Labyrinths of Space and Time

A Physics Walking Tour of Washington D.C.

2011-07-16T00:56:00.000-07:00

A Physics Walking Tour of Washington, DC
By Paul Halpern

Excerpted from “Washington: A DC Circuit Tour,” P. Halpern, Physics in Perspective 12, No. 4, (2010), pp. 443-466. All photos by Aden Halpern and Paul Halpern, except for the photo of the historic Van de Graaff generator at the Department of Terrestrial Magnetism, used by permission of the Carnegie Institution of Washington.

Stop 1: Joseph Henry Statue
We start our walk at the statue of Joseph Henry located in the National Mall directly in front of the “castle” housing the headquarters of the Smithsonian Institution (Smithsonian Metro Station). Designed by William Wetmore Story, the statue was dedicated in 1883. A widely accomplished physicist, Henry served as the first Secretary of the Smithsonian Institution.

Stop 2: The Smithsonian Building
We now walk from the Henry statue to the castle-like edifice behind it, the Smithsonian Building, completed in 1855. On the south side of the Smithsonian Building is an area known as the South Yard where, from 1890 to 1955, a shed housed the Smithsonian Astrophysical Observatory, one of the first centers in the world for astrophysical research.

Stop 3: U.S. Department of Energy
Across Independence Avenue from the Smithsonian’s South Yard is the Forrestal Building, which was built in 1970 and today houses the U.S. Department of Energy.

Stop 4: The Continuum Sculpture and the National Air and Space Museum
Going east along Independence Aveue and crossing 7th Street SW, we see on our left the National Air and Space Museum. Directly in front of its entrance is the modern sculpture Continuum, which was commissioned in 1976 and designed by artist Charles O. Perry to represent a distorted region of spacetime in the vicinity of a black hole.

Stop 5: Koshland Science Museum
Crossing the National Mall and walking due north several blocks along 6th Street NW, we arrive at the corner of E Street and find ourselves at the entrance of the Marion Koshland Science Museum of the National Academy of Sciences, which specializes in contemporary scientific issues.

Stop 6: National Museum of American History
Walking six blocks west along E Street, and then the equivalent of three blocks south along 12th Street NW, we arrive at Constitution Avenue and see on the other side of it the entrance to the National Museum of American History (Federal Triangle Metro Station). Long a part of the Smithsonian, it has two significant collections on physics: the Physical Sciences Collection and the Modern Physics Collection.

Stop 7: Albert Einstein Memorial and the National Academy of Sciences
We exit the National Museum of American History and walk eight blocks west on Constitution Avenue, cross 21st Street NW, and see the Albert Einstein Memorial in a shady grove in front of the National Academy of Sciences. It features a 12-foot bronze statue of Einstein, weighing about 4 tons, that was sculpted by Robert Berks to depict the founder of relativity in his later years.

Stop 8: Corcoran Hall: George Washington University
We now stroll the equivalent of about four blocks north on 21st Street NW, cross G Street, and reach Corcoran Hall, home of the Department of Physics of George Washington University since 1924.. GWU’s Department of Physics rose to prominence internationally with the appointment of Russian physicist George Gamow in 1934 and of Hungarian physicist Edward Teller in 1935. Plaques honoring Gamow and Teller, along with the Fifth Washington Conference on Theoretical Physics are featured on the wall facing 21st Street. At that conference, which took place at GWU in 1939, Niels Bohr announced to the astonished participants the discovery of nuclear fission in Germany.

Stop 9: Carnegie Institution of Washington
We now leave GWU and stroll seven blocks north along 21st Street NW to P Street. Then we turn right and go five blocks east to the corner of 16th Street NW and P Street where the Carnegie Institution of Washington (also known as the Carnegie Institution for Science) is situated (Dupont Circle Metro Station). Its three divisions with the deepest connections to physics are the Observatories Department (originally just Mount Wilson Observatory), the Department of Terrestrial Magnetism, and the Geophysical Laboratory.

The Carnegie Institution’s Department of Terrestrial Magnetism, founded in 1904 under the directorship of American physicist Louis Agricola Bauer, is housed in separate quarters at 5241 Broad Branch Road NW in the leafy northwestern corner of the District. It includes a pioneering Van de Graaff accelerator, completed in 1933 by physicist Merle Tuve, and used to explore the realm of the nucleus.

The Geophysical Laboratory was founded in 1905 and was located on Upton Street NW before it was relocated to the Broad Branch Road campus near the DTM in 1990. (Mt. Wilson Observatory is in California and not included on this walking tour except for the very athletic.)

