Ancient Math and Hellentistic Poetry

Interesting item from a Stanford press release:

Like novelists, mathematicians are creative authors. With diagrams, symbolism, metaphor, double entendre and elements of surprise, a good proof reads like a good story.

Reviel Netz, a professor of classics and, by courtesy, of philosophy, is especially interested in exploring the literary dimensions of the textual artifacts left by the likes of Archimedes and Euclid. Netz, one of the world’s preeminent experts on the works of Archimedes, sees proofs as narratives that lead the reader turn by turn through an unfolding story that ends with a mathematical solution.

In his book Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic, Netz reveals the stunning stylistic similarities between Hellenistic poetry and mathematical texts from the same era.

Earlier this spring, Netz and other scholars engaged in the study of mathematics as text gathered at Stanford to discuss this growing area of academic inquiry.

[the article then goes into interview format]

How did you become interested in exploring the idea of mathematics as literature?

I was always interested in the ways in which mathematics – or science in general – is concretely experienced: not the abstract logic of it but the heartbeat-by-heartbeat sense of getting the piece of knowledge through one’s eyes, hands, thoughts. This gives rise very naturally to the thought of thinking of the taking-in of a mathematical text alongside the taking-in of a text in general, which is something literary scholars are sometimes interested in.

You have said that a math proof is more focused on the properties of text than any other human endeavor, short of poetry.

Mathematics is structured around texts – proofs – that have very rich protocols in terms of their textual arrangement, whether in the use of extra-verbal elements – diagrams – in the very layout, in the use of a particular formulaic language, in the structuring of the text. And its success or failure depends entirely on features residing in the text itself. It is really an activity very powerfully concentrated around the manipulation of written documents, more perhaps than anywhere else in science, and comparable, then, to modern poetry.

Can parallels be drawn between pre-modern mathematics and pre-modern literature?

Of course, and my book Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic is precisely about the manner in which surprise, remarkable juxtapositions and the hybridization of genres are key norms for both mathematics and poetry in the culture of the Hellenistic Mediterranean.

How does an aesthetic examination of a mathematical text differ from studying the mathematical information?

When you study the information, you may translate the contents to whichever form suits you and consider its validity, axiomatic underpinning, etc; when you study its aesthetics, you must remain focused on the text as perceived historically.

How do you define or identify literary-like elements like metaphors in a mathematical proof?

Metaphor is fairly standard in mathematics. Mathematics can only become truly interesting and original when it involves the operation of seeing something as something else – a pair of similarly looking triangles, say, as a site for an abstract proportion; a diagonal crossing through the set of all real numbers.

You have said that a proof can be seen as having a complex narrative and even elements of surprise much like how a story unfolds. Can you give me an example?

You tell me, “I’m going to find the volume of a sphere.” And then you do nothing of the kind, going instead through an array of unrelated results – a cone here, a funny polygon there, various proportion results and general problems; then you make a thought experiment that shows how a sphere is like a series of cones produced from a certain funny polygon and, lo and behold, all the results do allow one a very quick determination of the volume of the sphere. Here is surprise and narrative. That’s Archimedes’ “Sphere and Cylinder” proof; it’s a typical mechanism in his works. Other authors are often much more sedate and progress in a more stately manner; this is Euclid’s approach.

Why is there a growing interest in studying the “aesthetic dimension of human endeavor,” and why is this a valuable course of study, especially in relation to mathematics?

There is an interest in the embodied experience of various fields, which gives rise to an interest in aesthetic. The unfortunate thing is that many scholars who study culture share this feeling but instead of actually engaging in the study of the aesthetic of a given culture – which would mean, essentially, a study of the formal properties of a historically situated group of artifacts – they engage in the ideas people had about aesthetics.

Would you say there is an art to being a mathematician?

Yes, it’s a cliché really, nothing I came up with. Mathematicians are always intensely aware of the aesthetic dimension of their own craft. I basically just try to say this is no mere waxing lyrical, there’s a concrete reality that needs to be studied.

Netz has been often mentioned at rogueclassicism for his work with the Archimedes Palimpsest …

A Whispering Column of Jerash in Queens

Checking into a somewhat nutty item sent me to an interesting item from the New York Public Library a few months ago … some excerpts:

The Whispering Column of Jerash stands quietly in Flushing Meadows Corona Park, Queens. Many people walk pass this ancient treasure not realizing that it dates back to 120 A.D. Many do not know that this column is the second oldest outdoor antiquity monument behind the famed Cleopatra’s Needle in Central Park.

