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2005 Archives
| Weyl and
Emmy -- Posted by wostraub
on Wednesday, December 21 2005 |
Here's a photo taken in the early
1930s of Weyl and his wife Hella, their son Joachim, Emmy Noether
and several friends, colleagues and students. Reproduced from the
1981 book Emmy Noether: A Tribute to Her Life and Work,
James Brewer and Martha Smith (eds.).
 |
| Weyl
Left -- Posted by wostraub
on Tuesday, December 20 2005 |
Hermann Weyl was a patriotic
German citizen, but when Hitler came to power in 1933 Weyl saw the
writing on the wall. As a respected mathematical physicist and
law-abiding Christian, he had nothing to fear himself, but his wife
Helene had a Jewish background which placed her in jeopardy. They
gave up their bank accounts and all their possessions, packed their
bags, and left for Princeton. Albert Einstein and Emmy Noether
weren't far behind them.
Now that Bush is turning America into Nazified Amerika, where would
Weyl go? My guess is back to Germany or Switzerland. He wouldn't
have anything to do with this Bush regime.
It's still not so bad, they say. You can still speak out against the
Bush regime without worrying about being taken away in the middle of
the night.
Or can you? According to Bush, you're either with him or you're with
the terrorists. The Democratic and Independent parties are not with
Bush, so they must be for the terrorists. Bush's latest crime is to
spy on Americans without a court order. My guess is that he will now
authorize his goons at the NSA to spy on these parties to keep them
from gaining power in 2006 and 2008. The Republican Party, in the
guise of a Frist or Hastert or DeLay or Sessions or Hunter or Inhofe,
will then become Dictator for Life. George Orwell may have been off
by only 24 years.
If Bush is successful, and I see no reason to believe that he won't
be unless he is stopped, then you can say goodbye to the America you
once knew and loved. Say goodbye also to the Constitution, which
Bush recently referred to as "just a goddamned piece of paper." Say
goodbye also to the middle class, which will be taxed out of
existence to pay off Bush's monstrous deficits. You can also kiss
off human rights, the environment and legitimate science, because
these niceties have no place in BushWorld.
As for me, I'm going to fight like hell in 2006 to keep these
nightmares from becoming reality, and I hope your New Year's
resolutions are along the same lines. If we fail, we won't recognize
the place we're living in. God help us all.
 |
| Guns,
Germs and Steel -- Posted by
wostraub on Thursday, December 15 2005 |
One day in 1972, the UCLA
evolutionary biologist Jared Diamond was walking along a beach in
New Guinea with a local politician named Yali. At one point, the
native New Guinean asked Diamond the question, "Many years ago, you
white people developed many advanced goods and brought them here.
Why did we black people develop so little of own own?"
The answer to that question became the subject of Diamond's 1997
book, Guns, Germs and Steel. I have just finished reading
this award-winning book on human history and biology, and I am
astonished by how much I have learned about the human condition.
You might recall a book called The Bell Curve from about
ten years' back that basically posited the very contentious notion
that whites are more intelligent than blacks, and it is because of
this that Europeans ended up on top in the world-dominance game. But
Diamond completely destroys that idea by showing that it was a
series of accidents -- biological, geographical and otherwise --
that is the real explanation for why Africa and other dark-skinned
nations were plundered by whites. It could easily have been the
other way round.
Diamond capably argues that whites, on the whole, are probably
somewhat less intelligent than blacks, but the difference is
meaningless. What really counted when the world was being
"civilized" 500 hundred years ago was the confluence of numerous
accidents affecting human food production, mobility, disease
resistance/immunity, language development, animal domestication, and
availability of local resources.
For example, Europeans were able to domesticate most of their
indigenous animals for work and food. Pigs, sheep, cattle, oxen,
chickens, ducks and dogs were just some of the critters that were
domesticable. By contrast, sub-Saharan Africans had all assortment
of local widlife that could not be domesticated. As a case in point,
Diamond describes efforts that were made many years ago to
domesticate the zebra to pull carts and plow fields. These efforts
were quickly abandoned because zebras simply cannot be sufficiently
tamed to serve as beasts of burden. It goes without saying that no
hippo, lion or hyena ever had to pull a wagon.
Neither is inhuman brutality solely attributable to whites. In
societies where one band of indigenous natives had an advantage over
others, the advantaged peoples happily attacked, slaughtered and
enslaved their less-fortunate neighbors, regardless of the color of
their skin. In other words, Diamond explains, if things had been
different, black civilizations ably probwould not have restrained
themselves from brutally exploiting their less-powerful white
brothers.
However enlightening the book was for me, it does not adequately
take into account the apparent lack of compassion that humans are
capable of, if not altogether inclined to. And while the last
chapter of Diamond's book is titled The Future of Human History
as a Science, it does not touch on the need for humans to act
cooperatively and humanely in an age of diminishing resources and
greatly expanding human populations.
To me, reading about human history and all its compound tragedies
makes the words, teachings and acts of Jesus Christ all the more
remarkable. Christ's love, wisdom, compassion and humility represent
the most revolutionary kind of humanity I can imagine. It's
miraculous that anyone, god or mortal, could have so understood the
human condition.
Today, we live in an age of war, torture, deceit, secrecy and
disregard for our fellow human beings, perhaps more so now than ever
before. Worse, my own country has adopted these evils and somehow
found a way to justify them. It astounds me that we can attend
church, pray and worship to the God whose teachings constantly tell
us that we are doing great wrongs. Yet this is the way of hypocrisy,
a unique human failing that itself is as old as history. |
| The Spin
Connection in Weyl Space, Again -- Posted by
wostraub on Saturday,
December 10 2005 |
I've completely rewritten my
article on Weyl and the spin connection from the point of view of
non-metric-compatible geometry. In this article, I express my doubts
not only about the validity of Weyl's original theory but that of
non-metric-compatible theories as well.
Connection.pdf |
|
Connections in a Weyl Space -- Posted by
wostraub on Friday, December
2 2005 |
While updating my previous
write-up on Weyl's spin connection, I started looking seriously at
the concept of a generalized Weyl space and its relationship to
variable vector magnitude under parallel transfer. It does not look
encouraging, and I'm beginning to suspect that vector magnitude is a
fixed quantity after all.
In his 1918 theory, Weyl argued that vector length under physical
transplantation varies in an electromagnetic field. If the length of
some arbitrary vector Vμ is given by L2
= gμνVμVν, then Weyl's theory
basically says that under parallel transport this goes over to
2LdL = gμν αVμVνdxα
or dL = AμdxμL, where gμν α
is the covariant derivative of the metric tensor and Aμ
is the electromagnetic 4-potential. However, I have not been able to
find a symmetric connection term Γαμν (Weyl or
otherwise) that allows for a non-zero dL and a vanishing
Kronecker delta tensor under covariant differentiation. It goes
without saying that dL = 0 kills Weyl's theory before it
even gets started.
This is not deep stuff, and I'm surprised that I've seen no real
attempt in the literature to address what appears to be an obvious
discrepancy of Weyl space. At the same time, I've read Weyl for
years and never given this issue a second thought!
Of course, everyone knows that Weyl's 1918 was wrong anyway, but the
argument that killed it (due to Einstein) was based on physical, not
mathematical, considerations. Einstein himself got wrapped up years
later in the same old game when he tried to find a non-symmetric
connection for parallel transport in spacetime. Indeed, the last
sheet of paper he ever wrote on (while in the hospital where he
died) is covered with non-symmetric connections, which were integral
to his final (and failed) unified field theory. I like to think that
when Einstein stood before God, the Almighty asked him "With the
mind I gave you, why on Earth did you waste the last 30 years of
your life on this nonsense?!"
A colossal waste of time, but fun stuff.
"The use of general connections means asking for trouble."
-- Abraham Pais, Subtle is the Lord
PS: Very big game tomorrow for my old school, USC. I love my kids
(UCLA grads), but -- Go Trojans!! |
| Lev
Landau -- Posted by wostraub
on Thursday, December 1 2005 |
"I sing of Olaf glad and big ..."
Lev Landau was perhaps Russia's greatest physicist, and certainly
one of the world's leading scientists in the fields of atomic and
nuclear physics, astrophysics, low-temperature physics,
thermodynamics, quantum electrodynamics, kinetic theory, quantum
field theory, and plasma physics [whew]. His work on superfluid
helium garnered Landau the Nobel Prize in Physics in 1962.
Landau was born in Russia in 1908. After earning his undergraduate
degree at the age of 19 at LSU (that's Leningrad State University to
you Louisiana Tigers fans), he went on to get a PhD in physics in
1934 at Kharkov Gorky State University, where he was appointed head
of the department the following year.
Landau was not only a brilliant scientist, he was an idealist whose
negative statements against Stalin earned him a trip to a Russian
prison in 1938. The conditions there were so harsh (see photo taken
during his imprisonment) that Landau did not expect to survive even
one year. But repeated, impassioned (and politically motivated)
pleas from Niels Bohr and fellow Russian Petr Kapitsa to Stalin (who
wanted Landau shot) caused the Russian leader to back down, and he
grudgingly ordered Landau to be released in 1939.
After receiving the Nobel Prize in 1962, Landau was involved in a
car accident that left him with a fractured skull and eleven broken
bones. The accident destroyed his great mind, and he subsequently
passed away from the accident's complications in 1968.
Why bring up the subject of Landau? Because he had the courage to
openly criticize a national leader who ordered the deaths of as many
as 20 million Russians over his total reign. Under Stalin's despotic
rule, Landau must have known he was sticking his neck out. But he
spoke out anyway.
Today, US President George W. Bush has legalized torture, killed
tens of thousands of innocent civilians, turned the media into an
entertainment/propaganda machine, lied to the American people and
the world for corporate profit and political power, and taken from
the poor and given it to the wealthy, not to mention being the
source of a host of other uncountable scandals, misrepresentations
and falsehoods. The worst part is that he commits these crimes while
hiding behind our Lord and Savior Jesus Christ!
Where are the outraged scientists today? Where are the scientific
heroes that are willing to temporarily set aside their thoughts on
superstrings and brane theory (not to mention advanced weapons
design) and speak out against the untruths we're subjected to daily,
ranging from a criminal war in Iraq to the outrageous stupidity
being forced into the craniums of students regarding intelligent
design and other anti-science dogma?
Stalin was a lot more intelligent than Bush, but Bush is far more
dangerous because he's in charge of 10,000 nuclear weapons. Bush's
hatred of intellectual thought and rationality has made him the
darling of an increasing number of brain-dead Americans who cannot
think for themselves anymore. I have the same respect for President
Bush as I would have for a chimpanzee with a machine gun.
"I will not kiss your f***ing flag ..." ee cummings
 |
| Newton
Routs Einstein -- Posted by
wostraub on Friday, November 25 2005 |
Yesterday, the Royal Society
announced the results of a "popularity contest" between Sir Isaac
Newton and Albert Einstein. When asked which scientist made the most
contributions to science, 86.2% of the Royal Society's voting
scientists opted for Newton. When the same question was posed to the
general public, Newton again beat out Einstein, with 61.8% voting
for Newton.
Intestingly, when asked which scientist made the most contributions
to humanity, only 60.9% of the 345 Royal Society voting scientists
voted for Newton, while the public vote was virtually tied.
Newton was elected to the Royal Society in 1672, whereas Einstein
came in as a foreign member in 1921.
Although this is the 100th anniversary of Einstein's annus
mirabilis, or miracle year of 1905 (he wrote five fundamental
papers that year, including the ones on special relativity and the
photoelectric effect), Newton's achievements were deemed more
remarkable overall. |
| Black
Hole in the Milky Way -- Posted by
wostraub on Thursday,
November 3 2005 |
Chinese researchers using a bank of ten radio telescopes spread
across the United States have found further evidence that a
supermassive black hole inhabits the center of our galaxy, in the
constellation Sagittarius.
Most scientists now believe that galactic cores host such objects,
whose sizes may range from hundreds of thousands to many millions of
solar masses.
The object at the center of our Milky Way Galaxy was estimated to be
about 4 million times the mass of the sun. Using the formula for the
radius of a black hole, R = 2GM/c^2, the black hole's event
horizon would fit neatly between the earth and the sun.
This is great stuff, but in order to get the general public excited
about it, newspapers and magazines have to write stupid things like
"black holes are cosmic vacuum cleaners that gobble up stars and
everything else in their vicinity." But black holes do not suck!
They are collapsed stars whose gravity is so great that the star
literally shrinks down to ZERO VOLUME and INFINITE DENSITY. Outside
the black hole, however, these point-like objects behave like
ordinary stars, except they don't shine because they're essentially
dead stars (and any light couldn't escape their gravity, anyway). In
fact, if our sun were to suddenly become a black hole, the earth and
other planets would continue in their orbits as usual, although the
sky would be darker than we've ever seen it.
Also, these articles never talk about the true nature of a black
hole, which is one of the most bizarre physical objects of God's
creation the human mind has ever encountered. The mathematics that
describes them, Einstein's theory of general relativity, is of
course rarely mentioned to the public.
Event horizons, ergospheres, Hawking radiation, time travel? No --
give us talk about cosmic vacuum cleaners! |
| Theory
of Matter in a Weyl Manifold -- Posted by
wostraub on Sunday, October
30 2005 |
While cleaning out some boxes
today, I came across a reprint of a paper I received years ago
entitled Theory of Matter in Weyl Spacetime by David
Hochberg and Gunter Plunien of Vanderbilt University [Phys. Rev. D
43 3358 (1991)]. It's neat to see Weyl's original spacetime
gauge theory pop up from time to time in research papers, and this
is one of the better ones.
The authors demonstrate how a Lagrangian that is linear (not
quadratic) in Weyl's version of the Ricci scalar R can be
coupled with a scalar field $\phi(x)$ to derive Einstein's
gravitational field equations. But the authors then go on to develop
a Lagrangian in spinor form that couples the Weyl gauge vector to
fixed-chirality spinors that are identified with neutrinos. I think
Weyl would have found that really interesting, since his massless
form of the Dirac equation anticipated the existence and eventual
discovery of these guys!
Hochberg and Plunien conclude from their investigation that
spacetime is actually Weylian (and only approximately Riemannian)
and that the Weyl field is a form of dark matter. Neat stuff!
I have the article in pdf format and will post the thing if I can
get permission from the American Physical Society. It's a relatively
easy paper to follow and I think the effort is worth it (and it
might just take your mind off the Bush cabal for a while). |
| Atiyah
on Weyl -- Posted by wostraub
on Monday, October 24 2005 |
In 2002 the noted mathematician
Sir Michael Atiyah wrote a biographical sketch of Hermann Weyl that
included reflections on Weyl's interests in philosophy and writing.
Here is the article in pdf format:
Hermann Weyl |
| Weyl
Relativity -- Posted by
wostraub on Monday, October 10 2005 |
This morning I was contacted by
the great-granddaughter of Hermann Weyl, Elizabeth T. Weyl of Mount
Holyoke College in Massachusetts. She informed me that she is aware
of only several direct descendants of the great mathematician now
living in this country. Why so few?
Weyl was married twice. His first wife, Helene (nickname Hella)
Joseph, was a philosophy student at the University of Gottingen in
Germany under Edmund Husserl, who held the philosophy chair at the
school. Weyl's early love of philosophy appears to have sprung at
least in part because of the influence of his wife, whom he married
in 1913. Weyl and Helene subsequently had two sons, but I have not
been able to learn anything about their lives. (Elizabeth Weyl wrote
that she is the daughter of the son of one of Weyl's and Helene's
two boys.)
Helene passed away in 1948, and in 1950 Weyl remarried, this time to
Ellen Lohnstein (or Lowenstein) Bar of Zurich (she was a sculptor).
At the time, Weyl was 64 and not yet retired from his position at
the Institute for Advanced Study in Princeton, New Jersey. He did
retire in 1952, and the couple traveled between Zurich and Princeton
until Weyl's untimely death in 1955 while in Zurich. Even at the age
of seventy, God took him too soon!
I think I mentioned some time ago that during Weyl's days at the ETH
in Zurich (where he held the chair in mathematics), the German-born
Weyl was drafted by Germany to serve in the First World War.
Fortunately, the Swiss government secured an exemption for Weyl, and
he was allowed to stay in Zurich to continue his research. Also
during these days, Weyl and the 1933 Nobel Laureate Erwin
Schrodinger became best friends. I've read unsubstantiated (but
probably true) claims that Weyl was the source of mathematical
inspiration for Schrodinger's wave equation. Unlike many scientists,
Schrodinger was a good-looking, well-dressed bon vivant and
a Don Juan of sorts, and I've even seen some reports that Weyl's
first wife, Helene, fell under his spell, while, at the same time,
Schrodinger's (probably long-suffering) wife Anny was enamoured of
Weyl! |
| Weyl and
Antimatter -- Posted by
wostraub on Tuesday, October 4 2005 |
In his famous paper Eleckron
und Gravitation (Zeit.f. Physik 56), Weyl wrote
It is reasonable to expect that in the two-component pairs of
the Dirac field, one pair should correspond to the electron and
the other to the proton. Furthermore, there should appear two
electrical conservation laws, which (after quantization) should
state the separate conservation of the number of electrons and
protons. These would have to correspond to a two-fold gauge
invariance involving two arbitrary functions.
