Science > Physics > This Week's Finds in Mathematical Physics (Week 221)
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"John Baez" |
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19 Sep 2005 12:27:23 AM |
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This Week's Finds in Mathematical Physics (Week 221) |
Also available as http://math.ucr.edu/home/baez/week221.html
September 18, 2005
This Week's Finds in Mathematical Physics - Week 221
John Baez
After going to the Streetfest this summer, I wandered around China.
I began by going to a big conference in Beijing, the 22nd
International Congress on the History of Science. I learned some
interesting stuff. For example:
The eleventh century was the golden age of Andalusian astronomy
and mathematics, with a lot of innovation in astrolabes. During
the Caliphate (912-1031), three quarters of all mathematical
manuscripts were produced in Cordoba, most of the rest in
Sevilla, and only a few in Granada in Toledo.
<P>
I didn't understand the mathematical predominance of Cordoba when
I first heard about it, but the underlying reason is simple.
The first great Muslim dynasty were the Ummayads, who ruled from
Damascus. They were massacred by the Abbasids in 750, who then
moved the capital to Baghdad. When Abd ar-Rahman fled Damascus
in 750 as the only Ummayyad survivor of this massacre, he went
to Spain, which had already been invaded by Muslim Berbers in 711.
Abd ar-Rahman made Cordoba his capital. And, by enforcing a certain
level of religious tolerance, he made this city into *the place to
be* for Muslims, Jews and Christians - the "ornament of the world",
and a beacon of learning - until it was sacked by Berber troops in
1009.
Other cities in Andalusia became important later. The great
philosopher Ibn Rushd - known to Westerners by the Latin name
"Averroes" - was born in Cordoba in 1128. He later became a judge
there. He studied mathematics, medicine, and astronomy, and wrote
detailed line-by-line commentaries on the works of Aristotle. It
was through these commentaries that most of Aristotle's works,
including his Physics, found their way into Western Europe! By 1177,
the bishop of Paris had banned the teaching of many of these new
ideas - but to little effect.
Toledo seems to have only gained real prominence after Alfonso VI
made it his capital upon capturing it in 1085 as part of the
Christian "reconquista". By the 1200s, it became a lively center
for translating Arabic and Hebrew texts into Latin.
Mathematics also passed from the Arabs to Western Europe in other
ways. Fibonacci (1170-1250) studied Arabic accounting methods in
North Africa where his father was a diplomat. His book Liber Abaci
was important in transmitting the Indian system of numerals
(including zero) from the Arabs to Europe. However, he wasn't the
first to bring these numbers to Europe. They'd been around for over
200 years!
For example: Gerbert d'Aurillac (940-1003) spent years studying
mathematics in various Andalusian cities including Cordoba. On
his return to France, he wrote a book about a cumbersome sort of
"abacus" labelled by a Western form of Arabic numerals. This
remained popular in intellectual circles until the mid-12th century.
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".
I want to learn more about Andalusian science! I found this book
a great place to start - it's really fascinating:
1) Maria Rose Menocal, The Ornament of the World: How Muslims, Jews
and Christians Created a Culture of Tolerance in Medieval Spain,
Little, Brown and Co., 2002.
For something quick and pretty, try this:
2) Steve Edwards, Tilings from the Alhambra,
http://www2.spsu.edu/math/tile/grammar/moor.htm
Apparently 13 of the 17 planar symmetry groups can be found in tile
patterns in the Alhambra, a Moorish palace built in Granada in the
1300s.
If you want to dig deeper, you can try the references here:
3) J. J. O'Connor and E. F. Robertson, Arabic mathematics:
forgotten brilliance?,
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html
For more on Fibonacci and Arabic mathematics, try this paper by
Charles Burnett, who spoke on this subject in Beijing:
4) Charles Burnett, Leonard of Pisa and Arabic Arithmetic,
http://muslimheritage.com/topics/default.cfm?ArticleID=472
Another interesting talk in Beijing was about the role of the
Syriac language in the transmission of Greek science to Europe.
Many important texts didn't get translated directly from Greek to
Arabic! Instead, they were first translated into *Syriac*.
I don't understand the details yet, but luckily there's a great
book on the subject, available free online:
5) De Lacy O'Leary, How Greek Science Passed to the Arabs,
Routledge & Kegan Paul Ltd, 1949. Also available at
http://www.aina.org/books/hgsptta.htm
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!
