Larsguy47

Doubling the Cube

Doubling the Cube, the most famous of the collection, is often referred to as the Delian problem due to a legend that the Delians had consulted Plato on the subject. In another form, the story asserts that the Athenians in 430 B.C. consulted the oracle at Delos in the hope to stop the plague ravaging their country. They were advised by Apollo to double his altar that had the form of a cube. As a result of several failed attempts to satisfy the god, the pestilence only worsened and at the end they turned to Plato for advice.

Just wanted to see what the skeptics could come up with on this one. Plato was said to have been consulted in 430 BC but he wasn't born until 428BCE. So where does this reference come from? Why don't the dates match?

Any comments? Links to discussion on this?


Thanks.


Larsguy47

Gamera

The state of biography in antiquity is in disarray. Virtually everything we know about "famous" figures from Greece reside in mss that are written 1000 years after the events, and involved biased authors. No specific dates about Plato or Socrates or Pericles should be taken seriously.

Larsguy47

Thanks for your comment!

Larsguy47

aa5874

Did Josephus, Pliny the Elder or Philo write about the Essenes one thousand years afterwards. When was 'The Life of Flavius Josephus' written, one thousand years after Josephus died?

The state of biography in antiquity is NOT in disarray, except perhaps that of Jesus the Christ.

rob117

Traditions about famous figures from centuries later are not considered reliable sources for dating when all the contemporary material contradicts them.

RED DAVE

From Larsguy47:
The operative word is “legend.”

What is the source of this legend? What is the reliability of the source. The reliability is questionable as it runs up against standard scholarship.

http://www.iep.utm.edu/p/plato.htm#H1

By the way, the source for the Delian Problem legend is Theon of Smyrna, a second-century Platonist.

http://books.google.com/books?id=nMl...3YaEILGdO2mlkI

RED DAVE

Larsguy47

Thanks, RED DAVE, much appreciated! I found this suspicious from the Encylopaedia Britannica on Plato:

Yet if my theory is correct and the Delian Problem is accurage, Plato would have been 26 or 27 when Pericles died, so he would have been able to reflect these things from experience.

Further, you have the claim of Xenophon, who is about Plato's age that he knew Socrates in his youth and indeed was at this famous Symposium. Both Xenophon and Plato write about the Symposium, strangely. But Xenophon claims he was actually present. If so, he would have only been 8 years old, and Plato younger. But if the chronology is correct, they would have been able to both have been there with Socrates only 7 years or less older than the two. Xenophon claims he knew Socrates in his youth.

Both wrote about the Symposium, both preserved the dialogues of Socrates, and Xenophon writes about Persian history. Very suspicious. When the chronology is corrected, of course, both could have been at the Symposium, which is likely whey they both gave their versions of it, pretending not to be there but recording the important event.

Larsguy47

RED DAVE

From Larsguy47:
You need to start sourcing your quotes.

From Larsguy47:
As quoted above, the Delian problem is based on a single quote two or three hundred years later. It is not a legitimate basis to start revising Greek history.

Sorry, dude:

Xenophon – 427-355

http://en.wikipedia.org/wiki/Xenophon

Xenophon was 28 when Socrates died. I am unaware of any date for the actual Symposium, but this would seem to be an ample overlap.

From Larsguy47:
And since he was 28 when Socrates died, he was likely telling the truth.

From Larsguy47:
Plato does not claim to have been at the Symposium.


RED DAVE

post tenebras lux

If legend is correct, the Athenians consulted the oracle at Delos in 430BC, who gave them the puzzle. However, it wasn't solved until 350BC by a friend of Plato (Menaechmus).

Can I please have a reference to the claim that Plato was consulted on how to solve the problem immediately (i.e. in 430BC) rather than him working on the problem during his adult life (and then getting pissed off that his friend solved it just before he died)?

Pataphysician

Theon of Smyrna gives no dates to the origin of the problem, and relates it to Delos itself not Athens. There was a well known plaque in Athens in 430 BC, so some decided maybe this is what was referenced, though there is nothing in the text that says the plague was in Athens, or even if so that it was this specific plague, so really the date of origin is pure speculation. Also it doesn't say Plato solved the problem, merely that he articulated what the real problem was. Of course the story could be totally made up, as Theon was not a historian, but a mathematician.

"Eratosthenes, in his work entitled Platonicus relates that, when the god proclaimed to the Delians through the oracle that, in order to get rid of a plague, they should construct an altar double that of the existing one, their craftsmen fell into great perplexity in their efforts to discover how a solid could be made the double of a similar solid; they therefore went to ask Plato about it, and he replied that the oracle meant, not that the god wanted an altar of double the size, but that he wished, in setting them the task, to shame the Greeks for their neglect of mathematics and their contempt of geometry."

Eutocius, in his commentary on Archimedes gives a letter supposedly written by Eratosthenes, gives a mythical origin to the problem of doubling the cube.

"Eratosthenes to King Ptolemy, greetings.
The story goes that one of the ancient tragic poets represented Minos having a tomb built for Glaucus, and that when Minos found that the tomb measured a hundred feet on every side, he said "Too small is the tomb you have marked out as the royal resting place. Let it be twice as large. Without spoiling the form, quickly double each side of the tomb". This was clearly a mistake. For if the sides are doubled the surface is multiplied fourfold and the volume eightfold."

It might help if you read the primary sources for your supposed chronology problems