As for the drug bussines, I know the opium thing, but I
did not got the source when I wrote the tale. So I am happy
to see it is indeed a contemporary source! I have read a book
with some letters from Barrow in the last years, when he was
involved on divinity and theology, and he sounds very very
stressed.

You probably have noticed in the history the following remark.
"Perhaps he found the lost Method. Perhaps
he lost other books when his ship was burned in Venice."

Let me to sustantiate it a little bit.
Below it is the detailed chronology, from the appendix of
my http://arxiv.org/html/physics/0006065 article
in spanish. Isaac Barrow was in Constantinople in 1659. He
never wrote about his experiences in the city, except
for two remarks. One, irrelevant, that he was in charge of
looking for some antique medals. Another, very interesting, that
he was interested on Greek liturgy, especially the works
related to St John Chrysosthom. Now, the Archimedes Palimpsest
is an Euchologion, this is, a text about Greek Liturgy, that
even contains some rituals stablished by Chysosthom.

Modern notices claim then the Archimedes Palimpsest was
moved to Constatinople in the XIXth century, but I have
never seem a justification for this claim. To me it is
reasonable to suppose an importation of relevant manuscrits
in 1625, when the final destination of Mar Saba was
in doubt.

Lastly, if you are interested on other remarks in the
history, I suggest to browse my website :)

Small chronology Mar Saba information, got via web from the document http://www.doaks.org/typikaPDF/typ055.pdf [Broken]

1540: Joachim revitaliza el monasterio de Mar Saba.
1623: El monasterio, endeudado, es puesto a la venta.
1625: El monasterio es comprado por el Patriarcado Ortodoxo de Jerusalén.

1688: El patriarca Dositheos solicita autorización para restaurar Mar Saba.

Modern Information
1834: La biblioteca de Mar Saba contiene aún un millar de manuscritos.
Primer tercio del siglo XIX: Se efectúa al parecer un traslado de manuscritos desde Mar Saba al monasterio del Santo Sepulcro en Jerusalén, perteneciente al patriarcado.
1846: Von Tischendorf clasifica el palimpsesto en la biblioteca del Metochion del Santo Sepulcro en Constantinopla, “hija” de la monasterio de Jerusalén. La hoja segunda del manuscrito es llevada a Cambridge.
1899: Papadopoulos-Kerameos clasifica el Euchologion en su catalogo de manuscritos del Metochion.
1906 y 1908: Heiberg lee el texto matemático en Constantinopla. Lo publica en 1913.

It is almost as if JL Borges made up the story of Barrow

I cannot comment----you have thought of everything
and it is complex

Maybe Borges *did* write this story : )

Some posters will not be familiar with palimpsests which though they are real objects are also symbolic of layers-of-alternative-universes---a Borgestian idea made concrete.

The fact is, about palimpsests, that in middle ages not only books were expensive but even mere material
to write on was expensive. Parchment was recycled!

and the monks used to scrape the ink-marks off of
priceless and unique books, eg copies of Archimedes writings,
just to have something to write on.

Re-used parchment is called palimpsest----I think psest means "scrape" and palim means "again"----so it is a "re-scrape" parchment.

So in modern times people have used various means to obtain images of the pre-existing writing which was covered over. Maybe they use UV, I don't know what the techniques are.

Amazing world, where writings of Archimedes can be found underneath layers of Christian liturgy and sermons by people
like Saint John Chrysostom, where two conflicting ideas of what is sacred are superimposed in almost a mixed state.

And you say what if Barrow, Newton's teacher, who indeed WAS in Constantinople and read some Christian manuscripts there actually saw Archimedes method of calculus and imparted some of those ideas to Newton. Surprising and provocative thought.
Be careful such a thought does not bite you! It is lively.

excuse a footnote of a trivial sort
stoma means mouth
(the little pores on the surface of a leaf are, I think, called stomata)

chryso means golden

When John Chrysostom used to preach sermons
people would interrupt him with applause
the Britannica article on him says that he had to scold
people from the pulpit for applauding in church
this is a sign that he was an oratorical stylist or
a kind of poet, and he is responsible in part for the mass
(Barrow apparently says that he was interested in one time
in checking out the Eastern version of the mass
and read some about it, as you describe.)

