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Who Was Hermann Weyl?
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Weyl's Spinor and Dirac's Equation
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Weyl v. Schroedinger
Why Did Weyl's Theory Fail?
Weyl and the Aharonov-Bohm Effect
Weyl's Scale Factor
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Riemannian Vectors in Weyl Space
Introduction to Quantum Field Theory
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There Must Be a Magnetic Field!
Kaluza-Klein Theory
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Uncommon Valor

Sophie did not forget Jesus
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262728 visits since 11/1/2004.

My work always tried to unite the
Truth with the Beautiful, but when I
had to choose one or the other, I usually chose the Beautiful.

Hermann Weyl

I died for Beauty, but was scarce
Adjusted in the tomb,
When one who died for Truth was lain
In an adjoining room

Emily Dickinson

Hermann Klaus Hugo Weyl (1885-1955). German mathematical physicist. In 1918, proposed an early form of gauge symmetry in an attempt to unify electrodynamics and gravitation. Subsequently applied a similar approach to quantum physics and discovered what is today considered one of the most profound and beautiful concepts in modern physics -- the principle of gauge invariance.

Shortly after Einstein announced his theory of general relativity (gravitation) in November 1915, Weyl began an intensive study of the theory's mathematics and was soon publishing related scientific papers dealing with its physical applications. In 1918 Weyl published his book Raum-Zeit-Materie (Space-Time-Matter), which provided the first fully comprehensive analysis of the geometric aspects of the theory and its relationship with spacetime physics. One of the topics covered in the book was Weyl's idea that gravity and electromagnetism might both be derivable from a generalization of Riemannian geometry, the mathematical basis from which Einstein had developed his relativity theory. Weyl's idea was based on a new mathematical symmetry that he called gauge invariance.

I came across Weyl's book in 1975, but it didn't impress me very much because I didn't know general relativity. However, in the summer of that year I stumbled across Misner-Thorne-Wheeler's massive Gravitation during a one-week work assignment in the microscopic rural town of Lone Pine, California (which then had a population of perhaps 500 people). Miraculously, the town's tiny public library somehow had this book, which is now regarded as a classic graduate text on general relativity. I checked out the book and brought it back to the hotel room to read in the off-hours. The book took immediate and total possession of me, and motivated me to learn everything I could about general relativity. (I spoke with co-author Kip Thorne about this in 1994, and he was quite amused to learn where one of his books had ended up.)

But Gravitation is not an easy read, and I had to look for more introductory texts. I soon came across Adler/Bazin/Schiffer's Introduction to General Relativity, which besides being easier had a chapter on unified field theory, including Weyl's 1918 theory of the combined gravitational-electromagnetic field. For whatever reason, the theory's mathematical beauty absolutely fascinated me. I had known about local and global phase invariance from my studies of quantum mechanics, but I was not aware that Weyl's theory was the origin of this powerful symmetry principle in quantum physics.

I have since read all of Weyl's books and many of his papers. Although today I believe that my interest is now based more on an appreciation of modern gauge theory (easily the most profound and beautiful concept of physics), I credit Weyl for having initiated the idea in 1918 and for his subsequent (1929) seminal application of the idea to the then still-developing quantum theory.

In his 2002 biographical memoirs, the great contemporary mathematician Sir Michael F. Atiyah praised Weyl as the discoverer of the gauge concept and as the driving force behind the current emphasis of gauge theories on modern theoretical physics:

The past 25 years have seen the rise of gauge theories--Kaluza-Klein models of high dimensions, string theories, and now M-theory, as physicists grapple with the challenge of combining all the basic forces of nature into one all embracing theory. This requires sophisticated mathematics involving Lie groups, manifolds, differential operators, all of which are part of Weyl's inheritance. There is no doubt that he would have been an enthusiastic supporter and admirer of this fusion of mathematics and physics. No other mathematician could claim to have initiated more of the theories that are now being explored. His vision has stood the test of time.