Stop 10: Oak Hill Cemetery in Georgetown
From the main headquarters of the Carnegie Institution on the corner of 16th Street NW and P Street, we go two blocks north to Q Street and then the equivalent of eight blocks west, crossing the bridge over Rock Creek, to reach Oak Hill Cemetery in venerable Georgetown. Among the notables buried there is Joseph Henry whose grave is prominently located in the section called “Henry Crescent” near the East Gate.

Stop 11: American Center for Physics in College Park
Visiting the American Center for Physics, the final stop on our tour, requires a trip by Metro to the College Park Metro Station and a brief walk. Established in 1993 under the leadership of Kenneth W. Ford, the American Center for Physics houses the American Institute of Physics, the American Physical Society, the American Association of Physics Teachers, the American Association of Physicists in Medicine, and the Society of Physics Students. The ACP also houses the AIP Center for History of Physics with its Niels Bohr Library and Archives and the Emilio Segrè Visual Archives.

Thanks to Roger Stuewer for suggesting and editing the article on which this guide is based, to Greg Good for helpful suggestions, and to Shaun Hardy for suggesting that I post a web version of my guide.

The Discreet Charm of the Discrete

2011-02-16T15:41:00.000-08:00

I've just written a new essay and submitted it to the FQXi Essay Contest: "Is Reality Digital or Analog?"

Here is a link to my essay, entitled:

The Discreet Charm of the Discrete

Book Review: The Matchbox that Ate a Forty-Ton Truck by Marcus Chown

2010-05-19T15:28:00.000-07:00

Marcus Chown has a marvellous gift for rendering cutting-edge science extremely accessible and entertaining. His latest work, "The Matchbox that Ate a Forty-Ton Truck," is a brilliant excursion through everyday life, showing what we might learn about the universe from things we see around us, including our own reflections in window glass, the variety of chemical elements, darkness at night and so forth. From simple phenomena, Chown transports readers on spectacular journeys through the realms of quantum physics, cosmology and other topics in modern science, explaining difficult concepts in a clear, methodical fashion. He weaves each tale with fascinating and humorous anecdotes about pivotal figures such as Fred Hoyle, Wolfgang Pauli and many other scientific luminaries. "Matchbox" will truly ignite your interest in science! Highly recommended!

The Cave of Portents

2010-05-01T07:31:00.000-07:00

Author's Note: I wrote this short fictional piece in 1999 as part of the same project that led to my book "The Pursuit of Destiny: A History of Prediction."

THE CAVE OF PORTENTS by Paul Halpern (1999)

Deep within the cave of portents, carved out over the eons by the currents of possibility, lies a chamber known for its auspicious acoustic qualities. Explorers stumbling upon that cavern have reported hearing beautiful melodies played out among the stony columns like the sonorant tones of wind chimes. Some have also recalled hearing soft whispering sounds, almost like the murmur of human voices. They have attributed these strange phenomena to peculiar resonant effects--a remarkable auditory illusion.

What makes matters even more intriguing are the presence of rocky formations in the chamber that seem to resemble human visages. Throughout the years since the cave was discovered, adventurers have nicknamed each of the stone faces after a historical or scientific figure.

One explorer, with a passion for philosophy, nicknamed one of the figures, “Pythagoras,” and another neighboring image, “Cicero,” because of their marked resemblances to those illustrious personages. A German exchange student, who gained admission to the caves as part of a summer research project, dubbed a craggy pillar close to the others, “Johannes Kepler,” after the 16th century astronomer of whose portrait it reminded him. A French spelunker, with a fondness for astrology, proudly selected the nickname “Nostradamus” for another rockface that seemed to have fiery, visionary eyes. Finally, to add to the eclectic mix of personalities, another caver, who knew modern physics very well, swore he saw the wild-haired image of Albert Einstein in one column, and the warm smile and deep, expressive glance of Richard Feynman in another.

With lanterns positioned well, these illusions were often enhanced by the strange rhythmic movements of shadows near the figures--suggesting the graceful gestures of musicians. Some have jokingly attributed the "concerts" and "conversations" seen and heard in the cavern to apparitions of the late scientists and philosophers, hovering near their stony likenesses. Hence the nickname for the chamber "harmony of the spirits."

Imagine the glorious music that would be made, and the striking and curious conversations that would resonate throughout the chamber, if the cave’s illusion suddenly and magically became real...

* * *

One Sunday morning, after an especially tuneful performance on his limestone "piano," the spirit of Kepler sighed and uttered, "Did you ever think we'd all end up here making music together?"