I find it remarkable that only one year after the appearance of
Dirac's relativistic electron theory, Weyl had the temerity to infer
that the four-component Dirac spinor referred to the electron and
the only other positively-charged particle then known, the proton.
Of course, Dirac had also considered this possibility, but I am not
aware of any rash statements he made to that effect so early in the
game. Neither scientist at that time knew the correct explanation
intimately involved the existence of the positively-charged
antielectron or positron, the first antimatter particle to
be discovered (which was found by Anderson in 1932).
Nevertheless, Weyl's gutsy if incorrect 1929 prediction shows how
bold an erstwhile pure mathematician could be in a field
not originally his own. Courageous, too, because Weyl's
equally-erroneous 1918 metric gauge theory had seemingly predisposed
him to mockery when he resurrected the idea (although as quantum
phase invariance) in his 1929 paper. |
| Birthday
Quiz -- Posted by wostraub
on Thursday, September 29 2005 |
Here's a photo of Einstein and
some friends taken at the Institute for Advanced Study at Princeton
on the occasion of Einstein's 70th birthday (March 14, 1949). Weyl
is the gentleman in the back, third from the left. Can you identify
the others? The answer is below.
Yes, it's the film director Visconti, 5 points. Oops, that's from an
old Monty Python routine. From the left, they are: H.P. Robertson,
Eugene Wigner, Hermann Weyl, Kurt Gödel, Isador Rabi, Einstein, R.
Ladenburg, J.R. Oppenheimer, and G.M. Clemence.
Note how these gentlemen range in appearance from dapper to advanced
geek. Particularly geeky is the mathematician Gödel (pronounced like
girdle), whose famous 1931 incompleteness theorems
proved that in principle not all math problems are solvable.
Einstein looks not only nerdy here but ancient as well; maybe it's
just his hair. He got the Nobel Prize in Physics in 1921. Rabi won
the prize in 1944, I believe, while Wigner got it in 1963. Some
pretty smart folks. |
| 30K for
Katrina Relief -- Posted by
wostraub on Wednesday, September 28 2005 |
My son Kristofer's Internet site
BlankLabel raised
almost $30,000 for Hurricane Katrina disaster relief. The money went
directly to the American Red Cross.
May God bless the efforts of you and your colleagues, Kris! |
| Warped
Universes, Warped Lives -- Posted by
wostraub on Monday, September
26 2005 |
I've been in Dana Point for
several weeks sailing and just goofing off, but during this time I
had the opportunity to read Lisa Randall's fascinating new book
Warped Passages: Unraveling the Mysteries of the Universe's Hidden
Dimensions. Randall is Professor of Theoretical Physics at
Harvard University. A Harvard PhD at 25, she's exceptionally
intelligent (as well as young and beautiful) and has some neat ideas
to share, which is why she wrote the book.
I'm thinking of writing and then posting a "book report" on this,
but we'll see about that. For now, I'll share an observation I've
had for some time about women scientists (hopefully you've already
read my comments about Emmy Noether).
When I was in physics graduate school, there was a fellow student I
got to know who was simply light years beyond everyone else. Angelyn
was only 20 at the time (and also beautiful), but she knew ten times
as much then as I do now about quantum mechanics. She seemed to
always know the answers, and they came off the top of her head
seemingly without any effort. She finished her PhD in physics at UC
Riverside, and is now a senior scientist at JPL.
Later, a female civil engineer worked for me who likewise stood head
and shoulders above all the others in the office (she was also
beautiful). Julie had the highest GRE score of anyone I'd ever seen,
and when she decided to go to graduate school she was immediately
picked up at Stanford, where she received her doctorate a few years
later.
(I could also add that my daughter Sheryl, a California
attorney-at-law, is also smart and beautiful, but I'm too biased to
say it.)
It boggles my mind to think that Randall is almost certainly several
orders of magnitude beyond these gals. How can some women be so
smart (and beautiful)?
I think the answer lies in the fact that they're really no different
than men, at least intelligence-wise. I also think all this talk
about male mathematical/science superiority is a lot of nonsense.
Women can do anything men can do, and often better. They also seem
much less prone than men to start wars. [Note: I am not suggesting
that Laura "Stepford" Bush run for president, though she'd probably
be an infinitely better pick than her s**t-for-brains husband.]
In the introduction to Randall's book, she briefly describes how she
became hooked on science and her lifelong fascination with math and
physics. I think that's all it takes -- a few brains, an
unquenchable curiosity of the world we live in, and a burning desire
to understand it from first principles (this is almost a direct
quote from Einstein). It's a shame that great women scientists like
Noether, Lise Meitner, Rosalind Franklin and scores of others were
denied Nobel Prizes and other honors simply because of their sex.
In closing, I can't help but make an additional (though negative)
comment pertaining to female achievement, as I feel it's very
appropriate. Dana Point, California is a beautiful place, but it's
marred by legions of idle "Orange County women" whose goals in life
seem to revolve around shopping, beauty parlors, constant cell phone
use, and the acquisition of expensive cars and homes -- all on a
middle-class income. In Orange County, they justify these excesses
by calling them "family values."
Enough said, I'm in trouble now! |
| Weyl's
Theory and Early Quantum Theory -- Posted by
wostraub on Wednesday,
September 21 2005 |
Weyl's 1918 gauge theory
essentially stated that the magnitude of a vector quantity was not
absolute but variable from point to point in a 4-dimensional
manifold, and that the electromagnetic four-vector was responsible
for this variability. Einstein at first lauded Weyl's idea, but then
realized that time, not just length, would also be variable.
Einstein noted that time would then depend upon a
particle's history, and that atomic spectral lines (which are fixed)
would vary from atom to atom depending upon their individual
histories.
Correspondence between Weyl and Einstein on this point has been
preserved, and it shows how desperate Weyl was to reclaim his theory
despite the fact that Einstein was obviously correct. Out of his
desperation, Weyl suggested that particle time and position were in
some sense unobservable, and he briefly postulated that his
gauge theory was correct after all and that certain gauge-affected
observables (like time) required a more general definition. Of
course, it was all nonsense.
Or was it? Weyl's basic idea was that Nature employs a gauge
symmetry in which a rescaled metric tensor does not affect any
essential physics:
$g_{\mu \mu} --> \lambda(x) g_{\mu \nu}$
where $\lambda(x)$ is an arbitrary function of spacetime. Of course,
the components of the metric tensor $g_{\mu \nu}$ are real and
observable.
As is well-known, Weyl's theory was reinvented as the phase
invariance concept of quantum mechanics, perhaps the most profound
symmetry known in modern physics. Weyl's gauge theory works in QM
precisely because the wave function is unobservable and can involve
an arbitrary phase function.
My contention is that Weyl's original gauge idea didn't work only
because the metric tensor is a real, observable quantity, and that
Weyl actually anticipated the existence of the wave function eight
years prior to Schrodinger's celebrated wave equation. After all, it
was only one year after the 1926 wave equation that physicists
(including Weyl, London, and even Schrodinger himself) began to
realize that Weyl's gauge concept was workable in QM and that it was
in fact required in order to incorporate electrodynamics into the
then-developing quantum theory. |
| Amalie's
Ashes -- Posted by wostraub
on Tuesday, September 6 2005 |
This year marks the 70th
anniversary of the death of Amalie (Emmy) Noether, colleague of Weyl,
Einstein and countless other great 20th-century scientists, and
generally regarded as the greatest female mathematician who ever
lived.
I just finished reading a chapter on Noether in Nobel Prize
Women in Science: Their Lives, Struggles, and Momentous Discoveries,
Second Edition, J.H. Henry Press (1993). I realize now that I did
not give her adequate credit in my little write-up (see Weyl &
Higgs), and I now stand in awe of the woman, both in terms of
her gifts as a mathematician and as a human being.
In spite of the harsh, ongoing prejudice she experienced firsthand
even as one of Germany's top mathematicians in the teens and 1920s,
Noether doggedly pursued her field with little or no regard for her
own well-being. In recognition of her greatness as a mathematician,
she was invited by Hilbert and Weyl to teach at the University of
Gottingen. But for many years she was an unpaid, untenured,
unpensioned nichtbeamteter ausserordenticher Professor,
which roughly translates to "unofficial, unprivileged third-class
instructor" (not unlike adjunct faculty!) Out of a total faculty of
237, Noether was one of only two female professors at the school
(the other was a physicist).
As I mentioned in my earlier write-up, Noether was a pacifist,
left-wing Jewish female, and these traits did not endear her to the
Nazis. When Hitler was appointed Chancellor of Germany in January
1933, Noether was one of the first professors to be fired. She and
numerous other colleagues at the University of Gottingen tried to
hang on, but brownshirted Nazi students successfully boycotted her
and other Jewish professors -- “Aryan students want Aryan
mathematics, not Jewish mathematics!.” Denied of a livelihood,
Noether (with the assistance of Weyl) formed the German
Mathematicians’ Relief Fund, and for a while taught secretly from
her apartment.
Even Weyl (a Christian) was forced to leave, as his wife was a Jew.
Moving to the Institute for Advanced Study in Princeton in 1933,
Weyl mourned the resulting Nazification of science and mathematics
and witnessed the destruction of German preeminence in science,
philosophy, psychology and mathematics with a broken heart.
In 1933, Noether too fled, to Bryn Mawr College in Pennsylvania,
where she was given a limited professorship at three-quarters pay.
She died there in 1935 following the surgical removal of a large
ovarian cyst. Although the college neglected to preserve her papers,
it did manage to preserve her ashes. In 1982, on the centennial
anniversary of her birth, the school buried her ashes under a brick
walkway near the library’s cloisters.
I see a terrible parallel to the madness Noether faced in Germany
with events in this country today: anti-intellectual, fundamentalist
fervor is demonizing stem-cell research and evolution (even geology)
in favor of mystical, irrational, evangelical creationist theories,
including “intelligent design.” Like the anti-intellectual,
anti-feminist Nazis, narrow-minded idealogues like Pat Robertson,
Jerry Falwell and Bill Frist are beating the drums for the
destruction of modern science and rational thought in America. In
their foaming hatred of feminism, I hear clear echoes of the words
of Nazi Propaganda Reich Minister Josef Goebbels: “The mission
of women is to be beautiful and to bring children into the world.”
In a recent issue of Physics Today, physicist Lawrence
Krauss addressed the lack of any contemporary Einsteins. Sadly, no
one of the moral and intellectual stature of Noether, Einstein or
Weyl exists today. No doubt, if these great people were alive now,
they would be quickly ostracized by the Bushies and their media
whores as intellectual peaceniks. They would also be ignored by the
American public, which largely prefers reality TV to reality.
The Republican War on Science |
| Dirac's
Burial Plaque -- Posted by
wostraub on Sunday, August 28 2005 |
Just thought I'd show this, which is located in Westminster Abbey,
not far from where Newton rests. This and Boltzmann's headstone are
the only markers I know of that celebrate great scientists with
famous equations! The grave of Boltzmann (who committed suicide in
1906) is honored with his entropy equation S = k log W,
while the above photo expresses Dirac's relativistic electron
equation, which is arguably the most beautiful equation in
physics. The "OM" stands for Order of Merit, an honor that
Dirac was particularly proud of. He was also elected a member of the
Royal Society in 1930 at the age of 28.
One of the utter shames of this world is that the average person has
never heard of Paul Dirac, whose name should be as well-known as
Newton's and Einstein's. For more information on Dirac and his
equation, see my write-up on Weyl spinors. |
| Weyl and
Overdetermination -- Posted by
wostraub on Saturday, August
27 2005 |
In one of my write-ups I glossed
over the fact that Weyl's theory of the combined gravitational-electrodynamic
field relies upon the square of the Ricci scalar, $R^2$. In terms of
the metric tensor, this quantity is of the fourth order in
$g_{\mu \nu}$ and its first and second derivatives. Einstein and
many others objected to Weyl's theory for this reason, since
solutions of the Weyl action tend to be overdetermined (i.e.,
non-physical "ghost" fields can appear).
I've looked all over for a detailed response from Weyl on this
issue. Clearly, he understood its relevance yet he didn't seem to be
overly concerned about it. However, if you calculate the equations
of motion from the free-field Weyl action principle, you find that
you can divide out an R term (assuming it is a non-zero constant),
which leaves second-order equations of motion! I don't know if Weyl
was aware of this or whether he dismissed the overdetermination
issue out of preference for the essential beauty of his theory.
Nature seems to prefer second-order equations, whether one is
dealing with classical physics or quantum mechanics. There are
exceptions, however. The one that comes immediately to my mind
(which any structural engineer will instantly relate to) concerns
the equations governing the elastic bending of beams. Indeed, loaded
beams are described by a fourth-order differential equation.
Fourth-order equations also result from perturbative expansions in
quantum mechanics, but these don't qualify!
Ghost fields in quantum mechanics are generally frowned upon. I've
always looked upon the scalar Higgs field as a kind of ghost field,
but it results from symmetry breaking rather than any inherent
defect in the associated action quantity. |
| The
Snapping of String Theory? -- Posted by
wostraub on Friday, August 5
2005 |
This month's Discover
magazine has an article by Michio Kaku on the future of string
theory. Kaku addresses the fact that string theory has now been
around for over 35 years without a shred of experimental evidence to
back up the theory's many predictions. He also recognizes the fact
that most of the world's top physicists seem to be gravitating
toward string theory, thus depriving other fields (notably particle
physics) of upcoming talent. Many notable physicists, including
Lawrence Krauss and Sheldon Glashow, feel that string theory is a
mathematically beautiful but ultimately empty concept that should be
either verified once and for all or abandoned.
Kaku describes a few experiments that might provide some support for
string theory (involving dark matter, gravitational waves, and the
Large Hadron Collider), but for now the theory's only support seems
to be its beautiful mathematics. I for one disagree, because I feel
that the math is just too confounding (but I'm a mediocre hack, so
who am I to judge?)
String theory verification may ultimately require energies that are
simply beyond what mankind will ever muster. We can currently probe
spacetime down to a distance of around 10(-18) meter, but strings
typically involve distances a billion billion times smaller than
that. What good is a theory if it predicts structures and hidden
dimensions that are on the order of the Planck scale? We'll never
get own that far!
It's too bad that Kaku's article wasn't handed to Scientific
American, which always goes into things much deeper than
popular science magazines like Discover. Popularized
accounts of the quantum theory and gravitation are rarely
interesting nowadays, mostly because the mathematics can be
understood by undergraduates. But string theory is so damned
confounding that only experts can work in the field, and even they
have confessed that they don't know what the hell they're doing.
Consequently, popularized accounts of strings are so dumbed-down
that they're essentially useless. Kaku (himself one of the experts)
is one of the better expositors, but his article in Discover
really doesn't tell me anything. |
| Weyl and
Higgs -- Posted by wostraub
on Sunday, July 24 2005 |
Here's a very simple derivation
of the Lagrangian for quantum electrodynamics along with a
description of the Higgs mechanism (and why Weyl should get a lot of
the credit for both of them).
Weyl/Higgs |
| Net
Energy -- Posted by wostraub
on Tuesday, July 19 2005 |
The July 17 Los Angeles Times
Magazine ran a great article on the likely future of hybrid
cars, focusing primarily on rapidly-developing technologies will
allow these cars to be plugged in overnight to charge batteries,
rather than have the cars' own gas engines do the charging.
AeroVironment, a Monrovia, California company (www.AeroVironment.com)
has received a $170,000 grant to retrofit Toyota Prius hybrids with
an additional 180-lb battery pack that can be charged separately.
Additional tinkering with the car's electronic controls allows the
car to run on battery power only for the first 30 miles or so (I
have a new Prius, and I think this is a fantastic idea). Overall,
the company's prototype Prius is getting slightly over 100 MPG using
the new system. While messing with the hybrid energy drive voids the
car's warranty, Toyota appears smitten with the idea and has
indicated a willingness to work with the company regarding the
warranty issue.
The article goes on to state that jazzed-up hybrid vehicles might
soon achieve up to 500 MPG and beyond. Great news, when gasoline is
running around $2.67 a gallon (at least here in Pasadena, CA).
However, that 500 MPG figure does not take into account the gasoline
energy equivalent to charge a hybrid's batteries off the grid. A
more recent article, put out by the Environmental News Network,
demonstrates that the net energy output of a system needs to take
such things into account. This is especially true when considering
the production of ethanol from corn, which has lately been widely
touted as a cost effective new gasoline additive.
The article states that researchers at Cornell University and the
University of California at Berkeley have concluded that it takes 29
percent more fossil energy to turn corn into ethanol than the amount
of fuel the process produces. Similarly, it requires 27 percent more
energy to turn soybeans into biodiesel fuel, while more than double
that to do the same to sunflower plants, the study found.