I want to read this book, too:
6) Scott L. Montgomery, Science in Translation: Movements of
Knowledge through Cultures and Time, U. of Chicago Press, 2000.
Review by William R. Everdell available at MAA Online,
http://www.maa.org/reviews/scitrans.html
The historian of science John Stachel, famous for his studies of
Einstein, says this book "strikes a blow at one of the founding
myths of 'Western Civilization'" - namely, that Renaissance Europeans
single-handedly picked up doing science where the Greeks left off.
As Everdell writes in his review:
Perhaps the best of the book's many delightful challenges
to conventional wisdom comes in the first section on the
translations of Greek science. Here we learn why it is
ridiculous to use a phrase like "the Renaissance recovery
of the Greek classics"; that in fact the Renaissance recovered
very little from the original Greek and that it was long before
the Renaissance that Aristotle and Ptolemy, to name the two most
important examples, were finally translated into Latin. What
the Renaissance did was to create a myth by eliminating all the
intermediate steps in the transmission. To assume that Greek
was translated into Arabic "still essentially erases centuries
of history" (p. 93). What was translated into Arabic was
usually Syriac, and the translators were neither Arabs (as
the great Muslim historian Ibn Khaldun admitted) nor Muslims.
The real story involves Sanskrit compilers of ancient Babylonian
astronomy, Nestorian Christian Syriac-speaking scholars of
Greek in the Persian city of Jundishapur, and Arabic- and
Pahlavi-speaking Muslim scholars of Syriac, including the
Nestorian Hunayn Ibn Ishak (809-873) of Baghdad, "the greatest
of all translators during this era" (p. 98).
And now for something completely different: the Langlands program!
I want to keep going on my gradual quest to understand and explain
this profoundly difficult hunk of mathematics, which connects
number theory to representations of algebraic groups. I've found
this introduction to be really helpful:
7) Stephen Gelbart: An elementary introduction to the Langlands
program, Bulletin of the AMS 10 (1984), 177-219.
There are a lot of more detailed sources of information on the
Langlands program, but the problem for the beginner (me) is that
the overall goal gets swamped in a mass of technicalities.
Gelbart's introduction does the best at avoiding this problem.
I've also found parts of this article to be helpful:
8) Edward Frenkel, Recent advances in the Langlands program, available
at math.AG/0303074.
It focuses on the "geometric Langlands program", which I'd rather
not talk about now. But, it starts with a pretty clear introduction
to the basic Langlands stuff... at least, clear to me after I've
battered my head on this for about a year!
If you know some number theory or you've followed recent issues of
This Week's Finds (especially "week217" and "week218") it should make
sense, so I'll quote it:
The Langlands Program has emerged in the late 60's in the form of
a series of far-reaching conjectures tying together seemingly
unrelated objects in number theory, algebraic geometry, and the
theory of automorphic forms. To motivate it, recall the classical
Kronecker-Weber theorem which describes the maximal abelian extension
Q^{ab} of the field Q of rational numbers (i.e., the maximal extension
of Q whose Galois group is abelian). This theorem states that Q^{ab}
is obtained by adjoining to Q all roots of unity; in other words,
Q^{ab} is the union of all cyclotomic fields Q(1^{1/N}) obtained
by adjoining to Q a primitive Nth root of unity
1^{1/N}
The Galois group Gal(Q(1^{1/N})/Q) of automorphisms of Q(1^{1/N})
preserving Q is isomorphic to the group (Z/N)* of units of the
ring Z/N. Indeed, each element m in (Z/N)*, viewed as an integer
relatively prime to N, gives rise to an automorphism of Q(1^{1/N})
which sends
1^{1/N}
to
1^{m/N}.
Therefore we obtain that the Galois group Gal(Q^{ab}/Q), or,
equivalently, the maximal abelian quotient of Gal(Qbar/Q),
where Qbar is an algebraic closure of Q, is isomorphic to the
projective limit of the groups (Z/N)* with respect to the system
of surjections
(Z/N)* -> (Z/M)*
for M dividing N. This projective limit is nothing but the direct
product of the multiplicative groups of the rings of p-adic
integers, Z_p*, where p runs over the set of all primes. Thus,
we obtain that
Gal(Q^{ab}/Q) = product_p Z_p*.