Weyl was an exceptionally gifted mathematician and physicist, but he was also a highly cultured man in the classical German tradition. He studied and wrote extensively on philosophy and was a serious student of German poetry and literature. His mathematical writing style could be exceedingly obtuse, but his other writings reveal a genuinely warm person who truly understood the human condition. Weyl was also very human himself; he could be overly thoughtful and cautious, often to the point of being unable to take action or make even basic decisions, and sometimes with the result that he became physically incapacitated. He was a devoted and loving husband and father, yet he could also be persuaded to stray, in accordance with the surprisingly liberal attitudes of post-World War I Weimar society.  

This website is my feeble attempt to document (and in many cases expand on) Weyl's ideas and thoughts on gauge symmetry in a manner that will be accessible to anyone with a basic understanding of calculus. Not a lot has been written about the original theory's underlying mathematics, and I wanted to provide a fairly detailed and complete mathematical description for those who want to learn about Weyl's ideas and to appreciate the beauty of his gauge theory (I'm even of the opinion that much of Weyl's work can be understood and appreciated at the high school/beginning university level). As this site progresses, I will also include discussions of other topics in mathematical physics (as well as some related scientific philosophy) which exhibit a similar mathematical beauty and elegance.

Exaggerating Eddington — Posted Thursday, 29 January 2015

On 29 May 2014 I posted an article on the 2009 BBC film Einstein and Eddington, which dramatized Eddington's 29 May 1919 solar eclipse expedition to Principe, an island on the west coast of Africa. I included a screen capture of the "evidence" of starlight deflection around the Sun (right photo, above), thinking it was an enlargement of one of Eddington's few good photographic plates (shown on the left).

This morning I learned from Delft University's Leo Vuyk that the photo I posted is a probably a fabrication created by the filmmakers to exaggerate the deflection effect. I've actually seen the real photographic plates, which show only a few stars in the Sun's field along with tiny deflections, and I have a several good reproductions of the photos, but the one from the film is so patently false that I'm ashamed I didn't suspect "artistic license" from the filmmakers from the beginning.

The starlight deflections that Eddington actually measured were indeed tiny, and his results just barely proved out Einstein's general theory of relativity (later, more careful photographic examination showed that Einstein's gravity theory was indeed upheld). As this article on the film notes, Einstein was a relative unknown prior to 1919, and Eddington's Principe expedition made Einstein a worldwide scientific superstar.

It's still a good film, and noted Shakespearean actor David Tennant (Hamlet) is excellent as Eddington. But I promise to be more careful in what I post in the future.
Ants — Posted Wednesday, 28 January 2015
When I was around ten years old I became fascinated with ants. Ants were everywhere in my world of 1959, my back yard in particular, where I would watch colonies of large black ants (friendly and harmless) and red ants (aggressive and stinging), always separated by a safe distance, as if they had polite, formal, established borders beyond which neither species ventured beyond. In view of their behavior, I often wondered about their intelligence — they were so wonderfully coordinated and ordered — and a few years later I actually wrote a short story about how ants had developed a rudimentary religion. I actually preferred the red ants, even though I got stung many times over the years of observing and playing with them.

I moved on, but in high school I had a friend (Dan E.) who was nuts about ants, and he resolved to major in entomology when he got to university. Entomology, the study of insects, is a lot broader than the study of ants (myrmecology), but ants are probably what factored in my friend's decision for a college major, which eventually took him to the University of California at Davis (he was a lot smarter than me — I could only get into Cal State Long Beach). But he ended up with a PhD in art history, of all things, while I left chemistry for physics and engineering, but that's another story.

But the real expert on ants today is undoubtedly E.O. Wilson, the noted Harvard entomologist, sociobiologist, evolutionary biologist and biodiversity advocate, whose latest book is The Meaning of Human Existence. That's a rather ambitious (or even pretentious) title for an ant expert, but quite appropriate for a brilliant 85-year-old scientist whose passions and expertise stretch far beyond anthropods. I only recently purchased the book and, having read only the chapters on religion and free will thus far (though it's a short book), I cannot predict how much success it will have with the general public. But what I have read makes a lot of sense.

