seek echo

The Antikythera Mechanism... in Lego

2012-01-18T03:25:00.000-08:00

I like the idea of recreating things like this in Lego. It brings it within reach. Anyone who can afford to order the bricks and cogs could, in principle, try it. In 2010, a fully-functional replica of this 2000-year-old analogue computer was constructed out of Lego by Andrew Carol. It predicts the year, date, and time of future solar and lunar eclipses accurately to within two hours. All using plastic gears.

The machine has been studied in great detail, and we now know that it predicted eclipses. I've already blogged it twice before (first, second).

These Nature videos give us more detail on the mechanism itself:

more circles

2012-01-08T13:04:00.000-08:00

In this one, you're told that the area coloured yellow is the same as the area coloured orange, but the challenge is to prove it:

irrational

2012-01-08T12:56:00.000-08:00

I like the next one. Here you have five circles of radius 1, and area pi, and a small circle.

The challenge is to find which area in the figure is rational:

same area

2011-12-28T05:45:00.000-08:00

It somehow seems remarkable that the orange area in this diagram is equal to the yellow. One so curved, one so straight.

Knowing a few simple things (mentioned in the last post) it is not hard to prove their equality.

circles and squares

2011-12-28T04:27:00.000-08:00

Let's say the area of the small circle is

π.

So, because area =

πr²,

the radius must be 1.

The small square has a side length of 2r = 2.

So its area is 4.

Its diagonal, by Pythagoras' theorem, is √(2² + 2²) = √8.

So, the middle size circle has a radius of ½√8.

And the area of that circle is (½√8)²π = 2π.

The middle size square has an area of √8 x √8 = 8.

So...

each circle is twice the area of the one smaller than it.

And...

each square is twice the area of the one smaller than it.

That seems really neat to me!

thyrsus

2011-11-19T03:07:00.001-08:00

The thyrsus was a staff of giant fennel covered with ivy vines and leaves, topped with a pine cone.

Baudelaire:

What is a thyrsus? According to the moral and poetical sense, it is a sacerdotal emblem in the hand of the priests or priestesses celebrating the divinity of whom they are the interpreters and servants. But physically it is no more than a baton, a pure staff, a hop-pole, a vine-prop; dry, straight, and hard. Around this baton, in capricious meanderings, stems and flowers twine and wanton; these, sinuous and fugitive; those, hanging like bells or inverted cups. And an astonishing complexity disengages itself from this complexity of tender or brilliant lines and colours. Would not one suppose that the curved line and the spiral pay their court to the straight line, and twine about it in a mute adoration? Would not one say that all these delicate corollæ, all these calices, explosions of odours and colours, execute a mystical dance around the hieratic staff? And what imprudent mortal will dare to decide whether the flowers and the vine branches have been made for the baton, or whether the baton is not but a pretext to set forth the beauty of the vine branches and the flowers?

foreignness

2011-11-19T02:45:00.000-08:00

Dionysos:

"His origins are uncertain, and his cults took many forms; some are described by ancient sources as Thracian, others as Greek. In some cults, he arrives from the east, as an Asiatic foreigner; and in others, from Ethiopia in the South. He is a god of epiphany, "the god that comes", and his "foreignness" as an arriving outsider-god may be inherent and essential to his cults."

The Bacchae

2011-11-19T02:23:00.000-08:00

The Bacchae with its mysterious, fearful maenads:

"The Bacchae of Euripides gives us the most vital picture of the wonderful circumstance in which, as Plato says in the Ion, the god-intoxicated celebrants draw milk and honey from the streams. They strike rocks with the thyrsus, and water gushes forth. They lower the thyrsus to the earth, and a spring of wine bubbles up. If they want milk, they scratch up the ground with their fingers and draw up the milky fluid. Honey trickles down from the thyrsus made of the wood of the ivy, they gird themselves with snakes and give suck to fawns and wolf cubs as if they were infants at the breast. Fire does not burn them. No weapon of iron can wound them, and the snakes harmlessly lick up the sweat from their heated cheeks. Fierce bulls fall to the ground, victims to numberless, tearing female hands, and sturdy trees are torn up by the roots with their combined efforts."

Pythagorean triples

2011-11-12T12:17:00.000-08:00

The pattern of the triples...

3   4   5 
6   8  10  [3 - 4 - 5] 
5  12  13 
9  12  15  [3 - 4 - 5]
8  15  17
12  16  20  [3 - 4 - 5] 
7  24  25
15  20  25  [3 - 4 - 5]
10  24  26  [5 - 12 - 13]
20  21  29
18  24  30  [3 - 4 - 5]
16  30  34  [8 - 15 - 17]
21  28  35  [3 - 4 - 5]
12  35  37
15  36  39  [5 - 12 - 13]
24  32  40  [3 - 4 - 5] 
9  40  41
27  36  45  [3 - 4 - 5]
14  48  50  [7 - 24 - 25]
30  40  50  [3 - 4 - 5]
24  45  51  [8 - 15 - 17]
20  48  52  [5 - 12 - 13]
28  45  53
33  44  55  [3 - 4 - 5]
40  42  58  [20 - 21 - 29]
36  48  60  [3 - 4 - 5]
11  60  61
16  63  65
25  60  65  [5 - 12 - 13]
33  56  65
39  52  65  [3 - 4 - 5]
32  60  68  [8 - 15 - 17]
42  56  70  [3 - 4 - 5]
48  55  73
24  70  74  [12 - 35 - 37]
21  72  75  [7 - 24 - 25]
45  60  75  [3 - 4 - 5]
30  72  78  [5 - 12 - 13]
48  64  80  [3 - 4 - 5]
18  80  82  [9 - 40 - 41]
13  84  85
36  77  85
40  75  85  [8 - 15 - 17]
51  68  85  [3 - 4 - 5]
60  63  87  [20 - 21 - 29]
39  80  89
54  72  90  [3 - 4 - 5]
35  84  91  [5 - 12 - 13]
57  76  95  [3 - 4 - 5]
65  72  97

As well as the eye shapes, there are what appear to be curious little circles in there...

tiling a circle

2011-11-12T12:05:00.000-08:00

Pythagorean triples give plenty of scope for play. Here the tiling fits exactly in the circle.
Because:

3² + 4² = 5²

and the radius of the circle is 5.

This time:

3² + 4² = 5²

and so (multiplying everything by 5):

15² + 20² = 25²

there are two 15 x 20 rectangles that fit in this circle, radius 25.

And because

7² + 24² = 25²

there's also two 7 x 24 rectangles.

There must be bigger pythagorean triples that do the same thing and allow more of the circle to be tiled. It could begin to be a way of approximating pi.

65 is a good candidate:

16  63  65
25  60  65  [5 - 12 - 13]
33  56  65
39  52  65  [3 - 4 - 5]

This is a total of 12380 squares.
Counting the remnants as triangles (which clearly they are not; as there is a curved side we are doing an underestimate) the triangles occupy 798 squares.
That gives a total area estimate of 13178 squares.
So as Area = pi x r²
our estimate of pi is 13178 / 65² = 3.119.
Not that good, but bigger grids with more rectangles on it should get us closer (the first image gives a pi of 2.96)..

85 gives us four triplets too:

13  84  85
36  77  85
40  75  85  [8 - 15 - 17]
51  68  85  [3 - 4 - 5]

1105 gives us lots:
 47 1104 1105
105 1100 1105  [21 - 220 - 221]
169 1092 1105  [13 - 84 - 85] 
264 1073 1105
272 1071 1105  [16 - 63 - 65]
425 1020 1105  [5 - 12 - 13]
468 1001 1105  [36 - 77 - 85]
520  975 1105  [8 - 15 - 17]
561  952 1105  [33 - 56 - 65]
576  943 1105

Seikilos epitaph

2011-11-12T09:31:00.000-08:00

The Seikilos epitaph:

Ὅσον ζῇς, φαίνου,

Hoson zês, phainou,

While you live, shine,

μηδὲν ὅλως σὺ λυποῦ·

mêden holôs su lupou;

don't suffer anything at all;

πρὸς ὀλίγον ἐστὶ τὸ ζῆν,

pros oligon esti to zên,

life exists only a short while,

τὸ τέλος ὁ xρόνος ἀπαιτεῖ.

to telos ho chronos apaitei.

and time demands its toll.

"I am an icon, not a stone
Seikelos placed me here
as a deathless remembrance
an everlasting monument."

midwifery

2011-11-06T09:59:00.000-08:00

Socrates' father was Sophroniscus, said to be a sculptor, and his mother Phaenarete was a midwife.

Heaven constrains me to serve as a midwife, but has debarred me from giving birth. So of myself I have no sort of wisdom, nor has any discovery ever been born to me as the child unintelligent, but, as we go further with our discussions, all who are favoured by heaven make progress at a rate that seems surprising to others as well as to themselves, although it is clear that they have never learned anything from me. The many admirable truths they bring to birth have been discovered by themselves from within. But the delivery is heaven's work and mine.

halls of Hades

2011-10-15T12:16:00.000-07:00

photo: Samuli Lintula

Tim Severin in his The Ulysses Voyage find the Halls of Hades on the river Acheron at the site of the ancient Necromanteion.

Odysseus had been instructed to 'make a journey of a very different kind, and find your way to the Halls of Hades...across the River of Ocean'. Odysseus finds his way there and, in the eeriest and darkest part of the whole tale, sacrifices a black lamb and lets the priest and prophet Tiresias drink its blood.

He asks Tiresias about the means to return home to Ithaca.

Tiresias answers, "Though you survive alone, bereft of all companions, lost for years, under strange sail shall you come home, to find your own house filled with trouble: insolent men eating your livestock as they court your lady."

When Odysseus' troubles were over and he was a happy old man, he was to take an oar from his ship and walk with it until he came to a place where people knew nothing about the sea or boats and someone asked him what the oar was, mistaking it for a winnowing fan.

I loop around this bollard
The beeline of cormorants,
The diver’s shifts in air
And secure my idea
Of the island: rigging
Slanted across the sky,
Then a netting of sunlight
Where the thin oar splashes,
Stone steps down to the water
And a forgotten ferry.

Michael Longleyhttp://seekecho.blogspot.com/2011/09/ulysses-voyage.html

wild silk

2011-10-15T09:34:00.000-07:00

diaphanous

We don't even know for sure what fabrics they wore in Antiquity. We know about wool and linen, but what about silk?

In Aristophanes' comedy Lysistrate the women are told to captivate men by appearing "naked in their Amorgion chitons" and assured they will get their men with the help of paint, perfume and "diaphanous garments". Some see this as a reference to wild silk cultivated on Amorgos and Cos.

Amorgos

walls of bronze

2011-09-25T13:56:00.000-07:00

Gramvousa by Wolfgang Staudt.

Aeolus' island is surrounded by "great walls of bronze" - where to find that, in the real world?

Coming back from the south where the winds had taken Odysseus to the land of the lotus eaters, Crete would be the logical stopping off point. But the winds were blowing mostly from the north; Odysseus would have had to wait for a rare favourable southerly. And where to wait? Tim Severin on his "Ulysses Voyage" thought it's the north west corner of Crete, and in particular the island of Gramvousa. Here, 'by some trick of the westering light, the entire rock wall of Gramvousa, which faced west, was changing colour - Gramvousa's rampart turned a rich red, the colour of new bronze, the metal of Aeolus "island"'.

View Larger Map

The Ulysses Voyage

2011-09-17T14:16:00.000-07:00

Tim Severin's book The Ulysses Voyage is a different kind of history, a more practical kind.

How is it possible to retrace the journey home of Odysseus?

When I read the Odyssey I read it as myth, metaphor, a little like Cavafy when he writes:

When you set out on your journey to Ithaca,
pray that the road is long,
full of adventure, full of knowledge.
The Lestrygonians and the Cyclops,
the angry Poseidon -- do not fear them:
You will never find such as these on your path,
if your thoughts remain lofty,
if a fine emotion touches your spirit and your body.
The Lestrygonians and the Cyclops,
the fierce Poseidon you will never encounter,
if you do not carry them within your soul,
if your soul does not set them up before you.

But Severin tried it literally, looking to find the route his galley would be most likely to take given the winds and currents.

He was not put off by Eratosthenes words, ""You will find the scene of the wanderings of Odysseus when you find the cobbler who sewed up the bag of the winds."

He locates the wanderings around Greece rather than further afield:

And it is true for Severin, again as Cavafy says:

Ithaca has given you the beautiful voyage. Without her you would have never set out on the road.

opposite?

2011-07-21T11:53:00.000-07:00

I wrote about this before...

So Xenophon thought hunting was a great education because it was a training in "the real world of actual things".
Plato meanwhile, famously, had
LET NO-ONE IGNORANT OF MATHEMATICS ENTER
inscribed over the entrance to the Academy.

He too had a lot to say about education. He wanted it to be pleasurable, reasonable paced, and, naturally, politically acceptable. And he wanted it to involve maths:

“Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.”

He had high hopes for maths too:

“... arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument.”

Were the two ideas, Xenophon's and Plato's, opposites? Or did they have something in common?

isopsephy

2011-06-08T04:35:00.000-07:00

So, if Milesian numerals perhaps were used right back in the 7th century BC, with each letter of the alphabet being a number:

maybe they were used to hide numbers in text too?
Like this inscription on a votive stele for a boy who won a competition in singing, an example of isopsephy, where each letter's value is added up:

ΟΡΘΕΙΗ ΔΩΡΟΝ ΛΕΟΝΤΕΥΣ ΑΝΕΘΗΚΕ ΒΟΑΓΟΣ ΒΨΛ
ΜΩΑΝ ΝΙΚΗΣΑΣ ΚΑΙ ΤΑΔΕ ΕΠΑΘΛΑ ΛΑΒΩΝ ΒΨΛ
ΚΑΙ Μ ΕΣΤΕΨΕ ΠΑΤΗΡ ΕΙΣΑΡΙΘΜΟΙΣ ΕΠΕΣΙ ΒΨΛ

The words in each line add up to ΄ΒΨΛ, that is 2730, and, perhaps in case anyone does't notice, that total is also given at the end of each line.

Although this, and other examples, are from much later, AD rather than BC, if isopsephy was used in secret, maybe as a kind of code, perhaps it could date from much earlier...?

The tomb of the diver

2011-06-01T11:17:00.000-07:00

The Tomb of the Diver was found not so long ago, a couple of kilometres south of the Greek city of Paestum in Magna Graecia, now southern Italy. It's the only example of Greek painting with figured scenes dating from the Classical period to survive in its entirety.

Inside the tomb were a turtle shell that was perhaps part of a lyre, the dead man's oil flasks, the ones he used to oil himself for wrestling practice, and his favorite drinking cup. This last object, in black-figure technique helped scholars to date the tomb to about 470 BC.

I like this picture on the lid best of all. It probably celebrates the man's life. But it also seems to me that he is diving into death from that stone platform, into the cool still water below, diving gracefully and confidently.

any old letters?

2011-01-30T08:34:00.000-08:00

Like Ϝ and Ϙ and ϡ - digamma, koppa and sampi. They aren't really needed for writing and they weren't used very much. Except for maths. As in the Milesian numerals.

Α Β Γ Δ Ε Ϝ Ζ Η Θ
Ι Κ Λ Μ Ν Ξ Ο Π Ϙ
Ρ Σ Τ Υ Φ Χ Ψ Ω ϡ

The picture at the top, called the "Abecedarium of Samos" is ‘one of the oldest if not the oldest of all the inscriptions from Ionia’ . It's the complete alphabet of 27 letters, dated to 660 BC, engraved on fragments of a clay cup. It was discovered in a well for rubbish in the Heraion, Samos, among various things which the priests had considered useless back then. The well had been sealed up in 640 BC.

According to a very interesting article by Dimitris K. Psychoyos, it was probably written to help with maths.

Shipwrecks Offer Clues

2010-12-26T07:05:00.000-08:00

Here's a shipwreck off the coast of Chios, the 'Chios-Oinousses wreck'.

According to DNA data, one of the amphorae held an olive product (probably olive oil), flavored or perhaps preserved with oregano. The other most likely
contained wine, because it appeared to contain fragments of DNA from mastic, a plant that grows on Chios and was used to preserve wine. (Hansson notes that the team wasn’t certain of this latter hypothesis because the same DNA sequences are also found in pistachio nuts.)