The abelian class field theory gives a similar description for the
maximal abelian quotient Gal(F^ab/F) of the Galois group Gal(Fbar/F),
where F is an arbitrary global field, i.e., a finite extension of
Q (number field), or the field of rational functions on a smooth
projective curve defined over a finite field (function field).
Namely, Gal(F^ab/F) is almost isomorphic to the quotient A(F)*/F*,
where A(F) is the ring of adeles of F, a subring in the direct
product of all completions of F. Here we use the word "almost"
because we need to take the group of components of this quotient
if F is a number field, or its profinite completion if F is a
function field.
When F = Q the ring A(Q) is a subring of the direct product of the
fields Q_p of p-adic numbers and the field R of real numbers, and
the quotient A(F)*/F* is isomorphic to
R+ x product_p Z*_p.
where R+ is the multiplicative group of positive real numbers.
Hence the group of its components is
product_p Z*_p
in agreement with the Kronecker-Weber theorem.
One can obtain complete information about the maximal abelian
quotient of a group by considering its one-dimensional
representations. The above statement of the abelian class field
theory may then be reformulated as saying that one-dimensional
representations of Gal(Fbar/F) are essentially in bijection with
one-dimensional representations of the abelian group
A(F)* = GL(1,A(F))
which occur in the space of functions on
A(F)*/F* = GL(1,A(F))/GL(1,F)
A marvelous insight of Robert Langlands was to conjecture that
there exists a similar description of *n-dimensional
representations* of Gal(Fbar/F). Namely, he proposed that those
may be related to irreducible representations of the group
GL(n,A(F)) which are *automorphic*, that is those occurring in
the space of functions on the quotient
GL(n,A(F))/GL(n,F)
This relation is now called the *Langlands correspondence*.
At this point one might ask a legitimate question: why is it
important to know what the n-dimensional representations of the
Galois group look like, and why is it useful to relate them to
things like automorphic representations? There are indeed many
reasons for that. First of all, it should be remarked that
according to the Tannakian philosophy, one can reconstruct a
group from the category of its finite-dimensional representations,
equipped with the structure of the tensor product. Therefore
looking at n-dimensional representations of the Galois group is
a natural step towards understanding its structure. But even
more importantly, one finds many interesting representations of
Galois groups in "nature".
For example, the group Gal(Qbar/Q) will act on the geometric
invariants (such as the etale cohomologies) of an algebraic variety
defined over Q. Thus, if we take an elliptic curve E over Q,
then we will obtain a two-dimensional Galois representation on its
first etale cohomology. This representation contains a lot of
important information about the curve E, such as the number of
points of E over Z/p for various primes p.
The point is that the Langlands correspondence is supposed to
relate n-dimensional Galois representations to automorphic
representations of GL(n,A(F)) in such a way that the data on
the Galois side, such as the number of points of E over Z/p,
are translated into something more tractable on the automorphic
side, such as the coefficients in the q-expansion of the modular
forms that encapsulate automorphic representations of GL(2,A(Q)).
More precisely, one asks that under the Langlands correspondence
certain natural invariants attached to the Galois representations
and to the automorphic representations be matched. These
invariants are the *Frobenius conjugacy classes* on the Galois
side and the *Hecke eigenvalues* on the automorphic side.
Since I haven't talked about Hecke operators yet, I'll stop here!
But, someday I should really explain the ideas behind the baby
"abelian" case of the Langlands philosophy in simpler terms than
Frenkel does here. The abelian case goes back way before Langlands:
it's called "class field theory". And, it's all about exploiting
this analogy, which I last mentioned in "week218":
NUMBER THEORY COMPLEX GEOMETRY
Integers Polynomial functions on the complex plane
Rational numbers Rational functions on the complex plane
Prime numbers Points in the complex plane
Integers mod p^n (n-1)st-order Taylor series
p-adic integers Taylor series
p-adic numbers Laurent series
Adeles for the rationals Adeles for the rational functions
Fields One-point spaces
Homomorphisms to fields Maps from one-point spaces
Algebraic number fields Branched covering spaces of the complex plane
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twf.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
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| User: "" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
19 Sep 2005 03:19:19 PM |
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In article <dgli7r$fb9$1@glue.ucr.edu>,
John Baez <baez@math.removethis.ucr.andthis.edu> wrote:
The eleventh century was the golden age of Andalusian astronomy
and mathematics, with a lot of innovation in astrolabes. During
the Caliphate (912-1031),
Actually the Caliphate began in 929 when Abd al-Rahman declared
himself caliph, though he assumed power in 912.
three quarters of all mathematical
manuscripts were produced in Cordoba, most of the rest in
Sevilla, and only a few in Granada in Toledo.