The inscription on the plaque states:

“This column was presented to the New York Worlds Fair and the City of New York by his Majesty King Hussein of the Hachamite Kingdom of Jordan on the occasion of Jordan’s participation in the Fair. The column was received by the Hon. Robert Moses, President, New York World’s Fair 1964-65 Corp. This is one of many columns in a temple erected by the Romans in 120 A.D. that stood in the Roman City of Jerash. The columns are known as the Whispering Columns of Jerash.”

Details of the Column

The Whispering Column of Jerash stands 30 feet tall, topped with a Corinthian capital. The Column is located east of the Unisphere in Flushing Meadows Corona Park. During the New York World’s Fair 1964-65, the Jordanian Pavilion stood adjacent to the column. The Kingdom of Jordan gifted the column so that the column would serve as a permanent monument in the post-Fair park (NY Worlds Fair records, 1964-65, box 278)

This tells only part of the story. The column was transported over 5,700 hundred miles from Jerash, Jordan, to become an attraction of the New York World’s Fair 1964-1965.

[...]

The Whispering Columns of Jerash are part of the temple of Artemis. Artemis is the daughter of Zeus and Leto, and the twin of Apollo. She is the goddess of the hunt, known to assist in childbirth.

When you stand in the middle of the temple and whisper, the sound of your voice reverberates. Whispering galleries or amphitheaters that are naturally curved may result in the effect of having your voice bounce off the walls.

[...]

Note to self: look into ancient ‘whispering galleries’ … I thought they were a Renaissance thing.

Whispering Column of Jerash: 120 AD

Whispering Column of Jerash: 120 AD (Photo credit: Rebexta)

Missing Bits from the Cadeby Hoard Turn Up

Adrian Murdoch mentioned this one on Twitter … from the Star:

PART of a treasure-trove dating back to Roman times has mysteriously surfaced at an antiques fair – almost 30 years after the rest of it was found in a Doncaster wood.

A silver bracelet dating back to the third century is now wanted by Doncaster Museum so they can reunite it with the rest of the famous Cadeby Hoard discovered by a local metal detector enthusiast in 1981.

Yesterday the way was cleared for the Chequer Road museum to acquire it from the owners – an ancient artefacts dealer in Essex – after Doncaster Coroner Nicola Mundy declared the bracelet to be treasure-trove.

Experts from the British Museum, who will now decide its value, are convinced it would have been hidden in the same place as 112 silver Roman coins and four silver bracelets in Pot Ridings Wood, Cadeby, in the period after AD 250.

The Cadeby Hoard, which attracted national interest at the time, was found hidden in a rock crevice in October 1981 by Brendan Kennedy, of Victorian Crescent, Town Moor, while using his metal detector.

But the hearing was unable to shed any light on how the bracelet came to change hands separately at the Newark Antiques Fair in 2009 – where it was sold by Nottingham man Kevin Darby, who has no knowledge of the finder.

He was unable to attend yesterday’s hearing because he is recovering from a heart attack.

In a statement Mr Darby said he had had the bracelet for many years, and bought it t because he liked it.

The bracelet is 85 per cent silver with a carnelian gemstone. At almost 62mm wide it weighs 62.8g. It is believed to have been made by a silversmith in Lincoln or York between 250 and 280AD.

While researching on the internet Mr Darby found a similar bracelet in the Doncaster Museum collection and visited to see the others from the Cadeby Hoard.

He also showed it to museum staff and added: “I have done everything by the book.”

The bracelet was bought by Essex-based dealers Timeline Originals, whose chief executive, Brett Hammond, said they were told it had been excavated prior to 1975 and before treasure hunters’ legislation was tightened up.

Ms Mundy received an expert’s report from the British Museum, with Ian Richardson saying the bracelet dated from the third century and bore ‘strong similarities’ with two found in Pot Ridings Wood.

“Analysis suggest this bracelet is another element of the Cadeby Hoard and should be considered retrospectively as treasure-trove,” he stated.

The coroner concurred, saying the bracelet had ‘strong similarities’ with the Cadeby Hoard bracelets.

She said: “I believe it was part of that earlier hoard and would have been deposited under the same rock.”

The treasure-trove declaration means the object – currently in the custody of the British Museum – is now owned by the Crown and will be valued by experts before being offered for sale.