Nostradamus, who was chanting verses at the time, responded, "I knew. I pictured this strange cave, where great minds might harmonize, during one of my psychic excursions into the time of the third millennium. Like my other prophecies, it appeared to me during my nightly meditations upon water-filled glass. Through such exercises, I have witnessed all of history until the year 3797."

Cicero winced. "Another one of your preposterous claims. As usual, with unmatched zeal, but without a crumb of proof, you purport that the future is wholly predictable."

Nostradamus remarked in a huff, "It is predictable only to those who possess the powers of prophecy. Only those who lack the God-given vision to foresee the unraveling of the ages call my work preposterous."

At that point Pythagoras put down his lyre and joined in on the conversation. "Oh that vision thing again," he sneered. "You act as if the skill of foretelling the future is your exclusive domain. The gods have revealed man's destiny in the miraculous properties of numbers, and in the harmonious relationships between musical tones. Like a child taught the alphabet, any intelligent individual, properly trained in a superior academy, might be made aware of the wonders of the cosmos, deciphering its marvelous code."

Kepler spoke up. "Indeed, like Nostradamus, I've offered my share of horoscopes. The public expected me to provide such a service. But I've never claimed to be a prophet. My most fulfilling task, the discovery of the patterns of planetary orbits, I can attribute to my background in classical geometry. Simple, beautiful mathematics, not superstition, was the key to my success."

Pythagoras nodded his head. "Exactly. The cosmos is a vast fruit and mathematics is its pith. Those who peel off the outer layers of corporeal illusion, and savor the rich pulp of numerical truth, might truly taste their destinies."

Cicero looked up. "But what then. Suppose you use instinct, mathematics, examining animal entrails, or whatever your favorite method to discern the future. Does that mean, then, that you have discovered what must be in times to come or what could be in times to come? If you have found the former--the immutable future, then what's that point? What's the purpose of knowing something that you can't change? Just to be depressed? If Caesar knew his fate well in advance, but couldn't change it, perhaps he would have been an unhappy, ineffective leader. Bitter certainty would have engulfed him in a cloak of despair. And he would have been assassinated anyway.

On the other hand, if through your prognosticative abilities you have found mere possibilities or probabilities for the future--then there also would be no point. The winds of destiny could blow in another direction, and your prediction would be dead wrong anyway. You'd be chasing after specters in the dark, while reality passes you by."

Feynman, who had been banging his beloved bongo drums, glanced over when he heard the word "probability."

"Well that's all you can really know. Probabilities."

Cicero replied, "What do you mean?"

Feynman assumed his familiar pedagogical role. "Its too bad I don't have a blackboard here, but I'll try to explain without diagrams. Let me point out some of the ways classical physics and quantum mechanics fundamentally differ in how they treat basic interactions between particles. I’d like to consider the simple case of one electron exerting a force on another electron by means of exchanging a photon.

In classical physics, which is extraordinarily more intuitive than quantum theory, given their initial locations and speeds, one can map out the exact paths that the two electrons first take. Then one can examine how the first electron gives off a photon, and then recoils, like a gun firing off a bullet. Next, one can calculate precisely how the second electron absorbs the photon. Lastly, by means of the principles of conservation of energy and conservation of momentum, one can determine the ultimate trajectories and velocities of the particles. In short, by knowing the initial conditions one can infer exactly which routes are traveled, knowing with perfect precision the position and speed of each object for all times."

Kepler looked at Feynman and smiled. “Richard, I wish I could explain things so well. It all makes such perfect sense.”

Feynman chuckled. “Unfortunately everything I just said was wrong. Why? The reason is crazy, and I expect no one to believe it, not even the eminent thinkers in this chamber. Sometimes I don’t even know if I believe it myself. Physicists have given up to trying to predict anything exactly, because experimental evidence tells us that we just can’t do it. The uncertainty principle, a built in law of nature, restricts what we might know at any given moment. If we know a particle’s position perfectly well, then we don’t know its speed, and vice-versa.

In general, until we make an observation, all we can determine about a system is a set of probabilities. Then after we measure one particular quantity, the mere fact that we have observed the system shakes it up and affects its other properties, altering the probabilities that they have certain values. In other words, the future state of a system depends upon the choices made by observers.”

Kepler and Pythagoras exchanged puzzled glances. “But surely the magnificent harmony of nature has little to do with the decisions made by mortals,” stated Pythagoras.

“One would think,” replied the great theorist. “But one would get the wrong answer. For instance, in the scattering example I just mentioned one cannot assume that the electrons and photons followed only one trajectory. Rather, in quantum theory, one must consider the likelihoods of all possible exchanges between the particles, including bizarre situations such as photons traveling backward in time to meet electrons. Only by summing up these probabilities, in a special manner that takes a bit of mathematical juggling, might one be able to estimate likely outcomes.”