Wilson ties much of the meaning of human life to religion (which he views as a colossal mistake), specifically humans' reverence regarding deific creation myths and tribalism. As Wilson notes, there are many creation stories, no two of which can be simultaneously correct, but it goes without saying that the universe did indeed somehow come into being. Of the twenty or so "eusocietal" organisms that have arisen on Earth — the ones that form caring, long term, multi-generational familial bonds — humanity is the only one that became self-aware. Yet even intelligent sentience was not enough to protect that single organism from self-deceit. Wilson believes that tribalism resulted purely as an evolutionary survival trait, especially when regional human populations grew to the extent that cut-throat competition became more advantageous to survival than cooperation, but humans even today do not recognize the fact that tribalism carries with it the same innate barbarity that its altruistic alter ego, religion, invariably has failed to correct.

Wilson's book tries to answer what meaning, if any, the emergence of sentient human life has on the totality of terrestrial existence, if not the universe itself. As noted earlier I have not read the entire book, but from the book's reviews I gauge that Wilson has not been very successful. It's a subjective issue, after all, one that to date no one has been able to overcome. To even pose the question of the meaning of human life is not only ambitious but probably self-defeating — every writer's effort is doomed from the start.

In my own life of rather shallow philosophical wandering I have come to liken humanity as a slave of ancient Roman times who finds himself permanently shackled to a Roman warship, ceaselessly pulling the oar while being both whipped and fed. It's a hopeless situation, true, but he still manages to find hope in the form of a miraculous release (recall the story of Ben-Hur) or, that failing, in the belief of an eternal afterlife of heavenly bliss. From that perspective Wilson believes mankind has utterly failed itself by retreating into the habit of wishful thinking, which to this day has overcome all attempts, including rational science, to defeat it. It's a resilient fall-back position because it requires no education, experience, logic or even intelligence to grasp it, and the fact that wishful thinking — like religion itself — cannot be disproved adds to its effectiveness.

I will finish Wilson's book, but I'm not optimistic that I will really learn anything from it.
Religion is regarded by the common people as true, by the wise as false, and by the rulers as useful. — Lucius Seneca, Roman statesman, 5 BCE - 65 CE
Science in the Media — Posted Monday, 26 January 2015

Numerous European readers have written to express their utter disbelief that American voters have placed science in the hands of rabid congressional science deniers and incoherent religious fundamentalists, many of whom believe the Earth is only 6,000 years old. I tell them that you always get the government you deserve. Sadly, the the same appears to apply to humans and their planet, which is getting hotter and deader as we speak.

(Thanks to Tom Tomorrow at
Daily Kos)
Math in the Media — Posted Friday, 23 January 2015
The movies The Theory of Everything and The Imitation Game are getting rave reviews from critics and viewers alike right now, and while it's neat to see the public getting interested in such things, the stories told in the films leave much to be desired.

Last night I saw The Imitation Game with Benedict Cumberbatch as the famous Bletchley Park mathematician Alan Turing, who was primarily responsible for cracking the seemingly impenetrable German Enigma cipher during World War II. The film of course focuses on Turing's homosexuality and his efforts to decipher Enigma, and what I thought was best about the film was how it related Turing's sexual "otherness" to how he approached mathematics — his thinking processes were quite different from those of the other (quite talented) Bletchley mathematicians, and this is certainly what gave Turing the edge. It rather reminded me of how people have described Caltech physicist Richard Feynman, whose thinking was "orthogonal" to everyone else's (there's being smart and there's being a genius, but some geniuses are just off the scale completely). In that regard, Turing and Feynman shared a true commonality.

However, as a film it doesn't match the acting, drama and storyline of 2001's fictionalized but highly underrated Enigma, with Dougray Scott and Kate Winslet portraying essentially the same characters (although Scott's character is not gay in the film, it's obviously based on Turing). Enigma's last scene is quite moving emotionally, and the music is heartrendingly beautiful (I often listen to the soundtrack while at the gym). Sadly, it was composer John Barry's (Midnight Cowboy, Dances with Wolves, Out of Africa) last film score. Enigma also has numerous scenes which explain how the Enigma code worked, along with scenes that attempt to explain the sheer beauty of mathematics — two important aspects of Bletchley Park that are completely lacking in The Imitation Game. Plus, in Enigma you can watch them manipulating an actual German Enigma machine, owned by the movie's co-producer, Mick Jagger.