Of course that should be "Granada and Toledo".
By the way, you can see a very romantic view of Granada,
and lots of other links, by going to the website version
of this week's finds:
http://math.ucr.edu/home/baez/week221.html
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| User: "Uncle Al" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
19 Sep 2005 03:31:39 PM |
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wrote:
In article <dgli7r$fb9$1@glue.ucr.edu>,
John Baez < > 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".
By the way, you can see a very romantic view of Granada,
and lots of other links, by going to the website version
of this week's finds:
http://math.ucr.edu/home/baez/week221.html
Islam created worlds of wonder, progress, and intellectual ferment.
Muslim Spain's architecture still outshines that of Catholic Spain.
While Europe was up to its diseased and willfully ignorant chin
drowning in the One True Church, Islam had created an equitable rule
of law that worked - for everybody in its dominions.
Islam then turned inward, embracing its Koran and denying empirical
reality. Pity. Protestantism in reply to Catholicsm has had no
better long-term luck.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
20 Sep 2005 05:33:48 PM |
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Uncle Al wrote:
Islam created worlds of wonder, progress, and intellectual ferment. > Muslim Spain's architecture still outshines that of Catholic Spain.
[...]
Islam then turned inward, embracing its Koran and denying empirical
reality. Pity.
No. Not pity. Inevitability.
All great civilizations eventually settle down and then, locked into
their self-imposed prison of settled-down confinement, begin to
increasingly manifest the symptoms of cabin fever, and go into
stagnation and a "fatigue of spirit" petering out.
This happened to China too, starting in the 1300's so that by 1900 it
China -- once the greatest civilization in the world -- became
everybody else's *****; with the notable event of the year being the
parade of armies from a dozen nations and constituencies in September
in Shanghai. That made the locals feel so good, they still commemorate
the indignity of being bitched by outsiders in the preamble of their
present-day constitution.
Islam was worse: the printing press, itself, was outlawed in much of
the Islamic world as late as the 19th century ... while the rest of the
planet so thoroughly passed it by that today it has become the one part
of the world holding everyone else back the most.
Only in the past few years have many of the nations in this part of the
world even gotten legislatures or parliaments; some don't even have
female suffrage, some only granting it in recent times ... some don't
even have MALE suffrage, either!
It's a shame the constitution proposed in Iraq had to be such a
shambles. The Sunnis' 13 objections were for the most part entirely
appropriate and (in fact) run closely parallel to many of the
substantial issues that emerged during the US's convention in 1787.
The document looks like complete rush job; like a high school essay
written by diletantes and the only thing worse than it being voted down
would be for it to be ratified. There could have been an opportunity
to rise above the mean vagaries of the time to erect a new foundation
for a "United Islamic Republic" setting the way for a future that
accommodates modern insight with the older legacy of the cradle of
civilization.
Some times the only way to do a job right is to do it yourself. So,
you'll see or hear about MY version of a prospective "United Islamic
Republic" constitution, to be widely distributed in the near future,
elsewhere, probably shortly after the ratification fails in October ...
and the launching underground of the Green Tide movement.
The "all great civilizations" includes the United States, which (as has
been widely noted the past 50 years or more) is showing striking
parallels to Rome. It's almost to the point where you can even draw
time equivalences and a time compression ratio, the 1940's being
roughly equivalent to the late 2st century, the 1970's to the early to
late 3rd century; and the present day to around the turn of the 5th
century, with a ratio on the order of 3:10. With the equivalence
2000=400, that puts 476 at around 2020.
Feudalism, serfs, dukes and counts were NOT the creation of Medieval
Europe by the way. They were well in place in the Empire by the time
of the 5th century. Duke and Duchy; Count, (Pontiff), Serfdom are all
Roman in origin. Similarly, the first outcroppings of the breakdown of
fatigue and stagnation, whatever they may be, should start to manifest
themselves sometime in the Future: In The Year 2000.
The question that should be on everyone's mind is: after the US, then
what?!
Progeny -- The Future World Federation
http://federation.g3z.com/FedSeries/Progeny.htm
Stay tuned for future developments...