Kepler was intrigued, "Ah, I see. What I think you are saying, my spirited companion, is that nature is like a safe. To unlock its riddles, you must try each of the possible combinations it presents."

Feynman smiled. "Well, I would only need to try a few combinations--but I've had plenty of practice cracking open document drawers in Los Alamos. Nature, on the other hand, probes an infinite range of possibilities. But remarkably, one often can add up these infinite sums and obtain finite solutions to physical problems."

Einstein, who had been listening to the conversation while tuning his violin, looked dismayed.

"Ach, mein Freund. Gott ist im Himmel, nicht in Monte Carlo. Do you mean that there is only a finite probability that we are here, and that our energies might simultaneously occupy other configurations as well. Then how do we know precisely where we are?"

"Well if an observer were around to take a measurement of our locations, our wave functions might collapse to a particular position value. We may find ourselves still here, or conversely, we might not be here at all."

"An observer? Why, who might be here to observe us? I don't think anyone is paying attention to our proceedings?"

At that point the chamber became strangely silent. The winds seemed to shift, a lamp blew out, and the remarkable acoustical and optical illusions were no more.

The Science of Prediction

2010-04-10T20:02:00.001-07:00

Last year I was interviewed about the science of prediction on the Discovery Channel for a show called Nostradamus Decoded. The show aired in November 2009 and is now available online.

My short segment starts at about 3:06 into the episode.

Interview on the Discovery Channel (3:06)

More about the science of prediction is in my book:

The Pursuit of Destiny: A History of Prediction

Technology, Privacy and Choice

2010-04-10T19:48:00.000-07:00

I've been thinking much in recent years about the state of communications technology, as it has advanced so rapidly that I sometimes find it overwhelming. Years ago, Alvin Toffler, in the book Future Shock, imagined how societal changes could be so rapid that people would find it hard to keep up. As a scientist, who was always ahead of the game in terms of computers, I never imagined a time when technological change would just fly by.

In some ways recent changes in technology are miraculous and amazingly useful. Hear a few lyrics of a song, do a Google search, and find out the title. Within a few minutes, it can be purchased and downloaded. Amazing. Or it is remarkable to be able to find certain research articles electronically instead of having to make day-long ventures to libraries (although that was fun too).

However, modern communications technology brings many privacy concerns. I'm not sure how many people realize the growing ability of government agencies (or businesses if they were ever allowed access to such information) to track where people carrying phones or other electronic devices are at anytime, and to link together the electronic trails people leave whenever they use an ATM (automatic teller machine), supermarket discount cards, and so forth. Separately, that information seems pretty harmless. But it is truly scary to think of records that include a list of someone's eating habits, everywhere they like to take walks, and (thanks to Facebook) a list of many of their friends and relatives, with similar information about those people too. Now imagine an agency having a complete record of all this for everyone. What seemed inconceivable years ago, is well within technological abilities right now.

The other aspect of technology I've been ruminating about is choice. I think that no one should be forced to use any given technology. I know people, who for various reasons, don't own televisions, or never use the internet. I think that is fine -- it offers more time to read books. Personally, I treasure handwritten letters and notes. Some people nowadays don't have home phones but just use mobile phones, while others prefer only home phones and avoid the use of mobile phones. Those sound like reasonable choices to me. However, I do hear some people reacting in a state of veritable shock if some individual doesn't use a certain technology. I really think it should be up to individuals to decide how much technology feels comfortable for them.

Finally, communications technology can erode the boundary between home and work. Once again, that is fine for some, but it should be a matter of choice. People have the right to draw a line between the two, and enjoy unfettered relaxation or family time, unless their profession requires an immediate response to emergency situations, such as doctors on call.

A visionary writer who anticipated many of the issues of technology and privacy was Ray Bradbury. In "The Pedestrian" he imagined people being arrested for taking walks instead of driving, and in "The Murderer" he pictured a world where no one can escape the noise of people chatting constantly on wrist phones, and there is no privacy or quiet left to be seen.

Anyway, just some thoughts on technology. I would be interested in hearing reactions.

The Strange Story of Atomism: From Blasphemy to Science

2009-08-18T18:17:00.000-07:00

Atomism, the concept that things have smallest constituents, was introduced at the time of the ancient Greeks. To us moderns, it makes perfect sense. Yet for almost two millennia, mainstream European philosophers ignored or even shunned the idea. Why did it take so long to catch on?