The Theory of Everything is well acted, but the true sense of what Stephen Hawking accomplished mathematically in his problematic life is just not there. It rather reminded me of some episodes of Cumberbatch's Sherlock series, in which his character is shown rapidly going through logical combinatoric exercises that I found confusing and even pretentious. In the end, the purpose of The Theory of Everything seems to be to simply entrance the viewer with Hawking's brilliance without trying to explain what he actually did.

Still, these two films are far better than 2013's Gravity and last year's Interstellar, both of which were highly rated but relied more on fancy computer graphics than on story or science. Noted Caltech physicist Kip Thorne served as science advisor on Interstellar and he absolutely insisted on scientific accuracy (often to the annoyance of director Chris Nolan), but I found the film to be highly improbable on a number of questionable scientific points, not least of which being that I don't believe wormholes exist (Nolan also considered faster-than-light travel as an alternative, but Thorne quickly quashed that one). Meanwhile, I found Gravity to be just so much computerized eye candy (not to mention my opinion that actors Sandra Bullock and George Clooney are also used as such), while Bullock's miraculous survival at the end belies what would have certainly been a quick death for all the astronauts if it had been real life.

But again, it's great to see so much science and math on the big screen today.

The last scene of Enigma. It's Trafalgar Square in London, after the war, and Tom (Dougray Scott) is waiting for Hester (Kate Winslet). In the crowd he spots the erstwhile love of his life, Claire (Saffron Burrows), the British spy who broke his heart. But things have changed since Tom and Hester left Bletchley Park, and for the better.

(© Manhattan Pictures International, 2001)
Today's Quote — Posted Wednesday, 21 January 2015

Chuck Easttom is a computer security consultant and professor at Collin College in Texas. (He should have added "semi-nomadic," and the Old Testament was actually written in the middle and late Iron Age, but you get the point.)
Scientific Conservatism? — Posted Sunday, 4 January 2015
Harvard history professor Naomi Oreskes' recent New York Times article Playing Dumb on Climate Change talks about the dangers of conservative scientific thinking — conservative in the sense that even when evidence is overwhelming, scientists are often still loathe to accept a rational, evidence-based conclusion. This type of conservatism, she asserts, is making the threat of anthropomorphic climate change seem less dangerous than it really is.

Oreskes provides a very understandable definition of Type 1 and Type 2 errors: scientists make a Type 1 error when they conclude that an effect is real when it is not, and they commit a Type 2 error when they claim an effect is unreal when it actually exists. Whether scientists make either error has a lot to do with the incidental consequences of making a bad claim; thus, "extraordinary claims require extraordinary evidence" is the rule, and it is better to miss a real effect, since their careers will suffer less. And when scientists do make an extraordinary claim, they like to back it up with as much statistical support as they can muster; as Oreskes explains, this is typically done using "confidence limits." A statistical confidence limit of 95% means that the odds that a claimed effect is due to random chance alone is 5%, while that of a 99% CL is only 1%.

In the case of global climate change, Oreskes notes that atmospheric scientists already have all the physical and statistical evidence they need to confidently demand political and industrial change regarding human activities. So why don't they? Her answer:
Why don't scientists pick the standard that is appropriate to the case at hand, instead of adhering to an absolutist one? The answer can be found in a surprising place: the history of science in relation to religion. The 95 percent confidence limit reflects a long tradition in the history of science that valorizes skepticism as an antidote to religious faith.
Oreskes also notes that
Moreover, while vigorously denying its relation to religion, modern science retains symbolic vestiges of prophetic tradition, so many scientists bend over backward to avoid these associations. A vast majority of scientists do not speak in public at all, and those who do typically speak in highly guarded, qualified terms. They often refuse to use the language of danger even when danger is precisely what they are talking about.
With regard to what many scientists rightly consider the existential threat of global warming, we would seem to have a case of scientists choosing to "scrootch back" in the corner of the debate room either to avoid being noticed, to avoid a classic Type 1 error, or to avoid offending religious fundamentalists, who need offer no evidence whatsoever of any scientific claims they choose to make.