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| User: "Uncle Al" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
20 Sep 2005 08:48:53 PM |
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wrote:
Uncle Al wrote:
Islam created worlds of wonder, progress, and intellectual ferment. > Muslim Spain's architecture still outshines that of Catholic Spain.
[...]
Islam then turned inward, embracing its Koran and denying empirical
reality. Pity.
No. Not pity. Inevitability.
All great civilizations eventually settle down and then, locked into
their self-imposed prison of settled-down confinement, begin to
increasingly manifest the symptoms of cabin fever, and go into
stagnation and a "fatigue of spirit" petering out.
[snip good stuff]
The "all great civilizations" includes the United States, which (as has
been widely noted the past 50 years or more) is showing striking
parallels to Rome. It's almost to the point where you can even draw
time equivalences and a time compression ratio, the 1940's being
roughly equivalent to the late 2st century, the 1970's to the early to
late 3rd century; and the present day to around the turn of the 5th
century, with a ratio on the order of 3:10. With the equivalence
2000=400, that puts 476 at around 2020.
[snip]
I put the crash at 2015 driven by the Baby Boomer retirement hump and
"discovered" embezzlement of the whole
Social Security fund. SS has always been "money out is only from
money in." Elasticity into embrittlement is amplified by the
$trillion Iraq fiasco, the $500 billion New Orleans fiasco, the $300
billion NASA fiasco including Apollo II... and insane escalation of
energy and raw material costs driven by an impotent US and a hungry
China translating into exponential stagflation, interest rate
explosion, and precipitated massive real estate and credit debt
defaults. How many more hundreds of fiat $billions can Bush the
Lesser extrude into Wall Street? Gold tells the tale - the US dollar
is withering.
I wouldn't be averse to Ragnarok being dated 21 December 2012 as
predicted by the Maya. The Great Depression was precipitous. The
plebeian mythos of prosperity suddenly disappeared. A nation that
thought it was comfortable was suddenly destitute without anything
much changing. Roosevelt's obscene universal socialism was impotent.
Revival required WWII. We killed off a bunch of young males to open
opportunities for the survivors. SOP European history.
Los Angeles had a rainstorm last night. Massive blackouts, flooding,
bureaucratic panic. On-time arrival of the annual rainy season, as it
has arrived every year for the past 120 years documented, requires
emergency STUDIES.
It's already over. Only paperwork remains to be filed to begin the
unending night.
C'mon hurricane Rita! Another Force 5 slam into New Orleans will
short-circuit Halliburton corruption.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Schoenfeld" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
21 Sep 2005 02:42:02 AM |
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Uncle Al wrote:
markwh04@yahoo.com wrote:
Uncle Al wrote:
Islam created worlds of wonder, progress, and intellectual ferment. > Muslim Spain's architecture still outshines that of Catholic Spain.
[...]
Islam then turned inward, embracing its Koran and denying empirical
reality. Pity.
No. Not pity. Inevitability.
All great civilizations eventually settle down and then, locked into
their self-imposed prison of settled-down confinement, begin to
increasingly manifest the symptoms of cabin fever, and go into
stagnation and a "fatigue of spirit" petering out.
[snip good stuff]
The "all great civilizations" includes the United States, which (as has
been widely noted the past 50 years or more) is showing striking
parallels to Rome. It's almost to the point where you can even draw
time equivalences and a time compression ratio, the 1940's being
roughly equivalent to the late 2st century, the 1970's to the early to
late 3rd century; and the present day to around the turn of the 5th
century, with a ratio on the order of 3:10. With the equivalence
2000=400, that puts 476 at around 2020.
[snip]
I put the crash at 2015
Nine years late.
http://www.aljazeera.com/cgi-bin/review/article_full_story.asp?service_id=9752
http://www.csmonitor.com/2005/0830/p03s01-wome.html
driven by the Baby Boomer retirement hump and
"discovered" embezzlement of the whole
Social Security fund.
2015 social security liabilities are relatively a small slice of the US
GDP and not the catastrophic issue some would have others believe. The
real problem is the depreciating value of the petrodollar and its
inevitable demise. Central bankers have been preparing for the currency
flight from USD to Euro's for years, and the ***** is to hit the fan
very soon. Volatility in oil prices show more weakness in petrodollar
than oil supply.