The reason has perhaps more to do with who ended up trumpeting atomism than it has to do with the notion itself. In the battlefield of ideas, if a leading advocate is tremendously unpopular, opposing armies often see to it that all the notions he bears are equally trampled.

It is to atomism’s misfortune that its standard bearer for a time was Epicurus of Samos, founder of the much-maligned Epicurean school. He advocated atomism along with a set of widely scorned doctrines about the supremacy of pleasure over piety. Also he believed that the gods did not intervene in the lives of men. Thus he was widely condemned as a godless hedonist, discounting his atomist ideas.

Epicurus used atomism as a cleaver to divide the physical and spiritual realms. According to his theory, our bodies are composed of coarse atoms and our souls made of fine atoms. The gods consist of the most delicate atoms of all, floating in the spaces between physical worlds. Only in our thoughts and dreams do the mundane and godly come into contact. They do so in a way that the gods have no influence over people. Earth came into being through the random assembly of its own atoms and will pass away once they scatter into the void. The same with living beings; each must eventually perish due to material causes. Hence, Epicurus concluded, the gods have nothing to do with mortal existence and we need not fear or worship them.

In 56 B.C., a prominent Epicurean of the Roman era, Lucretius, wrote an epic Latin poem De Rerum Natura (On the Nature of Things) expounding upon atomism, materialism, and mortal life. Although his contemporaries seem to have valued his work, once the Roman Empire became Christian, his writings were denounced for their support of atheism and no longer published. Only a single copy survived the medieval period and was re-published in 1417.

Throughout the Middle Ages in Europe, the Church continued to treat Epicurean philosophy as blasphemous. As an indication of Europeans’ disdain toward Epicurean philosophy as late as the 14th century, note Italian poet Dante Alighieri’s description of the sixth circle of his fiery Inferno where Epicurean souls are forced to reside forever with their rotting corpses:

“The private cemetery on this side
serves Epicurus and his followers,
who make the soul die when the body dies.”

For those tormented spirits, it seems, their original sin was atoms not Adam’s. By contrast, according to Dante, non-atomist Aristotle has a relatively cushy spot in Limbo (non-Christians cannot enter Paradise), where he is sad but not tormented. Such was the attitude toward materialism in Dante’s times.

Atomism was resurrected in the 17th century, largely due to the writings of French philosopher Pierre Gassendi (1592-1655), an avid reader of Lucretius. Gassendi muted theological objections to the subject by speculating that God created atoms as the building blocks of nature. His work coincided with a growing recognition among Christian believers that scientific experimentation provided a way of understanding and appreciating creation. Along with the discoveries of German mathematician Johannes Kepler, Italian astronomer Galileo Galilei, and others of his day, Gassendi’s sharp observations prodded Europe away from blind belief in Aristotle’s theories and toward an empirical view of nature. Ultimately these trends led to the founding of the modern scientific concept of atoms.

More about the extraordinary quest for the most fundamental components of nature can be found in:

Collider: The Search for the World's Smallest Particles

Happy 96th Birthday to a Pioneering Biochemist

2009-07-24T17:31:00.000-07:00

Last year I had the pleasure of interviewing (by phone) the groundbreaking biochemist, Mildred Cohn, who lives in an apartment in Philadelphia. The reason was to gather information for an article I wrote about physics in Philadelphia. I had just found out that Cohn's late husband was the well-known American physicist Henry Primakoff. She was gracious in answering my questions about her husband's career. Only later did I find out that Mildred Cohn is a pioneering scientist in her own right, an expert in enzymes who had worked with nuclear chemist Harold Urey. Throughout her career, she has helped young women chemists get their start. She continues to contribute to the history of chemistry through her recollections archived by the Chemical Heritage Foundation. Cohn turned 96 on July 12. Happy 96th Birthday to a pioneering scientist!

Here is a link to more information about her work:
Mildred Cohn Biography

The Twittering Minister

2009-06-10T05:44:00.000-07:00

Imagine posting a message on a blog or on the microblogging site Twitter about a government official and having him respond directly back to you within an hour. That's what happened yesterday when writer P D Smith (who reviews for the Guardian and maintains various blogs) posted a "tweet" about Lord Paul Drayson, British Science Minister and race car driver. While Drayson was preparing for a big race in France he saw the tweet, posted back and kept the conversation going. Smith's account of what transpired is posted here: The Man from the Ministry The story has appeared in various news venues including: The Times Online: Science Minister Takes to Twitter

Physics in Philadelphia

2009-05-23T17:40:00.001-07:00

[This is an advanced excerpt of an article I will be publishing in June, called Philadelphia: Life, Liberty and the Pursuit of Physics (to appear in Physics in Perspective).]

