Emmy Noether

One of the great intellectual heroes of the 20th century was German-Jewish mathematician Emmy Noether. She was remarkable in that her accomplishments in the field of abstract algebra emerged despite considerable prejudice against her, first because of being a woman, and second because of her ethnic background. During the 1920s and early 1930s the great mathematician David Hilbert tried to secure her a professorship at the University of Goettingen, but could only obtain for her dozent (lectureship) status because of her gender. When she taught classes, he had to list himself as the official professor. Then in 1933, with the rise of the Nazi regime, an act was passed "The Law of the Restoration of the Civil Service" forbidding those of Jewish background to teach in Germany, unless they had been World War I veterans (a concession made to placate Hindenburg). Noether fled Germany and obtained a position at Bryn Mawr College in the US. She died two years later.

Einstein wrote a beautiful obituary about her in the New York Times:

"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians. Pure mathematics is, in its way, the poetry of logical ideas." (Albert Einstein, New York Times, May 1, 1935)

Today I visited the site of her grave for the first time. It is in a quiet, monastery-like part of Bryn Mawr campus, known as The Cloisters. At first I didn't see the grave marker, as it is very plain and right in the pavement. Here are photos of The Cloisters and Emmy Noether's grave:

Quantum Horror in the Tales of H.P. Lovecraft

In his day H.P. Lovecraft was known purely as a pulp fantasy and horror writer, and only in recent years has the quality of his writing come to be respected. Though he was largely self-educated, it is remarkable how often this American writer of otherworldly horror instills genuine science into his prose.

Take for example his chilling 1933 tale "The Dreams in the Witch House" about a physics student living in an ancient house that used to be inhabited by a witch familiar with higher dimensions and non-Euclidean geometry.

The story has wonderful lines connected with modern physics:

“Non-Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of the Gothic tales and the wild-whispers of the chimney corner, one can hardly expect to be wholly free from mental tension.”

"some circumstance had given a mediocre old woman of the seventeenth century an insight into mathematical depths perhaps beyond the utmost modern delvings of Planck, Heisenberg, Einstein, and de Sitter."

I used the first as the opening quote for my book The Great Beyond, a study of the scientific and cultural history of higher dimensions.

Einstein and Borges

A recent conference in Buenos Aires commemorated Einstein's miracle year of 1905. Interestingly the meeting focused on some of the cultural aspects of Einstein's work, including his influence on Borges. Recordings of some of the conference sessions (in Spanish) can be found at:

El Universo de Einstein

Wellsian Prophecies

From childhood, one of my favorite books has been "Seven Science Fiction Novels," a collection of some of the greatest and most imaginative novellas by H.G. Wells (and indeed some of the best science fiction of all time). The copy I have was published in 1934, bought by a school library, discarded and then brought home by my dad. When I was old enough to read it, it became a source of endless wonder. Each novella was a glimpse of eerie spectres of things to come: Martian invasion. A man who is utterly transparent. Journeys through time to the last days of Earth. Moon creatures living beneath its surface. The collision of a comet. It's all in there, written in a uniquely intelligent style, as if from the vantage point of someone who has stepped out of time and encompassed the past, present and future of all things.

As I delved further into Wells' career, I discovered that his books seem to alternate between prophecies of doom and predictions of an utopia beyond imagination. Sometimes, as in the Time Machine, what seems at first glance to be paradise reveals itself to be an utter nightmare. Other times, it takes complete devastation to clear the ground for a brave new order, as in one of Wells' lesser known works, "The World Set Free." That 1914 tale of destriction and restoration is notable for its prediction of atomic warfare and the first use of the term "atomic bomb"

What I didn't know until recently was that reading that frightening story helped inspire physicist Leo Szilard to work out the details of the concept of a chain reaction himself, become avidly interested in the possibilities and ramifications of nuclear weaponry in the 1930s, and contribute to the theory behind the development of the first atomic bombs in the Manhattan project. Szilard and Einstein wrote a famous letter to Roosevelt about the dangers of the Nazis developing the bomb first, and this led to the Allied effort and ultimately to the horrors of Hiroshima and Nagasaki (which the theorists had emphatically absolutely nothing to do with--it was strictly a presidential and military decision under Truman).

I'm currently reading a fascinating and important book, called Doomsday Men, written by the historian of science, reviewer, Einstein biographer, photographer and blogger PD Smith. I've been delighted to discover in his new work ample references to Wells and science fiction, woven into a riveting chronicle of how superweapons capable of mass destruction were pondered, developed and justified. Talk to any child about the idea behind nuclear weapons and he or she is likely to recoil in horror, and seriously wonder why any madman would consider building such devices. Yet in the 20th century the concept of a "war to end all wars" stimulated thoughts amongst serious-minded people that the existence of weapons too horrifying to use would bring about world peace. And at least some of this, as Smith writes, can be traced back to Wells and other writers who imagined that a world after devastation would be one of wise leaders guiding the masses to peace.

