Monday, July 30, 2007
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:
Wednesday, July 18, 2007
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.
Sunday, July 1, 2007
El Universo de Einstein
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):
It will also be published by St. Martin's Press in December.
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 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.
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.
Explosions and magnet problems likely due to math errors have delayed the opening of the long-awaited Large Hadron Collider (LHC) in Switzerland. We'll need to wait a bit longer to see if the Higgs particle, supersymmetric companion particles and a number of other theoretically predicted collision byproducts turn up.
I was very much impressed by his keen memory of certain events of the 1930s through the 1950s, particularly his interactions with Einstein who was his neighbor. Einstein was kind to Wheeler's children and later to Wheeler's students. For one of the first relativity classes ever offered, Einstein offered a friendly hand. In 1948, after Wheeler's student Feynman proposed Quantum Electrodynamics, Wheeler recalled how Einstein was dubious.
Wheeler's sense of humor and gracious attitude were readily apparent. It was easy to see why he was so beloved by his students. At one point I commended him for his book (with Thorne and Misner) Gravitation. He proceeded to show me a copy in Chinese, and dryly commented that I could use the book to learn that language.
He showed me some of the photographs of him with certain notables such as Yukawa, and explained his current interest in discerning the "why" of life. What a remarkable figure in physics, who contributed so much to modern thought.
Shadows of Reality
The Fourth Dimension in Relativity, Cubism and Modern Thought
By Tony Robbin
Reviewed by Paul Halpern
In the early decades of the 20th century the world of art underwent a radical - and some might say anti-aesthetic - transformation. Banished were the bathers of Renoir, the landscapes of Cézanne, and the sensuous tropical vistas of Gauguin. In their place, Picasso, Braque and other members of the Cubist movement brought to life a new kind of artistic creation - sewn together like Frankenstein's monster from disparate images of the human form. Bizarre shapes and arrangements were suddenly de rigueur; postcard panoramas were out.
In Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, New York artist Tony Robbin dissects the Cubist revolution and reveals the mathematical method underlying its juxtapositions, bringing to light how Picasso, Braque, et al., derived their subversive style from geometric discoveries of the previous half-century. The Cubists, Robbin explains, were trying to view all facets of an object at once, as if simultaneously illuminated from many different vantage points - even the inside. This could be achieved only by transporting the viewer to a higher dimensional perch - or at least presenting the illusion of such.
With deft strokes piled layer upon layer, Robbin portrays how the concept of the fourth dimension grew increasingly tangible and relevant over the years. He shows how it began in the early 19th century as the abstract notion that length, width and height could be supplemented by an unseen perpendicular direction. The mathematician August Möbius, for example, speculated that a left-handed glove could flip into a right-handed glove if flung over something like a four-dimensional fence.
All this remained ethereal until visionary geometrists, such as Washington Irving Stringham and Victor Schlegel, showed how polytopes - three-dimensional representations of four-dimensional geometries - could be constructed. These representations are the equivalent of using flat X-ray scans to model three-dimensional skeletal structure.
The Cubists, Robbin argues, developed their strange compositions by applying such mathematical methods to portraiture. He envisions Picasso painting works such as Seated Woman With a Book, with texts about four-dimensional geometry literally in view.
Picasso's revolution paralleled bold changes in physics, initiated by Russian-German mathematician Hermann Minkowski in response to breakthroughs by Einstein. In 1908, Minkowski proclaimed the fusion of space and time into a single, four-dimensional structure called spacetime. In his synthesis, yardsticks and clocks measure different aspects of the same thing. The power of this discovery inspired Einstein and others to try to unite all of nature in a five-dimensional amalgam.
Einstein's ultimate quest, though unsuccessful, has inspired many other scientists to try their hand at a multi-dimensional "theory of everything." Robbin methodically shows that projective geometry has been the common principle connecting all these endeavors - linking fleeting shadows with a more solid truth. Illustrating each of his major points with his own colorful designs, rendered through state-of-the-art graphics, the avant-garde designer makes a compelling case.
So there you have it. Art, math, physics, history and computer graphics all in the same book. This splendid volume is an outstanding contribution to all these subjects by an innovative artist who himself is part of the story.
The Tramp, the Professor and Frankenstein's Brain Surgeon
The past century has been an era of labyrinthine complexity: a time of devastating warfare, massive population displacement, rapid advance in technology and tremendous political upheaval. With the century barely in its teens, World War I, one of the most destructive wars in human history, brought on the decimation of the major continental European Monarchies and led to the chaos of the Russian Revolution. The years leading up to World War II were hardly more placid; rather, they were times of unprecedented economic turbulence and dictatorial conquest. In more recent times humankind has witnessed even more terror and destruction, confusion and despair.
In the twentieth century the world was set aflame. The carcasses of the nineteenth century ideals of linear progress, rigid social order and scientific determinism all but vanished in this raging fire. Taking their place, new forms of art, music and the universe, constructs which they hope will help to explain the mechanisms of cosmic creation and destruction. New cosmological theories include the possibility that time is continually forking, that our universe is just one of many and that wormholes connect different cosmic sectors in a sort of inter-universal web.
As radical as these notions may sound, their implications have already been explored by a wide range of modern writers. From the fragmented universe of Joyce's Finnegan's Wake to the statement by Borges that "time forks perpetually toward innumerable futures," innovative writers have demonstrated much foresight in realizing new "shapes" of time and space. Along with the universe models developed by cosmologists, these literary creations provide powerful metaphors by which we may understand the new spatial and temporal conceptions of our society. They point the way for the consideration of a new paradigm of nature and culture, based on the image of the labyrinth.
In Time Journeys: The Search for Cosmic Destiny and Meaning (Mc Graw-Hill, 1990), I showed how the circular time notions of agricultural society evolved during the Middle Ages and Renaissance into the linear temporal viewpoints of the early industrial era. Interestingly, this paradigm shift took place both in physics and in society. However, that was just the beginning of the story.
In modern times, literature and science have increasingly assumed labyrinthine structures. Physics, art and literature have all been discarding the linear temporal and spatial notions of the past in favor of structures of far more complexity.
In the history of humankind there have been two major paradigm shifts regarding space-time perception. The first was the replacement of cyclical time and space with linear models, roughly following the transformation from stable agricultural to dynamic industrial societies. In physics this change came about with the discovery of the law of increasing entropy, a law which dictated that time must have an arrow of directionality. In literature, cyclical, epic stories in which there was no character development were replaced by novels in which real change occurred. So, linear models of space and time (ideas of unidirectional progress or decay) dominated science and literature until quite recently.
However, as Alvin Toffler, among others, has pointed out, we have moved far beyond the old industrial era into a post-industrial age, an age in which complexity and compartmentalization predominate. I assert that this change in society has heralded a second paradigm shift in both literature and science, in effect bringing on the "age of the labyrinth."
What characterizes the literature of this new era? Fragmentation, multiple speakers, shifts in perspective, stream of consciousness, random imagery and forking timelines are some of the key features of the writings of modern authors such as Joyce, Calvino, Borges, Garcia Marquez, Eco and Vonnegut. These writers set out to model a universe of boundless possibilities--a world in which anything can happen and chance is god.
The fullest expression of the age of the labyrinth is in the complexity of the internet. Linear encyclopedias no longer function as favored information sources, having been replaced by a colossal web of hypertext links. At this point, to navigate the full extent of this maze would take many lifetimes.
I hope that this blog offers a stable vantage point for observing the modern labyrinth of science and literature, space and time.