The southern portion of Chios island is known as the 'mastichora'. It was the primary and perhaps sole source of high-quality mastic in the ancient world, as first recorded by the Roman natural philosopher Pliny, circa 60 A.D. Modern scholars have hypothesized that mastic resin preserved the famous Chian wines and provided their distinctive flavor. If the resin in the unattributed amphora recoverd from the Chios-Oinousses wreck is indeed mastic, it is the first direct suggestion for mastic cultivation in the Classical era. This would shift the suspected origins of mastic production back in time at least 400 years. Because the source of mastic was so highly localized in the southern part of Chios Island, this suggests that this particular jar and by association the others in its class were produced either on the island itself or at a site nearby. Similarly to oregano, species in the Pistacia genus have been experimentally demonstrated to possess strong antioxidant and antimicrobial abilities, containing several different substances which prevent oxidation processes and microbial activity. This could have facilitated preservation of the jars' ancient contents, as well as the genetic material within the amphora walls.

An Ancient Nas

2010-12-06T14:35:00.001-08:00

An Ancient Nas
Originally uploaded by angeloska.

Ikaria is in the hands of the pirate-tyrant Polycrates. One of his triremes is in Nas. The harbour and its temple is guarded. How do Pythagoras and his pupils, on the run from Polycrates, land there?

At night? - no there are guards, lanterns...

No, there is fog, come from nowhere. Artemis of the swift arrows has watched over them, covered them in a cloak of mist.

a bit like Homer says:

"Some god guided us for we could barely see our bows in the dense fog around us and no moonlight filtered through the overcast. No lookout, nobody saw the island dead ahead, not even the great landward-rolling billow that took us in; we found ourselves in shallows, keels grazing shore, so furled our sails and disembarked where low ripples broke."

See also: Guided Tour in Ancient Nas

Paul's shipwreck

2010-11-20T03:05:00.000-08:00

One good description of Mediterranean sea travel is in the Bible:

The Storm
When a gentle south wind began to blow, they saw their opportunity; so they weighed anchor and sailed along the shore of Crete. Before very long, a wind of hurricane force, called the Northeaster, swept down from the island. The ship was caught by the storm and could not head into the wind; so we gave way to it and were driven along. As we passed to the lee of a small island called Cauda, we were hardly able to make the lifeboat secure, so the men hoisted it aboard. Then they passed ropes under the ship itself to hold it together. Because they were afraid they would run aground on the sandbars of Syrtis, they lowered the sea anchor[b] and let the ship be driven along. We took such a violent battering from the storm that the next day they began to throw the cargo overboard. On the third day, they threw the ship’s tackle overboard with their own hands. When neither sun nor stars appeared for many days and the storm continued raging, we finally gave up all hope of being saved.

Shipwreck
On the fourteenth night we were still being driven across the Adriatic Sea, when about midnight the sailors sensed they were approaching land. They took soundings and found that the water was a hundred and twenty feet deep. A short time later they took soundings again and found it was ninety feet deep. Fearing that we would be dashed against the rocks, they dropped four anchors from the stern and prayed for daylight. In an attempt to escape from the ship, the sailors let the lifeboat down into the sea, pretending they were going to lower some anchors from the bow. Then Paul said to the centurion and the soldiers, “Unless these men stay with the ship, you cannot be saved.” So the soldiers cut the ropes that held the lifeboat and let it drift away.
Just before dawn Paul urged them all to eat. “For the last fourteen days,” he said, “you have been in constant suspense and have gone without food—you haven’t eaten anything. 34 Now I urge you to take some food. You need it to survive. Not one of you will lose a single hair from his head.” After he said this, he took some bread and gave thanks to God in front of them all. Then he broke it and began to eat. They were all encouraged and ate some food themselves. Altogether there were 276 of us on board. When they had eaten as much as they wanted, they lightened the ship by throwing the grain into the sea.

When daylight came, they did not recognize the land, but they saw a bay with a sandy beach, where they decided to run the ship aground if they could. Cutting loose the anchors, they left them in the sea and at the same time untied the ropes that held the rudders. Then they hoisted the foresail to the wind and made for the beach. But the ship struck a sandbar and ran aground. The bow stuck fast and would not move, and the stern was broken to pieces by the pounding of the surf.

The soldiers planned to kill the prisoners to prevent any of them from swimming away and escaping. But the centurion wanted to spare Paul’s life and kept them from carrying out their plan. He ordered those who could swim to jump overboard first and get to land. The rest were to get there on planks or on other pieces of the ship. In this way everyone reached land safely.

This book is good too.

ships and weather

2010-10-26T05:16:00.000-07:00

"Give me a mattress on the poop, and an awning overhead with the patter of the spray on it; a pot on the fire with the turmoil of bursting bubbles and a boy turn the meat, and a ship's plank for my table, and a game of pitch and toss, and the boatswain's whistle..." Herodotus, The Histories: "The Persian fleet put to sea and reached the beach of the Magnesian land, between the city of Casthanaea and the headland of Sepia. The first ships to arrive moored close to land, with the others after them at anchor; since the beach was not large, they lay at anchor in rows eight ships deep out into the sea. They spent the night in this way, but at dawn a storm descended upon them out of a clear and windless sky, and the sea began to boil. A strong east wind blew, which the people living in those parts call Hellespontian. Those who felt the wind rising or had proper mooring dragged their ships up on shore ahead of the storm and so survived with their ships. The wind did, however, carry those ships caught out in the open sea against the rocks called the Ovens at Pelion or onto the beach. Some ships were wrecked on the Sepian headland, others were cast ashore at the city of Meliboea or at Casthanaea. The storm was indeed unbearable. 7.189. The story is told that because of an oracle the Athenians invoked Boreas, the north wind, to help them, since another oracle told them to summon their son-in-law as an ally. According to the Hellenic story, Boreas had an Attic wife, Orithyia, the daughter of Erechtheus, ancient king of Athens. Because of this connection, so the tale goes, the Athenians considered Boreas to be their son-in-law. They were stationed off Chalcis in Euboea, and when they saw the storm rising, they then, if they had not already, sacrificed to and called upon Boreas and Orithyia to help them by destroying the barbarian fleet, just as before at Athos. I cannot say whether this was the cause of Boreas falling upon the barbarians as they lay at anchor, but the Athenians say that he had come to their aid before and that he was the agent this time. When they went home, they founded a sacred precinct of Boreas beside the Ilissus river. 7.190 The most conservative estimate of how many ships were lost in this disaster is four hundred, along with innumerable personnel, and so much valuable property that a Magnesian called Ameinocles the son of Cretines, who owned land near Sepias, profited immensely from this naval catastrophe. In the following days and months gold and silver cups were washed ashore in large numbers for him to pick up." the rising of the Pleiades, Arcturus, Orion and the Kids Pleiades winter stars:

"And if longing seizes you for sailing the stormy seas,

when the Pleiades flee mighty Orion

and plunge into the misty deep

and all the gusty winds are raging,

then do not keep your ship on the wine-dark sea

but, as I bid you, remember to work the land."

(Works and Days 618-23)

The Pleiades would "flee mighty Orion and plunge into the misty deep" as they set in the West, which they would begin to do just before dawn during October-November.

Virgil: Then first did rivers feel upon their backs boats of hollowed alder, then the mariner grouped and named the stars, Pleiads and Hyads and Lycaon’s daughter, the radiant Bear. - - - Theopharastus: On Weather Signs From the Greek Anthology

1.— LEONIDAS
It is the season for sailing; already the chattering swallow has come, and the pleasant Zephyr, and the meadows bloom, and the sea with its boiling waves lashed by the rough winds has sunk to silence.
Weigh the anchors and loose the hawsers, mariner, and sail with every stitch of canvas set. This, O man, I, Priapus, the god of the harbour, bid thee do that thou mayst sail for all kinds of merchandise.

2.— ANTIPATER OF SIDON
It is the season for the ship to travel tearing through the waves ; no longer does the sea toss, furrowed by dreadful fret. Already the swallow is building her round houses under the roof, and the tender leaves of the meadows smile. Therefore, ye sailors, coil your wet hawsers and drag the anchors from their nests in the harbour. Haul up your well-woven sails. This is the bidding of me, Priapus of the harbour, the son of Bromius.

3. — Anonymous
The way down to Hades is straight, whether you start from Athens or whether you betake yourself there, when dead, from Meroe. Let it not vex thee to die far from thy country. One fair wind to Hades blows from all lands.^

4.— MARCUS ARGENTARIUS
Loose the long hawsers from your well-moored ships, and spreading your easily-hoisted sails set to sea, merchant captain. For the storms have taken flight and tenderly laughing Zephyr now makes the blue wave gentle as a girl. Already the swallow, fond parent, is building with its lisping lips its chamber out of mud and straw, and flowers spring up in the land ; therefore listen to Priapus and
undertake any kind of navigation.

5.— THYILLUS
Already the swallows build their mud houses, already on the flood Zephyr is bosomed in the soft sails. Already the meadows shed flowers over their green leaves, and the rough strait closes its lips in silence. Wind up your hawsers and stow the anchors on shipboard, and give all your canvas to the sheets. This is the advice that Priapus of the harbour writes for you who sail the seas seeking merchandise.

6.-SATYRUS
Already the moist breath of Zephyr, who giveth birth to the grass, falls gently on the flowery meads. The daughters of Cecrops ^ call, the becalmed sea smiles, untroubled by the cold winds. Be of good heart, ye sailors, loose your hawsers and spread out the delicate folds of your ships' wings. Go to trade trusting in gracious Priapus, go obedient to the harbour god.

7.— ARCHIAS
Stranger, I, Priapus, was set up on this sea-beaten rock to guard the Thracian strait,^ by the sailors, whom I had often rushed to help when they called upon me, bringing from astern the sweet Zephyr.
Therefore, as is meet and right, thou shalt never see my altar lacking the fat of beasts or crowns in the spring, but ever smoking with incense and alight. Yet not ever a hecatomb is so pleasing to the gods as due honour.

8.— By the Same
Little am I to look on, Priapus, who dwell on this spur by the beach, companion of the gulls, denizens of land and sea, with a peaked head and no feet, just such as the sons of toiling fishermen would carve on the desert shore. But if any netsman or rod-fisher call on me for help, I hie me to him quicker than the wind. I see, too, the creatures that move under the water, and indeed the character of us gods is known rather from our actions than from our shapes.

9. — Anonymous
Ye fishermen^ who pulled your little boat ashore here (Go^ hang out your nets to dry) having had ahaul of many sea-swimming gurnard (?) and scarus, not without thrissa,^ honour me with slender first-fruits of a copious catch, the little Priapus under the lentisc bush, the sea-blue god, the revealer of the fish your prey, established in this grove.

10.— ARCHIAS THE YOUNGER
The fishermen dedicated me. Pan, here on this holy cliff, Pan of the shore, the guardian of this secure haven. Sometimes I care for the weels, and sometimes for the fishers who draw their seine on this beach. But, sti*anger, sail past, and in return for this beneficence I will send a gentle south-west wind at thy back.

11.— SATYRUS
Whether thou walkest over the hills with bird-lime spread on the reeds to which the birds resort, or whether thou killest hares, call on Pan. Pan shows the hound the track of velvet-paw, and Pan guides higher and higher, unbent, the jointed reeden rod. 2

12. — Anonymous
Come and rest your limbs awhile, travellers, here under the juniper by Hermes, the guardian of the road — not a mixed crowds but those of you whose knees ache from heavy toil and who thirst after accomphshing a long day's journey. There is a breeze and a shady seat, and the fountain under the rock will still the weariness that weighs on your limbs. Escaping the midday breath of Autumn's dog-star, honour Hermes of the wayside as is meet.

13.— SATYRUS
How lovely are the laurels and the spring that gushes at their feet, while the dense grove gives shade, luxuriant, traversed by Zephyrs, a protection to wayfarers from thirst and toil and the burning sun!

14._AGATHIAS SCHOLASTICUS
The deep lies becalmed and blue ; for no gale whitens the waves, ruffling them to a ripple, and no longer do the seas break round the rocks, retiring again to be absorbed in the depth. The Zephyrs blow and the swallow twitters round the straw-glued chamber she has built. Take courage, thou sailor of experience, whether thou journeyest to the Syrtis or to the beach of Sicily. Only by the altar of Priapus of the harbour burix a scarus or ruddy gurnards.

15.— PAULUS SILENTIARIUS
Now the heart-entrancing spring in all the beauty of her meadows opens the closed folds of her bosom to the Zephyrs ; now the ship slides down the wooden rollers, pulled from the beach into the deep. Gof forth fearlessly, ye sailors, your sails strutting with the wind, to the gentle task of loading the merchandise ye gain by barter. I, Priapus, am faithful to ships, since I boast that Thetis was the hostess of my father Bromius.^

16.— THEAETETUS SCHOLASTICUS
Already the fair-foliaged field, at her fruitful birth-tide, is aflower with roses bursting from their buds ; already on the branches of the alleyed cypresses the cicada, mad for music, soothes the sheaf-binder, and the swallow, loving parent, has made her house under the eaves and shelters her brood in the mud-plastered chamber. The sea sleeps, the calm dear to the Zephyrs spreads tranquilly over the expanse that bears the ships. No longer do the waters rage against the high-built
poops, or belch forth spray on the shore. Mariner, roast first by his altar to Priapus, the lord of the deep and the giver of good havens, a slice of a cuttle-fish or of lustred red mullet, or a vocal scarus, and then go fearlessly on thy voyage to the bounds of the Ionian Sea.

17.— ANTIPHILUS
Blest god of the harbour, accompany with gentle breeze the departing sails of Archelaus through the undisturbed water as far as the open sea, and thou who rulest over the extreme point of the beach, save him on his voyage as far as the Pythian shrine. From thence, if all we singers are dear to Phoebus, I will sail trusting in the fair western gale.

Cycle of Venus

2010-08-15T12:02:00.000-07:00

This graphic is an approximation of the 586 day cycle of Venus: giving Venus and Earth circular orbits, instead of their slightly oval orbits. The eight days when Venus disappears in front of the sun, and fifty when it disappears behind are shown. Above the line is the Evening Star, below is the Morning Star.

Ancient records of Venus

2010-07-26T03:07:00.001-07:00

The Venus tablet of Ammisaduqa dates from the 17th century BC. It records the rise times for Venus over a period of 21 years.

Venus to the Babylonians was Ishtar, goddess of Love and War. Her symbol, the eight pointed star appears on at least one stele in the Louvre. Other artifacts in the Louvre give us more clues to this deity, as do objects in the British Museum.