Philadelphia's downtown district, called Center City, is laid out in a grid pattern with four squares. Interestingly, three of these squares, Logan, Franklin and Rittenhouse, have some association with physics.

James Logan was secretary to William Penn when Pennsylvania was founded. He was a lover of books and interested in all manner of scholarly topics, including physics. In 1709 Logan purchased a copy of the first edition of Newton’s Principia, and later he also acquired copies of the second and third editions, thus playing a pivotal role in introducing Newton’s work to the colonies. During a trip to London in 1710, Logan witnessed Newton performing an experiment before an audience at St. Paul’s Cathedral.

Benjamin Franklin made monumental contributions to the physics of electricity. In 1746, the London merchant and Fellow of the Royal Society Peter Collinson sent Franklin a package containing a glass tube used in electrostatic experiments and an article by the Swiss naturalist Albrecht von Haller describing current knowledge in the field, which sparked Franklin’s interest and led him to embark upon an intensive investigation of electricity. Franklin went on to define the concept of positive and negative charge, to establish that electrical attraction and repulsion of materials can act over a distance and not only by contact, and to enunciate the idea of conservation of charge. The most famous of Franklin’s experiments, however, was his lightning-kite experiment in 1752 in which he proved that lightning consists of an electrical discharge.

David Rittenhouse, as a child, demonstrated great mathematical and scientific aptitude, studying Newton’s Principia in English translation, building mechanical devices, and establishing his reputation as a maker of clocks and instruments on the family farm in Norriton, about twenty miles north of Philadelphia. His primary scientific field of study was astronomy, and in 1767 he built an orrery (solar system model) using Kepler’s laws as a guide. In 1769 he gained recognition as a leading member of the American Philosophical Society by using a refracting telescope he had made to measure the exact time of the transit of Venus. He also constructed the first diffraction grating.

So we see that three of Philadelphia's squares have a connection with physics. The next time you are in Philadelphia and find yourself passing Logan's Square's fountain, watching Franklin Square's carousel, or enjoying the sculpture in Rittenhouse Square you may wish to think about the accomplishments of their namesakes.

The Passing of a Great Historian of Science

2009-03-29T12:53:00.000-07:00

I was saddened to read that one of the great historians of science, Martin J. Klein of Yale University, passed away yesterday at the age of 84. He was a very down to earth and generous man, and was gracious in offering advice for one of my books. The first volume (of a planned two volume set) of a biography he wrote about physicist Paul Ehrenfest is a classic. (He never completed the second volume because he it was becoming too depressing for him to dwell on Ehrenfest's tragic final years.) Klein was also instrumental in the Einstein papers project and was the first recipient of the Pais Prize for the History of Physics. I remember him as a kindly, gray-mustached figure who was almost always surrounded by adoring former students.

Essay Contest Results

2009-03-10T10:06:00.000-07:00

The results of the "Nature of Time" essay competition have been posted.

There are many luminaries among the winners, including first-place winner Julian Barbour, an independent researcher who lives near Oxford.

If you are interested in reading any of the winning essays, including my own essay "The Garden of Forking Paths" (which I am delighted to announce has won a fourth juried prize) here is a link:

The Nature of Time Essay Competition Results

The Mystery of Time: An Essay Contest

2008-12-01T13:51:00.001-08:00

The nature of time is one of the deepest mysteries. In a new paper, submitted to an essay contest for the Foundational Questions Institute, I offer my own thoughts on this riddle:

The Garden of Forking Paths: Time as an Expanding Labyrinth

Einstein's Last Assistant

2008-07-24T13:33:00.000-07:00

Dr. Bruria Kaufman, Einstein's last research assistant at the Institute for Advanced Study in Princeton, turns 90 years old this year. She has had an extraordinary career, including collaborations with an amazing number of well-known scientists from various fields.

As a young researcher, she worked with Lars Onsager, a famous statistical physicist and Nobel-Prize-winning chemist, and John von Neumann, the Hungarian mathematician who was one of the great geniuses of the 20th century and helped invent the computer. She then spent time working with Einstein during his final days.

At the age of 27, during the 1955 Jubilee (50th anniversary) of relativity in Bern, she had the sad task of delivering Einstein's final paper on unified field theory. Her brilliant mentor had just passed away.

These varied areas of research are impressive in and of themselves. But then she collaborated with and married Zellig Harris, the founder of structural linguistics who advised Noam Chomsky. So she had yet another career as a prominent linguist.

Harris died in 1992, at the age of 82. In 1996, Kaufman married Nobel laureate physicist Willis Lamb, who was 83 at the time. She had known him from years earlier. Lamb was famous for having discovered the quantum phenomenon known as the Lamb shift, one of the earliest indications of virtual particles in the vacuum. They collaborated, later divorced, and Lamb recently died.

