## This Week's Finds in Mathematical Physics (Week 221)

In article <dgli7r$fb9$1@glue.ucr.edu>,
John Baez <baez@math.removethis.ucr.andthis.edu> wrote:

>The eleventh century was the golden age of Andalusian astronomy
>and mathematics, with a lot of innovation in astrolabes. During
>the Caliphate (912-1031),

Actually the Caliphate began in 929 when Abd al-Rahman declared
himself caliph, though he assumed power in 912.

>three quarters of all mathematical
>manuscripts were produced in Cordoba, most of the rest in
>Sevilla, and only a few in Granada in Toledo.

Of course that should be "Granada and Toledo".

In response to this:

>So, medieval Europe learned a lot of Greek science by reading Latin
>translations of Arab translations of Syriac translations of
>second-hand copies of the original Greek texts!

a friend of mine wrote:

| This all seems so precarious a process that it makes me wonder whether
| there was ten times as much valuable ancient math and philosophy as we
| know about, most of which got *completely* lost.

Something like this almost certainly true.

Like Plato, Aristotle is believed to have written dialogs which presented
his ideas in a polished form. They were all lost. His extant writings
are just "lecture notes" for courses he taught!

Euripides wrote at least 75 plays, of which only 19 survive in their
full form. We have fragments or excerpts of some more. This isn't
philosophy or math, but it's still incredibly tragic (pardon the pun).

The mathematician Apollonius wrote a book on "Tangencies" which is lost.
Only four of his eight books on "Conics" survive in Greek. Luckily, the
first seven survive in Arabic.

The burning of the library of Alexandria is partially to blame for
these losses.

There's some good news, though:

Archimedes did more work on calculus than previously believed!
We know this now because a manuscript of his on mechanics that had been
erased and written over has recently been read with the help of a
synchrotron X-ray beam!

This is a great example of modern physics helping the history of physics:

http://www.mlahanas.de/Greeks/ArchimedesPal.htm
http://news-service.stanford.edu/new...es-052505.html

This manuscript, called the Archimedes Palimpsest, also reveals for
the first time that he did work on combinatorics:

http://www.mlahanas.de/Greeks/ArchimedesComb.htm

Also: a team using multispectral imaging has recently been able to read
parts of a Roman library that was "roasted in place" - heavily carbonized -
during the eruption of Vesuvius that destroyed Pompeii in AD 79. By
distinguishing between different shades of black, they were able to
reconstruct an entire book "On Piety" by one Philodemus:

http://magazine.byu.edu/article.tpl?num=44-Spr01

The same team is now studying over 400,000 fragments of papyrus found
in an ancient garbage dump in the old Egyptian town of Oxyrhynchus. They've
pieced together new fragments of plays by Euripides, Sophocles and Menander,
lost lines from the poets Sappho, Hesiod, and Archilocus, and most of
a book by Hesiod:

http://www.papyrology.ox.ac.uk/multi/procedure.html

If you just want to look at a nice "before and after" movie of what
multispectral imaging can do, try this link.

George Baloglu recommends the following book:

Dimitri Gutas, Greek Thought, Arabic Culture: The Graeco-Arabic
Translation Movement in Baghdad and Early 'Abbasid Society
(2nd-4th/8th-10th Centuries).

Finally:

In article <dgnka4$get$1@dizzy.math.ohio-state.edu>,
Noam Elkies <elkies@math.harvard.edu> wrote:

>>Amusingly, Arabic numerals were also called "dust numerals" since
>>they were used in calculations on an easily erasable "dust board".
>>Their use was described in the Liber Pulveris, or "book of dust".

>This is even more amusing than you may realize: the word "abacus"
>comes from a Greek word "abax, abak-" for "counting board", which
>conjecturally might come from the Hebrew word (or a cognate word
>in another semitic language) for "dust"! See for instance
><http://education.yahoo.com/reference/dictionary/entry/abacus>.
>So these "dust numerals" replaced a reckoning device whose name
>may also originate with calculation a dust board...

Interesting! While "calculus" refers back to pebbles.