One object, a tablet, tells the story of Ishtar's descent into the Underworld:

To the Land of No Return, the realm of Ereshkigal,
Ishtar, the daughter of the Moon, set her mind. To the dark house, the abode of Irkalla, To the house which none leave who have entered it, To the road from which there is no way back, To the house wherein the entrants are bereft of light, Where dust is their fare and clay their food, Where they see no light, residing in darkness, Where they are clothed like birds, with wings for garments, And where over door and bolt is spread dust. When Ishtar reached the gate of the Land of No Return, She said to the gatekeeper: "O gatekeeper, open thy gate, Open thy gate so I may enter! If thou openest not the gate so that I cannot enter, I will smash the door, I will shatter the bolt, I will smash the doorpost, I will move the doors, I will raise up the dead eating the living, So that the dead will outnumber the living." The gatekeeper opened his mouth to speak, Saying to exalted Ishtar: "Stop, my lady, do not throw it down! I will go to announce thy name to Queen Ereshkigal." The gatekeeper entered, saying to Ereshkigal: "Behold, they sister Ishtar is waiting at the gate, She who upholds the great festivals, Who stirs up the deep before Ea, the king." When Ereshkigal heard this, her face turned pale like a cut-down tamarisk, While her lips turned dark like a bruised kuninu-reed. What drove her heart to me? What impelled her spirit hither? Lo, should I drink water with the Anunnaki? Should I eat clay for bread, drink muddied water for beer? Should I bemoan the men who left their wives behind? Should I bemoan the maidens who were wretched from the laps of their lovers? Or should I bemoan the tender little one who was sent off before his time? Go, gatekeeper, open the gate for her, Treat her in accordance with the ancient rules." Forth went the gatekeeper to open the door for her: "Enter, my lady, that Cutha may rejoice over thee, That the palace of the Land of No Return may be glad at they presence." When the first gate he had made her enter, He stripped and took away the great crown on her head. "Why, o gatekeeper, didst thou take the great crown on my head?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the second gate he had made her enter, He stripped and took away the pendants on her ears. "Why, O gatekeeper, didst thou take the pendants on my ears?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the third gate he had made her enter, He stripped and took away the chains round her neck. "Why, O gatekeeper, didst thou take the chains round my neck?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the fourth gate he had made her enter, He stripped and took away the ornaments on her breast. "Why, O gatekeeper, didst thou take the ornaments on my breast?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the fifth gate he had made her enter, He stripped and took away the girdle of birthstones on her hips. "Why, O gatekeeper, didst thou take the girdle of birthstones on my hips?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the sixth gate he had made her enter, He stripped and took away the clasps round her hands and feet. "Why, O gatekeeper, didst thou take the clasps round my hands and feet?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." When the seventh gate he had made her enter, He stripped and took away the breechcloth round her body. "Why, O gatekeeper, didst thou take the breechcloth round my body?" "Enter, my lady, thus are the rules of the Mistress of the Underworld." As soon as Ishtar had descended to the Land of No Return, Ereshkigal saw her and burst out at her presence. Ishtar, unreflecting, flew at her. Ereshkigal opened her mouth to speak, "Go, Namtar, lock her up in my palace! Release against her the sixty miseries: Misery of the eyes against her eyes, Misery of the sides against her sides, Misery of the heart against her heart, Misery of the feet against her feet, Misery of the head against her head - Against every part of her, against her whole body!" After Lady Ishtar had descended to the nether world, The bull springs not upon the cow, the ass impregnates not the jenny, In the street the man impregnates not the maiden. The man lies in his own chamber, the maiden lies on her side. The countenance of Papsukkal, the vizier of the great gods, Was fallen, his face was clouded He was clad in mourning, long hair he wore. Forth went Papsukkal before Ea, the king: "Ishtar has gone down to the nether world, she has not come up. Since Ishtar has gone down to the Land of No Return, The bull springs not upon the cow, the ass impregnates not the jenny, In the street the man impregnates not the maiden. The man lies down in his own chamber, The maiden lies down on her side." Ea in his wise heart conceived an image, And created Asushunamir, a eunuch: "Up, Asushunamir, set thy face to the gate of the Land of No Return: The seven gates of the Land of No Return shall be opened for thee. Ereshkigal shall see thee and rejoice at thy presence. When her heart has calmed, her mood is happy, Let her utter the oath of the great gods. Then lift up thy head, paying mind to the life-water bag: "Pray, lady, let them give me the life-water bag that water therefrom I may drink." As soon as Ereshkigal heard this, She smote her thigh, bit her finger: "Thou didst request of me a thing that should not be requested. Come, Asushunamir, I will curse thee with a mighty curse! The food of the city's gutters shall be thy food, The sewers of the city shall be thy drink. The threshold shall be thy habitation, The besotted and the thirsty shall smite they cheek!" Ereshkigal opened her mouth to speak, Saying these words to Namtar, her vizier: "Up, Namtar, knock at Egalgina, Adorn the thresholds with the coral-stone, Bring forth the Anunnaki, seated them on thrones of gold, Sprinkle Ishtar with the water of life and take her from my presence!" Forth went Namtar, knocked at Egalgina, Adorned the thresholds with coral-stone, Brought forth the Anunnaki, seated them on thrones of gold, Sprinkled Ishtar with the water of life and took her from her presence. When through the first gate he had made her go out, He returned to her the breechcloth for her body. When through the second gate he had made her go out, He returned to her the clasps for her hands and feet. When through the third gate he had made her go out, He returned to her the birthstone girdle for her hips. When through the fourth gate he had made her go out, He returned to her the ornaments for her breasts. When through the fifth gate he had made her go out, He returned to her the chains for her neck. When through the sixth gate he had made her go out, He returned to her the pendants for her ears. When through the seventh gate he had made her go out, He returned to her the great crown for her head. "If she does not give thee her ransom price, bring her back. As for Tammuz, the lover of her youth, Wash him with pure water, anoint him with sweet oil: Clothe him with a red garment,
let him play on a flute of lapis. Let the courtesans turn his mood." When Belili was stringing her jewelry, And her lap was filled with "eye-stones," On hearing the sound of her brother, Belili struck the jewelry on... So that the "eye-stones" filled the... "My only brother, bring no harm to me! On the day when Tammuz comes up to me, When with him the lapis flute and the carnelian ring come up to me, When with him the wailing men and wailing women come up to me, May the dead rise and smell the incense."

The Mayans also had a detailed calendar for Venus, covering its 8 year cycle; the Dresden Codex, the oldest pre-columbian text we have.

Hesperus and Phosphorus

2010-07-26T02:31:00.001-07:00

goodnight moon
Originally uploaded by simonsterg.

So Pythagoras is mentioned as the discoverer that the Evening Star ("Hesperus") is the same planet as the Morning Star ("Phosphorus")?

(Diogenes Laertius: "... and it is believed that he [Parmenides, 400 B.C.] realized, as the first, that the Evening and Morning stars were one and the same star, which Favorinus relates to us in his fifth book of `Worthwhile thoughts'. Others claim that it was Pythagoras.")

Apparently, the Morning Star moves away from the sun and then closer again for about 263 days then disappears in its brightness. About 50 days later the Evening Star appears and for about 263 days moves away from the sun and then closer, disappearing in its brightness. About 8 days later the Morning Star appears again, and cycle repeats, taking a total of 584 days.

You wouldn't think it would take much of a leap, would you, to realise that they were one and the same planet?

pebbles are the thing

2010-01-10T13:43:00.001-08:00

golden rectangle

2009-12-03T08:26:00.000-08:00

A possible insight into the minds of the early mathematics of Pythagoras.

The famous "golden rectangle": here it is made by starting with a small square (1 unit long) and adding another the same next to it. Then alongside those two another, 2 units long, and then another 3 units long.

1, 1, 2, 3, 5, 8, 13 - - - the Fibonacci sequence.

The resulting rectangle approximates to the Golden Rectangle, it's sides the golden ratio.

Here's wikipedia:

"Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. The Greeks usually attributed discovery of this concept to Pythagoras or his followers. The regular pentagram, which has a regular pentagon inscribed within it, was the Pythagoreans' symbol.

Euclid's Elements (Greek: Στοιχεῖα) provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e. the golden ratio. Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio. Some of these propositions show that the golden ratio is an irrational number."

Whether or not, as some people conjecture, the Parthenon was built with these proportions is hard to say.

Hyperbolic Crochet Coral Reef

2009-04-21T05:28:00.001-07:00

I watched the TED talk given by Margaret Wertheim with great pleasure. Here is a project that links to so many interests, the mathematical, the playful, the environmental, the practical, the educational. It connects them together with beauty and surprise. These beautiful crocheted corals are part of a hugh ("viral") project to model a coral reef in wool. They model hyperbolic space by the clever crochet trick of regularly adding number of stitches to each row. And this works because corals have hyperbolic shapes.

She describes mathematicians as the "free-est of thinkers", but they never noticed that these-hard-to-model hyperbolic planes were in front of them on their salad plate. She also mentions the work of Froebel in inventing Kindergarten. Have a look at the twenty gifts, through which he instilled mathematical thinking through physical play.

There's a lot of really good stuff on the Institute for Figuring's site, for instance the explanation of hyperbolic space.

In the interview with her on TED, she describes her own school learning and her discovery of pi:

I think that my love of figures and figuring is a thing that's bound up with my childhood. When I was in grade three or four, my mathematics teacher, a man named Mr. Marshall, gave us a mathematics lesson about circles. The whole point of this lesson was to teach us about pi; the magical number that is at the heart of all circles.
Instead of simply telling us the formula for the circumference of a circle and the area of a circle, he gave us an entire lesson letting us discover pi for ourselves. For me, the exercise worked. I looked around me and I realized that every time I see a dinner plate, every time I see the sun or the moon, every time I see the wheel of a car, every time I see a circle in the world around me, that this magical number pi is embedded in it.
I will never forget this moment; it was truly like a revelation to me, that this almost angelic thing pi was hovering magically, like an angel behind the material world. I had several experiences like that during my childhood.

This all seems to link back to the beginnings of maths in Europe with Thales, Pythagoras and co. They had a way, ways, of figuring - using arrays of pebbles to explore number theory, and the straight line and edge to explore geometry. There were limitations to these ways of modelling, but even the limitations were creative. They created a ludic quality - as in recreational maths - "what spaces can I get to within the constraints of this structure". Like origami, certain things are possible, certain things are not possible. And as "ontogeny recapitulates phylogeny"so education can recapitulate history; just as maths was invented or discovered through these games, so in the present it can be discovered anew by children or adults. Time to get crocheting...

♓

2009-04-03T13:18:00.000-07:00

A cord joins the tails of Pisces, the two fishes.

From the Atlas Coelestis of John Flamsteed.

It's never interested me before, my star-sign, Pisces. But there is, naturally, some kind of story behind it...

See for instance this page...

"The mythological events concerning this constellation are said to have taken place around the Euphrates river, a strong indication that the Greeks inherited this constellation from the Babylonians. The story follows an early episode in Greek mythology, in which the gods of Olympus had defeated the Titans and the Giants in a power struggle. Mother Earth, also known as Gaia, had another nasty surprise in store for the gods. She coupled with Tartarus, the lowest region of the Underworld where Zeus had imprisoned the Titans, and from this unlikely union came Typhon, the most awful monster the world had ever seen.

According to Hesiod, Typhon had a hundred dragon’s heads from which black tongues flicked out. Fire blazed from the eyes in each of these heads, and from them came a cacophony of sound: sometimes ethereal voices which gods could understand, while at other times Typhon bellowed like a bull, roared like a lion, yelped like puppies or hissed like a nest of snakes.

Gaia sent this fearsome monster to attack the gods. Pan saw him coming and alerted the others with a shout. Pan himself jumped into the river and changed his form into a goat-fish, represented by the constellation Capricornus, also inherited from the Babylonians.

Aphrodite and her son Eros took cover among the reeds on the banks of the Euphrates, but when the wind rustled the undergrowth Aphrodite became fearful. Holding Eros in her lap she called for help to the water nymphs and leapt into the river. In one version of the story, two fishes swam up and carried Aphrodite and Eros to safety on their backs, although in another version the two refugees were themselves changed into fish. The mythologists said that because of this story the Syrians would not eat fish. An alternative story, given by Hyginus in the Fabulae, is that an egg fell into the Euphrates and was rolled to the shore by some fish. Doves sat on the egg and from it hatched Aphrodite who, in gratitude, put the fish in the sky. Eratosthenes wrote that the two fishes represented by Pisces were offspring of the fish that is represented by the constellation Piscis Austrinus.

In the sky, the two fish of Pisces are represented swimming in opposite directions, their tails joined by a cord. The Greeks offered no good explanation for this cord, but according to the historian Paul Kunitzsch the Babylonians visualized a pair of fish joined by a cord in this area, so evidently the Greeks borrowed this idea although the significance of the cord was lost.

Pisces is a disappointingly faint constellation, its brightest stars being of only fourth magnitude. Alpha Piscium is called Alrescha, from the Arabic name meaning ‘the cord’. It lies where the cords joining the two fish are knotted together. Pisces is notable because it contains the point at which the Sun crosses the celestial equator into the northern hemisphere each year. This point, called the vernal equinox, originally lay in Aries but it has now moved into Pisces because of a slow wobble of the Earth on its axis called precession."

Could it mean anything, Aphrodite and Eros under threat, swimming in opposite directions, but held together with a cord to escape together?

It seems full of meaning, but am I just projecting my own meaning onto the myth??

Maybe it's time to read about the other star signs...

♈ ♉ ♊ ♋ ♌ ♍ ♎ ♏ ♐ ♑ ♒ ♓

money and knowledge

2009-03-10T01:32:00.000-07:00

Some people see it as no coincidence that the 'Greek Miracle", the explosion of science, maths, arts from the 6th Century BC onwards, coincided with the beginnings of standardised currency in gold-rich asia minor.

But though it may, along with the network of coastal Greek colonies linked to the Ionian city states, must have contributed to the material prosperity of the times (especially if you ruled a pirate state), and allowed surplus wealth to be dedicated to the arts and learning, the new kind of money must have brought its own worries. And of course wealth and increased individual choice had existed before, with its own problems, which continue to this day.

aristotle

2009-02-26T13:34:00.000-08:00

Picking up Aristotle is not always entertaining. Apparently, according to Wikipedia, all his more entertaining pieces were lost, although the encyclopedia does acknowledge, "a few modern scholars have actually admired the concise writing style found in Aristotle's extant works."

But these words of his about the earliest scientists (he means Thales & co.) caught my eye:

"It is owing to their wonder that men both now begin and at first began to philosophize; they wondered origanally at the obvious difficulties, then advanced little by little and stated difficutlties about the greatest mattres, e.g. about the phenomena of the moon and those of the sun and of the stars and about the genesis of the universe. And a man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover of Wisdom, for myth is composed of wonders)..."

(Notice that even Aristotle knows that myth is not just bad science, pre-science, as some people imagine. It is not, even if from time to time it appears to be, really trying to explain the sun and the moon and their movements. That story about the Tortoise and the Geese might seem like it's trying to explain how the tortoise has a cracked-looking shell, but that's not what it's about at all.)

So, leaving aside that question of "greatest matters", Science, Myth are the same in this, they are both about, or at least begin with, Wonder and Puzzlement.

'Why do those isands appear above the horizon when we climb the mountain? Why are the stars different when we sail north or south? ...'

And the maker of myth, the poet, the storyteller, makes his myth because he wants his hearer to wonder and puzzle about human life.

Take... at random, take the tale of Narcissus and Echo. Strange story. What's it on about? That's the first question. People talk about narcissism - so it's about a distorted self-regard? Perhaps, but why stop wondering there? What else is it about? Echo is in the tale too, what does she represent?

The myths, the stories are made to be many-faced. If they weren't, they wouldn't cause any puzzlement, any wonder. There is not meant to be a moral at the end of the fable. Or if there is, it should be a red herring, something that makes the story more puzzling still.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Narcissus, the beautiful young man who one day parted some reeds and looked into a still pool and when he saw his reflection fell in love with it. He went back again and again to stare into the pool, into his own reflection. He was too much in love with it to even notice that Echo loved him. She spoke to him, but he did not hear, did not reply and so she just faded away. Even her voice faded away, until all it could do was repeat a little of what was said. “Oh, how I love me!” Narcissus said. “Love me!” Echo replied. “”You, in the water, be mine!” Narcissus said. “Be mine!” was Echo’s answer. Narcissus of course became the yellow flower beside the pool. And Echo – well, she is Echo.

Heraclitus

2009-02-03T02:22:00.000-08:00

Among all the much later writings that we rely on for our picture of Pythagoras there are often fragments of earlier authors that seem to go back, sometimes to the actual time of Pythagoras. Examples: a few of the sayings of his contemporary, Heraclitus:

-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:

"Much learning does not teach understanding, otherwise it would have taught Hesiod and Pythagoras, Xenophanes and Hecataeus."

"Pythagoras, the son of Mnesarchus, practiced inquiry most of all men and having made a selection from these writings made for himself a wisdom, a polymathy, an evil trickery.”

-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:

He gives the appearance of having a low estimation of Pythagoras, but in passing gives us an impression of him:

having "much learning"
practicing "inquiry" more than anyone else,
using the writings of others,
developing a "wisdom"
being a polymath

These things, almost more than any "content" to the learning, interest me most. I don't think it was "academic" learning that he had. A better picture might come from the reported sayings of the "Seven Sages". Their "learning" was more concerned with - what can we call it? - - how to live well?