The Constitution talks about the tyranny of both the majority and the minority, but it implicitly assumes rationality of thought behind whatever issue is being discussed or whatever law is being implemented. As Oreskes implies in her article, scientists are committing a dangerous act by underestimating the threat of climate change out of conservatism, while the religious crowd is doing the same by denying it for totally irrational reasons.
Strange Bedfellows — Posted Saturday, 3 January 2015

Since the 1930s, George Washington University has convened a series of informal annual conferences on theoretical physics, each focusing on a specific topic. Hermann Weyl, then at the Institute for Advanced Studies in Princeton, was an invited attendee of several of these conferences. In November 1947, the topic at hand was gravitation and electromagnetism, so of course Weyl was there. Here's the group photo, with the 62-year-old Weyl seated at the left end. Also prominent in the photo are Edward Teller, John A. Wheeler, J.R. Oppenheimer and Richard Feynman, all fresh from Los Alamos, where they developed the atomic bomb. At this conference they discussed more mundane issues like quantum electrodynamics and unified field theory. The man with the enormous cranium standing fifth from the left is David R. Inglis of the University of Massachusetts. A nuclear physicist and ardent weapons-ban advocate, he seems to be glaring at Edward Teller (sitting next to Weyl), who was arguably more responsible for the widespread proliferation of nuclear weapons than any other scientist. It was also Teller who infamously betrayed Oppenheimer (seated, right center), a noted pacifist, thus destroying his career.

Much thanks to David Marans, the author of Logic Gallery, for alerting me to this photo. (David welcomes comments and suggestions for his online book. He can be reached at davidjan43@aol.com.)
Generalizing General Relativity — Posted Thursday, 1 January 2015
This year marks the 100th anniversary of Einstein's general theory of relativity (gravitation), and I still find it remarkable that efforts to generalize the theory remain in vogue to this day. The non-Riemannian theory of Hermann Weyl (1918) was the first of many such theories, notable today if only for the fact that its gauge aspects and application to quantum physics a decade later became the foundation for all modern quantum theories. Einstein himself resorted to non-Riemannian formalisms in his own 30-year-long effort to unify gravity with electromagnetism and quantum physics. And yet, sadly, the hoped-for unification of gravitation and quantum mechanics today remains as elusive as ever.

Ten years after Einstein announced his theory, mathematician Luther Eisenhart of Princeton University published an interesting book on non-Riemannian geometries, which to this day represent perhaps the oldest, purely-classical approach to generalizing the theory. Such geometries necessarily involve vector and scalar additions to the Riemannian connection term \(\Gamma_{\mu\nu}^\alpha\) and, while at times fascinating, the approach is best summed up by the noted physicist and Einstein biographer Abraham Pais, who wrote "the use of general connections means asking for trouble." Indeed, there seems to be no end of problems with generalized connection coefficients, which at the very least invariably wipe out many of the cherished symmetry properties of the Riemann-Christoffel tensor \(R_{\,\,\mu\nu\lambda}^{\,\alpha}\) while providing no discernible benefits.

Weyl's 1918 theory arguably came closest to describing a consistent, all-encompassing theory (although it involved only gravity and electromagnetism), but his death in 1955 preceded a perhaps more lucid approach to generalization, which was the 1961 theory developed by Princeton's Carl Brans and Robert Dicke, who used a combination scalar-tensor approach within a wholly Riemannian geometrical framework. While this avoided the non-Riemannian pitfalls previously alluded to, it was rather ugly and unable to successfully reproduce the predictions made by Einstein's original theory. Over the ensuing decades the Brans-Dicke theory itself has been generalized by numerous researchers to include scalar and spinor quantum fields, producing a variety of even uglier theories that have yet to produce any meaningful predictions.

