2005-2007 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 V^μ is given by L² = g_μνV^μV^ν, then Weyl's theory basically says that under parallel transport this goes over to 2LdL = g_{μν α}V^μV^νdx^α or dL = A_μdx^μL, where g_{μν α} is the covariant derivative of the metric tensor and A_μ is the electromagnetic 4-potential. However, I have not been able to find a symmetric connection term Γ^α_μν (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 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 th