-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:

ancient computer

2008-12-21T08:24:00.000-08:00

I blogged this device a long time ago:

The accompanying New Scientist article discusses how people have seen a new angle to this:

"MARCELLUS and his men blockaded Syracuse, in Sicily, for two years. The Roman general expected to conquer the Greek city state easily, but the ingenious siege towers and catapults designed by Archimedes helped to keep his troops at bay.
Then, in 212 BC, the Syracusans neglected their defences during a festival to the goddess Artemis, and the Romans finally breached the city walls. Marcellus wanted Archimedes alive, but it wasn't to be. According to ancient historians, Archimedes was killed in the chaos; by one account a soldier ran him through with a sword as he was in the middle of a mathematical proof.
One of Archimedes's creations was saved, though. The general took back to Rome a mechanical bronze sphere that showed the motions of the sun, moon and planets as seen from Earth.
Special admiration
The sphere stayed in Marcellus's family for generations, until the Roman author Cicero saw it in the first century BC. "The invention of Archimedes deserves special admiration because he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with their different rates of speed," he wrote. "The moon was always as many revolutions behind the sun on the bronze contrivance as would agree with the number of days it was behind it in the sky."
Until recently, historians paid scant attention to this story: the description suggests a sophisticated mechanical device, beyond anything the ancient Greeks were thought to have been capable of. Furthermore, Cicero had no technical training, and did not explain how the device worked. He could have made the story up for effect.
Now, however, research on the battered remains of a mysterious ancient device suggests that Cicero was telling the truth. While the Antikythera mechanism is not the same one seen by Cicero - it was not made until a century later - it proves that clockwork mechanisms like the one he described really did exist, and that ancient Greek technology was far more advanced than thought. Freshly deciphered inscriptions on its dials also hint at the origins of this technology..."

and another thing

2008-11-23T14:13:00.000-08:00

saying of the Pythagoreans:

"Two-footed is a human being, and a bird, and a third thing as well."

irrational

2008-10-30T15:47:00.000-07:00

The story of the discovery of irrational numbers is shrouded in mystery, and linked with a certain early Pythagorean named Hippasus. The popular version has rumours of cover-up, betrayal, perhaps even murder.

I have taken the proof of their existence, and, seeing that the Socratic dialogue is still a contemporary form, re-created a later conversation between Socrates and the slave boy we meet in Meno.

Socrates: So you’ve kept going with your mathematical studies?
Boy: Yes, you made me see that it was possible, Socrates. I have, as you said, approached the same questions in many different ways, and have indeed gone far beyond what we talked about last time.
Socrates: And what in particular have you been studying?
Boy: Too many things to say.
Socrates: Tell me at least one or two of the areas.
Boy: Where can I begin? Factors, square numbers, whole numbers, fractions…
Socrates: So, many of the kinds of numbers…
Boy: You could say all of the numbers, as all numbers are either whole numbers, or a fraction of some kind.
Socrates: Well that’s an interesting suggestion. Are you sure you’ve included all possible numbers?
Boy: How could there be any other?
Socrates: Well, you remember that diagonal we talked about last time?
Boy: When we were doubling the size of the square, yes.
Socrates: I think I can prove to you that the side of a square and its diagonal could not possibly both be whole numbers or fractions.
Boy: How could that be?
Socrates: Well let’s draw that same diagram again.

Socrates: Let’s propose that the side and diagonal of the small square are both whole numbers, the smallest possible whole numbers they could be. Do you understand what I am proposing?
Boy: Yes, I do.
Socrates: So they could not both be, let’s say, even, could they?
Boy: Obviously not. You would be able to halve both numbers and still have whole numbers, and you proposed that they were the smallest possible whole numbers.
Socrates: I see that you have indeed, as you say, been studying. Now, if the side of the small square is a whole number, you will agree that the square itself must be whole a whole number.
Boy: Yes, that’s obvious.
Socrates: Forgive me if I move in steps that are too obvious. I only want to be sure that we have not taken some wrong turning. Now we saw last time, did we not, that the square on the diagonal is twice the size of the small square?
Boy: Yes, how could I forget!
Socrates: Then that square on the diagonal, as it is double a whole number, must be an even number?
Boy: Agreed.
Socrates: And would you agree too that if the square is even, then the side of the square must be even too?
Boy: I’ll need to think about that a moment, let me see…

Boy: Yes, I can see now that all even squares will have an even side.
Socrates: So, we have established that the diagonal must be an even number.
But the way you’ve drawn those squares, shows something else, did you see? – They are always multiples of four too?
Boy: Yes…
Socrates: And the little square is half the size of the square on the diagonal, so it must, you’ll agree, be half a multiple of four?
Boy. Yes… which will be a multiple of two.
Socrates: I can see it’s not so easy for me to race ahead of you anymore. Yes, it will be an even number. And even squares have even sides as we said, so the side of the small square is even too.
Boy: Yes.
Socrates: But don’t you see, there is something absurd here? We started by saying the side and the diagonal would be the smallest possible numbers. But now we find that they are both even.
Boy: Yes, which means they could both be divided by two to get smaller whole numbers. How can that be?
Socrates: How indeed? Are you sure that all the steps we have taken are acceptable? I haven’t moved you on too quickly, making you agree with something that is uncertain by sheer force of personality, have I?
Boy: No, Socrates, each step was clear enough. And yet we arrive at an absurdity…?
Socrates: The only way out of it that I can see – tell me if you can see another – is that the proposition we started with, that there are two smallest whole numbers that could measure the side and diagonal of the square is an impossibility: there are no such numbers.
Boy: But that seems illogical. These lines must after all have a particular length?
Socrates: That I do not deny. But both of them cannot be whole numbers – or, as it is simple enough to demonstrate, fractions for that matter.
Boy: Is there not something unreasonable about that proposition, that there are measurements which cannot be expressed either as whole numbers or as fractions?
Socrates: We cannot exactly call it a proposition, since it is something more certain that we have arrived at by carefully following the trail left by the numbers themselves. But I know what you mean about it’s seeming unreasonableness, and with your permission I propose to call such numbers “irrational numbers”.

not so ideal

2008-10-28T01:15:00.001-07:00

I really shouldn't carp at any supposed shortcomings in Socrates' method of questioning.
Any real attempt to do the same, even tidied up, with interruptions removed, would be something more like this real conversation...

Socrates: Could you make a square twice the area of that square?

Boy: No.

Socrates: What sort of square could you make then?

Boy: You could make a rectangle.

Socrates: OK, so there’s one square, there’ another, there’s a third, then a fourth. You could also draw lines from corner to corner like that…

Boy: I also thought that maybe if we squished that up, if I squished them together, we could make the rectangle into a square. Like play-doh™.

Socrates: So you’d keep the same area, and push in the short side of the rectangle?

Boy: Yes.

Socrates: OK, so there’s a line from that corner to that corner… and do you see those triangles now?

Boy: Yes. There, there, there… there’s eight. Because I know that there’s two here, so that must be four, so that must be eight.

Socrates: Good. Are all these triangles the same size?

Boy: Yes.

Socrates: Do you see this square in the middle?

Boy: Yes. It’s a diamond. Well, it’s not a diamond. Because that is a square. And a diamond… Say this (draws) was a square, even though it isn’t, and then we do that (rotates)… that wouldn’t be a diamond. But this (draws) … that would be a diamond.

Socrates: A diamond has to be longer one way than the other?

Boy: Yes

Socrates: Right. So that’s a square.

Boy: That’s a square on its point.

Socrates: How many triangles were in that first square I showed you?

Boy: Two.

Socrates: And this last square on its point has…?

Boy: Four.

Socrates: So what can we say about the squares, their two sizes?

Boy: Er… they’re the same size…

Socrates: What did I ask you to do in the beginning?

Boy: You asked me to…

Socrates: Make a square that was double. So the first square has how many triangles?

Boy: Two.

Socrates: And the last one?

Boy: Four.

Socrates: Two... and four?

Boy: …

Socrates: So isn’t that middle square double the first one?

Boy: Oh yeah!

doubling a square

2008-10-26T08:29:00.000-07:00

Looking at that famous part in Plato's Meno:

SOCRATES: Tell me, boy, is not this our square of four feet? You understand?

BOY: Yes.
SOCRATES: Now we can add another equal to it like this?

BOY: Yes.
SOCRATES: And a third here, equal toeach of the others?

BOY: Yes.
SOCRATES: And then we can fill in this one in the comer?

BOY: Yes.
SOCRATES: Then here we have four equal squares?
BOY: Yes.

SOCRATES: And how many times the size of the first square is the whole?
BOY: Four times.
SOCRATES: And we want one double the size. You remember?
BOY: Yes.
SOCRATES: Now does this line going from comer to comer cut each of these squares in half?

BOY: Yes.
SOCRATES: And these are four equal lines enclosing this area?

BOY: They are.
SOCRATES: Now think. How big is this area?
BOY: I don't understand.
SOCRATES: Here are four squares. Has not each line cut off the inner half of each of them?
BOY: Yes.
SOCRATES: And how many such halves are there in this figure?

BOY: Four.
SOCRATES: And how many in this one?

BOY: Two.
SOCRATES: And what is the relation of four to two?
BOY: Double.
SOCRATES: How big is this figure then?

BOY: Eight feet.
SOCRATES: On what base?
BOY: This one.

SOCRATES: The line which goes from comer to comer of the square of four feet?
BOY: Yes.
SOCRATES: The technical name for it is 'diagonal'; so if we use that name, it is your personal opinion that the square on the diagonal of the original square is double its area.
BOY: That is so, Socrates.
SOCRATES: What do you think, Meno? Has he answered with any opinions that were not his own?
MENO: No, they were all his.
SOCRATES: Yet he did not know, as we agreed a few minutes ago.
MENO: True.
SOCRATES: But these opinions were somewhere in him, were they not?
MENO: Yes.
SOCRATES: So a man who does not know has in himself true opinions on a subject without having knowledge.
MENO: It would appear so.
SOCRATES: At present these opinions, being newly aroused, have a dream-like quality. But if the same questions are put to him on many occasions and in different ways, you can see that in the end he will have a knowledge on the subject as accurate as anybody's.
MENO: Probably.
SOCRATES: This knowledge will not come from teaching but from questioning. He will recover it for himself.
MENO: Yes.

Not being a mathematician, I like the simplicity of this demonstration.

And I also like it that way back then, this careful, step-by-step approach was being used. In "hindsight" I think the steps could have been a little different, a little more time taken to talk round the figure, to avoid the "I don't understand".

But Socrates makes up for any shortcomings in his questioning (!) by acknowledging the need for "many different ways" and "many different occasions".

evidence

2008-10-13T09:01:00.001-07:00

The Zones
Originally uploaded by jovike.

I touched on the question of empirical evidence before. And these were empirical people - they - Thales, Pherecydes, Anaximander - were busy with sundials, and day lengths and the like.

I must have mentioned this abstract before:

"Abstract. Probably the most direct observation of the Earth’s curvature is how objects appear from over the horizon when we approach them and disappear as we get further away from them. Similarly, the portion of a high object (a building or a mountain) that is visible depends on the height of the site where the observation is made. Based upon these very obvious facts, a simple method to estimate the Earth's radius R has been applied. The method does not need either sophisticated instrumentation or complex mathematics. In our application of the method presented here, the result is R = 6600 ± 600 km in the best case. A discussion is presented about the possible use of this method in ancient times. Surprisingly enough, we have not found any reference to the use of this method despite its being simpler than, for example, the classical approach of Eratosthenes."

And other evidence??

Here's a list I put together when I started thinking about this:

height of stars, sun, moon, planets varies with latitude
ships disappearing at a set distance from port
the moon is a sphere
the sphere of the sky rolls ‘under’ the earth (support impossible)
eclipse
sun on mountain?
Islands missing their bottom half
More islands becoming visible as one climbs
Sunrise and sunset at different longitudes
Apparent curvature of earth up high mountains
Mountains appearing shorter than they ought to be
The pattern of day length through the year
Time zones (?!)
Variation in day length through year?
The clouds, light on them at dawn and dusk, the way they appear at the horizon

Some of them I'm not so sure of, some are glaringly obvious. To us, now - and would have been for whoever looked then, and many people did.

explanatory power

2008-10-13T08:16:00.000-07:00

Wikipedia says that Pythagoras "saw harmony in the universe and sought to explain it. He reasoned that Earth and the other planets must be spheres, since the most harmonious geometric solid form is a sphere."

But is there really any evidence that this was his reasoning? Why shouldn't everything be spherical if this is so perfect?

Aside from all the observational reasons he could have had for thinking the Earth is a sphere, there is the sheer explanatory power.

Coldness in the north is explained, and hotness in the south. The height of the sun and the stars changing with latitiude.

And if you tilt the axis of the Earth (or for that matter of the Heavens) you explain even more - the seasons, temperature changes, day length varying from north to south and through the years, the skies changing through the year.

You'd have to play with a sphere for a while to see all this.

Corvus

2008-09-14T15:14:00.001-07:00

He asked us what constellations we could see and we named them. When we came to the Raven and the Snake, Rhoda told us that she used to sing the song of the Raven and the Snake, called ‘Apollo’s Command’.

Pythagoras got up and gave her the lyre.

‘Sing Apollo’s Command for us now.’

‘I can’t,’ she said, trying to give the lyre back.

‘But you must. Sing it,’ he insisted and she took the lyre from him and began to pick the strings. She sang out to the stars:

‘Apollo prepared a feast for Zeus,

Sent Raven down to earth with a golden cup

“Fetch me some fresh spring water,” he said,

Raven went down, found the spring

Landed on a fig tree.

Looked at the figs, hard and green.

Forgot the cup, forgot the spring,

Thought only of the figs on that tree.

And waited, waited,

Waited till they were soft and sweet,

And with ripe figs filled his belly.

Then Raven saw the golden cup,

Remembered Apollo’s command,

Picked up the cup and filled it up,

Wondering what to say when he saw the god.

Just then Snake shot over the pool;

Raven saw his chance and grabbed it,

And with water and Snake flew back to the god.

“You’ve been gone so long, what kept you?”

Raven dropped down the snake.

“It was this evil thing that was guarding the spring

I told him he would be punished.”

Apollo, who knows truth from lies,

Said “I see your belly, Raven.

It’s full of the figs you waited for.

It’s you, not Snake, I’ll punish.

From now on your cry will always be rasping and dry;

No spring will ever quench your thirst.”

And to remember this

Apollo took Raven, cup and Snake

Reached up to the night sky

And hung them for all to see.’

Rhoda finished, stood up and gave the lyre back to Pythagoras.

‘Now I know why Aesop sent you to me,’ he said. ‘It was so that we could sit up here, high up on Mount Kerkis and hear you sing. Do you know more like that?’

donkeys and sitting

2008-09-11T14:00:00.001-07:00

Still on the question of 'why maths', why in ancient history or prehistory did someone start it up? Why did the 'Milesian Philosophers' go in for it? ...

There is the story of Nasrudin and the donkeys.

His friend had asked him to bring nine of them back from the market. He found that when he was riding on them there were eight. But when he got off there were nine.

(The picture is to be found here, along with a fuller telling of the tale.)

When Nasrudin got seated on a donkey, the counting went wrong. When he did the counting properly, he wasn't sitting on a donkey.

So the link? Walking and counting go together. Sitting on donkeys goes with getting the wrong answer.

So, maths as a way of getting a man off his donkey?

Speakers' corner

2008-07-18T15:42:00.001-07:00

Speaker's corner ~ Silently waiting for an audience
Originally uploaded by Boreio Selas.

When I was just a teenager Paul used to speak to big audiences at Speakers' Corner. Now, in the noisy show of the place he just, like Diogenes with his lamp, stands and waits for an individual human being.

A story retold from back then:

A girl who had been in London for some time, from Germany -
She was asked "Where is Virgin Records?"
She pointed the way.
"Where is MacDonald's?"
She pointed it out.
- "Oxford Street?" - "Picadilly?" - she knew all these.
Then she was asked, "And where can I find wisdom?"
She got out her dictionary.
Paul said "You've been wasting your time. It's things like Wisdom, Courage, Beauty that makes you human, not these other things. You've been here all this time - and you haven't learnt the essential things."