… not sure why I can’t find anything of substance about the Cadebury Hoard … (should be Cadeby)

Roman Salting Factory from Denia/Dianum

While poking around for more details about the Villajoyosa finds (see next item), I came across another item of interest in Euroweekly from back in February that I missed:

FOLLOWING on from the recent discovery of archaeological remains in the heart of Denia, a new excavation has brought to light the structures of an ancient salting factory under the town’s modern buildings.

The remains appear to be late Roman, dating from the 4th and 5th centuries, when old Denia went under its Roman name of Dianium, and consisted of “ a set of four contiguous pools of regular ground, dug into the earth, and have a strong coating of signinum opus (a heavy lime based plaster)” said local architect and the head of Denia’s Municipal Architecture Department, Josep A Gisbert.

These structures “are related to a common type of late Roman factory, the likes of which have been well documented along the coast of the Levante, and coastal enclaves of Andalusia and Tarragona “ continued Sr. Gisbert.

Archaeological excavations in this area have not yet been completed.

And this week works are commencing on a new ‘dig’ in Denia in an attempt to expose more of the extensive factory remains and so gain better understanding of the factory and its workings.

The factories were coastal based to give easy access to salt beds, and so also were conveniently situated to offer instant salting for the locally caught fish trade.

“It’s (the salting works) special location is in an area close to the old city centre, adjacent to the forum (the main square in Roman times). This proves a strong urban regression from the classical city, which has overlapping ruins of industrial and domestic architecture, as well as fifth and sixth century cemeteries,“ said Sr. Gisbert.

The discovery “leads to another conclusion” he said, “this small salting factory which ran for almost one thousand five hundred years and was part of the fabric of Dianium, is a historical reference that confirms the presence of salted fish in the diet and work of the people’s daily lives.” In short, archaeology is not simply the study of old rocks. It tells us things. It explains life.

Excavating Allon/Villajoyosa

One of those items from EuroWeekly which is crying out for more detail:

THE archeological excavations in front of the gas station and plaza de la Generalista ton Avenida del Pais Valenciano in Villajoyosa have been completed.

They were carried out to be able to reconstruct the history of the ancient Roman city of Allon.

“This has been one of the most difficult excavations in the history of the area,” said Councillor Pepe Lloret.

“Despite this, the team has been able to uncover key aspects to help us understand this ancient city.”

The limit of Allon was discovered, although not all of it can be seen as some is below the national motorway.

Part of the ancient town was destroyed in the 1930s when roads were built.

It was found it was a unique town of its time in that the homes had their own private bathrooms at a time when communal toilets were common.

via: Villajoyosa Roman city excavation finished (EuroWeekly)

… looking for more details, I find that back in February, there was a report on this dig that I missed, however, so:

THE rich historical heritage of the Costa Blanca surfaced again, when it was reported that a 2,000-year-old pen was discovered in Villajoyosa during the excavation of a storm drain on the outskirts of the town.

The find coincided with works on a deposito – rain collector tank – when an ancient grain silo was exposed. It was within this ancient space that the bone stylus was discovered.

The item dates from an estimated 2,200 years ago in the area of Villajoiosa which sits on the old settlement which the Romans called Allon.

The bone instrument was carved to be sharp at its writing tip, and beveled flat at the opposite end to be used to erase errors, by smearing smooth the wax tablet on which the script was written – rather than modern paper – and the granary space was 1.8m across.

The finds were made by the town’s municipal archeology team when alerted to the presence of the old structure.

The storm drain is set to run for 800m, and following this first find, parts of the works have been cordoned off for archeological surveys to be carried out, and so ensure no other items of archeological significance are damaged by the works.

Ninety per cent of the drain is to be surveyed, illustrating the expanse of historical riches in the area. “The area of the find was special in giving good views out over the Bay of Allon (Villajoyosa),” said Antonio Espinosa, head of Villajoyosa’s heritage museum.

“And for this reason the place grew into an important settlement, being an Iberian community even before the arrival of the Romans.”

“The silo was a large hole sunk deep into the ground which would have been lined with burnt clay and plastered, before storing roasted grain that could then be used throughout the year,” said Villajoiosa’s Councillor Pepe Lloret.

In addition to the stylus and grain store, recent municipal works in the town have bared a Roman road that led north to Valencia, as well as hundreds of tombs in a substantial Roman graveyard.