"Ethanol production in the United States does not benefit the
nation's energy security, its agriculture, the economy, or the
environment," according to the study by Cornell's David Pimentel and
Berkeley's Tad Patzek. The universities concluded that the country
would be better off investing in solar, wind and hydrogen energy.
The researchers included such factors as the energy used in
producing the crop, costs that were not used in other studies that
supported ethanol production, and they also took into account some
$3 billion in omitted state and federal government subsidies that go
toward ethanol production in the United States each year.
Believe me, I'd love to see America producing cars that get 100 MPG,
and I sincerely think it's technologically possible. But like all
things, let's consider the whole picture before we get too
optimistic.
Article |
| More
Fizzicks Fun -- Posted by
wostraub on Monday, July 18 2005 |
You gotta just love the new
Hewlett-Packard Pavilion notebook computer commercial.
The setting is a university lecture hall. A physics professor is
droning on monotonously (a la Ben Stein as the teacher in "The
Wonder Years") on atomic physics. The cute young thing in the front
row is busy with her new HP Pavilion computer, but she's not taking
notes -- she's watching DVD videos, including tattooed rock singers
who magically jump out and writhe suggestively on her desk,
obliterating the boring physics lecture.
Remember Malibu Stacy's response to a Simpson's math question?
"Don't ask me -- I'm only a girl (tee hee)!" Ms. Stacy must be HP's
target demographic.
No wonder America's students are going down the drain in math and
science. If a student of mine had acted like this, I'd have kicked
her out of the class forthwith (and probably gotten myself fired in
the process).
Earlier I gave a bad review of Tom Friedman's new book The World
is Flat, but one of the book's many good points is that it
accurately assesses the awful state of math & science education in
the United States and how we are being rapidly being taken over
academically by other countries, notably China.
Hewlett-Packard is a high-tech US firm. What in hell are they doing
putting out ads like this?!
Update 19 Jul 2005 HP announced this morning that it would
lay off 14,500 workers and freeze employee pensions. Guess the
commercial's not working. |
| Speaking
of Uranium -- Posted by
wostraub on Saturday, July 16 2005 |
I've always been fascinated with
heavy metals. As a kid, I used to play around with mercury (warning:
it's very toxic, and has a relatively high vapor pressure, so don't
mess with it!), rubbing it onto silver coins to make amalgams (this
was pre-1964), mixing up explosive fulminates for fun (I still have
all ten fingers and two eyes, thank the Lord), or just being awed by
its "divine heaviness" (to quote Auric Goldfinger).
There are other neat heavy metals. Platinum is pretty dense; gold
somewhat less so. Neater by far is iridium, which is
reasonably safe and even more divinely dense than gold, and another
is osmium, which is arguably the densest stable element in
nature, although it has a nasty habit of erupting into flames in the
presence of oxygen and giving off toxic fumes of osmium tetroxide.
Still another is gallium, although its main claim to fame
is not density but its tendency to melt in your hand (unlike M&Ms).
Alas, outside of the Exploratorium, Los Alamos or Sandia Labs,
you're likely never to heft a sample of iridium or osmium or
gallium, so mercury remains the poor man's (or kid's) heavy metal of
choice.
But every kid's holy grail, at least when I was growing up, was
uranium. To this day I have never held any, though I've seen
samples behind glass. I've heard that enriched uranium is actually
warm to the touch (and plutonium even more so), but despite its
inherent dangers I've always wanted to own some, maybe as a paper
weight. U-238 is used as cladding for armor-piercing artillery;
there's a lot of it lying around in Iraq now, though most of it has
probably vaporized. Depleted uranium poisoning is a candidate cause
of Gulf War Syndrome.
Like all elements past bismuth in the periodic table, uranium is
radioactive. It occurs naturally in isotopic form, mainly U-238 (the
most common and boring variety), followed by U-235 and U-234; only
U-235 is fissionable. Uranium can actually be mined; because U-238
has a half-life of about 4.5 billion years, there's still enough of
it in the earth's crust that it can be mined economically. About
0.7% of what's mined consists of the isotope U-235, and this is
where humankind gets its nuclear fuel (and bomb material).
Plutonium-239 cannot be found in the elemental or chemically-bound
state, but it can be made by transmuting uranium via neutron
bombardment. Every garden-variety nuclear power plant is in fact a
plutonium factory. Pu-239 is also fissionable, and has several
advantages over U-235 in terms of bomb potential. If you can manage
to fashion a sphere of Pu-239 metal about 5 inches in diameter,
you'll have a critical mass of the stuff (but you won't have it for
very long).
The density of mixed uranium metal is about 19.05 g/cc, somewhat
less dense than gold and about 15% less dense than osmium or iridum,
but much more so than mercury (13.6 g/cc). People who have actually
hefted a chunk of the metal have stated that it seems almost unreal.
Now for the point of all this. When God created the universe, he
allowed nature to make all kinds of elements, but only one
fissionable variety that could be mined in quantity. In my opinion,
without U-235 and its 0.7% concentration in mined uranium metal,
thermonuclear weapons would probably never have come into being.
What was God's reasoning behind all this?
He may have provided it as a means of giving mankind a source of
long-term energy, one that would last far longer than the all
too-finite resources of the fossil fuels we're rapidly depleting. Or
he could have placed it on earth as a means of ensuring Armageddon.
Both possibilities seem to be tailor-made for mankind, either in
view of his need for energy, or his assured destruction. I'm not
thanking God or blaming him for this situation; I'm just raising the
issue.
Today, we have many thousands of megatons of thermonuclear weapons
stockpiled and ready to roll, whereas the peaceful uses of nuclear
energy are relatively insignificant. (Well, I guess Europe has a
good deal of nuclear power, but the United States, China, India and
Russia still prefer fossil fuel.)
I for one don't have a good feeling for where we're headed, but I
have been spectacularly wrong on lots of things. My advice: Continue
to ask God for his protection, guidance and salvation, and hope that
some idiot like Bush doesn't try to force Christ's return by blowing
everyone up.
By the way, journalist Frank Rich of The New York Times has an
excellent article on uranium (hint: the Niger kind):
Follow the Uranium
Also BTW: Has anyone read the book How to Survive the Coming
Global Thermonuclear Holocaust and Make a Stinking Profit to Boot
(Republican Neoconservative Press, 2005). |
| Goenner
Again -- Posted by wostraub
on Thursday, July 14 2005 |
If you have any real interest in
physics, particularly its evolution from Einstein's geometrical
approach to quantum theory, you simply must read On the History
of Unified Field Theories by Hubert Goenner of the University
of Gottingen. Pretty much all of this involves the progress of
theoretical physics from 1920 to 1929, concluding with Weyl's
historic 1929 paper on gauge symmetry. Of particular interest are
the efforts to to incorporate Dirac's relativistic electron theory,
which appeared in 1928, into Einstein's ideas of spacetime geometry.
Even the five-dimensional theory of Kaluza-Klein was given the
Einstein treatment, to no avail. By the end of 1929, it was all too
clear that Einstein's general relativity just did not mesh with
quantum mechanics.
I mentioned Goenner's paper earlier on this site. I finally finished
reading the whole thing, and I have to admit that he's got a lot
more in his one paper on Weyl than I have on my whole stupid website
(at least he doesn't seem to be adversely distracted by the Bush
Reich, like I am).
Early Field Theories
I cannot get over the sheer amount of intellectual effort that went
into the various attempts to reconcile gravitation with quantum
theory, or the optimism that reigned regardless of the fact that
nobody really seemed to know what was going on. I think it can be
traced to the fact that there were only two forces known at the
time: gravitation, which was elucidated by Einstein, and
electrodynamics, which Weyl had seemingly unified with gravity in
1918. In the end, neither could be reconciled with quantum theory,
at least in terms of what was known by the time the 1920s ended.
Part 2 of Goenner's excellent overview of unified theory is yet to
come; I welcome it enthusiastically. |
| World
Oil Production -- Posted by
wostraub on Sunday, July 10 2005 |
The attached link summarizes
world oil production data for the period 1860-2003, as obtained from
the US Department of Energy (Energy Information Agency). I assume
it's reliable, although the numbers are a tad higher than those
given by Deffeyes. My statistical analysis for the Gaussian
regression is included; the graphic shows the data (open circles)
along with the superimposed regressed normal distribution curve (grey
line), which fits rather nicely. However, note that, according to
this analysis, Peak Oil occurred in 1998!
Production Analysis for 1860-2003
[Note: I used a non-linear multivariate regression program called
NLREG to do the analysis.] Obviously my preliminary analysis is not
very realistic, but it's intended only to get you thinking about the
Peak Oil issue, anyway. The actual situation is more complicated
because it involves oil reserves and discoveries (that may or may
not be included in the EIA data) and not just produce-and-use data.
At any rate, this will give you some idea of how the data are being
viewed by a number of researchers (and many of them are alarmed at
what they're seeing).
One thing that is not in question is that once the oil production
curve starts to fall over from its exponential rise, the Peak Oil
phenomenon will be inevitable. This will then signal the end of
cheap oil, the commodity that runs the modern world. What will
replace it? I haven't a clue. God gave us something like 2 trillion
barrels of oil, and we've gone through about half of that. God's
gift should have been used to develop a more sustainable energy
source (such as solar), but instead it went to Hummers and their
kin. Now it looks like oil wars are inevitable.
My advice is that you get up on the issue and decide for yourself. |
| Peak Oil
-- Posted by wostraub on
Wednesday, July 6 2005 |
Recently, I compiled a table of
world oil production data for the period 1860 to 2004 and did a
regression analysis on the data assuming a normal distribution (Gaussian)
model. I think I know why the Peak Oil doomsayers do not use this
model. Using a nonlinear regression program called NLREG for the
Gaussian model, my results show a decent data fit (the r^2 statistic
is about 0.98) with a standard deviation of approximately 25 years
and a total production of about 1.7 trillion barrels (this is the
amount of oil contained in all the planet's reservoirs). However,
the peak year comes out to be 1998, seven years ago! [This
really isn't as embarrassing as it may seem, because it's doubtful
that any simple model will be within 10 years of the actual peak,
anyway.] Of course, oil production hasn't peaked yet, as far as we
know. For my pathetic little model, post-1998 oil production data
overshoot the model, but this doesn't necessarily mean it's wrong.
Most of the models I've seen use the logistic function,
which is often used in population projections. I have absolutely no
idea why it should be preferred over the Gaussian function for
making oil projections. The logistic models typically give the peak
year at around 2005 to 2015, with a total production of about 2
trillion barrels. Since these peaks are in the future, maybe that's
the reason.
I've found a way to express the data as a rate plot, a
device that Deffeyes explains in his excellent book Hubbert's
Peak. It's basically just an x-y plot using specially
transformed data, which gives a straight line. The x-intercept
provides another method of obtaining the total production. It too
gives 1.7 trillion barrels.
What's not in doubt is the amount of oil we've burned since the
famous Titusville, Pennsylvania oil well started producing in 1860
(the "Ur well" of the oil age). It's hard to believe, but humans
really have burned about half the oil that was formed in the earth
over the past few billion years. [Side note: I once asked a
new-earth creationist friend how all that oil got formed in just
6,000 years, since no chemical or physical process known to man
could have done it in that short of time. Her answer: "God put it
there for our use." May the Lord preserve us from this incredible
ignorance!]
While curve fitting is great fun, I'm trying not to take things too
seriously, at least not yet. Still, if there's any truth to this at
all, it portends a terrible future for mankind. The worst part of it
is that it may not be more than a few years away. Either way, we're
not doing much about it.
Dr. Albert Bartlett, Professor Emeritus of physics at the University
of Colorado at Boulder, has been warning us of the peak oil issue
for many years. He claims (and I believe he is correct) that one of
mankind's greatest failures is his unwillingness to appreciate (or
even understand) the exponential function. Because we tend to use
untapped resources initially at an exponential rate, we naively
adopt the misconception that unrestrained growth is always good and
can be sustained indefinitely. To me, that's one of the stupidest
aspects of human beings -- we think only in the short term and
believe that God, technology or luck (or that old standby, the
"indomitable human spirit") will somehow bail us out when things go
to hell.
I'll put up what I have so far in a few days and you can decide for
yourself if world oil production is peaking. |
| Pauli
-- Posted by wostraub on
Monday, July 4 2005 |
I finally finished reading
Penrose's book (The Road to Reality), which is a remarkable
text in terms of the sheer amount of material it covers. It doesn't
go into a lot of detail, but if I were stuck on an uninhabited
island somewhere I would probably like to have it with me. Alas, I
never quite got through Zwiebach's A First Course in String
Theory, despite a rather gallant effort on my part. The math is
not too difficult (remember, this is a very introductory text), but
the physical models it presupposes are simply beyond my
comprehension. Yes, strings are actually strings, but they have this
peculiar habit of attaching themselves to membranes in a God-awful
number of dimensions. What the hell are these membranes other than
highly-abstract boundary conditions? It's a right brain/left brain
thing, I believe, and I've been forced to grudgingly accept the very
serious limitations of my little grey cells, as Poirot puts it.
Again, I emphasize that this is an introductory text. Lord,
is there any hope for me?
So in utter defeat this evening I pulled down my crumbling Dover
copy of Pauli's Theory of Relativity, which always holds
something that I had overlooked the last time I got it down.
Although I am enamored of Weyl, his writing style (or at least the
German translations of his writing) very much leave something to be
desired. In short, Weyl's ideas are beautiful, but his writing is
not, at least in my opinion. Pauli, on the other hand, is a joy to
read, at least the stuff I understand, and this is especially true
for his relativity book.
I may be stretching things here, but the book actually covers about
35 years of progress on basic general relativity. Pauli wrote the
first version in 1921 as a lengthy German encyclopedia article, then
appended it in the mid-1950s with supplementary notes. The book
includes a section on Weyl's theory of the combined electrodynamic-gravitational
field, and as such was only the second book I acquired that provided
details on Weyl's theory.
The book is a pleasure to read, from Pauli's clear exposition of
special relativity to general relativity and beyond. I was
absolutely dumbstruck when I learned that Pauli had written the book
when he was only a 21 year-old graduate student. Talk about grey
cells!
An oft-told anecdote about Pauli concerns his admittance to the
hospital for cancer treatment in 1958. His lifelong fascination with
physics included a similar fascination for the fine-structure
constant of quantum mechanics, which is very nearly the pure number
1/137. He always wondered why God had created such a number. In
quantum mechanics, constants tend to be truly microscopic (Planck's
constant is about 6 x 10^-34, for example), so the appearance of a
number that is about 0.008 boggles the mind. What also boggles the
mind is that Pauli, who passed away in the hospital at the
relatively young age of 58, died in Room 137. Don't ever think that
God doesn't have a great sense of humor!
Every high school student gets introduced to Pauli through his
Exclusion Principle in chemistry. But the man was such a gigantic
figure in the field of physics that he deserves so much more. He was
an irrascible and impudent curmudgeon who was famous for his
crushing verbal put-downs of lesser physicists who dared to expose
their ignorance, but he could also be caring and supportive. He was
fond of Weyl and truly loved Einstein, despite the great scientist's
ill-fated rejection of quantum mechanics.
The Dover book is still available as a paperback for maybe $10. I
heartily recommend it. |
| Weyl and
Chalabi -- Posted by wostraub
on Saturday, June 25 2005 |
You cannot apply mathematics
as long as words still becloud reality. -- Hermann Weyl
I don't know what context Weyl intended in this quote, but I'm
tempted to think that he saw empty rhetoric as the enemy of truth
and reason.
You cannot lie with mathematics because you will quickly be found
out. It is far easier to lie with words, because until someone can
check out what you're saying (which may not even be possible),
people have to assume that you're telling the truth.
Mathematics and words both come from the heart, but only one is
required by its own nature to be true. It is true that one can lie
with statistics, but the lie is sold through the interpretation of
the meaning of the numbers, which gets us back to words again.
Jesus Christ warned us to be careful about what comes out of our
mouths, but it wasn't mathematics he was concerned with.
Most people are not aware that years ago, the designated Iraq
Minister of Oil Ahmad Chalabi was a professor of
mathematics at the American University of Beirut, Lebanon. The son
of a wealthy banker, Chalabi studied at MIT and the University of
Chicago, where he received his PhD in mathematics in 1969 (I believe
his specialty was ring theory). Of course, you're certainly aware
that Chalabi, an Iraqi Shi'a Muslim, is a notorious liar who stuffed
Bush's head full of lies (as if it wasn't already full of them)
about Iraq's non-existent weapons of mass destruction. He is also
under warrant for arrest in Jordan for embezzlement and money
laundering. After all of his "disassembling," Chalabi still managed
to wrangle the job as oil minister on the new Iraqi cabinet, largely
on the basis of his ongoing connections with Bush, the CIA, and the
Pentagon. He's their kind of people!