§§§§§

It is related that when Socrates first met Xenophon, then a boy, in the street he stopped him and asked where various articles could be got.

Xenophon told him. Socrates then asked, ‘Where can you get brave and virtuous men?’ and when Xenophon was puzzled told him to come with him.

connections

2008-06-12T02:18:00.001-07:00

the tube
Originally uploaded by simonsterg.

As a kid I got to know various bits of London. Often I got to them by Tube. Starting from my home in Paddington, I popped up in South Kensington or Tower Hill or Baker Street. They seemed like very separate places, unconnected, with their own climates and moods. Only later when I moved about overground a lot more did the islands of familiarity join up into one London.

I'm not a mathematician, but you can get a sense of how the world of number interconnects.

Take this picture from two posts back:

I thought "what if I tidy this up a bit? - make a nice neat diagonal across the rectangles - what then?" Like this:

This is an intriguing shape...

The triangles, with sides 3,4,5 (the first and most familiar "pythagorean triple") have an area of 6 squares.

The diagonal square in the middle is a 5 by 5 square and has an area of 25 squares.

And - yes -it connects with this proof of The Theorem - See!

"See!"

"don't wear a god's image on your ring"

2008-06-03T14:26:00.000-07:00

I'm going into windbag territory here... I've got my special ring on... If I don't come out in a few days, come and get me...

Academics naturally are tuned into ideas. They want to read what people believed, what their "philosophy" was.
But like Borges they / we could be missing everything.

Wikipedia has a very typical derivation for the word "philosophy":

The word philosophy is of Ancient Greek origin: φιλοσοφία (philosophía), meaning "love of knowledge", "love of wisdom".

The Pythagoras page says that:

He was the first man to call himself a philosopher, or lover of wisdom.

But going back to what Diogenes Laertius said:

The first... to call himself a philosopher (lover, friend of wisdom) was Pythagoras. "For no one," he said, "is wise (sophos) except god."

(Lives of the Philosophers, i. 12)

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

He wanted to contrast himself with "the wise", the sophists, and adopt a name that was more modest. He called himself a (mere) friend of wisdom.

Still, even to be the cousin, or acquaintance, or next door neighbour of wisdom would be a fine thing.

Wisdom takes the study of the ancients out of the academic realm. We all know, even we who are not all that wise, that wisdom can't be a matter of merely accumulating knowledge, or comparing it, or tracking it back. We have some feeling that it must be:

practical - it will help us make the most of the situation as it actually is, to do something that can be done;

to do with balance - puting things in their place - so much of this kind of knowledge is useful, so much of this ignorance, so much of this activity, so much of this inactivity, and so on;

must involve a fair amount of self-knowledge - as it's our own biases and blindnesses that skew decisions.

You wouldn't especially expect to find it in an academic, but perhaps it was there in those first "philosophers"

You wouldn't really expect to arrive at wisdom through reading lots of books, or writing essays on them. But the ancient philosophers seem to have been (obviously Socrates is our clearest example) very interested in how to find an education that would develop some wisdom in their young friends. It was by no means a fixed curriculum, and it wasn't necessarily what we would think of as education.

why maths???

2008-05-29T02:30:00.001-07:00

coming down from moni evangelistrias
Originally uploaded by simonsterg.

As a kind of hiking.

Someone once said:

"All the corruption in the world arises from this - someone believed in
someone out of imitation or disbelieved in someone out of imitation."

Well, there should be lots of imitation, , learning a language, learning songs, learning to cook. And then you should be doing things where you don't imitate, where there is a world to explore.

It can be like this with numbers.

An example...

I read the other day that if you square an odd number and take away one you always end up with a multiple of 8.

So, for example you square 5, that's 5 times 5, which is 25. Take away 1 and you get 24 - which is a multiple of 8.

Now doesn't that seem curious? There's an eight hidden away in all those squares of odd numbers? A mysterious eight that nobody put there, but is just waiting for someone to pass by?

This intrigued me. Why was that eight there? Why wasn't it seven, or nine?

So what do you do? You follow the trail...

How many eights are there in the squares?

Make a table:

And then you notice those numbers in the last column...

1 3 6 10 15 21 ...

The triangle numbers!

So, eight triangles are hidden away in the squares.

This must make a good drawing. Hang on...

There they are, the "triangles", eight of them, all fitting neatly into the square!

A hidden terrain opens up!

What next?

Perhaps to prove that however big the square there will always be eight triangles.

And so there is a path you follow, a footpath - only one person at a time. But it could be sociable too if other people were doing that kind of walking.

It's not unique to maths. It could be hunting. Or poetry. Or music. Or science. Or people-watching. Or hiking.

maths

2008-05-08T15:54:00.000-07:00

There's the obvious question: What did they see in maths, as it wasn't practical gain??

I don't know, but I like the few tiny snatches of conversation we hear, famously, from old man Euclid...

§§§§§§§§§ §§§§§§§§§ §§§§§§§§§

New student: "How do I benefit by learning these things?"

Euclid to slave: "Give him threepence, since he has to make a profit out of what he learns".

§§§§§§§§§ §§§§§§§§§ §§§§§§§§§

Ptolomy: "Is there a shorter way to study geometry than your book?"

Euclid: "There is no 'royal road' to geometry."

a figure and a sixpence

2008-05-04T13:37:00.000-07:00

Proclus (450 AD!) says:

Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures.

Considering the previous post alongside this, he examined the principles in a material manner too - on a particular beach, with particular stones to play a game, making a circle in a particularly smooth stretch of sand, with particular pupils. He built the road from particular ephemeral arrangements of pebbles all the way to the abstract and immaterial.

Proclus goes on to talk about the motivation for all this:

I emulate the Pythagoreans who even had a conventional phrase to express what I mean "a figure and a platform, not a figure and a sixpence", by which they implied that the geometry which is deserving of study is that which, at each new theorem, sets up a platform to ascend by, and lifts the soul on high instead of allowing it to go down among the sensible objects and so become subservient to the common needs of this mortal life.

on the beach

2008-05-02T07:43:00.001-07:00

beach
Originally uploaded by simonsterg.

returning to Pherecydes, this marvel is reported of him:

"For it is said that he was walking along the sea-shore at Samos, and that seeing a ship sailing by with a fair wind, he said that it would soon sink; and presently it sank before their eyes. "

Is it possibe, that what has come through to us here is Pherecydes talking about the horizon, just a few kilometers away at sea-level...

Could he be talking about how the bottom of a ship disappears, and then the whole ship disappears, when it goes down 'behind' the horizon??

So how about the other 'marvellous story'? -

'At another time he was drinking some water which had been drawn up out of a well, and he foretold that within three days there would be an earthquake; and there was one.'

Wkipedia says that experts are of the opinion that you can't predict earthquakes, but someone suggested to me that perhaps the water in the jug rippled, amplified a tremor that gave Pherecydes good reason to think there could be a bigger one on the way.

Part of what I like about these tantalising tales is that they happen in a place, the first one on a beach. Perhaps Pythagoras was walking on the sea-shore with his teacher? Maybe he reported the story? There's no stopping speculation now... It's this 'outdoors science' that I want to pick up on, to conjure up. With no end of unhistorical speculation of course.

part of a circle

2008-04-26T13:30:00.001-07:00

When we went to the beach one afternoon I took the cord, a ring and a stick. The others watched as I staked the stick in the sand, tied the cord to the ring and put the ring over the stake so it would turn freely.

‘Dorcas, this will be easy for you,’ I said. ‘It’s the hexagon.’
Dorcas stood back from me and announced in a loud voice to the other two:
‘The amazing Leon will now create a perfect hexagon, using only circles and a straight stick.’
‘First of all we need to make the sand flat and get the stones out of the way,’ I said.
We threw the stones towards the sea and smoothed the sand out with sticks.
Then the others stood back while I walked the cord round the stake, digging a circle into the sand just as Pythagoras had done. I made the second and third circle, and then with a stick linked the points to make the hexagon.
Dorcas cheered. She made us all gather up stones and lay white ones along the three circles, and black ones for the hexagon.
After that she made the other two have a go at creating their own hexagons just as I had.
Somehow because she was excited the others agreed straight away, and not only made the hexagons, but were enjoying it as well.
‘This is a kind of game too,’ she said. ‘You have to ask yourself: Can I make a square? Can I make a pentagon? Then the challenge is to make them just using the rope and the stick.’
I’d learnt to make many shapes like this with Anaximenes, but using paper and ink. Over the next weeks the four of us made a lot of them in the sand, and carefully laid stones in the lines of sand to make them last longer. No one moved our stones. The beach became our beach, a giant scroll, its stones not scattered randomly any more but mapping out figures in circles and lines.

tyrant

2008-04-10T07:39:00.000-07:00

It was people like Polycrates that gave us the name 'tyrant'.

The part of Aristotle's Politics which mentions Polycrates is worth quoting:

Tyrannies are preserved two ways most opposite to each other, one of which is when the power is delegated from one to the other, and in this manner many tyrants govern in their states. Report says that Periander founded many of these. There are also many of them to be met with amongst the Persians. What has been already mentioned is as conducive as anything can be to preserve a tyranny; namely, to keep down those who are of an aspiring disposition, to take off those who will not submit, to allow no public meals, no clubs, no education, nothing at all, but to guard against everything that gives rise to high spirits or mutual confidence; nor to suffer the learned meetings of those who are at leisure to hold conversation with each other; and to endeavour by every means possible to keep all the people strangers to each other; for knowledge increases mutual confidence; and to oblige all strangers to appear in public, and to live near the city-gate, that all their actions may be sufficiently seen; for those who are kept like slaves seldom entertain any noble thoughts: in short, to imitate everything which the Persians and barbarians do, for they all contribute to support slavery; and to endeavour to know what every one who is under their power does and says; and for this purpose to employ spies: such were those women whom the Syracusians called potagogides Hiero also used to send out listeners wherever there was any meeting or conversation; for the people dare not speak with freedom for fear of such persons; and if any one does, there is the less chance of its being concealed; and to endeavour that the whole community should mutually accuse and come to blows with each other, friend with friend, the commons with the nobles, and the rich with each other. It is also advantageous for a tyranny that all those who are under it should be oppressed with poverty, that they may not be able to compose a guard; and that, being employed in procuring their daily bread, they may have no leisure to conspire against their tyrants. The Pyramids of Egypt are a proof of this, and the votive edifices of the Cyposelidse, and the temple of Jupiter Olympus, built by the Pisistratidae, and the works of Polycrates at Samos; for all these produced one end, the keeping the people poor. It is necessary also to multiply taxes, as at Syracuse; where Dionysius in the space of five years collected all the private property of his subjects into his own coffers. A tyrant also should endeavour to engage his subjects in a war, that they may have employment and continually depend upon their general. A king is preserved by his friends, but a tyrant is of all persons the man who can place no confidence in friends, as every one has it in his desire and these chiefly in their power to destroy him.

Ikaria 249

2008-03-28T11:18:00.001-07:00

Ikaria 249
Originally uploaded by isl_gr.

This paper says about Ikaria:

"The island was originally densely forested. Icaria was a shipbuilding centre and a charcoal exporting country. Throughout history it has attracted the dominant powers of the eastern Mediterranean, each of which, in its own way, influenced the forest. The flourish cities of antiquity among them Samos, put pressure on its local resources.
These demands have continued through out the vicissitudes of history. Aristotle (4th century BC) mentions in Politics that Polycratis tyrant of Samos, as he strengthened his power and over neighbouring islands, he create a great navy force.
The construction of boats named «samaina» would cause the destruction of Ikaria’s forests."

- although looking through The Politics I can only see one mention of Polycrates, comissioning huge public works to keep his people poor and occupied.

It sounds very likely though. All that wood for the hundreds of boats had to come from somewhere. The paper mentions the trees found here:

"Quercus Ilex (oak tree) is the dominant tree species. Other species include Quercus Pubescens, Arbutus Unedo, Arbutus Andrachne and Phillyrea Latifolia."

+++

This video by Jernej Burkeljca (see here for details) focuses on the present problem with the forest, and attempts to solve it.

dog days

2008-03-27T13:29:00.000-07:00

Sirius the dog star is the brightest star in the sky.

It's usually shining brightly up there, but it has a little break in Summer, when the sun's in it's part of the heavens and its little light is mingled with the sun’s daytime light, making the summer even hotter.

Then as the sun moves away it 'rises'.It becomes visible after its absence in the heat of the summer, the 'dog days'.

In the past, when the stars were the calendar, this was a turning point in the year.Listen to Hesiod in his 'Works and Days'

When the piercing power and sultry heat of the sun abate, and almighty Zeus sends the autumn rains , and men's flesh comes to feel far easier, -- for then the star Sirius passes over the heads of men, who are born to misery, only a little while by day and takes greater share of night, -- then, when it showers its leaves to the ground and stops sprouting, the wood you cut with your axe is least liable to worm. Then remember to hew your timber: it is the season for that work. Cut a mortar three feet wide and a pestle three cubits long, and an axle of seven feet, for it will do very well so; but if you make it eight feet long, you can cut a beetle from it as well. Cut a felloe three spans across for a waggon of ten palms' width. Hew also many bent timbers, and bring home a plough-tree when you have found it, and look out on the mountain or in the field for one of holm-oak; for this is the strongest for oxen to plough with when one of Athena's handmen has fixed in the share-beam and fastened it to the pole with dowels. Get two ploughs ready work on them at home, one all of a piece, and the other jointed. It is far better to do this, for if you should break one of them, you can put the oxen to the other. Poles of laurel or elm are most free from worms, and a share-beam of oak and a plough-tree of holm-oak.

and then again

But when the artichoke flowers, and the chirping grass-hopper sits in a tree and pours down his shrill song continually from under his wings in the season of wearisome heat, then goats are plumpest and wine sweetest; women are most wanton, but men are feeblest, because Sirius parches head and knees and the skin is dry through heat. But at that time let me have a shady rock and wine of Biblis, a clot of curds and milk of drained goats with the flesh of a heifer fed in the woods, that has never calved, and of firstling kids; then also let me drink bright wine, sitting in the shade, when my heart is satisfied with food, and so, turning my head to face the fresh Zephyr, from the everflowing spring which pours down unfouled thrice pour an offering of water, but make a fourth libation of wine.

Too much of Hesiod and he can get a tiny bit self-satisfied, but I love these little snatches of life from back then, the right tree for the right job, the times of year, the plants and sounds... and the stars.

equinox

2008-03-20T14:41:00.001-07:00

They watched the skies, and were part of a long tradition of sky-watching. People used the skies a lot more. They would have understood the celestial equator and the ecliptic, and of course the equinox. I have to really bend my mind to grasp the ideas...

interview with Thales

2008-03-18T09:34:00.000-07:00

Thales is known best as one of the founders of maths and science, but, like all the 'philosophers' didn't confine himself to 'natural philosophy', as his reported answers to these questions perhaps shows:

What is very difficult?

To know one's self.

And what is easy?

To advise another.

What is most pleasant?

To be successful.

What is the divinity?

That which has neither beginning nor end.

What hard thing have you seen?

An old man a tyrant.

How might a man most easily endure misfortune?

If he saw his enemies more unfortunate still.

How might men live most virtuously and most justly?

If we never do ourselves what we blame in others.

Who is happy?

He who is healthy in his body, easy in his circumstances, and well-instructed as to his mind.

from Diogenes Laertius

Pherecydes of Syros

2008-03-17T16:07:00.000-07:00

Once again, there are tantalizing clues, stories perhaps misconstrued…

Diogenes Laertius writing many centuries later says:

“A sun-dial is also preserved, in the island of Syra, of his making.”

“Pherecydes was a Syrian… the first person who ever wrote among the Greeks on the subject of Natural Philosophy and the Gods. And there are many marvellous stories told of him. For it is said that he was walking along the sea-shore at Samos, and that seeing a ship sailing by with a fair wind, he said that it would soon sink; and presently it sank before their eyes. At another time he was drinking some water which had been drawn up out of a well, and he foretold that within three days there would be an earthquake; and there was one.”

Marvellous, or bizarre?