Also, SS liabilities are in the form of government bonds, and when
hyperinflation hits this debt will trivially dissolve thus technically
fixing Social Security (the people will get their money but it won't be
worth anything).
Looks like the US will soon need to export real goods and services to
participate in the global economy - hamburgers and legal services won't
do.
[...]
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| User: "Schoenfeld" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
21 Sep 2005 03:07:32 AM |
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wrote:
The question that should be on everyone's mind is: after the US, then
what?!
A century of prosperity.
Progeny -- The Future World Federation
http://federation.g3z.com/FedSeries/Progeny.htm
Stay tuned for future developments...
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| User: "Joseph Hertzlinger" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
26 Sep 2005 12:31:52 AM |
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On 20 Sep 2005 15:33:48 -0700, <>
wrote:
The "all great civilizations" includes the United States, which (as has
been widely noted the past 50 years or more) is showing striking
parallels to Rome. It's almost to the point where you can even draw
time equivalences and a time compression ratio, the 1940's being
roughly equivalent to the late 2st century, the 1970's to the early to
late 3rd century; and the present day to around the turn of the 5th
century, with a ratio on the order of 3:10. With the equivalence
2000=400, that puts 476 at around 2020.
Time for my standard capsule comparison of America and the
archetypical has-been empire:
If we take Rome as the model, those parts of Roman history that look
eerily familiar to present-day Americans occurred between the time of
Tiberius Gracchus (an analog of JFK) and the time of Crassus (an
analog of H. Ross Perot). I think the best analog for the Current
Unpleasantness occurred about 100 BCE when Rome was attacked by a
bunch of barbarians nobody had heard of before and was defended by
Marius (who made his reputation by jailing a previously untouchable
crook and was subsequently known for professionalizing the armed
forces). In that case, we can expect it will be five hundred years
before Washington is sacked.
As for time scales...
Rome overthrew its absolute monarchy in 509 BCE. If the closest
analogy to that is the execution of Charles I (this is consistent with
the Napoleon--Alexander analogy), we're only fifty years ahead of
schedule.
Feudalism, serfs, dukes and counts were NOT the creation of Medieval
Europe by the way. They were well in place in the Empire by the time
of the 5th century. Duke and Duchy; Count, (Pontiff), Serfdom are all
Roman in origin. Similarly, the first outcroppings of the breakdown of
fatigue and stagnation, whatever they may be, should start to manifest
themselves sometime in the Future: In The Year 2000.
The question that should be on everyone's mind is: after the US, then
what?!
We'll have to arrange to put the world in reponsible hands after the
American Empire collapses in another five hundred years.
What would a last Will and Testament for an empire look like?
We the people of the United States leave...
To Europe: Custodial care over the museums containing the by-then
fossilized triumphs of Western Civilization.
Who should we leave our kick-butt military to?
--
http://hertzlinger.blogspot.com
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| User: "Robert J. Kolker" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
19 Sep 2005 05:17:26 PM |
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Uncle Al wrote:
baez@math.removethis.ucr.andthis.edu wrote:
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".
By the way, you can see a very romantic view of Granada,
and lots of other links, by going to the website version
of this week's finds:
http://math.ucr.edu/home/baez/week221.html
Islam created worlds of wonder, progress, and intellectual ferment.
Muslim Spain's architecture still outshines that of Catholic Spain.
While Europe was up to its diseased and willfully ignorant chin
drowning in the One True Church, Islam had created an equitable rule
of law that worked - for everybody in its dominions.
Islam then turned inward, embracing its Koran and denying empirical
reality. Pity. Protestantism in reply to Catholicsm has had no
better long-term luck.
The immediate result of the Protestant Reformation was the rescinding of
usury laws and the burgeoning of capital investment. Capitalism in
Europe, at least in its initial phase was a child of the Protestant
Refermation.
The Counter Refromation undertaken by the Church to clean up its act in
turn promoted the development of commerce and capitalism, so for a
period during and following the Renassance Europe began to develop.
After the plauge reduced the excess population and drove up wages Europe
really began to flourish.
In our own day, the Fundies have attempted to squash science, but they
have not succeeded. The U.S. is a secular nation. If we fail, we fail
for reasons not directly related to religion. I suspect are huggy kissy
love affair with the Welfare State has done its work to send us down the
toilet bowl of history. As we exist the stage, a de-communized by
authoratarion China enters stage right which completes the cycle. For a
long time China was several parsecs ahead of the West and Islam.