This serves to show that while mathematics doesn't lie,
mathematicians certainly can.
My guess is that Chalabi will be assassinated when the Bush
administration begins to siphon off large quantities of oil from the
Iraqi oil fields to supply all the military bases we're constructing
in that country. He certainly doesn't have the interests of the
Iraqi people at heart, and his role as a Bush oil puppet is certain
to get him into trouble. Before he dies, I hope the last thing that
goes through his head (other than a bullet) will be the sincere
regret that he didn't stay in mathematics.
Sorry that I mentioned Weyl and Chalabi in the same breath; Weyl
deserves better. |
| Grace
S., 1924 -- Posted by
wostraub on Friday, June 24 2005 |
Here lies a most beautiful lady:
Light of step and heart was she;
I think she was the most beautiful lady
That ever was in the West Country.
But Beauty vanishes; Beauty passes;
However rare -- rare it be;
And when I crumble, who will remember
This lady of the West Country?
Epitaph, Walter de la Mare, 1873-1956
 |
| Weyl and
Philosophy -- Posted by
wostraub on Friday, June 24 2005 |
I have been having great
difficulty lately understanding Weyl. Not his physics (which is
pretty straightforward) nor his math (which can be exceedingly
difficult for a non-mathematician like me), but his extensive
philosophical writings.
During his life, Weyl went through various stages of philosophical
speculation. Each was important to him in its own time, as Weyl aged
and became wiser, from phenomenology to what might be called
religious existentialism. He consequently devoted an enormous amount
of time and effort to philosophy, no doubt a result of his deep
reflections on the interconnectedness of mathematics, physics and
the human mind.
Unfortunately for me, I'm having one hell of a time understanding
Weyl's philosophical musings. I'm inclined to state that he is very
deep, but at times it all seems like a bunch of mumbo jumbo. The
same thing happened when I tried to learn category theory,
which has been described as both the fundamental basis of all
profound mathematical theories and "generalized abstract nonsense."
Being trained neither in formal mathematics nor philosophy, I'm at a
distinct disadvantage to criticize (never mind fully comprehend)
Weyl's efforts in either field. But I keep trying.
In 1954, near the end of his life, Weyl reflected on what he had
learned over the years in physics and philosophy, as necessarily
colored by two world wars in which his native country, Germany, had
participated in rather shamefully:
"I did not remain unaffected either by the great revolution which
quantum physics brought about in natural sciences, or by
existentialist philosophy, which grew up in the horrible
disintegration of our era. The first of these cast a new light on
the relation of the perceiving subject to the object; at the center
of the latter, we find neither a pure "I" nor God, but man in his
historical existence, committing himself in terms of his existence."
This is the philosophical Weyl that I can relate to. |
| No Weyl
in Pasadena -- Posted by
wostraub on Monday, June 13 2005 |
Well, I tried. This was the
response I received from the Institute for Advanced Study:
Dear Dr. Straub:
Thank you for your inquiry to the Archives of the Institute for
Advanced Study. I have searched the documentary evidence that we
have for mention of any visits by Professor Weyl to Caltech. I'm
sorry to report than I find none, though there is other travel
documented, including west to Colorado, where Professor Weyl
apparently went to escape allergies that plagued him in New Jersey.
From my review of the literature, he seems to have been a reliable
presence on the Institute campus during the academic year, and
regularly gave lectures here. Of course, that does not preclude a
brief trip here or there, and his summers were his own. I have
searched for literature you might consult to advance your research,
but don't find anything to add to what your website indicates you've
already seen. I'm very sorry not to be able to be of more help, but
I will keep your inquiry in mind, and be in touch if I find anything
that might be of interest to you.
Regards,
Erica Mosner
Library Assistant
Historical Studies-Social Science Library
Institute for Advanced Study
Einstein Drive
Princeton, New Jersey 08540
Thanks, and God bless you, Erica! |
| Weyl in
Pasadena? -- Posted by
wostraub on Saturday, June 11 2005 |
I recently contacted Dr. Judith
Goodstein at Caltech to see if Hermann Weyl had ever visited the
school. Goodstein is the University Archivist and author of
Millikan's School, a history of Caltech, and co-author (with
husband and fellow Caltech professor David Goodstein) of
Feynman's Lost Lecture, so if anyone can help me, I thought she
could. Although Weyl went to the Institute for Advanced Study (IAS)
in Princeton when he left Germany in 1933, I figure that his
wanderings over the the years must have brought him to Pasadena at
least once.
Unfortunately, Goodstein told me that Caltech has no record of any
visits by Weyl. She suggested that I contact the IAS to see if
anyone there keeps a listing of Weyl's domestic travels. I'm in the
process of doing that, and will pass along whatever I find. |
| Jesus on
Truth and Lies -- Posted by
wostraub on Thursday, June 9 2005 |
From John 8:
42Jesus said to them, "If God were your Father, you would
love me, for I came from God and now am here. I have not come on my
own; but he sent me. 43Why is my language not clear to
you? Because you are unable to hear what I say. 44You
belong to your father, the Devil, and you want to carry out your
father's desire. He was a murderer from the beginning, not holding
to the truth, for there is no truth in him. When he lies, he speaks
his native language, for he is a liar and the father of lies.
45Yet because I tell the truth, you do not believe me! 46Can
any of you prove me guilty of sin? If I am telling the truth, why
don't you believe me? 47He who belongs to God hears what
God says. The reason you do not hear is that you do not belong to
God."
Why doesn't America truly follow Jesus? Why are we embracing the
torture and imprisonment of innocents? Why are we spending half a
trillion dollars annually on weapons of death and destruction? Why
are we throwing away our Constitutional rights? Can't we recognize
hypocrisy when it stares back at us in the mirror? Why are we
following the Devil? |
| Science
and Patriotism -- Posted by
wostraub on Monday, June 6 2005 |
Johannes Stark was a great German
scientist who won the 1919 Nobel Prize in Physics for his discovery
of the "Stark effect," the splitting of atomic spectral lines by
electric fields. He was a prolific researcher who published over 300
scientific papers in his lifetime. He was also a fanatical German
patriot who early on embraced the Nazi belief that Jews were
inferior human beings. He became a member of the Nazi Party in 1930.
Stark was a strong proponent of "Deutsche physik," or Aryan physics,
which be felt should be used solely for the purpose of advancing
national defense and prestige. By comparison, he scorned what he
termed "Judische physik" (Jewish physics) on the basis that
non-Aryan physics was not scientifically objective (by this I
suppose he meant that physics was not objectified unless it had a
nationalistic purpose). In 1934, Stark wrote a book, "National
Socialism and Science," in which he explained his views (I am going
to read that book). He hated Einstein and was no friend of the loyal
(but not rabid) German physicist Werner Heisenberg, whom Stark
referred to as a "white Jew." In 1947, a court sentenced Stark to
four years in prison for his contributions to anti-Jewish hatred
before and during World War II.
Stark's is a classic case of scientific inquiry gone mad. Pure
science and mathematics are completely objective when their pursuit
involves discovering the truth. I will take that statement one step
further by adding that objectivity cannot exist when a political
agenda is attached to the research. The most heinous example I can
think of involves the research and development of weapons of mass
destruction for purely military and/or political purposes. But a
more common example would be the selective and deliberate
misrepresentation or skewing of scientific data for the purpose of
convincing someone that something is true when in fact it is not.
But Stark, Phillip Lenard and other noted German scientists first
had to convince themselves that Einstein's theories were wrong
before they could convince others. How did they do that? Einstein
wasn't right about everything, but his special and general
relativity theories were thoroughly tested and found to be valid.
Also, these theories were, as Paul Dirac once put it, mathematically
"beautiful" (and they are). I believe that this is where ethnic and
political hatred made their way into the picture. Stark believed
that Einstein was of an inferior race, so his ideas had to be wrong.
This was no small effort -- he almost had to convince himself that
2+2=5 in order to erase the truth of relativity from his mind.
Fortunately for Stark, he easily found others that shared his Nazi
mindset. Einstein's works quickly found themselves among the
thousands of other papers and books that the Nazis burned during
Hitler's reign.
My younger son and I discussed a related topic today. I asked him
why a seemingly-disproportionate amount of funding is being spent on
HIV/AIDS research today. My straw-man argument was that AIDS is
primarily a behavior-related disease while, say, malaria threatens
everyone, so why not stress the preventive aspects of HIV. His
response is that the human immunodeficiency virus is a threat to
mankind simply because it now affects so many people. He felt that
dwelling on issues like behavior-based prioritization of funding is
too closely tied to moralizing, which is subjective. Subjectivity is
the enemy of science and mathematics. It is also, sadly, a very
human trait.
I see the same thing happening to science today, and it is truly
frightening. HIV/AIDS, evolution and cellular research are all being
attacked on the basis of subjective moral and political arguments
that have nothing to do with the scientific method. The Dobsons,
Frists, and Falwells of this country fervently believe that HIV/AIDS
is a punishment from God designed to strike down immoral people.
They have forgotten that when God warned us "the wages of sin is
death" he was referring to all sin, not just homosexual sin (and
yes, I do believe it is a sin). If I look at a woman the wrong way,
I have committed a sin that can put me in hell along with every
other unforgiven sinner; will I then feel somehow more "sanctified"
than the other lost souls?
Because they demand logical, organized and rational thinking,
science and math are giving Americans fits these days. Although we
have some great (and objective) expositors like Weinberg, Kaku,
Lederer, Davies, Hawking and Penrose around to explain things, we
also have idiots like Dr. Frist whose subjective pseudo-science
represents an enormous threat to America. I'm sure he's already
compiled a long list of books that he plans to have burned when he's
president. God save us!
I hope he and his ilk can be stopped in time, but I truly fear for
the scientific future of this country. |
| "Rods
from God" -- Posted by
wostraub on Thursday, June 2 2005 |
"Full-spectrum dominance."
That's the term the US military is using to describe a proposed
planet-wide system of nuclear-tipped intercontinental ballistic
missiles and orbiting weapons utilizing what insiders call "Rods
from God." RFGs are heavy metal cylinders that would be fired from
orbiting space platforms to take out enemy fortifications on earth's
surface. The rods would be made from dense metals like depleted
uranium or tungsten and fired at such high velocities that they
could penetrate many meters of soil and concrete.
However, a half-dozen distinguished scientists, including Nobel
prize winners Steven Weinberg (physics) of the University of Texas
at Austin and John Polyanni (chemistry), professor at the University
of Toronto, claim that the proposed defense system would be a
"criminal" waste of hundreds of billions of dollars that would be
better spent on public welfare programs. They go on to say that the
system would be unworkable anyway and would offer only the illusion
of absolute security if deployed.
Weinberg is the author of an excellent book on the general theory of
relativity and a three-text series on quantum field theory. The
latter is a tough read, but Weinberg's response to the RFG proposal
is easy to understand -- assuming that you're sane.
RFG represents only one facet of Bush's "space exploration program."
Of course, conservative faith groups are ecstatic over the proposal
because it has the word "God" in it. Also, they don't generally
trust math and science, because it's hard to understand and promotes
stuff like evolution and all, but "Rods from God" has a nice
Christian ring to it. Just the thought of evil doers being
righteously blasted to smithereens warms their hearts.
But the proposal has another, equally ominous aspect. Imagine you're
the leader of a nuclear country like Russia or China (or even
France). You see the United States being led by dangerous
"Christian" fascists determined to take over the earth and enslave
countries owning the resources needed by the United States to
maintain its preposterous standard of living. What have you got to
lose? In coordination with the other nuclear members, you fire off
everything you've got, and hope for the best. It's madness, of
course, but it would at least guarantee the destruction of the
United States as a functioning society.
Is this the American Taliban's real game plan -- to provoke a
worldwide nuclear Armageddon and thus force Jesus Christ to make an
early return?
http://www.nuclearpolicy.org |
| Early
Unified Field Theory and the Quantum -- Posted by
wostraub on Wednesday, June 1
2005 |
I’ve been reading lately about
the efforts of Einstein, Weyl, Rainich, Eddington and others around
1925 to find a unified theory of gravitation and the electromagnetic
field. To my mind, these guys were the flip side to Bohr, Dirac,
Pauli, and Fermi, who of course were almost solely focused on
quantum physics at that time.
In my opinion, Einstein’s discovery of general relativity in 1915
came at a really bad time. When the theory was brilliantly confirmed
by the explanation of the perihelion shift of Mercury and the solar
eclipse expeditions of 1919, there was no doubt whatsoever that
general relativity was a valid description of spacetime physics. In
those simple days, the only known forces of nature were gravitation
and electrodynamics, and the only known particles were electrons,
protons and photons. Following the brilliant but failed “near miss”
of Weyl’s theory in 1918 and Rainich’s subsequent discovery of the
algebraic similarities of gravity and electromagnetism, Einstein and
his colleagues must have felt that a consistent unified theory was
imminent.
However, the theory stubbornly resisted discovery. In hindsight, we
know that Einstein and the others were doomed to failure. Nature is
not as simple as Einstein had presumed; instead, it hosts a dizzying
array of elementary and composite particles, forces and fields
requiring a much more sophisticated physical and mathematical
approach.
I get a real kick out of reading Einstein’s correspondence to the
other early field theorists of that time. One idea after another is
proposed – distant parallelism, bivectors, n-beins, a generalized
(and traceless) Einstein tensor – and each one is subsequently
tossed aside. Einstein constantly refers to the sublime secrets of
nature and “the Old One,” and on occasion waxes quite philosophic
about the nobility of the search. In spite of the failures he is not
discouraged, and continues to press on. Most of his colleagues,
however, begin to realize that it is probably a waste of time, and
so they move on. But even as late as 1929, rumors spread that
Einstein had finally achieved his goal. Several newspapers even
printed the theory with all its mathematics for their undoubtedly
puzzled readers. It was all a big fuss over nothing.
By comparison, the development of quantum mechanics in the 1920s was
met with one astonishing success after another. I’m inclined to feel
that Einstein’s eminence in those years ultimately hurt physics,
because his unification efforts were sidetracking himself as well as
the talents of numerous great colleagues. Remember that when
Einstein’s general theory appeared, about the only quantum theory
that existed was that of Bohr’s hydrogen atom, which even then was
seen as a hodgepodge of classical and quantum ideas. It wasn’t taken
seriously until Heisenberg’s matrix mechanics and Schrödinger’s wave
equation arrived in 1925, and it was about that time that real
interest in unified theory was on the wane.
Today, physicists are hard at work on unified theories that Einstein
couldn’t have comprehended. String theory made its appearance in the
1970s, followed by supersymmetry, supergravity, superstrings,
M-theory, and loop quantum gravity. Recall Einstein’s initial
support of Kaluza-Klein theory in the 1920s, which sported a total
of five spacetime dimensions. Would Einstein have been equally
enthusiastic about ten, eleven and even twenty-six dimensions? I
wonder.
To my mind, God displayed a wonderful sense of humor when he let
Einstein discover general relativity theory in 1915. God knew that
scientists would initially think they were close to knowing
everything. At about the same time he opened our eyes to quantum
physics, and then probably watched with much amusement as we tripped
over ourselves trying to sort things out. But eventually we did --
thanks to these wonderful, curious minds God gave us.
Einstein once famously remarked that “God is subtle, but not
malicious” (Raffiniert ist der Herrgott, aber boshaft ist er nicht).
Recently, a noted physicist (darn it, I just can’t remember the the
guy’s name offhand) dared rephrase Einstein’s remark as “God is not
malicious, but he is subtle.” This makes much more sense to me. The
maddening complexities of modern unification theories are all too
real, but they follow a kind of simplicity involving spacetime
symmetries and their evil cousins, the internal symmetries. Surely,
this is what God had in mind for mankind – we’ll try our damnedest,
but, even if we never find the true unified field theory, we’ll have
glimpsed God’s glory along the way.
And this would have surely pleased Einstein. |
| A
Lagrangian for Evolution? -- Posted by
wostraub on Thursday, May 26
2005 |
I was talking to my son the other
day about Lagrangians and the action principle in physics.
Lagrangians are mathematical quantities (usually integral scalar
densities) that, when extremalized, define the actual dynamical path
that a particle or wave function takes under a given set of
conditions. These paths generally result when something like energy
or time is minimized. William Hamilton was the first to formalize
the mathematics (Hamilton's Principle), although Fermat knew about
the minimum-time principle of ordinary light propagation. Because
minimal principles represent the most efficient or "best" ways that
Nature can conduct her business, many early scientists saw this as
direct evidence of God's existence, and many still do.
Lurking behind the Lagrangian formalism are mathematical symmetries.
A symmetry is simply a modification in a Lagrangian quantity that
leaves the quantity unchanged. For example, translation symmetry
(the requirement that physics be the same on Earth as it is on some
extragalactic planet) leaves the Lagrangian mathematically
unchanged. I won't go into it, but this symmetry is also responsible
for the conservation of linear momentum. There is a very powerful
theorem (by Emmy Noether) which states that for every Lagrangian
symmetry there is a corresponding conservation law. It was Weyl, in
1929, who showed that the conservation of electric charge is due to
gauge symmetry, which was a brand new kind of symmetry in those
days. Since symmetry is a form of beauty (and it may even be a
definition of beauty), one may indeed argue that God is behind all
of this.