Pherecydes’ epitaph is given, on this webpage:

"All knowledge that a man may have had I:
Yet tell Pythagoras, were more thereby,
That first of all Greeks is he; I speak no lie."

Which doesn’t make complete sense to me. What the translator meant by ‘were more thereby’ I really don’t know.

Another translator has it:

“The end of all wisdom is in me. If aught befall me, tell my Pythagoras that he is the first in all of Hellas. In speaking this I do not lie.”

But then Pythagoras is said to have gone to be with him and look after him when he was dying. The epitaph seems strange in the light of this.

But anyway…

The Wikipedia page on Pherecydes mentions among his legacies a sundial:

“A 'heliotropion', or 'shadow-chaser': The first example of this instrument, which was a more advanced kind of gnomon used to determine midday and to calculate the length of the year and the geographical latitude, was built by Pherecydes in Samos."

(How does a sundial do those things? I’ve never used one, but thinking about it it seems clear: The sundial shows you the direction of the sun and also how long the shadow is. It tells you it’s midday when the shadow is shortest. It tells you it’s midsummer when the midday shadow is shortest. And this midsummer midday shadow gets shorter as you go south.)

It looks as if, like his contemporary Thales, Pherecydes was making observations of the sun’s behaviour through the year and at different latitudes.

And he is said to have travelled widely. Also to have gone to Samos, and been the teacher of Pythagoras...

Ikaria 231

2008-03-05T04:58:00.001-08:00

Ikaria 231
Originally uploaded by isl_gr.

This beautiful picture (the comments should be read too!) shows Atheras, the long spine-mountain on Ikaria, and in the haze, almost invisible, Kerkis, the massive white mountain of Samos.

Stand on Kerkis and see a star set. It will be, I think, around ten minutes before they see the same star set on the highest peak of Atheras.

At that moment, the moment the star sets, light a beacon on Kerkis: On Atheras they will see the beacon light, but the same star will not set for them for another ten minutes.

When they see the star set on Atheras and light their own answering beacon , you on Kerkis will see it ten minutes after the star set for you.

What does this mean? It means the times are different on the two islands, the heavens at any one moment are different.

And what does that mean? It means that the world curves from east to west. (you can, too, work out the size of the world.)

Imagine the moment. In the dark you light the flax, soaked in oil, at the bottom of the tall pine structure of the beacon, dry reeds catch the flame in an instant, the crackle changes to a roar as dry branches burst into flame. Sparks fly. You stumble back from the sparks and heat. And then wait. Wait for the answering beacon in the west. Ten minutes and then it comes...

curves and confusion

2008-03-05T04:20:00.000-08:00

Things get confused, garbled. You try to describe something with shapes, people get the wrong idea. You should have drawn a picture.

Everyone says that Anaximander said the world was drum shaped, floating in space. Like this, with all the land and sea on the flat circular 'skin' of the drum:

But I think he didn't say that. I think he said it was drum on its side like this, with the land and see on the curved surface:

The flat circular ends would have been east and west.

Why do I think this?

Well, I think we don't give them quite enough credit for being smart. We think they lived a long time ago so they were not quite as bright as us. Actually, because we have a lot of things done for us, they were quicker than us. And the ionian philosophers were gathering a lot of empirical evidence. They knew the path of the sun, planets and stars in the sky. They had heard about places further south and further north and knew many of the differences you get with latitude. The sun is higher in the sky as you go south, and lower as you go north. The pole star is nearer to the northern horizon as you travel south, and higher in the sky as you travel north. It is hotter as you go south and colder as you go north.

The easiest way to explain all this is that the earth curves from north to south.

However there are no such changes when you travel east or west. You can't even detect differences in time zone because there was A. no way of instantly communicating with people at a different longitute and B. no way of keeping time accurately enough as you travelled to see that the time was different in the place you came to.

So let's say there is no curve to the earth from east to west.

What do you get? A drum on its side.

If you say it is curved both ways, say a sphere, you will have to find evidence for an east-west curve.

first

2008-03-05T00:24:00.000-08:00

Sailors would of course have known about the earth's curve before everyone else.

at Delphi

2008-02-15T06:23:00.001-08:00

there were supposedly three things carved above the entrance to Apollo's temple:

KNOW YOURSELF

and

NOTHING TO EXCESS

and

These three things seem to be an entrance into all the philosophy and tales of the Greeks (take Plato's Apology and Ovid's Metamorphosis as examples). The E being a little bit of mystery.

Ikaria 001

2008-02-09T11:30:00.001-08:00

Ikaria 001
Originally uploaded by isl_gr.

Two Februaries ago, I was looking through flickr photos, I don't know what tag I was searching. Perhaps it was Apollo, Delos, I don't remember. Anyway, the god was smiling on me, and I came across another picture by isl_gr looking out from the island of Ikaria towards Delos on a beautiful afternoon.

Her blog - "Eleni in Ikaria - this blog is about the stupid side of me, that's my love for nature, loneliness and Ikaria island" was just clocking a thousand visits, making her headache worse. She had almost been carried away by a wave clicking her camera on a cliff. It had been a snowy stormy January on Ikaria, telephone lines were down, the cat was out all night with its boyfriends, she dreamt she was a grouvalina on Livadi beach fighting the bourgois holidaymakers where secret salty lilies make the best fragrance like they did back on Knossos, a big black raven called from the sky where Icarus had flown intoxicated by the games of sunlight and cloud and reflections...

It was the first conversation I had on flickr, and it went like this:

	simonsterg (that's me) says: Wonderful. One of the things that intersts me is what you can see of other islands? You must be able to see Vigla, the big mountain on Samos. Can you see Naxos? Do the islands appear on certain days? Here where I live, the Pyrenees appear on some days when the air is clear. Other days, even when the sky is blue, they are hidden. They are 100 km away. Tomorrow we head up there to ski. Or fall over in my case. Posted 24 months ago.
	isl_gr says: you see them as visions. Like the oasis look in the deserts or like the remote mountain tops of a sierra look like when you are above a sea of clouds. I could see Mykonos (and Delos behind it). The time to get my camera, and the vision faded. In return, I got a godly colour and texture. Posted 24 months ago.
	simonsterg says: where is the camera when you need it! I have just been looking at your picture of cloud topped Kerkis / Vigla. I think Pythagoras, creditied with being the first to say the world is a sphere, saw it from the top of that mountain, visions of tops of islands with the lowlands hidden below the horizon. They say his cave is lower down the mountain. Posted 24 months ago.
	isl_gr says: mountain tops are very important>> philosophers, scientists, dreamers etc. -and saints (mt. Athos) I tell stories=>like deep dens with running water and where land meets the sea. Also love the sound of wind in the forests ... but weren't you supposed to be in the Pyrenees? Posted 24 months ago.
	simonsterg says: Back. Three days of hurtling ungracefully through snow. My five year old boy now skis better than me. Talking of Athos, I like the story that news of the fall of Troy was relayed to Argos by mountaintop beacon, from Ida to Lemnos to Athos and down the mainland. I wonder if beacons were really used like that? Posted 24 months ago.
	isl_gr says: yes they were until they installed telegraph. The castle on this mountain was a beacon. From there they transmitted signals from post to post as far as Constantinople.
	simonsterg says: How did that work then? And where did it connect to from Ikaria? In my local forest there is an old tower from the time before telegraph. LinkText It worked with a sort of semaphore on top and a series of towers. Posted 24 months ago.
	isl_gr says: Yes, the French system was the last of a long tradition. It takes an empire to build a system like this. Can't find a good link for Greece now. Just: 67.18.47.148/com/index/convert/morse/history/friktories.asp for Troy-Mycenae, and for Ikaria: www.island-ikaria.com/culture/history.asp Posted 24 months ago.
	simonsterg says: Thanks. Apollo, the Far-Shooter, would have liked that kind of communication, I think. Posted 24 months ago.
	simonsterg says: I came across a picture on: www.latein-pagina.de/ovid/ovid_m8.htm (nearly halfway down this slow loading page) It is similar to your one (not as good of course!) I wonder if you would have a look and tell me where you think it might be. I don't speak german or know the shapes of islands. The page has lots of great pictures of the Icarus story too... (I have always liked the Matisse cutout one.) Posted 24 months ago.
	isl_gr says: Apollo would have also liked the internet ! The link is amazing ! (I can't read German ...but I understand a bit of Latin) I'll add it as link in groups.yahoo.com/group/hikingIkaria/links/ Thank you

ten

2008-02-06T12:57:00.001-08:00

ten
Originally uploaded by optick.

What actual, real, significance can ten have??
This triangle is reputed to have been of special significance to the Pythagoreans, perhaps to Pythagoras too.
Yes, it's 1 + 2 + 3 + 4.
Yes, we have ten fingers.
Is there more? Does maths in-itself relate to human experience or the human condition or even the metaphysical realm?
I don't know. Already I am out of my depth.

into the distance

2008-01-29T13:48:00.001-08:00

The air was clear; dark blue sea and light blue sky met at a horizon far away. We looked down on the Fourni Islands below as if we were birds flying above them. To the west was the Long Island. Icarus had seen the island like this when he and his father Daedalus had made wings with birds’ feathers and wax. Escaping from the labyrinth of King Minos they flew over the choppy seas of the Aegean.
The blue sky all around us dizzied me. Pythagoras took my hand and pointed out to the west where the sun was making its way to the horizon.
‘Delos is just to the right a bit, behind the Long Island. Can you see Paros in the distance to the left? And there’s Naxos.’
Turning round slowly I saw far out, as Icarus would have seen flying in the sky, islands, mainland, Samos itself.
The air was still and silent.
‘It was by coming up here,’ said Pythagoras, ‘that I could see for certain that the world is a sphere. It was here that I could know the true size of the world.’
I looked at the horizon.
‘It does look curved,’ I said.
‘It’s not that. Up here you can see islands that are invisible down below. On the clear days you can see the tops of distant mountains, just the tops, their feet hidden behind the horizon.’
‘And it wouldn’t be like that if world was flat?’
‘Of course not. How could anything be hidden behind the horizon if it were flat?’
He seemed right; it was as if we could see the whole sea from up here.
We stood quietly and watched as the sun went down to the horizon. The western sky yellowed and the sun turned orange, and became fat as it touched the sea. We watched it disappear.
Daedalus had warned Icarus not to fly too close to the sun, but Icarus who loved being a bird too much could not resist flying higher and higher. Here, flying above the Long Island, Icarus felt the wax in his wings melt and saw the feathers begin to fall off. He fell down, down into the sea.
‘Look at the sky. Look at the whole sky,’ said Pythagoras. ‘What do you see?’
‘Pink clouds high up,’ said Dorcas.
‘Yes, what else?’
‘Red where the sun was,’ I said, ‘and above that yellow, and above that blue.’
‘What are we supposed to see?’ asked Zalmoxis.
Pythagoras turned to Zalmoxis and laughed. ‘Yes, that’s just what everyone wants to know. “If I knew what two and two was I would say four.” But just look at the sky.’ He turned Zalmoxis around to face the east. ‘It has many things to tell you, more than I can ever tell you. You must watch it by day and by night and you won’t need me to tell you anything. What do you see?’
Zalmoxis looked. ‘A dark blue band low down, above that pink, and above that blue again.’
‘That’s better. Watch the dark band.’
We stood facing east. The sun had set and it was getting colder.
‘Why did Thales say the earth is barrel shaped and you say it is a sphere?’ I asked.
‘The right answer is not what we want. If we thought you would just believe us and agree with us we wouldn’t take you as pupils. We want you to learn to look for yourself and think for yourself. You’re shivering – you’re making me feel cold. Come on let’s go down.’

tragic consequences

2008-01-24T07:20:00.000-08:00

"Thespis, the "inventor of tragedy" was born in Attica, and was the first prize winner at the Great Dionysia in 534 BC. He was an important innovator for the theatre, since he intoduced such things as the independent actor, as opposed to the choir, as well as masks, make up and costumes.

Thespis walked around Athens pulling a handcart, setting up a kind of one man plays, where he showed the bad behaviour of man. The word for actor " thespian" comes from his name. His contemporary Solon resented him, with the explanation that what he showed on stage soon would be acted out in reality as well."
from in2greece.com

Did the cart cause the bad behaviour, or was there a function in displaying the behaviour?

best and worst

2008-01-17T03:05:00.000-08:00

Between heaven and earth there flies a red bird that is always wet. Can you tell me what it is?

There are 32 white stools ranged around the long red room where this old gossip lives.

Hugh Lupton’s riddle book has a great Cuban tale in it that he heard from Mimi Barhélemey, called The Best and the Worst in All the World. I was pleased to discover that it is an descendant of a much older story told about Aesop:

Aesop, a slave to Xanthus on the island of Samos, was ordered one day to arrange the meal for a large banquet. He was to provide the choicest dainties that money could buy.
When the guests arrived they were treated to a starter of tongue, served with a variety of excellent sauces. The guests of course made a few jokes about this. But when the next course was tongue too, they were puzzled. And when the third and fourth courses turned out to be tongue too puzzlement turned to perplexity. Xanthus was embarrassed and turning to Aesop angrily demanded an explanation.
‘Didn’t I tell you to provide the best meat you could find?’
‘What could be better than the tongue?’ said Aesop. ‘It is the tongue that teaches and enlightens, the tongue that praises and entertains, it is the tongue that strikes bargains and makes promises.’
The guests liked what Aesop said and good feeling was restored to the meal.
Xanthus spoke up: ‘Well, perhaps all of you could do me the favour of coming again for another meal tomorrow?’ And turning to Aesop he added, ‘This time could you arrange a meal with the worst meat you can find?’
The guests liked the idea and returned the following evening. And, to their confusion, nothing but tongue was served again.
Xanthus seemed angry. ‘How,’ he said, ‘can you serve up tongue as the best possible meat one day, and then the worst meat the next?’
‘What,’ replied Aesop, ‘can be worse than the tongue? What evil is it not involved in? Violence, injustice and fraud are all debated and resolved upon and communicated by the tongue. It is the ruin of empires, cities and friendships.’
The guests were pleased by what Aesop had said, and pleaded with Xanthus to appreciate the wisdom of his slave.

I like the Aesop story, even though there is a slight feel of a sermon about it.

The characters in the Mimi Barthélemy version are crocodiles. It is spiced with riddles like the ones above. And it is, as the real Aesop of course was, more lyrical:
“It is the tongue – that can lull a baby to sleep, that can fill the ears and the heart with love and delight, that can make peace between two warring armies and can lead the world into truth. Truly it is the best thing of all.”

Pythagorean Symbols

2008-01-14T07:28:00.000-08:00

Many of these are completely opaque to me. Some seem to make obvious sense. And some tease a little. They are called 'symbols' - I wonder if they would have been in visual form, as reminders?

PYTHAGOREAN SYMBOLS, or MAXIMS (From Hierocles.)

1. Go not beyond the balance.

7. Go not by the public way.

9. Wear not the image of God on your ring.

10. Do not unload people, but load them up.

33 Do not sleep at noon.

41. Pick not up what is fallen from the table.

54. When the winds blow, adore echo.

62. Give way to a flock that goes by.

There is too another kind of 'symbol' that is linked with him; not that I really understand the link.

Prometheus

2008-01-13T12:30:00.000-08:00

Thanks to David for pointing me to this:

"A potent myth about the origin of mankind identifies the Titan Prometheus as our creator. Prometheus, trickster, rebel and hero, links the realm of the gods with the world of humanity, with which he had such close affinity. His act of stealing fire has been viewed as the foundation of all man's technologies. Google the name Prometheus and see how often it has been given to innovations in many different fields, notably science, medicine and space exploration. The fire he stole can be seen, too, as the spark generating all artistic creativity. As Tony Harrison has Hermes say in his film Prometheus (1998):

Constant theft! First fire, now this -
pinching poetic artifice!
How can Olympus stay intact
if poetry comes to Pontefract?

The fire can even be viewed as being life itself, given to men by Prometheus. One version of the story has him create the first man from mud and tears. It's not surprising that when Mary Shelley wrote Frankenstein she subtitled it "The Modern Prometheus".