Read -The Genius of China- by Robert Temple to see how smart the Chinese
were in their prime. Their time passed, yet it is coming again.
Bob Kolker
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| User: "Bruce Scott TOK" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
20 Sep 2005 11:58:37 AM |
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Bob Kolker wrote:
The immediate result of the Protestant Reformation was the rescinding of
usury laws and the burgeoning of capital investment. Capitalism in
Europe, at least in its initial phase was a child of the Protestant
Refermation.
[...]
Isn't this ignoring the ``first draft'' of capitalism that got going in
the 12th-13th Centuries? Large scale defaulting by the royalty brought
most of it down. It got going again in the 15th Century, well before
Luther and his consequences.
All this is extensively covered in The Pursuit of Power by W McNeill and
most expecially The Wheels of Commerce by F Braudel (he covers the
1400-1700 period mostly).
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
20 Sep 2005 05:36:30 PM |
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wrote:
By the way, you can see a very romantic view of Granada,
and lots of other links, by going to the website version
of this week's finds:
The marriage ceremony seen at the end of the 2nd Star Wars film was in
an actual setting, not something fabricated. It was filmed on location
in Spain.
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| User: "John Baez" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
20 Sep 2005 04:32:38 PM |
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Some addenda....
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 that had been erased
and written over has recently been read with the help of a
synchrotron X-ray beam!
http://www.mlahanas.de/Greeks/ArchimedesPal.htm
http://news-service.stanford.edu/news/2005/may25/archimedes-052505.html
This manuscript also reveals for the first time that he did work on
combinatorics:
http://www.mlahanas.de/Greeks/ArchimedesComb.htm
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$1@dizzy.math.ohio-state.edu>,
Noam Elkies <elkies@math.harvard.edu> wrote:
Amusingly, Arabic numerals were also called "dust numerals" since
they were used in calculations on an easily erasable "dust board".
Their use was described in the Liber Pulveris, or "book of dust".
This is even more amusing than you may realize: the word "abacus"
comes from a Greek word "abax, abak-" for "counting board", which
conjecturally might come from the Hebrew word (or a cognate word
in another semitic language) for "dust"! See for instance
<http://education.yahoo.com/reference/dictionary/entry/abacus>.
So these "dust numerals" replaced a reckoning device whose name
may also originate with calculation a dust board...
Interesting! While "calculus" refers back to pebbles.
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| User: "" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
21 Sep 2005 06:05:37 AM |
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In article <dgpv5m$p2s$1@glue.ucr.edu>,
(John Baez) wrote:
Some addenda....
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.
I know how much has been lost from our work. An extrapolation
added to knowing how people [do not] work is guiding what
I'm going now. A paperless society only interested in
the new and shiny is not a feature.
<snip>
/BAH
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| User: "" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
21 Sep 2005 10:28:37 AM |
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John Baez wrote:
The burning of the library of Alexandria is partially
to blame for these losses.
and the sack of Constantinople in 1204 during the 4th Crusade,
led by Enrico Dandolo, the Doge of Venice.
Can't say I blame the guy though - anyone would have done the
same in the circs: Years before, the rulers of Constantinople
had arrested several thousand Venetian traders based there,
essentially for being too successful, and when Dandolo visited
to negotiate their release the rulers had him blinded and sent
back to Venice:
http://en.wikipedia.org/wiki/Fourth_Crusade
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
If that refers to the "Philosopher's House", I read that the
Naples authorities have shamefully neglected the site and
allowed rainwater to seep through the carbonized remains.
But it's good news that something has been retrieved.
Cheers
John R Ramsden
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| User: "Shmuel Seymour J. Metz" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
25 Sep 2005 05:54:49 AM |
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In <1127316516.956530.204900@f14g2000cwb.googlegroups.com>, on
09/21/2005
at 08:28 AM, said:
and the sack of Constantinople in 1204 during the 4th Crusade, led by
Enrico Dandolo, the Doge of Venice.
Can't say I blame the guy though - anyone would have done the same in
the circs:
He could have ordered that all property be seized and that the books
be sent to Venice.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to
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| User: "John Baez" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 221) |
22 Sep 2005 11:34:18 AM |
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In article <1127316516.956530.204900@f14g2000cwb.googlegroups.com>,
<john_ramsden@sagitta-ps.com> wrote:
John Baez wrote:
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
If that refers to the "Philosopher's House", I read that the
Naples authorities have shamefully neglected the site and
allowed rainwater to seep through the carbonized remains.