Now switch from physics to molecular biology. Is there a minimal
principle behind biological processes? Most certainly, because the
behavior of biologically-important molecules (proteins, enzymes,
etc.) is governed by quantum mechanics, and QM itself follows
Lagrangian principles.
But what about large-scale biological processes such as genetics and
evolution (or, if you prefer, random mutations over large time
scales)? What minimal principle could possibly result in the
formation, adaptation and maintenance of complex living systems?
Given a supply of simple organic compounds, is life inevitable? Was
the formation of the first RNA or DNA molecule the result of God or
Nature minimizing something? And if so, what was the driving force
or symmetry behind it?
My argument with my son was that living systems today are so
unbelievably complex that concepts such as driving force and
symmetry are totally hidden from us. When physicists conduct
particle collision experiments, they now have a large collection of
theoretical tools that they can use to design the experiments and
interpret the results. By contrast, for living systems scientists
can only watch and maybe make educated guesses. There are no
readily-apparent symmetries or driving forces that can be utilized
to interpret what they see. No one asks "Why are there proteins?" or
"Why did Nature decide to develop this kind of enzyme for liver
function?" When my son conducts PCR experiments or sticks mutated
plasmids into cells, all he can do is say "Let's see what happens."
I happen to believe that God created life. I also believe that he
created evolution so that life could adapt to changing environmental
conditions. But how he did all this is a great mystery (maybe so is
why he did it). But seeing God's penchant for symmetry in physical
laws, my guess is that he employed a similar approach when he
designed life.
When I was very young, I remember asking my father why a flower
grows. What does it think it's doing? Why doesn't it just fall
apart? Why should it make other flowers? What's the purpose behind
all this? In later years I learned about things like Gibbs free
energy, the equilibrium driving force behind Newton's law of
cooling, statistical mechanics, and the action principle. But these
revelations told me nothing about why God did what he did, or why he
used the approaches he did.
At the same time, I very strongly believe that our striving to
answer these questions is one of the principal reasons why God put
us here in the first place. When we finally figure it out, we'll
know for sure what a great guy he is.
The computational physicist Kent Budge has a blogsite (Trolling in
Shallow Water) that includes a rather off-beat look at God,
Lagrangians, and why Jesus was needed. Odd, and probably not what
God actually had in mind, but it's worth a look (it's near the
bottom of the first page):
http://shallows.blogspot.com/2005/02/u1xsu2xsu3-part-2.html |
| John
Baez's Website -- Posted by
wostraub on Sunday, May 22 2005 |
| I've added a link on the menu for
the website of John Baez, professor of mathematical physics at the
University of California at Riverside. He specializes in quantum
gravity, but the guy seems to know about everything. His site has a
lot of neat stuff ranging from very easy to way over my head. His
enthusiam is contagious. Give him a look. |
| Einstein
on Nationalism -- Posted by
wostraub on Saturday, May 21 2005 |
Einstein hated militaristic
nationalism. He would have undoubtedly deplored living in America at
this time, and would have certainly detested our pathetic Cowboy
President, his love of war, and his pro-torture position on innocent
foreigners and "enemy combatants." In reaction to his views, the
Daughters of the American Revolution (which until recently excluded
all minorities from its nobel ranks) told Einstein to get out of
America. The House Committee on Un-American Activities (McCarthy's
little band of Nazis) similarly denounced Einstein, and the
cross-dressing transvestite J. Edgar Hoover had his FBI compile a
huge dossier on the scientist.
The attached Word file is a copy of a hand-annotated speech that
Einstein gave in May 1947 (I believe to the Emergency Committee of
the Atomic Scientists). Read it and ask yourself if these are the
words of a dangerous mind.
http://www.weylmann.com/einsteintalk.doc |
| Weyl and
Petrarch?! -- Posted by
wostraub on Friday, May 20 2005 |
Did you ever glimpse someone,
perhaps only for a moment, but it changed your life forever, and for
the better? Did you ever have one of those “Aha!” experiences or a
“Road to Damascus” moment that had the same effect? In the following
I present some random thoughts I’ve had about Weyl and Beauty; it
might even make for a passing grade on a high school composition.
Her name was Laura de Noves, and she lived and died almost 700 years
ago. She was exquisitely beautiful, and when he was twenty-three the
great Italian humanist Francesco Petrarcha (better known as Petrarch)
caught sight of her at the Church of St Clare in Avignon, France.
Although he saw her for only a few moments, he fell into lifelong
love with her. This was reportedly the only contact he ever had with
the woman. Yet she was his livelong inspiration and the true force
behind all of his great writings, including his Canzoniere, his
barely-concealed lyric poems in praise of Laura.
In the great Orson Welles classic, Citizen Kane, the elderly
attorney Bernstein has a similar story to tell to the shadowy
Reporter: “One day back in 1896, I was crossing over to Jersey on
the ferry. And as we pulled out, there was another ferry pulling in.
And on it there was a girl waiting to get off. A white dress she had
on. She was carrying a white parasol. I only saw her for one second.
She didn't see me at all. But I'll bet a month hasn't gone by since
that I haven't thought of that girl.”
And one cannot even mention the great Italian renaissance poet and
writer Dante without conjuring up the memory of his beloved
Beatrice. It is this Beatrice, who Dante saw once and remained
forever in love with, who guides Dante to Paradise from the depths
of Inferno and Purgatorio. Like Laura’s influence on Petrarch,
Beatrice was the inspiring force of Earthly beauty that compelled
Dante to seek out truth, God and salvation. His Divine Comedy is
considered by many to be the greatest literary work ever.
Finally, the noted Austrian physicist Erwin Schrödinger, while on an
extramarital fling in the mountains in 1925, came up with his
greatest discovery, the aptly-named Schrödinger wave equation, for
which he shared the 1933 Nobel Prize in physics. Who was the unnamed
lady (if she can be called that), and just how did she inspire Mr.
Schrödinger? Nobody knows.
What does all this have to do with Hermann Weyl? Well, as a young
man he too glimpsed Beauty, and the experience affected him for the
rest of his life.
I suppose I risk appearing to be the most blatant of intellectual
snobs if I admit that I see a parallel between Petrarch and Weyl. In
his book of self-revelation, "My Secret Book," Petrarch has a long
and intense imaginary dialog with St Augustine over Petrarch’s
sufferings as an errant human being who, though he has seen the
truth and glory of God, cannot get the idyllic but still very
fleshly memory of Laura de Noves out of his head. It is a wonderful
and profound dialog, comprising about 100 pages, in which Petrarch
argues with Augustine that his love for Laura is based in purest
admiration of beauty, and that this love has been the inspiration of
all his noteworthy achievements in life.
I won’t go into it, but Augustine will have nothing to do with
Petrarch’s imaginings. “It cannot be denied that the most beautiful
things are often loved dishonorably,” says Augustine. But, Petrarch
replies, “Loving her has increased my love for God.” In the end,
Augustine wins out handedly, and Petrarch admits his folly. It is an
amazing debate, all the more remarkable because it was written in
1347, at the dawn of humanistic thought.
Similarly, Weyl glimpsed Beauty in 1918 in his theory of metrical
gauge invariance, and then struggled to maintain his love against a
disbelieving and chiding Einstein. In a series of written
correspondences that stretched from 1918 to 1921, Weyl and Einstein
debated long and hard over Weyl’s 1918 theory. Try as he would,
Einstein could not get Weyl to acknowledge the theory’s fatal flaw.
Weyl sent a proof of the first edition of his book
"Space-Time-Matter" to Einstein for review. Along with the proof he
boldly tells Einstein that he has “succeeded in deriving electricity
and gravitation from the same source.” While Einstein is initially
ecstatic, he spots the flaw, for which there is no cure, and replies
“Regrettably, the basic hypothesis of the theory seems unacceptable
to me [although] the depth and audacity of which must fill every
reader with admiration.” Weyl counters with “Even if this theory is
only in its infant stage, I feel convinced that it contains no less
truth than [your] Theory of Gravitation.” In his book, Weyl
rhapsodizes rather poetically:
“…One Light and Life of Truth comprehends itself in Phenomena. Our
ears have caught a few of the fundamental chords from that harmony
of the spheres of which Pythagoras and Kepler once dreamed.”
But Einstein holds firm. Weyl weakens a bit: “Your rejection of the
theory for me is weighty [Weyl is all too aware of Einstein’s
renowned insight and scientific wisdom] … But my own brain still
keeps believing in it.”
Like Petrarch and his flawed love for Laura, Weyl is at last forced
to face the fact that his gauge theory is also flawed and, like
Petrarch again, Weyl tries to fix it up by a rather unsound
rationalization of what’s real and unreal in spacetime. For a time
this isolates him somewhat from Einstein, Pauli and others who are
all too aware that Weyl is grasping at straws.
But finally, and happily, Weyl concedes to the fatherly and caring
Einstein. Like Petrarch, Weyl picks up his life and moves on, and in
1929 he discovers the true gauge invariance principle, which lies
not in generalized Riemannian geometry but in quantum mechanics – a
profound and lasting discovery that represents Weyl’s reward for
having recognized at last the real truth behind the Beauty he had
glimpsed one day in 1918.
I suppose it would be the acme of naivete to compare the chiding
Einstein with Augustine, but I think the basic idea holds up. But if
you think I’m nuts, then go read "My Secret Book" and
"Space-Time-Matter" and decide for yourself. |
| A Final
Word on Majorana -- Posted by
wostraub on Friday, May 13 2005 |
In 1986 the German-born Italian
director Donatello Dubini released a film entitled "Das Verschwinden
des Ettore Majorana" (The Disappearance of Ettore Majorana), which
starred Jean Seberg. Well, Blockbuster Video didn't have this one as
it turns out, so I'm giving up.
If you premultiply a conjugated Dirac spinor with the purely
imaginary gamma matrix $\gamma^2$, you get a charge-conjugated
Majorana spinor. If this is set equal to the Dirac spinor, then the
object describes fermions that act as their own antiparticles (some
physicists believe the Majorana spinor provides an accurate
description of massive neutrinos). Well, I guess you could have
learned this from anybody, but it's about all I have on the guy. I
guess the story about him jumping into the Tirrenian Sea in 1938 was
the best part after all.
No doubt you're foaming at the mouth for more, but until I learn
Italian I'm going to have to pass on Mr. Majorana. If you come
across the movie, I'd appreciate an email. |
| More on
Ettore Majorana -- Posted by
wostraub on Thursday, May 12 2005 |
Earlier I mentioned the brief
life of Ettore Majorana, the brilliant Italian theoretical physicist
who mysteriously disappeared while on a short boat trip in 1938.
Off and on, for perhaps two years now, I have begun to study
supersymmetry theory, only to fall flat on my face. The material is
not that difficult; Dirac and Weyl spinors move in and around the
theory, so there's a feeling of comforting familiarity. But the
stuff gets so compounded and interwoven with so many details that I
always give up. Interspersed in this mess are references to "Majorana
spinors," which are very similar to Weyl spinors, but even closer to
the concept of neutrinos. I always figured Majorana was just some
inconsequential guy who happened to come across a neat kind of
spinor. Now I'm beginning to see how unappreciative and stupid I've
been.
Almost all of the biographical material I can find on Majorana has
to be translated from Italian websites, and the Google translations
just aren't very good. Here's what I found today:
Majorana was born in 1906 in Catania, Italy. He and his family moved
to Rome in 1923, where he studied engineering until 1928. He
switched to theoretical physics, obtaining a PhD in 1929 with a
dissertation entitled "Quantum Theory of Radioactive Nuclei." Many
considered Majorana to be brighter than Enrico Fermi, who worked
with him.
Immediately prior to his disappearance on 25 March 1938, a note was
found in his handwriting that included the plea "Do not condemn me,
for you do not know how much I suffer." Colleagues noted that on
occasion he regretted the knowledge he had acquired regarding
nuclear fission and the possibility of making an atomic bomb. Since
Majorana was not a sickly person, or in debt, or even lovesick, it
was assumed that he had committed suicide by throwing himself into
the sea. His mother did not buy this; she never mourned, but awaited
his return until the day she died.
A neat mystery! Why can't television produce a drama like this,
instead of the tripe it continues to air? |
| Who the
Hell Was Ettore Majorana? -- Posted by
wostraub on Wednesday, May 11
2005 |
I've been reading a fascinating
account of the life of the late Italian physicist, Ettore Majorana.
A colleague of the great Enrico Fermi, Majorana also worked on
spinor theory and came up with a type of spinor very similar to
Weyl's. Majorana was one of the first scientists to recognize the
role of the neutron in nuclear physics, especially nuclear fission.
At the age of 32, Majorana was appointed the Chair of Theoretical
Physics at the University of Palermo in 1938. However, he either
took French leave, committed suicide or was washed overboard on a
boat trip prior to taking up residence at the school. Since he was
privy to the inner secrets of nuclear fission, rumors abound to this
day that he was abducted or killed by the Nazis. His body was never
found. There have been unsubstantiated reports over the years of
Majorana being sighted in Italy and in South America. If he did
bail, he did a good job of covering his tracks.
Fermi noted that Majorana was an exceptionally gifted physicist who
was also exceedingly eccentric and severely lacking in common sense.
Majorana was therefore just your typical scientist.
There's a biography on the guy that I'm trying to locate. If I find
anything interesting on him, I'll put it up. |
|
Radioactive Decay Rates -- Posted by
wostraub on Friday, May 6
2005 |
This will be my last word on the
creationism vs evolution issue, as my sanity depends on it.
A creationist friend of mine once asserted that radioactive carbon
dating is subject to error, because the rate of C-14 creation in the
upper atmosphere depends upon the rate of cosmic ray influx from the
sun, which is not constant in time.
She was RIGHT. The concentration of C-14 in Earth's atmosphere has
varied with time, so the rate of uptake of C-14 by living organisms
has not been constant. However, the variation has not been overly
significant. That's one of the reasons why organic samples dated by
C-14 methods are qualified with +/- figures. This means that a human
bone dated by C-14 to be 33,500 years old plus or minus 1,500 years
is really about that old. It does NOT mean that the bone can be
post-Diluvian (younger than about 4,000 years). Live with it --
there are fossils that are undeniably human that predate Noah and
his ark by many tens of thousands of years.
Other creationists have used similar arguments regarding
potassium-argon dating, saying that the rate of radioactive decay of
unstable isotopic elements can vary with time.
These arguments are WRONG. The radioactive half-life of an unstable
elemental isotope is a fixed, unchanging constant. To argue
otherwise is akin to saying that the probability of a fair coin
coming up heads after an infinite number of trials is 25%, or that
the value of the transcendental number PI depends on the day of the
week. Live with it -- when an Archaeopteryx fossil is dated at 150
million years, it really is about that old. It cannot be 4,000 years
old. Noah did not stash a pair of Archaeopteryx dino-birds on the
ark.
To deny this is to deny reality. If you deny reality, you are either
insane or a Republican. The difference is not spacious.
An excellent article on radiometric dating from a Christian
physicist's perspective can be found at
http://www.asa3.org/ASA/resources/Wiens.html |
| The
Newtonian Moment, One More Time -- Posted by
wostraub on Friday, May 6
2005 |
| In an earlier post I described
the New York Public Library's exhibit on Isaac Newton, "The
Newtonian Moment." It must have been popular, because it followed me
home. The exhibit is now on display at the Huntington Library in San
Marino. Part I of the exhibit, "All Was Light," is on display until
June 12; Part II, "The Making of Modern Culture," will open here on
July 23. Admittance is $15, a little steep to see some six or seven
displays of Newtoniana, but then there's the rest of the Huntington
Library itself, which is a must if you're in town. I've been going
there for 40 years, and I never tire of the place. |
| Weyl's
Spin Connection -- Posted by
wostraub on Wednesday, May 4 2005 |
In his 1929 paper on quantum
mechanical gauge invariance, Weyl derived the spin connection for
Dirac spinors in curved manifolds (roughly akin to the affine
connection that is used in general relativity). Because spinor
transformations are limited to the SU(2) symmetry (that is, they are
neither scalars nor vectors), Weyl's spin connection, to the best of
my knowledge, is the only route we have to analyze the behavior of
spinors in spaces warped by gravitational fields.
In case you haven't noticed, I'm rather enamored of both Weyl's 1918
theory and the basic concept of particle spin. Particle spin is just
so damned fascinating to me! Some time ago I read a book that
examined the spin connection in what is known as a "Weyl space,"
which is the manifold that fell out of Weyl's 1918 effort. I noticed
that the spin connection could be described in two ways, depending
upon one's preferences for simplicity. Like Weyl, I keep looking for
ways to get his $\phi_\mu$ field into things; being retired, it's a
source of amusement to me. [Physics is amusing?! Maybe I've got
Alzheimer's.]