Prometheus's gift of fire was notoriously dangerous, if only because of the punishment Zeus meted out to him. The immortal was chained to a mountain and an eagle sent to tear at his flesh for all eternity. So Prometheus's name is associated with the daily effort involved in being human. He is clearly a martyr in mankind's cause, and his bravely borne suffering wrings the heart. Let us leave him in his torment, in Ted Hughes's poem Prometheus on his Crag:

Prometheus on his crag
Began to admire the vulture
It knew what it was doing
It went on doing it
Swallowing not only his liver
But managing also to digest its guilt
And hang itself again just under the sun
Like a heavenly weighing scales
Balancing the gift of life
And the cost of the gift
Without a tremor
As if both were nothing"

· Neil MacGregor is the director of the British Museum writing in The Guardian

On the subject of Prometheus, there are some great things from Aesop...

"This is also something that Aesop said. The clay which Prometheus used when he fashioned man was not mixed with water but with tears. Therefore, one should not try to dispense entirely with tears, since they are inevitable."

"Prometheus has given us two sacks to carry. One sack, which is filled with our own faults, is slung across our back, while the other sack, heavy with the faults of others, is tied around our necks. This is the reason why we are blind to our own bad habits but still quick to criticize others for their mistakes."

"Zeus once ordered Prometheus to show mankind the two ways: one the way of freedom and the other the way of slavery. Prometheus made the way of freedom rough at the beginning, impassable and steep, with no water anywhere to drink, full of brambles, and beset with dangers on all sides at first. Eventually, however, it became a smooth plain, lined with paths and filled with groves of fruit trees and waterways. Thus the distressing experience ended in repose for those who breath the air of freedom. The way of slavery, however, started out as a smooth plain at the beginning, full of flowers, pleasant to look at and quite luxurious, but in the end it became impassable, steep and insurmountable on all sides."

"Prometheus, that potter who gave shape to our new generation, decided one day to sculpt the form of Aletheia (Truth) , using all his skill so that she would be able to regulate people's behaviour. As he was working, an unexpected summons from mighty Zeus called him away. Prometheus left cunning Dolos (Trickery) in charge of his workshop, Dolos had recently become one of the god's apprentices. Fired by ambition, Dolos used the time at his disposal to fashion with his sly fingers a figure of the same size and appearance as Aletheia with identical features. When he had almost completed the piece, which was truly remarkable, he ran out of clay to use for her feet. The master returned, so Dolos quickly sat down in his seat, quaking with fear. Prometheus was amazed at the similarity of the two statues and wanted it to seem as if all the credit were due to his own skill. Therefore, he put both statues in the kiln and when they had been thoroughly baked, he infused them both with life: sacred Truth) walked with measured steps, while her unfinished twin stood stuck in her tracks. That forgery, that product of subterfuge, thus acquired the name of Pseudologos (Falsehood) , and I readily agree with people who say that she has no feet : every once in a while something that is false can start off successfully, but with time Truth is sure to prevail."

Cinderella?

2008-01-10T03:59:00.001-08:00

Rhodopis, 'Rosy-Cheeks', was taken as a slave from her native Thrace to Samos. There she worked for a man named Iadmon, as a fellow slave to Aesop the fabulist.

What stories did she hear?

Very beautiful, she was sold on to a trader named Xanthes who takes her to Naukratis in Egypt, the town that has been given over to the Greeks by Pharaoh Amazis.

What kind of journey was that?

She is bought by Charaxus, brother of the poet Sappho, who has come to Egypt with a shipload of wine from Lesbos (Sappho is thought to have writen a poem on the subject, calling the girl by her perhaps real name of Doricha).

What would that poem have been like?

And, from Wikipedia:

She works in the household of her Egyptian master. Though kind, her master spends most of his time sleeping, and is therefore unaware of her harsh treatment at the hands of his other servant girls. Because Rhodopis is both fair-complexioned and a foreign slave, the other servants tease her and order her around.

After her master sees Rhodopis dancing skillfully by herself, he gives her a pair of rose-gilded slippers. The other servants resent this treatment and use Rhodopis more harshly than before.
One day, Pharaoh Ahmose I invites the people of Egypt to a celebration in Memphis. The other servants prevent Rhodopis from attending with them by giving her a long list of chores to complete.

While she is down by the river washing clothes, her slippers become wet and she places them in the sun to dry. Suddenly, the falcon Horus swoops down, snatches one of the slippers, and flies away with it. Rhodopis stores the other slipper in her clothing.

During the celebration in Memphis, the falcon drops the slipper in the Pharaoh’s lap. Realizing that it is a sign from Horus, he decrees that all the maidens of the kingdom must try on the slipper, and that he will marry the one whose foot it fits.

The Pharaoh’s search for the owner of the slipper eventually leads him to Rhodopis’ home. Though Rhodopis hides when she sees the Pharaoh’s barge, he sees her and asks her to try the slipper. After demonstrating that it fits her, she pulls out its mate, and the Pharaoh declares that he will marry her.

a word, a spice, a heart

2008-01-07T07:56:00.000-08:00

One word - admittedly a very long word - has opened up a world of ancient Mediterranean foods to me.

It is the name of a dish mentioned in Aristophanes' comedy Assemblywomen.

The word, in English, is:

Lopadotemachoselachogaleokranioleipsanodrimhypotrimmatosilphioparaomelitokatakechy
menokichlepikossyphophattoperisteralektryonoptekephalliokinklopeleiolagoiosiraiobaphe
traganopterygon

or in the original:

λοπαδοτεμαχοσελαχογαλεοκρανιολειψανοδριμυποτριμματοσιλφιοκαραβομελιτοκατακε
χυμενοκιχλεπικοσσυφοφαττοπεριστεραλεκτρυονοπτοκεφαλλιοκιγκλοπελειολαγοσιραιο
βαφητραγανοπτερύγων

One of the ingredients of this delightful shark fricassee is the spice silphion or silphium. This is apparently a kind of giant fennel of a kind similar to asefetida. It was much prized, both as a spice and a medicine, and grew only in Cyrenaica.

Here's a picture of the weighing of silphium in the presence of King Arcesilaus II of Cyrene 560-c. 550 BC

This page says:

Aside from its culinary uses in sauces and garnishes, silphium was said to be effective in treating coughs, sore throats, fevers, indigestion, fluid retention, seizures, aches and pains. The sap was said to remove warts and other growths, and to be useful against snakebite. Pliny – who said it “was sold for its weight in gold” – mentions that mixed with wine it caused serpents to explode. He also said it put sheep to sleep, made goats sneeze, and was useful in treating leprosy, restoring hair, promoting menstruation and as a contraceptive. The timing of administration suggests it probably functioned as an abortifacient similar to preparations made from related plant species. Paradoxically, it is also referred to in some sources as an aphrodisiac.

However, apparently the plant died out.

Wikipedia says:

The reason for silphium's supposed extinction is not entirely known. The plant grew along a narrow coastal area, about 125 by 35 miles, in Cyrenaica (in present-day Libya). Much of the speculation about the cause of its extinction rests on a sudden demand for animals that grazed on the plant, for some supposed effect on the quality of the meat. Overgrazing combined with overharvesting may have led to its extinction. The climate of the maghreb has been drying over the millennia, and desertification may also have been a factor. Another theory is that when Roman provincial governors took over power from Greek colonists, they over-farmed silphium and rendered the soil unable to yield the type that was said to be of such medicinal value. Theophrastus reports that the type of ferula specifically referred to as "silphium" was odd in that it only grew in the wild, but could not be successfully grown as a crop in tilled soil. The validity of this report is questionable, however, as Theophrastus was merely passing on a report from another source. Pliny reported that the last known stalk of silphium was given to the Emperor Nero "as a curiosity".

There has also been some speculation about the connection between silphium and the traditional heart shape (♥).

"Silphium has left its mark in modern society in a way that has not previously been recognized. Have you ever wondered why the human heart - the repository and the embodiment of romantic love - is always drawn stylized instead of in the natural shape of the human heart organ? The answer is rooted in the ancient function of Silphium! And the connection between this artistic convention and Silphium is found in the coinage of Cyrene, which features a seed pod of the revered plant."
Emilio N Favority and Kurt Baty. The Celator, Vol 9, No.2 quoted here

Now, isn't that intriguing? The subject of a small quest perhaps...

from Agamemnon

2007-12-31T14:27:00.000-08:00

coming across Ted Hughes's Oresteia - not plays I know - but treasures, newly polished.

Here's the Chorus talking about the arrogance of Paris:

Everywhere
The concieted man
With his lofty scheme
Ruins himself
And everybody near him.

The house where wealth
Cracks the foundations
With its sheer weight
Is a prison
Whose owner dies
In solitary.

two dawns

2007-12-23T14:18:00.001-08:00

Mountains
Originally uploaded by markb120.

When David was at Sde Boker he had two experiences of sunrise.

He was on the prehistoric lake bed, completely flat with mountains around. To the west the mountains went red, really red, glowing. To the east there was a golden glow just over the horizon. He walked into an empty space and saw the shadow of the mountain flash across the landscape from west to east. Dawn had come.

Another time he had been wandering through the desert in the night and was sitting on one side of a canyon. The other side was about a hundrred metres away and it went bright red. He watched the shadow going down the cliffside. The golden sun lit up a birdsnest, and two birds flew away.

Theodorus

2007-12-21T07:53:00.000-08:00

Everyone at this time seems larger than life...

"Theodorus of Samos was a Greek sculptor and architect of the sixth century BC who is often credited with the invention of ore smelting and, according to Pausanias, the craft of casting. He is also credited with inventing a water level, a carpenter's square, and, according to Pliny, a lock and key and the turning lathe."

"The great Temple of Hera, or Heraion, had its origins in the 8th centuryBC, when it was the first Greek temple to be surrounded by a peristyle of columns; its 7th century successor was also innovatory in that it was the first temple to have a double row of columns across the front. But these were surpassed by the temple begun around 570 BC by Rhoecus and Theodorus, who built a colossal structure measuring some 45 m by 80 m, the earliest in the new Ionic order. It was supported by at least 100 columns, whose moulded bases were turned on a lathe designed by Theodorus."

Pausanius:

"Leading from the market-place is another road, on which they have built what is called Scias (Canopy), where even at the present day they hold their meetings of the Assembly. This Canopy was made, they say, by Theodorus of Samos, who discovered the melting of iron and the moulding of images from it."

"Theodorus of Samos made the first self-portrait, in bronze, remarkable for its "similitudo mirabilis" (Pliny 34. 83)

"how great is the toil of Theodorus' hand
For you will see the yoke-band, the
reins, the ring on the bit of the horses,
the axle, as well as the driver's
eye and the tips of his hands.
And you would see well.... and sitting on this
a fly the size of the chariot"

"Theodorus, who made the labyrinth at Samos, cast himself in bronze...
- In his right hand he holds a file, and with three fingers in his left hand he held a little chariot-team ... of such small size that a fly made at the same time covered the miraculously made team and the chariot and the charioteer with its wings."

dream city

2007-12-15T01:30:00.000-08:00

Where does this site get this information:

Polycrates did a lot of important things in Samos. This was, after all, his old dream and his great ambition. Everything was great and miraculous. But three of them stood out: The Asty ( Centre of Town ), the soil upon the sea and the Hereon. These works gave fame to Polycrates and Samos. Although now ruined, these have been admired by all people, Greeks and foreigners until now.

The Asty : The ancient city of Samos. The holy centre. It had been built by Tembrionas and Procles. But Polycrates decorated it and made it the first among all the other towns, both Greek and barbaric of that time.

The beach was particularly decorated. There, one could find the Agora, the Agoranomio ( the Town Hall ), the Archio, the Parliament House ( Vouleftirio ), the Prytanio, where the geomori gathered for their conferences, the Laura, the Heroon ( where they worshiped heroes ), the Andronas or Peditis etc. The splendid palace of Polycrates, built high up on the acropolis, was a great ornament. Scattered all over the town, one could find the Semi - circle of Pythagoras, various temples, schools, theatres, the Library, the Art Gallery, statues etc.

between cup and lip

2007-12-15T01:18:00.000-08:00

The first mythological king of Samos was Angeos, son of Apollo or Neptune and Nymph Astypalea. He was born on the banks of river Imbrasos just like Hera. He took part in the Argonaut expedition. He even became captain of Argo, after its first captain was lost during the return to Greece.

After returning to the island, he helped it progress a lot: he helped vineyard cultivation and had his own vineyard, which was cultivated by slaves. It seems that they were forced to work and got very badly treated. So, one of them, angry as he was, cursed Angeos secretly not to drink any wine from his own vineyards. The king heard the curse but he said nothing, keeping the curse in his mind. When the wine was ready, the king remembered the curse and teased the slave. He filled his glass with wine and sent for him. " See ? " he said. " Your curse did not work. Here is the wine which is going to cool my throat. " The slave answered calmly: " There is a great distance between the glass and your lips. Wait and see."

At that very moment another slave came running to tell the king that a wild boar was destroying the vineyards. The king immediately dropped the full glass, grabbed his bow and ran to the vineyard. But he never returned. He was wounded by the boar and died. So, he never drank his own wine. From the slave's words comes a proverb said even these days about those who are in a hurry to jump into conclusions before they see the end of something.

Artemon Periforetos

2007-12-15T01:08:00.001-08:00

I like the suggestion that

Anacreon is credited with a satire about the inventor of the throwing machine, Artemon Periforetos, who was so anxious for his security that he always had his slaves carry him around close to the ground in case he should fall out, and with a shield above him in case anything should fall from above.

Could it have been performed as a play at Samos, with Polycrates watching??

to be a mirror

2007-12-14T07:22:00.000-08:00

We don't know what stones and pots mean. Histories are unreliable. But there is no doubt what Anacreon, poet at the court of Polycrates means:

THE WISH

Niobe on Phrygian sands
Turn'd a weeping statue stands,
And the Pandionian Maid
In a swallow's wings array'd;
But a mirror I would be,
To be look'd on still by thee;
Or the gown wherein thou'rt drest,
That I might thy limbs invest;
Or a crystal spring, wherein
Thou might'st bathe thy purer skin;
Or sweet unguents, to anoint
And make supple every joint;
Or a knot, thy breast to deck;
Or a chain, to clasp thy neck;
Or thy shoe I wish to be,
That thou might'st but tread on me.

- or how about another poem and a more modern translation by Jon Corelis -

The women tell me,

'Man, you're old;

don't be so bold.

Look into a mirror

to make it clearer:

your hair

ain't there.

But I can't see what lies

above my eyes.

I do see more reason to play the game,

when Death takes aim.

that fishy story

2007-12-13T09:52:00.001-08:00

box
Originally uploaded by simonsterg.

has resonated down the ages....

'angeloska' says:

Polycrates was a pirate. Just think of that! He was a robber of the open
sea-routes in the same way as Croesus of Lydia was what we'd call today a
tycoon.You have been to Pythagorion, Polycrates city. It controls the straight
between Samos and Asia. In the 6th century BC that straight was as important for
international trade as Suez and Panama canal put together. From there Polycrates
could defy every god! It seems even the fish chose this passage to come and
go...

Happy Street

2007-12-13T09:34:00.000-08:00

At last, a few more juicy details...

But Clytus, the pupil of Aristotle, in his History of Miletus, says that

"Polycrates, the tyrant of Samos, collected everything that was worth speaking of everywhere to gratify his luxury, having assembled dogs from Epirus, and goats from Scyros, and sheep from Miletus, and swine from Sicily."

And Alexis, in the third book of his Samian Annals, says that

"Samos was adorned by Polycrates with the productions of many other cities; as he imported Molossian and Lacedaemonian dogs, and goats from Scyros and Naxos, and sheep from Miletus and Attica. He also sent for artists, promising them enormous wages. But before he became tyrant, having prepared a number of costly couches and goblets, he allowed any one the use of them who was preparing any marriage-feast or extraordinary entertainment."

And after hearing all these particulars we may well admire the tyrant, because it was nowhere written that he had sent for any women or boys from any other countries, although he was of a very amorous nature, and was a rival in love of Anacreon the poet; and once, in a fit of jealousy, he cut off all the hair of the object of his passion. And Polycrates was the first man who called the ships which he had built Samians, in honour of his country.