It is hard to think of a living scientist who has had a more diverse career than Dr. Kaufman.

Quantum Musicians

2008-07-24T13:29:00.001-07:00

A common metaphor in quantum mechanics relates the standing wave vibrations of electrons in atoms to the harmonics of plucked guitar strings. Apparently that image has resonated with some of the offspring of quantum theorists who have chosen musical careers.

A pioneer of this trend was Olivia Newton-John, the English-born Australian musician who captivated audiences in Grease and Xanadu. Her maternal grandfather was none other than one of the principal founders of quantum mechanics, Goettingen physicist Max Born.

In more recent years, the band Eels has attracted a loyal following. Its founder, (aka "Mr. E") is Mark Everett, son of Hugh Everett, developer of the Many Worlds Interpretation of quantum mechanics. He was recently featured in the BBC documentary "Parallel Lives, Parallel Universes."

Albert Baez, an X-ray pioneer, passed away last year. You can guess who his famous daughter, a prominent folksinger, is.

Then there are Brian May, guitarist and songwriter of the classic rock band Queen, and Brian Cox of the UK Synthpop Band D:ream. They have started a kind of reverse trend. May has become an astrophysicist and chancellor of Liverpool John Moores University and Cox has become a physicist at CERN.

Quantum harmonies are more than just a metaphor these days!

The Way of Science in the Labyrinth of Culture

2008-05-13T12:20:00.000-07:00

German historian of science Daniela Wuensch has just published a new book: The Way of Science in the Labyrinth of Culture

How can anyone resist a book with such a great title? It looks like an interesting read.
So far it is available only in German, however. So to travel through this labyrinth, those not fluent in that language may need a dictionary in addition to an Ariadne's thread.

Unifying the Forces of Nature

2008-01-27T10:59:00.000-08:00

It has been the physics community's long-standing dream to unify the natural forces into a single comprehensive theory. Two of the pioneers in unified field theory attempts were physicists Oskar Klein and Albert Einstein. In my new history of physics article, I explore connections between their quests for unification in five dimensions.

Here's a link to my recently published article (subscription required to see the full content; alternatively, paper copies available upon request):

Klein, Einstein and Five-Dimensional Unification

A Guide to Understanding the Bomb

2008-01-27T10:57:00.001-08:00

A book review I wrote of Doomsday Men by PD Smith has finally made its way into the pages of the Philadelphia Inquirer and also online:

A Guide to Understanding the Bomb

It is a fascinating book about the history and culture of superweapons and I highly recommend it.

Ironic Borgesian Textual Labyrinth with a Spam Minotaur

2007-11-01T08:56:00.001-07:00

In several of the short stories of famed Argentine writer Jorge Luis Borges, he imagined assembling books from random snippets of characters or text--like monkeys pounding away on typewriters haphazardly and seeing what strange passages they've typed. In such works, any semblance of meaning would be hidden amongst page after page of pure nonsense. In "The Library of Babel" Borges imagines an entire universe of such random books, and librarians seeking deeper truth in this labyrinth of meaninglessness.

Yesterday I discovered a new blog "labyrinths-921.blogspot.com" that at first glance seemed to be dedicated to Borges and labyrinths. However, after reading through the blog for a split second, it vanished and automatically shifted to a commercial chat site (the details of which I'll spare the reader). With some effort, I restored the original blog and found it to be a randomly organized collection of text snippets pertaining to the Argentine writer and mazes with absolutely no rhyme or reason. For example, the Saturday, October 27 entry reads:

"No description. Labyrinths It is impossible to imagine the former owner/occupant of this decaying Borgesian labyrinth of books, which still palpably pulsates with ideas and visions that only a lover of Borges can appreciate and understand, not having the . Paris, France: There are extensive networks of catacombs, quarries and other tunnels running under the capital of France. Some of these amazing photographs were taken by urban explorers who lit the scenes with candles, . Labyrinths Borges The inspiring Labyrinth, Memorial Wall and Sculpture Garden are located approximately 13 miles north of Weed, CA on Hwy 97."

That's either remarkably ungrammatical writing, or the random assembly of text by a computer algorithm craftily designed to lure intellectuals into a maze of prose, only to be whisked away by the minotaur of commercialism and spam. Isn't it ironic that a Borgesian blog could be assembled through shear chance?