Anyway, on the menu to the left of this site I've got a very rough
draft of a write-up on this subject. I'll add to it and fix it up as
time permits.
|
| 1924
-- Posted by wostraub on
Monday, May 2 2005 |
This has nothing to do with Weyl
or science, but I thought I'd toss it in --
My father, who would have been 100 years old in January (he died in
1981), graduated from high school in 1924. After years of searching,
I finally acquired a copy of his high school yearbook (along with
five others from the 1920s).
I don't have many photos of my father in his youth, but here he is
in the Class of 1924, at age 19, looking dapper and sharp in what
must have been a newly-purchased suit, and with carefully combed
hair. The biographical highlight concludes with "He was of the Prime
in Worth." Dad was far better looking than me, and when the picture
was snapped he must have thought his prospects in life were
boundless.
Mom graduated from the same school in 1932. Unlike Dad, she kept her
yearbook, which now sits right next to Wheeler's "Spacetime Physics"
on my bookcase -- a very odd juxtaposition, indeed.
Sprinkled around her and there in these yearbooks are photos of my
parents as undergrads and club members -- tiny, easily-overlooked
glimpses of my folks sitting and standing with their classmates,
almost all of whom are now certainly gone. Autographs and notes
abound in these books, with most saying things like "Have a
wonderful life."
Here is Violet Beer, who wrote that she remembered Dad. "He played
in the symphony orchestra, didn't he?" Indeed he did, and his
trumpet sits out in my garage. If alive, she must be 100 herself
now.
Here is my uncle, Dad's brother, who graduated in 1930 at the age of
22. He's gone, too.
And here ISN'T my father's other brother, who must have spent more
time playing hooky than attending class. He's also gone.
Here's Robert Piggott, my father's best friend. Dad used to tell me
about a certain Edna Piggott when Mom wasn't around. I assume Edna
was Bob's sister, but her picture's not in any of the books. Two
days before Dad passed away, his mind went back to the past, and he
mentioned these names to me before he died. Why were they important
to him?
Here's Thera Loomis, Mom's best friend at high school. Where is she
today? Or IS she today? (I know that she married a guy named Abbott,
and their son became a physics teacher.)
Looking over the notes the kids scribbled in these yearbooks, it's
easy to see that life was harder then, and graduation from high
school was not a slam dunk. Sickness, bad grades, excessive truancy,
the need to work -- even death -- kept many of my parents'
classmates from graduating. An example:
IN MEMORIAM
Lucille Bredeweg, Class of 1929
July 13, 1911 -- December 13, 1927
The memorial photo shows a beautiful 16 year old girl. Uncle Ivan
must have known her, and mourned for her.
And here's Mom as a junior in 1931 as a member of the "Alchemy
Club." I never knew she took chemistry, which was my undergraduate
major.
My mother was beautiful in her youth, and Dad was very handsome
(unfortunately, those genes didn't get handed down to me). They
married in 1932, and the marriage ended when Dad died 49 years
later.
One of my favorite poems is Buffalo Bill (ee cummings, I believe, so
I'll keep it lower case):
Buffalo Bill's defunct
who used to ride a watersmooth-silver stallion
and break onetwothreefourfive pigeons
justlikethat,
Jesus.
he was a handsome man, and what i want to know is,
how do you like your blue-eyed boy,
Mr Death?
My mother used to tell me not to put flowers on her grave, because
they wouldn't do her any good. And as I place flowers on my parents'
graves, I know she was right. May God save their souls. |
| Thoughts
on Drake's Formula -- Posted by
wostraub on Monday, May 2
2005 |
Some time ago I read the book "It
Must Be Beautiful: Great Equations in Modern Science," a collection
of articles by noted scientists and edited by Graham Farmelo. One of
the chapters in the book deals with Drake's Equation.
Frank Drake was a 1950s radio astronomer who worked at the National
Radio Astronomy Observatory in West Virginia. One day it occurred to
him that the intensity of domestic, commercial and military radio
and television transmissions far exceeded those arising from natural
processes in the Sun, and he began to think about how these
transmissions might be intercepted and analyzed by extraterrestrial
observers. Turning his thoughts around, he considered the
possibility that humans might be able to intercept similar
transmissions from other solar systems. By the 1950s, there were
numerous powerful radio telescopes in operation around the world
that could be pressed into service (at least part of the time) to
look for such transmissions. But where to look, and what was the
probability of finding them?
Drake addressed the problem by setting up a simple formula. First,
he set R equal to the average rate at which stars are formed in the
universe that are reasonably similar to Earth's Sun. He then let fp
be the fraction of star systems in the observable universe that have
planets. He then let fh be the fraction of fp that represents
planets suitable for habitation. Similarly, he let fl, fi, and fc
represent the fractions of those planets having life, intelligence
and structured technological civilizations. Lastly, Drake set L
equal to the average lifetime enjoyed by any given civilization. He
then postulated that the creation rate N of observable,
extraterrestrial radio-transmitting civilizations could be expressed
simply as
N = R x fp x fh x fl x fi x fc x L
Of course, N cannot be identically zero because there is at least
one such civilization, which is that of Mankind on Earth.
Since Drake first proposed this empirical (and perhaps even
meaningless) formula, there has been no end of respectable
scientists and crackpots alike that have come up with numerical
figures for the above fractions. There has been no consensus on the
fractions, but the number N has generally ranged from unity to a
billion.
If N = 1, then it is almost certainly hopeless that the transmission
source will ever be found. If a billion, then there is a chance,
though a small one, because the heavenly sphere is huge compared
with the number and size of our radiotelescopes.
Reflect for a minute on the possibility of finding such a source.
Let's say that one is confirmed in the Andromeda Galaxy, about 2.2
million lights years from Earth. Let's further assume that the
transmission is intended to convey a message, and we determine with
absolute certainty that the message is "Hello there." What exactly
would that mean to us?
I would argue that the message would be, for all intents and
purposes, meaningless. We would never be able to talk to the message
senders, or explore or analyze their world. All we'd be able to do
is consider the certainty that extraterrestrial life exists. Would
this improve Mankind's lot in any meaningful way? I doubt it. There
might even be a tendency to see life as cheap and common. We could
then blow ourselves to atoms, or destroy our environment, secure in
the knowledge that life, somewhere, would go on. This is not to say
that there might be some social disorientation created by the
knowledge that someone else is "out there." Religious leaders and
social scientists alike would have to sort out the consequences of
such knowledge, but I really can't see things going much further
than that.
Now consider the very real possibility that terrestrial Mankind is
the ONLY civilization that Drake's formula pertains to. Assume for a
minute that Mankind is unique to the universe. Would this knowledge
not make every man, woman and child on the planet an infinitely
precious thing? Would it not make every species now facing
extinction on the planet something to be protected and celebrated?
Would it not make war seem like the ultimate insanity?
I personally believe that God did indeed pull off other acts of
creation in the universe, and maybe a sizeable percentage of them
involve intelligent life. But it simply does not matter, because we
have to live out our lives here. I don't oppose the Search for
Extraterrestrial Intelligence (SETI), because I believe that one of
the things God wanted us to do was explore the universe we live in.
But I wouldn't waste too many of our already-limited resources in
the search.
As for UFOs and the like, consider this: We haven't found any
intelligent extraterrestrial radio messages yet (and we've been
looking for 50 years), so chances are the LGM (Little Green Men) are
quite far away. If so, then statistically speaking their own chances
of finding us (never mind the requirement that they'd need warp
drive technology to come here) is much worse than finding a
particular grain of sand in all the beaches of the world. And if the
LGM have indeed arrived, why are they making their presence so
difficult to confirm? If you're the least bit scientific about it, I
think you'd have to conclude, as I have, that UFOs either do not
exist or they are human time travelers who do not want their
presence known. If time travel to the past is possible, future
historians would absolutely love to visit past Earth (I know I
would!), but might have to face unfortunate consequences if their
presence or technology were discovered (just imagine George W. Bush
and his war machine with a time-travel device -- yike!). As unlikely
as this scenario is, it's vastly more believable to me than LGM.
|
| The
Accidental Scientist? -- Posted by
wostraub on Monday, May 2
2005 |
Tim Russert talked to New York
Times columnist and author Thomas L. Friedman on Meet the Press
yesterday. Friedman was there mainly to push his new book "The World
is Flat," which sounds a wake-up call to an America that seems to be
sleeping while the world undergoes radical globalization. I don't
always agree with what Friedman has to say, but the views he
promoted on the show are very close to my own.
Friedman's flat-world scenario really refers to the fact that new
technologies are allowing countries like India, China and Ireland to
compete with the United States on a playing field that is getting
leveled more and more to their advantage every day. He believes that
America's leadership in science and engineering has become eroded
due to an attitude of arrogant "entitlement." Meanwhile, other
countries are producing far more PhDs in technical fields, and
they're showing signs of leaving us in the dust. Up until perhaps 10
years ago, foreign students came here to study science and
engineering, but the enormous rise in the quality of foreign
universities (coupled with American travel restrictions imposed due
to 9/11) is keeping them in their own countries, which then get the
primary benefit of their efforts. As a result, Friedman is seeing an
steady and alarming erosion in America's ability to compete with
foreign markets in technological fields.
To get America back on track, Friedman recommends that we develop a
"Moon Shot" program similar to what JFK initiated in the early 1960s
(I would prefer something more akin to another Manhattan Project,
but perhaps it's all just symantics). And Friedman believes that
this program should be focused on energy self-sufficiency -- kicking
the oil addiction once and for all (because Peak Oil is almost
certainly going to happen), and developing cost-effective
alternative energy sources (including solar, wind, and nuclear). He
even went so far as to recommend that the President impose a $4 per
gallon price on gasoline, beginning in 18 months, with the generated
revenues going to finance the program. Friedman even told Russert
that if Americans want to drive Hum-Vees, they should go to Iraq,
implying that gas-guzzlers like Hummers have no economic or moral
place in the world. Right on, Tom!
Friedman sees global warming as a bigger threat to the world than
terrorism. I personally see the biggest threat to be waning energy
supplies and the increased militarism of countries to secure
whatever oil resources remain after Peak Oil kicks in. Many
scientists believe that we will run out of fossil fuels before
global warming becomes an acute threat to the planet.
Regardless of who's right, Friedman's plan is a giant step in the
right direction. Energy self-sufficiency would require an enormous
investment in scientific research and development. America is
probably the only country that has the financial capability of
undertaking such a task, and it consequently offers an ideal
opportunity for America to retake the lead in science and
technology.
Where I disagree with Friendman lies my belief that we should not
trust in technology alone to fix our problems. If you've ever
studied Lagrangians in math and physics, you already know that
Nature has cooked things up so that conjugate variables like
ENERGY-TIME are minimized. This means that humans should make every
effort to conserve resources and minimize waste. Also, we should
minimize the amount of energy we throw away into ENTROPY. This
simply means that it is far better to not make a mess (like an oil
spill or air pollution) than to make it and then clean it up.
Speaking system-wise, a cleaned-up mess is even worse than one that
is left alone. Of course, all this flies in the face of that great
god, Capitalism, so our current attitudes will necessarily have to
be adjusted -- and quickly.
As Friedman implies, all of this will require a hell of a lot of
scientific education. My belief is that when people are adequately
educated in science and math, they see the way things really should
be, and they make changes in their lifestyle. Friedman's thinking is
an example of this; his own background is in Mediterranean studies,
but he has gotten himself educated in science to the point where he
sees the truth about things. Science and math will do that to you.
Lastly, Friedman expressed his hope that President George W. Bush
will read his book and show the one thing that Friedman claims has
been missing in America to date -- true LEADERSHIP.
Lots of luck, Tom. |
| Weyl
Articles -- Posted by
wostraub on Monday, April 25 2005 |
Norbert Straumann, Professor of
Theoretical Physics at the University of Zurich, kindly sent me a
German reprint of his paper "On the Origin of Weyl's Gauge
Theories." I've been looking all over for a copy of this article, as
it gives an especially clear overview of Weyl's 1929 paper on
quantum-mechanical gauge invariance. [If I can get permission, I'll
translate it and post it as a pdf document on this site.] The paper
includes a reproduction of the postcard that Einstein sent to Weyl
regarding Weyl's original 1918 gauge theory. After I've translated
Einstein's comments, I'll post a photo of the postcard along with
the translation on the menu to the left.
Straumann (with Lochlain O'Raifeartaigh) has also written a very
readable overview of early gauge theories, including the
5-dimensional Kaluza-Klein theory. The article is available online
at
http://xxx.lanl.gov/abs/hep-ph/9810524 |
| When
Einstein Lived in Pasadena -- Posted by
wostraub on Monday, April 18
2005 |
KPAS (Cable 55 in Pasadena) has
got a great 45-minute video titled "When Einstein Lived in
Pasadena." It's shown frequently, but to date I've only seen about
half of it.
It includes a neat story about how Nobelist Robert Millikin
(remember the Millikan oil drop experiment in school?), Caltech's
president in the 1920s and 1930s, enticed Einstein and his wife Elsa
to visit Pasadena. They made three visits (all in December, I
believe) in 1931, 1932 and 1933. During Einstein's first visit, he
lived at 707 S. Oakland Avenue in Pasadena. The house is still
there, looking very much today as it did then. It's a fairly simple,
unassuming house in a neighborhood of nice, well-maintained homes
built in the 1920s and 1930s.
I stopped by Caltech this morning, and thought I'd also swing by and
take a picture of the Einstein house. You can download it from the
menu on the left (the file is about 550KB, so I hope you have a
decent Internet connection).
Of course, Millikin's plan was to get Einstein to join the Caltech
faculty, and he nearly succeeded. But Einstein was lured away by
Princeton's Institute for Advanced Study. When Einstein left Germany
for good in 1933, that's where he went. He died there on April 18,
1955, exactly 50 years ago today.
I used to have a next-door neighbor, Seth Baker (who sadly passed
away four years ago at the age of 92), who was a communications
professor at USC. He had lived in Pasadena since the 1920s, and he
saw Einstein during one of his visits (I think it was 1931).
Einstein gave a speech at the opening of Pasadena Junior College's
then-new telescope facility, and Seth snapped his photo (which
unfortunately got lost over the years). Too bad.
I haven't inquired about it, but you may be able to get a copy of
the Einstein video from Caltech. The website (which has lots of
other neat stuff) can be found at
http://www.archives.caltech.edu |
| Darfur
-- Posted by wostraub on
Thursday, April 14 2005 |
I rarely agree with anything that
neocon Max Boot (Council on Foreign Relations) writes, but in
today's Los Angeles Times he has hit on something that should touch
every American. That something is the genocidal situation in Sudan's
Darfur region.
Over the past two years, religious and ethnic differences in that
country have resulted in over 300,000 deaths and more than 2 million
displaced refugees, who literally have nowhere to run. But the worst
of it is the torture and rape of hundreds of thousands of people,
including children. The Sudanese government, which itself is
complicit in the crimes of radical Islamic militias, is otherwise
helpless to stop the crimes against humanity that are occurring
every day.
Boot bemoans the apparent lack of American will in mounting any
serious humanitarian assistance (military or otherwise), noting that
we are too bogged down in Afghanistan and Iraq to be of any real
help. But that does not absolve us of our Christian responsibility
to help out when a human crisis of this magnitude arises.
There are numerous charitable groups who are sincerely trying to
alleviate the suffering in Sudan. One of the best, in my opinion, is
Doctors Without Borders (DWB), which is already providing a wide
range of medical and humanitarian services to the region. However,
like many other such groups, its resources have been overstretched
by the Indonesian tsunami disaster.
You don't have to mortgage your house to help out; even a few
dollars can be put to good use -- whatever you can spare. This is a
chance for self-loathing liberals and hypocritical right-wingers
alike to do something right for a change! :)
DWB can be reached at:
Doctors Without Borders
www.doctorswithoutborders.org
1-888-392-0392 toll free
"Leave wringing of your hands: peace! Sit you down,
And let me wring your heart"
-- Hamlet |
| Fifty
Years After Einstein and Weyl -- Posted by
wostraub on Monday, April 11
2005 |
Believe it or not, I can just
barely remember Mrs. Webster, my Kindergarten teacher at Northview
Elementary School in Duarte, California, mentioning to her otherwise
oblivious little charges that Albert Einstein had just died. I
remember this only because she made a big deal about how smart the
guy was and how important it was to do well in school. I also
remember that I didn't know who the hell Albert Einstein was. Now,
if it was Sheriff John or Bozo the Clown that had died, I would have
have really taken notice.
That was fifty years ago this week.
It's odd that I can remember stuff that happened to me thirty, forty
and even fifty years ago (or at least I THINK I remember), but I
can't recall what I did last week to save my soul. Chalk it up to
advanced middle age.
Einstein died in Princeton on April 18, 1955. Weyl was to follow him
in death in December of that year. I certainly DON'T remember Mrs.