For those of you who recall the tumultous days of the 20th century that preceded the current Golden Age (as so we're told by the rock band U2, at any rate, who go on to say that "gold is the reason for the wars we wage), or even for those of you too young (or busy) to remember the 20th century at all, I suggest that you familiarize yourself with the past so that we're not doomed to repeat it. As you can probably tell, I highly recommend Doomsday Men, now available in the UK (through Amazon.co.uk. for example):

Doomsday Men

It will also be published by St. Martin's Press in December.

Either/Or

Written more than a century and a half ago, but possessing an honest and direct style more characteristic of modern works, Soren Kierkegaard's Either/Or is for me one of the best expressed statements of the stark choices in life. For those of you unfamiliar with the work, it is written in two parts, with each half purportedly written by a different author (but both actually penned by Kierkegaard himself). The first half, the "Either," beautifully describes the pleasures and anguish of the "aesthetic life:" a world of music, drama, art, and seduction, but also of chronic boredom and depression. The second part, "the Or," supposedly written by a married physician, succinctly argues for the pious and virtuous life of good clean hard work. It's written in the form of letters to the first chap.

The most famous sections of the book are the Diary of a Seducer (a chronicle of his meticulous wooing and subsequent abandonment of a young woman) and the Diapsalmata, a collection of fragmented thoughts about the boredom and restlessness in life -- what continuously drives the aesthetic appreciator to seek new forms of entertainment and stimulation. We realize what a futile quest the poor fellow is going through as nothing seems to satisfy him: "I do not care for anything," he writes. "I do not care to ride, for the exercise is too violent. I do not care to walk, walking is too strenuous. I do not care to lie down, for I should either have to remain lying, and I do not care to do that, or I should have to get up again, and I do not care to do that either. Summa summarum: I do not care at all."

So if the aesthetic side seems painful, then what about the ethical? Less stressful and easier on the heart, one surmises. However, while the second half seems the epitome of common sense it seems to lack color somehow.

Perhaps this dichotomy is a bit artificial, but in my mind Kierkegaard well depicts the sense of wonder about the roads not taken in life.

The Mystery of Dark Energy

In May 2007, I went to an interesting conference in Canada called Origins of Dark Energy. Dark energy is the part of the universe's content driving it to expand outward at a faster and faster pace--a universal acceleration discovered in 1998. No one knows what causes this effect. Brian Schmidt, one of the co-discoverers of the phenomenon, pointed out the enormously difficulties and costs involved in trying to unravel this mystery. To pin down this effect requires recording the energy released by supernovae billions of years in the past.

The simplest model of dark energy involves adding what is called a "cosmological constant" term to Einstein's equations of general relativity. This is a factor that was proposed by Einstein himself as an attempt to stabilize the universe, but later abandoned by him when he realized that the universe was expanding. Inserting that factor again leads to a kind of cosmological "anti-gravity." It is unclear, however, what physically motivates the inclusion of the term.

Dark energy should not be confused with dark matter. While both are invisible, the former pushes things apart and the latter helps glue them together.

Renegade Astronomer

In April 2007, I had the pleasure of meeting innovative astronomer Geoffrey Burbidge, one of the "B^2 HF" group that revolutionized thinking about the chemical elements some 50 years ago. Back then, some scientists were convinced that *all* of the elements were forged in a hot Big Bang. Others, such as the Burbidges (Margaret and Geoff) as well as Fred Hoyle didn't believe in the Big Bang. They favored a "steady state" universe that exists eternally. (In fact the term "Big Bang" was originally a put-down of the theory by Hoyle!)

The Burbidges, Hoyle and William Fowler set out to find an alternative mechanism for element production. Brilliantly, they deduced a process by which the higher elements are forged in the fiery cauldrons of stellar cores, then released in catastrophic supernova explosions. Thus, the oxygen we breathe and the carbon we burn were once in the belly of a long-gone giant star.

Geoff Burbidge still believes in a modified version of the steady state model, making him part of a dwindling minority amongst astronomers. He cautions an open mind toward cosmology, and notes that the Big Bang theory still has many gaps--such as the 96% of the matter and energy invisible to astronomical detection. Although few scientists agree with his solution to the great cosmological dilemmas, it is admirable that Burbidge is unafraid to voice his views, and serves as an exemplar of diversity of thought.