Shadows of Higher Dimensions

2007-10-17T08:12:00.000-07:00

During a visit to Goettingen, Germany several years ago, I visited the mathematics building, built during the height of the department, when brilliant figures like David Hilbert, Hermann Weyl, Emmy Noether and Richard Courant roamed its halls and discussed whether there could be a complete description of mathematics (a hypothesis that would be disproven by Kurt Goedel). I noticed a marvellous display case in the department's foyer, full of incredible models of polytopes (representations of higher dimensional figures).

I recently developed a presentation about the relationship between these "shadows of higher dimensions" and unified theories of nature:

Imagining the Fifth Dimension

The history of higher dimensions is described in my book:

The Great Beyond

Labyrinths of Tile and Concrete

2007-09-03T08:09:00.000-07:00

Our minds can craft beautiful kinds of labyrinths from a variety of distinct materials. While some of these are abstract, such as poetic verse assembled from a blend of images or musical passages derived from a mixture of folk melodies, others are more concrete. "More concrete" was certainly the motto of Henry Chapman Mercer as he constructed his labyrinthine mansion in eastern Pennsylvania almost a century ago.

Born to a wealthy family in 1856, Mercer studied law at Harvard and the University of Pennsylvania. After briefly practicing law, he decided that he was more interested in ancient artifacts and folk art, and began collecting these. He also became a master craftsman, and opened a tile works specializing in colorful, unusual designs.

In 1908, he decided to build a mansion for himself, Fonthill, which would also house at least part of his collection. To make it fireproof, and less costly, he elected to construct it from concrete. Concrete also had the advantage of malleability, so he could shape any room or hallway as his wished. Indeed, he crafted a house with passages and stairways leading in almost every direction conceivable, with manifold libraries, studies, bedrooms and so forth. Each room is at a different level, connected to at least a half-dozen others. Naturally there's a tall tower, and even separate stairs and doors for his dog Rollo. Strangely Mercer was to live in this massive castle virtually alone (except for Rollo). Apparently the one woman he proposed to thought he was way too odd!

Scattered throughout the house, and embedded directly in the concrete, are ancient tiles from Babylon and China. Other tiles include a variety of styles and periods. Alphabet tiles arranged on the walls and ceilings spell out numerous messages in Latin, German and English, characterizing the rooms and their collections. One bedroom prominently displays a gruesome tile mosaic of the story of Blackbeard's wives and their untimely deaths; which apparently further put off potential suitors.

When Mercer died in 1930, he bequeathed the house to a historical society, but willed that his housekeeper should reside there as caretaker. She lived there until her own death almost half a century later. When I was growing up I heard about this strange house where a housekeeper would let you in and show you around if it suited her that day! When she passed away, official and more conventional tours began of the house. It's a great place to get lost in a creative artist's dreams.

Emmy Noether

2007-07-30T16:47:00.000-07:00

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

2007-07-18T19:55:00.000-07:00

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

2007-07-01T16:48:00.000-07:00

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

2007-07-01T15:31:00.001-07:00

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

2007-07-01T15:28:00.000-07:00

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

2007-07-01T15:27:00.000-07:00

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

2007-07-01T15:24:00.000-07:00

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.

Still Waiting for the Higgs

2007-07-01T15:23:00.001-07:00

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.

Big Bang at the Atomic Lab

Meeting John Wheeler

2007-07-01T15:21:00.000-07:00

One of the joys of being a science writer is getting a chance to interview some of the greats in the field. A particular pleasure is meeting someone like John Archibald Wheeler who was a student, collaborator, and mentor of some of the most notable physicists of the 20th century. Professor Wheeler, who is now almost 96, still maintains an office at Princeton. When I was writing my book, The Great Beyond, he generously gave several hours of his time for a morning interview.

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.

Book Review: Shadows of Reality

2007-07-01T15:18:00.000-07:00

This book review appeared in the Philadelphia Inquirer:

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.

Fractaled Mirror Maze

2007-07-01T15:12:00.000-07:00

An American amusement pier has decided to teach about fractals and the Mandelbrot set through one of its attractions the "Dr. Mandel Broot's Fractaled Mirror Maze." Check this out:

Einstein and Chaplin

2007-07-01T15:08:00.000-07:00

Here's a link to a piece I wrote about Einstein and Chaplin:

The Tramp, the Professor and Frankenstein's Brain Surgeon

Einstein's Assistant

2007-07-01T14:56:00.000-07:00

Here is a link to an article about my interview with Peter Bergmann (Einstein's assistant from the 1930s and a well-known physicist in his own write) shortly before he died.

Desperately Seeking Einstein's Assistant

The Age of the Labyrinth

2007-07-01T14:20:00.000-07:00

The Age of the Labyrinth, by Paul Halpern

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.