Douglas (my first-grade teacher at Northview) telling us that
Hermann Weyl had passed away! |
| Weyl and
Vierbeins -- Posted by
wostraub on Saturday, April 9 2005 |
While reading Weyl's 1929 paper
for what seems to be the umteenth time (there are still parts of it
that I find puzzling), I began to wonder if it was Weyl who came up
with the VIERBEIN (or TETRAD) concept. Because there are no
finite-dimensional representations of spinors in gravity, the only
way of tying a flat-space spinor field to the curved spaces of
gravitation is through vierbeins. A vierbein is just a quantity
having a Lorentz (flat space) index (usually denoted by a Latin
letter like a,b,c...) and a general coordinate or tensor index,
which is denoted by a Greek letter. Vierbeins are also used to
express flat-space tensor quantities into curved-space forms.
The vierbein is written simply as $e^a_\mu$, although either index
can be up or down (or even juxtaposed with the other). We raise or
lower Latin indices with the flat-space metric $\eta_{ab}$, while
the curved-space metric tensor $g_{\mu\nu}(x)$ is used to raise and
lower Greek indices. We can therefore express the curved-space
metric tensor using the vierbein formalism with the Lorentz metric:
$g_{\mu\nu}(x) = e^a_\mu(x) e^b_\nu(x) \eta_{ab}$ (1)
Spinors can be viewed as flat-space fields that inhabit local
tangent spaces. They transform in general-coordinate spaces like
scalars, but in Lorentz space they transform using a certain unitary
2X2 matrix (see my write-up on Weyl spinors on the menu to the
left). This matrix involves the Dirac gamma matrices $\gamma^\a$,
which also live in a flat Lorentz space.
To get a spinor representation in a curved manifold, we use the
unitary transformation matrix as usual but with the gamma matrices
expressed in curved-space form, $\gamma^\mu(x)$. This is where the
vierbein comes into the picture:
$\gamma^\mu(x) = e^\mu_a \gamma^a$
Weyl used this vierbein approach in his 1929 paper. What puzzles me
is whether Weyl was the first to do this. I know that a year
earlier, Einstein (and maybe also Wigner) had used vierbeins, but in
a completely different application.
I do believe that Weyl was the first to derive the connection term
for the covariant derivative of a Lorentz vector. Using this term,
one can calculate the total covariant derivative of a mixed Lorentz-coordinate
tensor quantity. However, the covariant derivative of the vierbein
vanishes. In Weyl's 1918 theory, the covariant derivative of the
metric tensor is not zero, and this would also require a
non-vanishing derivative for the vierbein as well. I wonder if Weyl
ever considered what happens to the vierbein when the metric tensor
in (1) is rescaled via $g_{\mu\nu} -> \exp(\pi(x)) g_{\mu\nu}$. Do
the vierbeins get rescaled, or does the flat metric $\eta_{\ab}$ eat
the scale factor?
Had Weyl completely given up on his earlier theory by the time he
wrote his 1929 paper? I don't think so, because gravity was still
very much on Weyl's mind at the time. Indeed, the title of the paper
(Elektron und Gravitation) would have likely been Elektron und
Wellenmechanik if Weyl had completely sworn off his earlier effort.
It seems a shame to me that God called Weyl home in 1955 at the
relatively young age of 70, because so much neat physics was to
arise in the 15 years that followed his passing. I've often wondered
what role Weyl might have played in the development of this new
physics, because his gauge principle lies at the root of so much of
it. |
| "DEAD
WRONG" -- Posted by wostraub
on Thursday, March 31 2005 |
The cover letter of the
now-released report from the President's Commission on the
Intelligence Capabilities of the United States Regarding Weapons of
Mass Destruction claims that the government was "DEAD WRONG" in its
findings and that the intelligence information it dumped on the
American people and the world was either "WORTHLESS" or
"MISLEADING."
Analysis of the 618-page report (and I will read every word of it)
by the world's press has only just begun, but many are already
saying that 1,533 American servicemen and women died in vain in
Iraq, while more than 100,000 Iraqi civilians (innocent men, women
and children) died as "collateral damage." As Defense Secretary
Donald Rumsfeld has said, "Stuff happens" in war.
I am outraged by this report, and every American should feel the
same! PRESIDENT GEORGE W. BUSH IS A WAR CRIMINAL, AND SHOULD BE
TRIED FOR HIGH CRIMES AND MISDEMEANORS AGAINST THE AMERICAN PEOPLE
AND FOR CRIMES AGAINST HUMANITY. His cohorts in evil, CHENEY,
RUMSFELD, RICE, POWELL, WOLFOWITZ, PERLE, FEITH and MYERS should
also stand trial for treason.
The accessories to these crimes, in my opinion, are the AMERICAN
PEOPLE. You and I stood by and let a half-dozen monsters take over
this country, suspend the rights of American citizens, authorize the
seizure, imprisonment, torture and murder of innocent people, all
for political and corporate power. In doing so, these people lied
and lied and lied, and we let them. And we call ourselves
Christians! God forgive us!
In his recent book "The Sorrows of Empire," Chalmers Johnson
reluctantly and sadly admits that the only options available to the
American people to change the current administration are probably
through radical means. If nothing changes, America will become a
fascist empire that will enslave us all.
The Commission's report pulls at the curtain hiding the President
and his co-conspirators. What will it take to rip it away
completely? Will we wake up then, or will we go back to sleep? THIS
IS OUR COUNTRY, DAMN IT!!
Post Script: Notice how closely the announcements of the death of
Terri Schiavo and the release of the above report followed upon one
another. Is it a coincidence? Today's TV news is devoted almost 100%
to Schiavo's death, while the WMD report has been consistently
absent from the airwaves. I see this as more evidence that our
beloved leaders are relying upon the American public's addiction to
triviality as a means of avoiding culpability in issues that really
matter. |
| On
Bioethics and Related Matters -- Posted by
wostraub on Tuesday, March 22
2005 |
I apologize for the following
rambling, unstructured diatribe, but I have other things to do so
I'm making it quick.
The Op-Ed section of today's Los Angeles Times has several
interesting articles involving the interplay between science and
religion. One is "Why Science Can't Show Us God" by Margaret
Wertheim, the author of "Pythagoras' Trousers" (which I have not
read), which won a book prize funded by the John Templeton
Foundation (see my previous entry). Another article is by Jeremy
Rifkin, the noted scientist-ethicist and author of "The Biotech
Century" (which I have read). A third article is from Robert Scheer,
the political gadfly and notable Bush critic, whom I happen to
admire a lot in spite of the fact that (or perhaps because) he is
consistently hated by rightwingers because he happens to have a mind
and the courage to speak out against the mind-numbing hypocrisy of
our times.
These articles jumped out at me because not long ago I read "The
Beginning of Wisdom: Reading Genesis" by Leon R. Kass, MD, PhD, who
in 2001 was appointed by President George W. Bush to the Chair of
the President's Council on Bioethics. This 700-page book is
fascinating; it analyzes the first book of the Old Testament in
almost excruciating detail, and thus provides much insight into the
mind of God at the beginning of creation that I think many people
(myself included) were never aware of. For example, the order that
God chose to create the sun and moon, light, the Earth, and mankind
reflects much profound subtlety, while God's oft-repeated
pronouncement "...and He saw that it was good" was NOT made when he
created Adam. Very interesting, deep, neat stuff.
However, Kass elects to minimize the importance of several things
that reveal the author's shortcomings, which I believe spring from
his conservatism. For example, when Cain is sent away following
Abel's murder, he goes to Nod where "he knew his wife." Where did
the Land of Nod come from, and more importantly, where did his wife
come from? These are not new questions, and have in fact been asked
for many centuries, but Kass brushes them off with a single footnote
citing incest as the possible answer. He also admonishes the reader
to not think about these questions too much, but instead says "That
he [Cain] had a wife (and descendants), not where she came from or
who she was, is what we here need to know." In view of the
meticulousness with which Kass has developed his arguments (after
all, he has written 700 pages on the Book of Genesis ALONE), these
kinds of brush-offs are most annoying. The Cain story and footnote
appears on Page 144, and I was so annoyed at Kass' attitude at this
point that I almost stopped reading the book. It's almost as if Kass,
when faced with inconsistencies that he cannot explain within the
context of his own belief system, is saying "Let's not dwell on
this, because I don't want you to use your own mind. Just accept my
dogma without question."
While Kass does not address bioethics in his book at all, I feel
that to dismiss the possible early biology of humanity as
inconvenient IS unethical. God did not fix the time scale in Genesis
(he did not create the Sun until Day Four, so millions of years
could have been involved), and in my opinion it's very possible that
Cain's wife was an advanced australopithicine or other early human
biped that was capable of mating with Cain. But this view
presupposes evolution, which to any red-stater is a no-no. Kass
states that "None of these biblical teachings needs to be retracted
because of the findings of evolution." If Kass can acknowledge
evolution in this manner, why can't he simply acknowledge that
evolution is just a tool God invented to ensure that his creation
can adapt to changing environmental conditions? The denial of
evolution is, to me, a sin against bioethics because it denies
biological reality, and a sin against God because evolution is his
creation.
On a separate but related note, Scheer points out the hypocrisy of
the Bush sycophants in their rabid determination to save the "life"
of a brain-dead patient (Terri Schiavo) for purely political
purposes, in spite of the fact that Governor George W. Bush himself
championed a Texas law permitting spouses and significant others to
OK the withholding of extraordinary life-saving measures in just
these kinds of cases. This is most CERTAINLY a case of bioethics
that has been perverted by politicians for their own selfish ends.
The state courts have already weighed the Schiavo case to the nth
degree, and declared that Terri should be allowed her appointment
with God (and I have prayed that her soul is saved). Bush and his
fellow maniacs would rather Terri spend another few decades in a
brainless, lifeless limbo to further their own despicable causes.
And the fact that Congress jumped in to vote on this SINGLE case
tells me that our Constitution is in deep, deep trouble.
Meanwhile, Rifkin chimes in to voice his opposition to genetic
engineering. He reminds us that researchers are trying to create
hybrid creatures ("chimeras") using spliced human and animal DNA so
that they'll have more human-like laboratory animals to experiment
with. And why would such research be tolerated? So that
pharmaceutical companies can make billions by developing new drugs
tested on creatures like "humanzees," a truly horrendous cross
between humans and our closest genetic relative, the chimpanzee. It
seems that America's bioethicism can be stretched without limit
provided there's money to be made for the CEOs and the shareholders.
Here, I'm 100% behind Rifkin and presumably even Mr. Bush. God
created every living species to be separate and distinct, and by
literally monkeying around with this set-up we risk disaster.
Last but not least is Wertheim's otherwise excellent article,
although I really don't agree with what she says. She states that
"rational inference can never substitute for personal experience of
the divine," and claims that God should not be equated with the
structure and function of nature. I agree -- God is not nature. But
this avoids the real issue, which is whether science and religion
complement one another or must be kept separate. I believe Wertheim
is a proponent of the latter. Any person can justify anything by
simply claiming that "I received a message from God," which is
absolutely not scientifically verifiable. I defy anyone to take away
one's right to believe they have received divine instructions from
God, but this simply cannot be proved. As it stands, people like
this are locked up, unless they're the President of the United
States.
What Wertheim does not address is the fact that God gave us superb
reasoning organs called brains. The capabilities of our minds far
surpass the need to simply acknowledge God and the wisdom behind his
creation. I believe God gave us the ability to think because he
wanted to challenge us, to wonder about the physical world and to
figure out how he did it. This included questioning where we came
from, where we're going, and what our purpose is in life. It even
included wondering whether or not God exists. Otherwise, he could
given us minds like sheep -- then we wouldn't have sinned, and we'd
all spend our eternal ovine afterlives peacefully munching grass.
Wertheim seems to want to maintain the wall between religion and
science. That's why biology texts in red-state schools are being
rewritten to emphasize allegorical creation over evolution, and
that's why when Bush tells us that 2 plus 2 is 5, we'll
unquestionably accept it as divine revelation.
On a purely personal note, I confess that I was not able to accept
the existence of God until I studied science and math. Then God's
existence became a rational certainty to me. My belief in Jesus
Christ and personal salvation, on the other hand, is more
faith-based, but even there I see a sound scientific reason based on
the constraints imposed by God's gift of free will: Did God want man
to have free will? Yes. Did he know that free will would cause us to
know evil (because we have to know both good and evil to have a
choice)? Yes. Therefore, if mankind was to be saved from himself,
God had to provide a Savior. Without free will, there would be no
need for Jesus, but then we'd all be incapable of intelligent
thought.
The Sciavo case is way overblown, of course. The war in Iraq and a
host of other ills is far more important, and I suspect our
government is just using Schiavo as a screen to keep the sheep from
looking behind the curtains.
The apostle Paul admitted that he would rather be dead and be with
Jesus Christ than continue to live and be subjected to the world and
its temptations. I cannot speak for Terri Schiavo's parents, who
must truly love their daughter. But in this case I say let Terri be
with God, and I believe any compassionate Christian bioethicist
would agree with this. |
| More
About Growth -- Posted by
wostraub on Thursday, March 10 2005 |
I was a civil engineer for many
years, and one thing I did was try to predict water demand using
population growth rates. The idea was to extrapolate population
levels using regional economic and socio-demographic data, then
assign a per capita water demand (typically 150 gallons per day per
person). Multiplying one by the other gave us the total water
demand. The only trick is to get the future population right. Curve
fitting is fun!
Well, there are two ways to look as this type of planning. One
assumes that the population growth will occur no matter what, so the
water purveyors had better be ready for it. But the other way says
that there might be a cause-and-effect issue involved -- by planning
for growth, the growth occurs because we made it possible. No civil
engineer ever said to the Mayor, "This is all the water we'll ever
have available, and when that's allocated, the city must stop
growing." Civil engineers are a lot like politicians -- they'd
rather be employed than be out of work.
I forget who said that humans will always take a resource and use it
up as quickly as possible, regardless of how much was originally
available. If this causes a problem, they will form blue ribbon
committees consisting of experts to study the problem, then produce
a lengthy report that no one will read or take action on. It's just
human nature.
Take the infrastructure issue, for example.
The American Society of Civil Engineers (of which I've been a member
for 29 years) recently published a report on the state of America's
infrastructure (that's water systems, dams, treatment plants, roads,
bridges, etc.), and I sure as hell hope people read this one. It
gave the country a grade of "D" based on calculated estimates of
infrastructure deterioration, and added that it will take $1.6
trillion over the next five years to fix it nationwide (the grade is
slightly better than the "D-" ASCE gave it in 2001). Unfortunately,
repairing a bridge is not as "sexy" as designing and constructing
one -- after all, that's what we engineers went to school for! In my
opinion, the infrastructure problem will persist because it is a
reminder of the problems associated with growth, and people just
don't want to face it.
Well, eventually we will have to face these problems, and there's a
tried and true method that the government has historically resorted
to, and always will. It's this -- ignore the problem until you can't
anymore (a disaster, etc.), then raise taxes on the middle class to
pay for a partial fix. And believe me, with the Bush cartel in power
today, the middle class is gonna get slammed pretty hard this time
around.
ASCE's a great organization that's trying to do the right thing, and
you can help by at least getting educated. If you want to see the
infrastructure report, go to their website at
ASCE. |
| The Peak
Oil Issue -- Posted by
wostraub on Thursday, March 10 2005 |
Since retiring four years ago,
I've been following the Peak Oil issue with increasing interest and
concern. It began in 1999 after I spoke with Dr. Albert Bartlett of
the University of Colorado at Boulder, who is a vocal proponent of
the issue (and, alas, a Cassandra because the issue's being ignored
by the vast majority of humans). Since then I have read Dr. Kenneth
Deffeye's book, "Hubbert's Peak," and I don't know how many other
articles that have come out.
Dr. Bartlett is fond of quoting his Third Law of Experts, which is
"For every PhD there is an equal and opposite PhD." By this he means
that if an expert comes out for or against something, there is
another expert who will counter those claims. So I decided to look
at the data myself; there are several web sites that have summarized
the data.
There is no question that oil production is following a Gaussian (or
bell) curve. The oil gusher that began modestly enough in
Titusville, Pennsylvania back in 1859 grew into millions of oil
wells around the world, and the production of oil grew
exponentially. In spite of a few blips (the North Sea oil discovery
in the 1970s was a kind of unexpected gift), the world's production
rate does indeed look Gaussian. The production curve for the United
States fits a Gaussian curve almost perfectly (and it peaked in
1970, which is why we're importing most of our oil nowadays).
Unless you believe that the world is flat and infinitely
two-dimensional, the world's supply of oil is indeed finite and will
be exhausted at some point in the future. But this is not the real
problem; the problem is that when world oil production hits the peak
of the Gaussian curve, production can only go in one direction --
down. When that happens, there will be no such thing as CHEAP OIL
anymore, and then really bad things will start to happen.
