were sights to see, of course.  Why else would we come?  The old archeology museum stood proud and ignored across the street from the sports stadium.  The museum was had once boasted some of the finest mosaics in the world, but these had been moved to the new museum, so now it was a lonesome place, with emptied, echoing spaces, informational plaques whose corresponding objects were missing, plaster marks on the polished floor.

Gaziantep is arguably one of the oldest continuously inhabited cities on earth.  People first settled here in the third millennium B.C., and since then they have been trading, eating, marrying and dying, leaving behind the litter of their life which was then unearthed, identified, and set under glass for display.  We looked at the old cut-stone sarcophagi, the piles of old coins, the grave stele, the old glass-ware, the broken potsherds, the marble heads.

A lonely corridor was lined with grave stele from a half-dozen passed civilizations.  The rocks showed gods and warriors who had not been celebrated or worshipped for thousands of years.  Carved into the rock, their features worn by rain and the indifference of time, they eat, drink, banquet, fight, hold emblems and pieces of food and weapons, cups, trinkets and grapes.  Sometimes I caught a particularly fine detail—a eye that lifted with joy, a hand delicately holding a trident.

Kings enjoying themselves.  Photo by Jenna Staff.

But nobody else was at the museum.  I was a little indignant.  The stadium next door is busy with men eating kebabs and talking about sports, but here, where the monuments of history stand, there is silence. 

But then again, why should people care about the past, when the past is dead and they are alive?  Like the figures on the stele, they too must fight and drink and feast and die.  When the stele and the statues in the museum stood alive in the open air, they were not monuments, they were pieces of daily life.  The people of their time appreciated them with the same lazy eyes with which we now look at billboards and street signs.  So why should the musty virtue of antiquity make these cracked slabs of rock suddenly worthy?  Why should I expect people to turn their backs on the fun of their lives to look at dusty rubble?

After the old museum, we went to the new museum a twenty minute walk away.  We plodded along the tramway, passed under the train station, and skirted the slightly sketchy neighborhood around the train station.  Then out of the obscurity of the low-rent apartments, the mass of the museum imposed itself, huge and white, not yet even a year old.

Most of the mosaics had been rescued from Zeguma.  Zeguma was a Greek city perched on a crossing of the Euphrates river.  It became rich with trade, and over the centuries its citizens became rich, built their villas and their fountains, and laid their houses with mosaics of startling beauty.  Their patron god was Fortuna, the goddess of luck, and so the wheel of fortune repeats itself along the border of mosaic after mosaic, a tumbling interlocking circle.  Zeguma was taken by Rome and the city grew even more.  But the wheel of fortune turned, Rome became weak, and in the third century Zeguma was overrun by the Sassanid Empire, burned, its greatness lost.  People lived there, but they lived in the shadow of a great city, people unable even to remember the distant greatness of their ancestors.

The Wheel Of Fortune.  Photo by Jenna Staff.

The city wallowed in obscurity until the 1990s when archeologists discovered the city’s well preserved frescoes and mosaics.  But the careful excavation of the archaeologists was slow—faster were the antiquity traffickers who ravaged the new discoveries before they could be preserved.

Fortune was still crueler to Zeguma, the city who had once worshipped her.  A new dam was built, and the city was set to be flooded.  An international consortium of archaeologists flocked to the city to rescue what artifacts they could, finding seals and statues, lifting frescoes and tiles—but when the dam was finally opened over three tenths of the city was submerged and destroyed.

Those mosaics that had been salvaged were moved here, to the new museum in Gaziantep, and they stun the visitor with their incredble craftsmanship.  They show the strange gods of Asia Minor in all their glory and folly.  Oceanus and Tethys pose, swimming with dragons and snakes.  Europa is eternally being dragged off with Zeus the bull.  Eros and Psyche sit on a couch, and Aphrodite is birthed from a clam-shell.  These fine works were once on the floors of dining rooms and bedrooms, stepped on by the sandals of visitors, submerged with fountain water.  Now they were on the wall of a museum, to be admired.

Oceanus and Tethys pose.  Photo by Jenna Staff.

We see these gods marring, posing, eating and arguing.  Eros and Psyche sit on a couch and the expressions on their faces look like they are sitting at home and they can’t exactly decide what to watch on TV.  Eros has his hand lightly on Psyche’s back, and Psyche has her left hand open imploringly, like she’s just about to suggest that they put on a rerun of Olympus’ Got Talent.

They are like us.  And I imagine that the long-dead city of Zeguma must have once been a lot like the city of Gaziantep:  bustling, commercial, and hot; the citizen’s lives rich with traffic and trouble, the people only sometimes pausing to admire the work of their mosaics and fountains and frescos.  And then they move on to the real beauty of their daily lives.

The Amazing Awesome Anatolian Road Trip Diary continues...

You can also get the whole series as an e-book.

Spartan Jokes

The past is a broken, forgotten thing. We have only small pieces of it, which, with some effort, we might stick together roughly. Then we might find the shape of the past--but not its color, or heft.

Just think of this:  We have lost nine-thousand-nine-hundred-and-ninety-nine jokes out of every ten-thousand that have ever been told.  That means someone sometime has told the funniest joke in history.  And we can't laugh at it anymore.

But even if all the jokes of antiquity were preserved, we might not be able to understand them.  What will make one person laugh until they cry will make another merely scratch their head.  So much more with the wit of the ancients.

Take the Spartans, please!

Plutarch admires the Spartans for their dry, restrained wit.  Though the jokes he records do not exactly leave you rolling on the floor, laughing.

Here's one (slightly edited):

One day a Spartan was invited to hear a man imitate the nightingale.  He said: "I won't waste my time.  I have heard the bird with my own ears."

Here's a second:

Another Spartan, seeing men seated on stools in a privy, said: "May I never sit where I cannot give place to an elder."

Could you stand a third?

A youth, when someone promised to give him game-cocks that would die fighting, said, "Don't do that, but give me some of the kind that kill fighting."

Banter!

If you want some more very old jokes (including some that are actually funny), check out this post about the world's oldest jokes.