As many people noted in 2014, scientific progress seems to be stuck in a rut. One hundred years after Einstein gave us his profoundly beautiful theory of gravity, there has been little real progress made on unified field theory or on any theory that describes gravity within the equally beautiful and profound mathematical formalism of quantum physics. Despite the ongoing brilliant work of scientists like Edward Witten, Stephen Hawking and others, we're no closer to a truly comprehensive description of Nature than we were in the days of Weyl and his fellow generalists. Think about that for a minute — scientists have routinely cracked the mysteries of Nature, often only after long and arduous searching, but in the case of gravity all of man's ingenuity has yet to provide any real progress. We still do not know if gravity involves extra dimensions, extra forces, strings, branes, supersymmetry, quantum loops or other fanciful notions, while the Large Hadron Collider, which supposedly disclosed the Higgs boson (or something very like it) in 2012, provided no useful clues.

Gravity, undoubtedly the first of Nature's forces that mankind became aware of (often painfully), has turned out to be far more mysterious and elusive than we might ever have imagined.
Exodus: Believe the Lie — Posted Thursday, 1 January 2015

In the new blockbuster movie Exodus: Gods and Kings, Moses is only forty (not eighty) and there are only 600,000 fleeing Israelites, not millions, but faithful viewers will still think they've witnessed actual history. Thanks to superior computer-generated imagery, the Exodus myth lives on.

Let us go way back in time, to about 1250 BC, when Egypt's 19th Dynasty, under the reign of Pharaoh Ramses II, ruled much of what we today call the Middle East, including all of the land known as the Levant (Israel and its immediate neighborhood). It included all of Egypt, portions of Nubia (Sudan) and Libya, the entire region of Canaan (what is today Israel, the West Bank and areas to the immediate west), and all the way up to the border of what is today called Lebanon, Syria and Jordan. The lands outside of Egypt were controlled by garrisons of armed Egyptian soldiers, numbering in the tens of thousands, overseeing vassal states runs by local puppet governors and kings, all beholden to Pharaoh. Ramses, the greatest pharaoh of all time, ruled Egypt, economically and militarily the most powerful country in the world, and was a ruler to be reckoned with.

Impose now if you will the story of several million Israelite slaves held in Egyptian bondage, somewhere in the eastern Nile Delta, where a great city known as Pi Ramses (House of Ramses) was reportedly constructed by forced labor. According the the Old Testament Book of Numbers, 603,550 Israelite men revolted under the leadership of an Israelite-Egyptian noble called Moses, who had received the call of God to lead his people out of Egypt into the Promised Land, which we know today as Israel and its immediate environs. The Israelite men took their wives, children, parents and others, numbering certainly no less than 2 million souls, along with livestock and plunder taken from their Egyptian captors, and headed out into the western Sinai, by way of the shallow Sea of Reeds (not the Red Sea). According to the Bible, they avoided a more direct route along the Mediterranean coast, no doubt because of the Egyptian garrisons posted there; undoubtedly, a smart move on Moses' part.

Some 40 years later, with Moses dead, the Israelite general Joshua took what was now a large army into the land of Canaan, west of the Jordan River. They conquered the land, and by the direct mandate of God they killed every living thing they encountered — men, women, children, infants, slaves, livestock, fruit trees and crops.

Question: What was Egypt doing while all this was going on? Pharaoh Ramses II was the most powerful ruler in the world at the time, and it seems doubtful that he would have restrained his armies while Joshua marauded the Levantine countryside, which was under Ramses' reign and protected by legions of Egyptian soldiers. The Bible gives no account of Egypt's reaction; indeed, it doesn't even mention Egypt at this point in time, nor does it identify the name of the reigning pharaoh. And indeed, in the last several books of the Hebrew Torah, also known as the Pentateuch, Egypt doesn't seem to even exist.