But Clearchus says that

"Polycrates, the tyrant of the effeminate Samos, was ruined by the intemperance of his life, imitating the effeminate practices of the Lydians; on which account, in opposition to the place in Sardis called the beautiful Ancon, he prepared a place in the chief city of the Samians, called Laura; he made those famous Samian flowers in opposition to the Lydian. And the Samian Laura was a narrow street in the city, full of common women, and of all kinds of food calculated to gratify intemperance and to promote enjoyment, with which things he actually filled Greece. But the flowers of the Samians are the pre-eminent beauty of the men and women, and indeed of the whole city, at its festivals and banquets."

And these are the words of Clearchus. And I myself am acquainted with a narrow street in my native city of Alexandria, which to this very day is called the Happy Street, in which every apparatus of luxury used to be sold.

Xenophon goes hunting

2007-11-25T12:42:00.000-08:00

I've just read Xenophon's book On Hunting. I like it a lot and I'm going to use it. I like the close description of the ways of hunting dogs, of hares, deer and wild boar, the sense of the unpredictablilty and challenge of the sport. I also like the feeling for the landscape, for the seasons, for the weather.

Xenophon himself clearly loved hunting, and saw it as a great eduction. He says the ancients "saw plainly that among the many pleasures to which youth is prone, this one alone is productive of the greatest blessings. In other words, it tends to make them sound of soul and upright, being trained in the real world of actual things"

Yes, it's that sense of a training in "the real world of actual things" that comes through when Xenophon writes about dogs and hares. Though he doesn't seem to be discussing his teacher Socrates' tradition of philosphy, in fact he is.

sunrise on the mountain

2007-11-22T01:46:00.001-08:00

first blush
Originally uploaded by simonsterg.

If the horizon was clear, the sun on the mountain at dawn or dusk would have told the ancients not only that the world is round, but would have given them the size of the world. It's the speed that the sunlight moves up or down the mountain that does this.

See!

2007-11-16T07:09:00.000-08:00

Robert P Crease in his article on Pythagoras on physicsworld.com discusses the simple surprise involved in proving something in maths - one of the easiest things to prove being Pythagoras' Theorem itself.

For him it was the new thing that was happening in Ionian maths. I agree. And alongside this seems to be a beginning of maths for its own sake rather than for any particular utility.

Why they valued proof and maths-for-itself is another question...

The article mentions some of the people who have been captivated by the theorem and its proof. Thomas Hobbes at the age of 40 came across it and it changed his life.

'Hobbes was transformed. He began obsessively drawing figures and writing calculations on bed sheets and even on his thigh. His approach to scholarship changed. He began to chastise philosophers of the day for their lack of rigour and for being unduly impressed by their forebearers. Hobbes compared other philosophers unfavourably with mathematicians, who proceeded slowly but surely from "low and humble principles" that everyone understood.'

The indian mathematician Bhaskara had his own, visual, proof and was so pleased with it that underneath instead of any symbolic proof he simply wrote

"See!"

a discussion

2007-11-08T07:43:00.000-08:00

This question is posed on the Bad Astronomy forum:

"How can you tell that the Earth is round?

...Assuming you can't actually take a peek yourself, how do you convince somebody that the Earth is round? Explanations would ideally be easy enough to explain to a young person..."

There are a wide range of responses to the question, and some solutions, but not all are suggested.

It is, of course, exactly the question I want to explore - transposed to Samos in the sixth century BC.

east at sunset

2007-10-24T13:31:00.001-07:00

east at sunset
Originally uploaded by optick.

Why is there that band of blue-grey that rises in the east at sunset?

To me it looks like the shadow of the Earth. And I have the feeling it would rise much faster if the earth were flat...

Measuring the size of the sun

2007-09-09T01:10:00.000-07:00

This page takes us through the steps very simply.

Eratosthenes famously took the step of measuring the size of the Earth by comparing shadows in 235 BC.

Of course it could have been done a lot earlier by other means:

"Abstract. Probably the most direct observation of the Earth’s curvature is how objects appear from over the horizon when we approach them and disappear as we get further away from them. Similarly, the portion of a high object (a building or a mountain) that is visible depends on the height of the site where the observation is made. Based upon these very obvious facts, a simple method to estimate the Earth's radius R has been applied. The method does not need either sophisticated instrumentation or complex mathematics. In our application of the method presented here, the result is R = 6600 ± 600 km in the best case. A discussion is presented about the possible use of this method in ancient times. Surprisingly enough, we have not found any reference to the use of this method despite its being simpler than, for example, the classical approach of Eratosthenes."

Ancient Greek robot mechanism recreated

2007-07-23T23:55:00.001-07:00

Hero of Alexander does it again - first the steam engine, now this...

mountain top beacons

2007-07-19T06:44:00.000-07:00

You could signal the arrival of sunrise from a mountain top beacon, and demonstrate the curvature of the earth.

Homer:

Thus, from some far-away beleaguered island, where all day long the men have
fought a desperate battle from their city walls, the smoke goes up to heaven; but no
sooner has the sun gone down than the light from the line of beacons blazes up and
shoots into the sky to warn the neighbouring islanders and bring them to the rescue
in their ships.

Aeschylus:

Chorus--And at what time hath the city been sacked?
Clytaemnestra--I say in the night that hath now brought forth this day.
Chorus--And what messenger could come with such speed?
Clytaemnestra--Vulcan, sending forth a brilliant gleam from Ida; and beacon dispatched beacon of courier-fire hitherward. Ida, first to the Hermaean promontory of Lemnos, and third in order Athos, mount of Jove [Zeus], received the great torch from the isle, and passing over so as to ridge the sea, the might of the lamp as it joyously traveled, the pine-torch transmitting its gold gleaming splendor, like a sun, to the watch towers of Macistus. And the watchman omitted not his share of the messenger's duty, either by any delay, or by being carelessly overcome by sleep; but the light of the beacon coming from afar to the streams of the Euripus gives signal to the watchmen of Messapius, and they lighted a flame in turn and sent the tidings onward, having kindled with fire a pile of withered heath.
And the lamp in its strength not yet at all bedimmed, bounding over the plain of the Asopus, like the bright moon to the crag of Cithaeron, aroused another relay of the courier fire. And the watch refused not the light that was sent from afar, lighting a larger pile than those above mentioned; but it darted across the lake Gorgopis, and having reached mount Aegiplanetus, stirred it up in unscathing strength, they send on a mighty beard of flame, so that it passed glaring beyond the headland that looks down upon the Saronic frith, then it darted down until it reached the Arachnaean height, the neighboring post of observation, and thereupon to this roof of the Atreidae here darts this light, no new descendant of the fire of Ida.
Such, in truth, were my regulations for the bearers of the torch fulfilled by succession from one to another; and the first and the last in the course surpassed the rest. Such proof and signal do I tell thee of my husband having sent me tidings from Troy.

also

Watchman--I pray the gods a deliverance from these toils, a remedy for my year-long watch, in which, couching on my elbows on the roofs of the Atreidae, like a dog, I have contemplated the host of the nightly stars, and the bright potentates that bear winter and summer to mortals, conspicuous in the firmament. And now I am watching for the signal of the beacon, the blaze of fire that brings a voice from Troy, and tidings of its capture; . . .

archimedes tomb found

2007-07-02T08:02:00.000-07:00

When I was quaestor in Sicily I managed to track down
Archimedes' grave. The Syracusans knew nothing about
it, and indeed denied that any such thing existed. But
there it was, completely surrounded and hidden by bushes
of brambles and thorns. I remembered having heard of
some simple lines of verse which had been inscribed on
his tomb, referring to a sphere and cylinder modelled in
stone on top of the grave. And so I took a good look
round all the numerous tombs that stand beside the
Agrigentine Gate.

Finally I noticed a little column, just visible above the
scrub: it was surmounted by a sphere and a cylinder. I
immediately said to the Syracusans, some of whose leading
citizens were with me at the time, that I believed this
was the very object I had been looking for. Men were sent
in with sickles to clear the site, and when a path to the
monument had been opened we walked right up to it. And
the verses were still visible, though approximately the
second half of each line had been worn away.

So one of the most famous cities in the Greek world, and
in former days a great center of learning as well, would
have remained in total ignorance of the tomb of the most
brilliant citizen it had ever produced, had a man from
Arpinum not come and pointed it out!

But now to return to the point where I started that
digression. Surely anyone who has even the slightest
connexion with the Muses, that is to say with civilization
and learning, would rather be the mathematician Archimedes
than the tyrant Dionysius. If we weigh up the two men's
ways of life and behavior, we find that one of them fed
his brain on scientific research and discovery, with all
the satisfaction that comes with intense intellectual
exercise - which is the most wonderful spiritual
nourishment in the world - while the thoughts of the
other dwelt on murder and oppression, and fear was his
companion day and night. Compare Dionysius with
Democritus, Pythagoras, Anaxagoras. What thrones or
possessions on all the earth could you rank higher than
their philosophical achievements, and the satisfaction
they derived from them?

Cicero, quoted on this page.

"The fox is one hundred years old; its child is one hundred and ten."

2007-06-09T13:54:00.000-07:00

This Greek proverb is thought to come from a story (which I have changed a little from my source):

On a cold winter night a fox and her daughter were padding hungrily through the forest.

They saw a fire. Some men were cooking; the smell of roasting meat was in the air. The fox and her child stopped at a safe distance. There may be food there, but it was not safe to go too close to men.

Hungry or not, the mother fox decided to pull her cub's leg a little. She held up her front paws.

"What are you doing mother?"

"Warming myself from the fire."

The two were quiet for a wile. Then the fox cub began to open its mouth and take in big gulps of air.

"What are you doing, daughter?"

"Just eating the aroma of that meat," said the cub.

all these things

2007-05-09T05:10:00.000-07:00

found at the Hearaion on Samos, each votive offereing has a story - someone offered most of these things to Hera. Why was it chosen? What did it represent?

Something to get the imagination going.

offerings

2007-05-07T07:44:00.001-07:00

slow and steady
Originally uploaded by simonsterg.

The Arcaeological museum in Vathy, Samos (guarded by tortoises), as well as housing massive kouroi, is home to many of the small objects that were offered to Hera at her Temple. They give another angle on life in 6th Centruy BC Samos.

it's a fair cup

2007-05-06T10:16:00.000-07:00

This cup is sold to tourists in Samos. I bought one.

The piece of paper that comes with it says:

"CUP OF PYTHAGORAS

Tradition says Pythagoras, during water supply works in Samos around 530 BC moderated the workers' wine drinking by inventing the 'fair cup'. When the wine surpasses the line, the cup totally empties, so the greedy one is punished."

It does work. If you fill it below the line in the middle, all is well. If you fill it above the line - all the wine comes out of the bottom!

I played cynical with the young man in the shop, and said I doubted whether after all these years the story about Pythagoras inventing it were true. He said he believed it.

Strangely though, it does seem sort of like Pythagoras, this cup. It's the combination of respect for moderation, ingeniousness, and dramatic lesson that makes me say this.

So, let's drink to... Pythagoras' Cup!

that turban

2007-05-02T13:16:00.001-07:00

Pythagoras of Samos
Originally uploaded by mharrsch.

they say was because his father was a Phoenician trader...

The Phoenicians traded more and further than the Greeks. They went to Cornwall for tin, and probably the Baltic for amber.

A lot of knowledge comes from such wide travelling - different peoples, different latitudes, different stars...

the world

2007-04-26T23:12:00.000-07:00

It was when Pythagoras was young that just across the sea in Miletus the first world maps we know about were made.

Anaximander's may have been something like this. (It's hard to imagine that England, the south of it at least, wouldn't be part of it, so I have restored it in my version here.)

Pythagoras should have been able to work out that the world was a lot bigger than this!

The earth is a sphere

2007-04-25T08:06:00.001-07:00

Samiopoula Saturday 8am
Originally uploaded by simonsterg.

Evidence at last!

oxyrhynchus

2007-04-20T23:13:00.000-07:00

Amazingly, new information is coming to light about the classical world all the time.

For instance here is a fragment of papyrus by the poet Ibycus:

'With them you too, Polycrates,

shall have immortal fame for beauty

as long as my song and fame endure.’

pebbles

2007-04-20T07:31:00.001-07:00

pebbles
Originally uploaded by simonsterg.

‘The Pythagoreans explored the beauty of numbers by playing a sort of game’

This comes from this transcript of a radio program on science in ancient greece. It attributes the words to Herodotus, but I can't find them in my copy.

Despite the 2500 years that have passed, I have found out how they did it...

- - - UPDATE - - -

I've found something. According to p136 of this book, Aristotle says something about it. He describes the Pythagorean Eurytus as one who "decided what was the number of a thing... by immitating its form with pebbles. as some bring numbers into the shapes of triangle and square." Metaphysics 1092b10-14

horizon

2007-04-04T11:48:00.001-07:00

horizon
Originally uploaded by simonsterg.

How would the horizon look if the earth were flat? Just the same? What do you think?

What about the sky/ Would that look different if the earth were flat? What do you think?

dance

2007-03-29T14:30:00.000-07:00

"Did you came to me to learn about the stars and about number?
Apollo and the Muses forbid it!
You will learn to dance first!"

And from the Iliad, quoted on this page:

Here young men and the most desired young girls were dancing, linked, touching each other’s wrists, the girls in linen, in soft gowns.... Trained and adept, they circled there with ease, the way a potter sitting at his wheel will give it a practice twirl between his palms to see it run; or else, again, in lines as though in ranks, they moved on one another: magical.

The festival of Hera is soon. The girls get ready, dancing the Ierakio .

golden verses

2007-03-23T09:39:00.000-07:00

You can find the "golden verses" of Pythagoras in many places on the Web. They read to me like something that could go back to the man himself, though who knows through what filters they have passed - followers always overcook things, always caricature the original.
These maxims are "heavy stuff" for most tastes, but they perhaps give a flavour of what the man would have wanted from his disciples.

I will pick out:

7. Avoid as much as possible hating thy friend for a slight fault.

12. But above all things respect thyself.

15. But always make this reflection, that it is ordained by destiny that all men shall die.
16. And that the goods of fortune are uncertain; and that as they may be acquired, so may they likewise be lost.

21. There are among men many sorts of reasonings, good and bad;
22. Admire them not too easily, nor reject them.

30. Never do anything which thou dost not understand.

40. Never suffer sleep to close thy eyelids, after thy going to bed,
41. Till thou hast examined by thy reason all thy actions of the day.
42. Wherein have I done amiss? What have I done? What have I omitted that I ought to have done?

56. Few know how to deliver themselves out of their misfortunes.
57. Such is the fate that blinds mankind, and takes away his senses.
58. Like huge cylinders they roll to and fro, and always oppressed with ills innumerable.

63. But take courage; the race of man is divine.

seek echo

The Antikythera Mechanism... in Lego

more circles

irrational

same area

circles and squares

thyrsus

foreignness

The Bacchae

Pythagorean triples

tiling a circle

Seikilos epitaph

midwifery

halls of Hades

wild silk

walls of bronze

The Ulysses Voyage

opposite?

isopsephy

The tomb of the diver

any old letters?

Shipwrecks Offer Clues

An Ancient Nas

Paul's shipwreck

ships and weather

Cycle of Venus

Ancient records of Venus

Hesperus and Phosphorus

pebbles are the thing

golden rectangle

Hyperbolic Crochet Coral Reef

♓

money and knowledge

aristotle

Heraclitus

ancient computer

and another thing

irrational

not so ideal

doubling a square

evidence

explanatory power

Corvus

donkeys and sitting

Speakers' corner

connections

"don't wear a god's image on your ring"

why maths???

maths

a figure and a sixpence

on the beach

part of a circle

tyrant

Ikaria 249

dog days

equinox

interview with Thales

Pherecydes of Syros

Ikaria 231

curves and confusion

first

at Delphi

Ikaria 001

simonsterg (that's me) says:

isl_gr says:

simonsterg says:

isl_gr says:

simonsterg says:

isl_gr says:

simonsterg says:

isl_gr says:

simonsterg says:

simonsterg says:

isl_gr says:

ten

into the distance

tragic consequences

best and worst

Pythagorean Symbols

Prometheus