Imagine -- every now and then some politician suggests raising the
gasoline tax a few pennies a gallon to pay for some pet project, and
he/she gets crucified for it because opponents scream that it'll
hurt people and businesses. After Peak Oil kicks in, and it will at
some point, the base cost of gasoline might be $10/gallon. What will
we do then? Who wrote the law that says gasoline can never go higher
than $2/gallon?
Another thing that Bartlett says is that one of the saddest facts
about us humans is our unwillingness to understand the EXPONENTIAL
FUNCTION. This is a mathematical function that describes the rate of
growth or decay of something. Growth can be good or bad -- nobody
wants a malignant tumor to grow, for example -- but so-called "good"
growth can be bad, too.
My observation is that no one really seems to know what "good"
growth is. A small town with a population of, say, 10,000 people
might be desperate for growth, as it would attract more goods and
services as well as tax revenues to pay for the public works
infrastructure needed to sustain the citizens. After a period of
growth, the town's citizens might start to say "That's enough
growth, things are just right now." But that is never the case;
growth continues whether people want it or not. People are still
flocking to Los Angeles, where growth has truly destroyed the
lifestyle that once existed in the 1930s and 40s. Now it's just
smog, hellish traffic congestion, and high taxes. This is not what
folks wanted for LA, but it happened anyway. I think most people
believe there's an "ideal" growth rate at which nothing bad ever
happens.
There are currently several ads running on TV featuring Erik Estrada
hawking residential lots in Florida (and Arkansas, of all places).
The ads say that growth is explosive, with the Florida community
expected to increase its population by 33% by the year 2010, so come
on down! Good Lord, who would want to live in a place that's growing
like that?! I believe people tend to think of growth as they do
their bank accounts; nobody wants an annual rate of return of only
2%, they want more. This is understandable -- everyone wants more
money, more goods and services. But we humans do not know how to
stop growth when it's not wanted anymore. Housing developers now say
that "people have to have a place to live," and go on building. Or
they talk about "sustainable growth," which is a lame excuse to keep
on building because it sounds as if some smart person has a plan
that will fix everything. The term is also an oxymoron. Growth is
growth; something that grows at only 1% per year doubles itself in
about 69 years. A community experiencing 10% population growth (a
"nice" figure for bank accounts) will double in size in only 7
years. Do you want your city to grow that fast? How would you like
your doctor to tell you that your cancerous tumor is growing only a
few percent per year?
Peak Oil, if true, will abruptly stop growth, and it will stop it
all around the world. Unfortunately, it has the very real potential
to rapidly create chaos and human suffering of the kind not seen
since Noah's flood. Oil has been described as the nearest thing to a
free lunch. Its energy density surpasses all other sources of
cost-effective energy. We should have been using it to develop a
truly sustainable energy source, like large-scale solar power or
safe nuclear reactors, rather than burn it in 12-MPG automobiles.
Forget fusion -- it will never happen in our lifetime, and if it
does its development will require an enormous amount of energy just
to get it built and distributed.
To me, the only solution now is to conserve like we never have
before. But conservation is anathema to growth, and as long as
humans believe growth is good, we're doomed. That's one reason why I
drive a hybrid car. It's a drop in the bucket, but I'm trying to do
my share.
Bartlett has a wonderful term for the point in time that Peak Oil
proponents are talking about; it's called the "Dirac Delta Function
in the Darkness." Try to imagine the history of mankind over the
past 10,000 years or so. A space visitor looking down on Earth at
night during that time would see mostly darkness, because until
Titusville came along there were only scattered campfires and the
like to serve us and keep us warm. Then, a brilliant flash of light
for maybe 150 years or so, representing the Oil Age. After that,
darkness again. The Dirac function, which represents a sudden and
intense "spike" of activity on the axis representing time, is a very
appropriate analogy.
I urge you to Google "peak oil" and look at some of the many
websites that address this issue. Politically, environmentally and
economically, it might very well be the defining issue of our age --
and it's going to happen very quickly if it's true. A good site to
check out is www.fromthewilderness.com, which should open your eyes.
You don't have to believe everything you read, but at least get
yourself educated so you can decide for yourself. |
| Einstein
at the Skirball Museum -- Posted by
wostraub on Friday, February
18 2005 |
Today my older son and I visited
the Einstein exhibit at the Skirball Museum in West LA. Lots of neat
stuff -- Einstein's grade school report card; Einstein's handwritten
reproduction of his 1905 special relativity theory; original letters
to and from many famous scientists and statesmen; his brass
refractor telescope; his magnetic compass; his smoking pipes and
classical 78-rpm records; his erroneous light-deflection calculation
from 1912; and the "Holy Geometry Book," an elementary text in
German, given to Einstein as a child by his uncle, which Einstein
cherished as the source of his interest in science and mathematics.
Also on display are letters to extra-marital paramours, of which he
had many, and the list of demands he handed to his estranged first
wife, Mileva, instructing her to silently deliver hot meals to his
room and to not expect any tokens of intimacy from him. This is
Einstein, warts and all.
To me, the best part of the exhibit focused on his later years, in
which he became increasingly involved with nuclear weapons control
and human rights. He was caught up only marginally in the McCarthy
trials, but a paranoid American government nevertheless considered
Einstein to be a socialist subversive. The FBI spied on him and
compiled a 1,500-page file on his activities. Reading some of these
reports shows what a bunch of dangerous morons Americans can be when
they are frightened. That was 50 years ago and, alas, it is
happening in this country again.
Einstein lobbied strenuously for African Americans, whom he felt
were being disenfranchised of their civil and human rights. He was a
friend of the black actor Paul Robeson and the scholar-activist WEB
Dubois. And when she was barred from staying at a Princeton hotel
following a performance in 1937, Einstein put the great black
soprano Marian Anderson up in his own house. Einstein defended
Robeson and Dubois against McCarthy, and noted that the only place
they were referred to as "niggers" was in their own country.
The exhibit is a testament to a great scientist who hated militarism
and anti-intellectualism. Einstein reluctantly urged FDR to move
forward with the Manhattan Project, but was devastated when the
weapon was used on Japanese civilians. Because of his pacifist and
progressive beliefs, the Daughters of the American Revolution wanted
Einstein kicked out of America! If he were alive today, I believe
Einstein would be horrified and disgusted by the current mad-dog
militarism and pro-stupidity movement that is prevalent in America
now. May God save us!
The Einstein exhibit ends May 29, 2005. Admittance is only $12, and
it's well worth it, even if it has nothing on Hermann Weyl! |
| Beauty
and Truth -- Posted by
wostraub on Thursday, February 17 2005 |
I died for Beauty - but was
scarce
Adjusted in the Tomb
When One who died for Truth, was lain
In an adjoining room -
He questioned softly "Why I failed"?
"For Beauty," I replied -
"And I - for Truth - Themself are One -
We Brethren are," He said -
And so, as Kinsmen, met a Night -
We talked between the Rooms -
Until the Moss had reached our lips -
And covered up - our names -
One of my favorite poets, Emily Dickinson wrote this poem in 1862,
and I have long wondered about its exact meaning. The above version
represents the way she actually wrote it, with those exasperating
hyphens and a tendency to capitalize words that apparently didn't
need any emphasis. Her poems are usually presented in a "cleaned up"
format in modern anthologies of her works, and are sometimes even
almost rewritten.
The poem tells us that truth and beauty are the same thing, and that
they are worth dying for. But it also implies that they can fail --
Dickinson depicts Truth and Beauty lying powerless in the grave.
This bothers me a great deal, because to me truth and beauty, at
least from the scientific and mathematical point of view, transcend
the human experience. I doubt very much if Ms Dickinson thought
about it from that perspective.
The poem reminds me very much of the Old Testament, which describes
our own righteousness as filthy rags fit only for burning. It is
mainly because of this that I see Truth and Beauty in their noblest
aspects as coming from God, who is perfect. In a very real way,
righteousness is truth and beauty because it represents the way
things really are according to God.
It is an unfortunate fact that many of today's premier scientists
are atheists or agnostics, and I have never been able to understand
this. Perhaps they see themselves as the creators of truth and
beauty, rather than the holders of minds that have been awakened by
God. The book of Ecclesiastes notes that wisdom is meaningless
unless God is acknowledged as its true author. I would go so far as
to add that human wisdom is less than meaningless -- quantum
mechanics has given us a glimpse of God's mind, but it has also been
used by humans to build the most awful weapons imaginable.
And maybe this is what Dickinson was trying to tell us. |
| Beauty
and Symmetry -- Posted by
wostraub on Tuesday, February 8 2005 |
Needing a respite from Zwiebach's
string text, I read "Symmetry and the Beautiful Universe," a new
book by Leon Lederman and Christopher Hill. It presents a very
readable introduction to the various types of mathematical
symmetries that give rise to the physical laws we all know and love.
Although the book's authors mention the earth-shattering
achievements of Christina Aguilera, they more appropriately focus on
the work of a far more notable female, the mathematician Emmy
Noether. Noether is the wunderfrau whose 1918 theory revealed the
deep connection between mathematical symmetries (like gauge
invariance) and conservation laws. The book offers a substantive
narration of Noether's life and work and is worth reading only for
this. The authors do not overlook the sad truth that the public is
almost totally ignorant of Noether's achievements as both the
greatest female mathematician who ever lived and the travails she
bravely faced as a Jewish intellectual at the dawn of the German
hate machine in 1933.
Perhaps more importantly for a science book aimed at the general
public, the authors move past the usual grammar-school description
of symmetry (oh look, what a pretty snowflake!) and talk in relative
depth about how physical and mathematical symmetries lie at the core
of our understanding of matter and energy and their interactions.
I was disappointed that the book treats Hermann Weyl primarily as a
historical character who interacted with Noether, Einstein, Hilbert
and others. However, the authors appropriately put local gauge
invariance (Weyl's discovery) at the top of the symmetry list in
terms of importance. There's a nice description of the Higgs
mechanism which, if proved (and it will be, in my opinion), owes as
much to Weyl as Peter Higgs himself.
Unfortunately, the authors neglected to summarize the symmetries and
conservation laws we're currently aware of. To the best of my
knowledge, they consist only of these: translational and rotational
symmetry (conservation of linear and angular momentum); time
evolution and translation (conservation of energy); time-reversal
symmetry (conjugation of charge); space reflection (conservation of
parity); gauge symmetry (conservation of electromagnetic and other
types of charge); and permutation symmetry (invariance of quantum
statistics). There are several other symmetries (like Lorentz
invariance) and conservation laws (like conservation of baryon and
lepton number) that I am unable to place in specific categories like
the others. Gauge invariance was the last continuous symmetry to be
discovered, and that was in 1929. Are there any others? Time will
tell.
All of these symmetries and laws (either singly or in combination)
are absolutely inviolate. When fully understood and appreciated,
they constitute the best proof we have of the existence of a wise
and benevolent God. When we learn math and physics, we learn
something about how God's mind works. When we read the New
Testament, we learn how to live from Jesus Christ. It disturbs me
greatly to know that my country is now being run by a bunch of
dangerous fools who understand neither science nor the philosophy of
Christ. |
| Weyl and
String Theory -- Posted by
wostraub on Thursday, January 27 2005 |
I'm nearing the end of Zwiebach's
book, and it has been rough going at times, but I'm beginning to see
what all the fuss is about. The theory is really quite beautiful (at
least the parts I understand), but some of the math is still very
hard to swallow. It remains to be seen if string theory is anything
more than just a pretty mathematical construct.
I was heartened to find that Weyl's gauge symmetry idea has found a
place in string theory as well. Like the rescaling of the metric
tensor in ordinary 4-space, a Weyl transformation in string theory
comes about by rescaling the Polyakov world-sheet metric $h_{\mu\nu}(\tau\rho)$
with an arbitrary function of the surface parameters \tau and \rho.
The Polyakov action is invariant under such a transformation, so
there must be a conserved quantity associated with this symmetry
(but I haven't read that far yet). What would Weyl and Noether
thought of all this?
I'm very grateful that Zwiebach put this book out. It's clearer than
anything else I've seen, and I highly recommend it as a self-study
text.
|
| Strings
Attached -- Posted by
wostraub on Wednesday, January 19 2005 |
I bought Barton Zwiebach's book
"A First Course in String Theory," and am about a third of the way
through. If you're anything like me (relatively mathematically adept
but a klutz nevertheless), you might want to invest in this book, as
it's just about the most readable text of its kind.
Almost all of the "Popular Science" kind of stuff that has been
written on string theory is a total waste of time -- golly-gee stuff
that is nothing more than handwaving and gushing about tiny
vibrating strings in multiple dimensions. However, the only other
alternative is to actually do the math, which can be excruciatingly
difficult. Zwiebach's book was intentionally written for people in
between, and as far as I can seen he has succeeded admirably.
Could the world really be a ten- or eleven-dimensional place
connecting multiple (or infinite) universes? Is this what Jesus
meant when he said "In my father's house are many mansions ... I go
to prepare a place for you"? The theory seems to be mathematically
plausible, but there also seems to be no way of actually
demonstrating anything experimentally. Our particle accelerators can
now "see" down to about 10^(-18) meter, but this is a long way from
the so-called Planck scale of 10^(-35) meter where those hidden
extra dimensions may live.
At this time, string theory represents the only real candidate we
have for a unification of nature's fundamental forces. One of the
brightest aspects of the theory is that gravity falls out of it
naturally (indeed, it is actually necessary). The noted quantum
physicist Michio Kaku has expressed his hope that one day string
theory (or its modern variant, M-theory) will allow us to write down
a single, inch-long equation that describes how the physical world
works in its entirety. If this happens, I will see it not only as a
fantastic intellectual achievement in its own right, but also as the
ultimate proof of an Intelligent Designer. |
| Just
Reminiscing -- Posted by
wostraub on Thursday, January 6 2005 |
Not long ago, I visited the grave
of Richard Feynman, Caltech physicist extraordinaire, who's planted
in the Mountain View Cemetery right next door to me in Altadena,
California (coincidentally, his grave's about a stone's throw from
the house I was born in). My parents moved here from Missouri in
1944, no doubt to take advantage of the fantastic riveting and
welding opportunities at Lockheed during the war years. The house is
still there, though a tad worse for wear.
I mention this because my father would have been 100 years old on
January 11 of this year, and I guess it's starting to get to me (I
just turned 56 myself, so my own threescore and ten years are about
80% gone). In October of last year, I visited the midwestern house
my father was born in, the streets I had played in during annual
boyhood visits, and other sights and stuff. Earlier, I mentioned my
viewing of Newton's death mask in New York. So, maybe I'm just
feeling a little more mortal than usual.
On the return flight from New York, I stopped over in Missouri to do
some genealogical wandering. My parents and relatives are all from
the northeastern and southwestern parts of the state, and it took me
some time to find all the cemeteries they're buried in. I found them
all, but seeing their moss-covered headstones (some of them go back
to the late 1700s) was yet another reminder of my mortality. To make
matters worse, it rained constantly during my visit, and I was often
ankle-deep in mud. It reminded me of the joke in the PBS Civil War
series about Tullahoma, Tennessee -- "Tulla" is an Indian word
meaning "mud," while "Homa" means "more mud."
But there's good news, too. A side trip to a little German
tavern/restaurant in Springfield, Illinois brought my attention to a
brew called Straub's Beer, which was served with the meal. I don't
drink beer as a rule, but this was an earned exception. Anyway, it
turns out that Straub's operates a regional brewery in St. Mary's,
Pennsylvania, and it was founded by a guy named Peter Straub from
Baden-Wuerttemberg, Germany. Well, that's where my Dad's family is
from! As I can trace my father's family there back to the 1400s, I
have resolved that I will visit that area this year (though I will
try to stay away from the cemeteries). Now, wouldn't it be neat if I
found that Weyl had lived there at one time ... |
| Newton's
Face -- Posted by wostraub
on Wednesday, January 5 2005 |
I stopped by the New York Public
Library recently, which is exhibiting a small but neat collection of
original publications and memoirs by Isaac Newton. "The Newtonian
Moment" includes three copies of Newton's Principia and numerous
scientific notebooks, some of which have handwritten comments and
pre-publication editorial corrections by the man himself. One
describes an experiment he conducted in which he thrust a metal
probe along the side of his eyeball; he noted that it produced some
interesting optical effects!
The exhibit included what appeared to be one of the three original
plaster death masks taken of Newton within hours of his passing in
1727. I could not get over how small and delicate the man's features
were. He was elderly when he died, but he still looked remarkably
like the paintings I've seen of him as a younger man. The mask
faithfully captured facial artifacts like pockmarks, scars and other
defects that he had accumulated during his 84 years on earth.
Looking on Newton's face reminded me that no matter how great one's
achievements may be, things always end up this way. Newton, a devout
Christian whose prodigious religious writings far eclipsed his
extensive scientific output, would likely be amused by all this!
This excellent exhibit ends on February 5, 2005. |
|
She did not forget Jesus!
"Long live freedom!"