as an unreligious person I know of the mass only because my chorus
sings the Bach bminor and Mozart Cminor and Beethoven Cmass
and Mozart requiem and Haydn nelsonmass and all that good stuff----the greatest western music bar none, musical settings of a pretty great poem. and when it comes to where we sing sanctus sanctus sanctus dominus deus sabbaoth pleni sunt coeli et terra gloria tua, of whom or of what should one think? Archimedes certainly, and Aristarchus who first saw the heliocentric model, and people like that, and Kepler (who discovered that the coeli were pleni of geometrical glory) Really. For me, as I sing it, the Sanctus is a palimpsest and I hope the time comes when the specifically christian overlay flakes off and the word Sabbaoth, which originally meant the battle-array of angellic Host, will have a better meaning---something like "the laws of physics"

Fortunately my greek is null enough so I can not risk my life to search for the lacking pages :)

While it can not be proved (*) that Barrow read it, I still hope that the presence of the book in Constantinople in the XVIIth century could be. Or at least, I hope that the conjecture of a later, XIXth century arrival, will be discarded. Beyond that, I'll refrain.

Alejandro Rivero

(*)Well, an esoterist could accept that Barrow's reference about "checking out the Eastern version of the Mass and read some about it" was indeed a cryptic message.

here is a medicine that may cure your obsession
with whether he did nor didnt read the Method

the mainstream theoretical physicist Frank Wilczek says
that the number 13E18 is extremely important

It is the ratio of the planckmass to the proton mass.
Here is a link to the third of a series of articles which
are essentially about this number. This article in turn
has links to the previous two articles and other bibliography:

I have analyzed chandrasekhar's formula for his supernova
limit and found that if the chandra mass limit is expressed
in terms of planck mass then it is

[constant] times (M_planck/m_prot)^2

the constant involves the average fraction of the baryons that are protons, in the core. If the core is 1/2 protons and 1/2 neutrons then there is a factor of 1/4 (half times half)
The constant is approximately pi/4.

So a quick and dirty way to calculate chandra limit is

(pi/4) (13E18)^2

it comes to the usual 1.4 solar masses.

This is not numerology or numerical coincidence. I just cranked it out of Chandra's formula as presented in Frank Shu's book. It is an algebraically equivalent form, which happens to display this
nice number (which is more exactly 12.99E18.

I hope we both realize that it does not matter whether or not Barrow really studied the Method! Your tale is in the realm of literature, where coincidence, symbolic connection, and what if questions matter. To deny importance to literature is to court destruction and oblivion.

Congratulations on being restrained from folly by not knowing enough Greek. :)

It is the second time in this month that someone points out Frank Wilczek's trilogy (ah well, I checked, the first one come from you, too!). Also there are some interesting lectures from him in the ArXiv, by the way.

Of course, the question of existence of a fundamental scale is deeply related to this thread! One can bypass all the subtle issues of analysis if the sum in riemann integral is replaced by a finite sum of finite, but very small areas. In turn, such areas can be defined as multiples of a fundamental one. This approach is wrong (or naive), but it keeps appearing and disappearing.

Note the related thread on Plank area vs Plank length. It keeps asking what is fundamental in a integral process: is it the area or is it the interval?

Actually in the Riemann integral there are an interplay of scales, as any map of areas, lines &c. to numbers is associated to a set of units. But the integral has also a iterative process, the one of the limit, which does it less naive than a simple sum.

Barrow theorem is not very explicit about all these issues. Regretly it was published earlier than Newton/Leibnitz Calculus, and never retouched; Barrow got completely involved in church matters, avoiding further work in mathematics.

I confess i need more help finding Wilczek (general audience) lectures. I just now did a search for his stuff in ArXiv and found *too much*. More by him (and co-authors) than I can with limited skill sift through. I would be grateful for any URLs.

I like his writing because I sense that he can write with honesty from a broad perspective for a general audience. And he has a knowledge of history. I would sure like to find more articles comparable to that trilogy.

I am comfortable with defining things by going to the limit (which is the conventional mainstream way) instead of trying to give real existence to infinitesimals as they sometimes do in "non-standard" analysis (that I know very little about!)

I suspect that the Planck mass is an important *reference* mass for establish ratios. But it is 22 micrograms which is neither particularly small or large! It is the mass of a barely visible flea!
Oops, must run. Thanks for answering!

Fundamental scales dont have to be the smallest possible or the largest possible of anything, just good reference points for proportions. Or?