Fast forward to today. Israel occupies territories granted to it in accordance with the Partition Plan for Mandatory Palestine (a follow-up of the British Mandate for Palestine, first formulated in 1922 and implemented in May 1948). Arab countries adjacent to the region immediately went to war with Israel's army, which by some miracle happened to exist at the same time for just such an eventuality (the British, French and others supplied arms to Jewish guerrillas prior to 1948, but this hardly explains how they could have defeated half a dozen Arab states without help from those same countries). Israel won that war, and others that followed over the years, and today it continues to occupy disputed territories claimed by Palestinians displaced by the wars and by Israel's continued practice of seizing and building on what had historically and legally been Palestinian land (ultra-orthodox Jews, and many orthodox Jews, feel that Israel is still being cheated — according to the Old Testament, God granted Israel much more land than its occupies today, and they continue to agitate for greater Israeli territorial aggression).

More recently, the Palestinian Authority was denied nationhood by the United Nations, so today it applied for membership with the International Criminal Court (ICC), the Netherlands-based international judiciary that oversees crimes against humanity, war crimes and crimes of aggression, largely independent of the United Nations. To date, the United States, Israel, China, India and about 16 other nations have refused to join the ICC, primarily because of past or ongoing practices that would render those countries in violation of ICC humanitarian statutes. The Palestinian Authority is unquestionably guilty of war crimes and crimes against humanity, primarily against Israelis, so the Authority's joining with ICC would presumably help bring judgment against itself. But it could also petition the ICC to judge Israel for the same crimes, including crimes of aggression. It will be interesting to see how this all works out, since the United States and Israel have vowed to impose harsh sanctions against the Palestinians for seeking justice in the way they have.

But the upshot of all this is the fact that Israel's existence today is really based on the Exodus myth, which has never been substantiated archeologically, scientifically or even logically. I have written extensively on this topic elsewhere, but my conclusions are hardly my own, being backed up by many renowned archaeologists, scholars and investigators, notably Donald Redford, Israel Finkelstein and Neil Silberman. Even the noted Los Angeles Rabbi David Wolpe has admitted to his congregation that the story is allegorical myth, at best a metaphor symbolizing God's relationship with the Israelites, and not to be taken literally. To be brief: the Exodus story never happened.

Unfortunately, the Exodus story became the signature event of the Jewish faith, when the Pentateuch was penned around 600-800 BC, and the associated Passover observance has since become a sacred Jewish tradition, recognized even by Jesus of Nazareth. As is well known, his observance of the traditional Passover meal occurred during his tragic last visit to Jerusalem.

But it is far more tragic that the Exodus story is also the basis for Israel's presumed right to all the land it can get its hands on, which, with a population already at 8 million crammed into an area the size of New Jersey, will inevitably spur internal demands for more space (the Germans called it Lebensraum). The reason a two-state solution with Palestine will never occur is not because of political intransigence, religious differences or decades-long ethnic hatred, but because a fictional story written some 2,600 years ago has been taken literally by billions of people who should know better. It is ironic that the Palestinians, being predominantly Muslim, also believe in the Exodus tale, but I fear they can't see that the joke is on them.

America has a myth, too, along with its own Lebensraum. Called Manifest Destiny, it was employed in a similar manner to wrest land and resources from a supposedly savage race of inferior people who were also exterminated, and again God was used as the excuse. Acknowledgment of this atrocity was never formally made, much less any offer of reparations, but the few survivors were at least granted small allotments of unwanted land (provided nothing of value was ever later discovered there, in which case the vanquished were moved again).

Assuming the Palestinians are not exterminated outright by Israel, I wonder where they'll end up, as they sure as hell won't get their own nation as things stand today. God does work in mysterious ways, doesn't he?

The mummy of Ramses II (the Arabic pronunciation is rahm-SEIZE), born 1303 BC and died August 1213 BC, age 90. He ruled Egypt for 66 years, siring some 100 children along the way. I saw the guy a few years ago in his glass enclosure at the Egyptian Antiquities Museum in Cairo, and I wondered if this was the pharaoh who faced off with Moses. But no — Moses probably never existed, but this man certainly did.