But it's good news that something has been retrieved.
I'm referring to the "Villa of Papyri" in the old Roman town
of Herculaneum. I'm not sure if this is the same thing. It could be.
It's a pretty impressive story. Quoting from the above site:
"A sister city to Pompeii that was also buried in the volcanic eruption
of A.D. 79, Herculaneum was a seaside town that sat between Vesuvius'
fertile foot and the gleaming Bay of Naples. The collection of 2,000
carbonized Greek and Latin scrolls, primarily Epicurean philosophical
writings, was found in a luxurious Herculaneum house known as the Villa
of the Papyri, which was discovered in 1752.
The scrolls have endured a destructive path through history: first, rain
soaked the papyri, then a 570-degree swell of molasses-thick mud engulfed
the villa and charred the scrolls. They would remain buried under 65 feet
of mud for hundreds of years.
As a result, many of the fragile scroll cylinders are pressed into
trapezoidal columns; some are bowed and snaked into half-moons, others
folded into v-shapes.
After their discovery the mortality rate for the scrolls continued to climb
as would-be conservators struggled to find a way to unroll the fragile
manuscripts. Some scrolls were turned to mush when they were painted with
mercury; many were sliced down the middle and cut into fragments. Early
transcribers would copy the visible outer layer of a scroll, then scrape it
off and discard it to read the next layer.
Even today, scholars use metaphors of near impossibility to describe the
scroll unrolling process. It is like "flattening out a potato chip" without
destroying it, or like "separating (burned) layers of two-ply tissue," says
Jeffrey Fish of Baylor University.
The current unrolling methoddeveloped by a team of Norwegian conservators
involves applying a gelatin-based adhesive to the scroll's outer surface.
As the adhesive dries, the outer shell - which bears the text on its interior -
can be slowly peeled off. It can take days to remove a single fragment,
months or years to process a complete scroll. Some 300 of the library's
scrolls have yet to be unrolled, and many more scrolls are in various
stages of conservation and repair.
On the Herculaneum project, CPART researchers Steve and Susan Booras
conducted multispectral imaging (MSI) on 3,100 trays of papyrus fragments
and photographed them with a high-quality digital camera. The images will
be used to create a digital library that can be accessed by scholars
worldwide. Developed for NASA scientists, the imaging technique has only
recently been applied to the study of ancient texts. Rather than focusing
on light that is seen at wave lengths visible to the eye, MSI uses
filters to focus on nonvisible portions of the light spectrum. In the
nonvisible infrared spectrum, the black ink on a blackened scroll can be
clearly differentiated. In some cases clear, legible writings have been
found on fragments that researchers believed were completely blank.
[....]
Because most records from this period deteriorated long ago, the survival
of the Herculaneum scrolls is remarkable. Ironically, the forces that
burned the scrolls probably ensured their survival by converting unstable
organic matter to a more stable carbonized state.
"Would we have these scrolls if Vesuvius had not erupted? Probably not.
Papyrus left on the shelf for 2,000 years would probably have long
deteriorated," says Booras. In their current condition, however, there is
little hope that the physical remnants of these scrolls will survive.
Rapid deterioration underscores the importance of the CPART digital
library, which will provide a permanent archive and point of reference
for future study.
While the Herculaneum collection is already one of the world's largest
ancient libraries, the collection may grow even larger with continued
exploration. Many scholars believe that additional scrolls may be buried
in the Villa of the Papyri, which was only partially excavated in 1752.
Since the upper-floor library was found in a state of transition - as
if someone was moving the scrolls to safety at the time of the eruption -
many scholars believe the house's main library has not yet been found.
"The hope everyone has is that somewhere in one of these charred scrolls
is going to be found the writing of an ancient author that has been lost
for centuries," says Hall.
However, the hunt for that ancient library was abruptly suspended last
year. Just as modern excavations at the villa brought archaeologists
to the doorways of two new lower-level rooms, the Italian government -
opting to focus on preservation and restoration of existing sites -
banned new excavations. It was a devastating blow to scholars like
Gigante, the 50-year patriarch of the Herculaneum scrolls project and
a self-proclaimed "son of Vesuvius," who is anxious to continue the
search."
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