A striking consequence of the new picture of the world is that there should be an infinity of regions with histories absolutely identical to ours. That's right, scores of your duplicates are now reading copies of this article. They live on planets exactly like Earth, with all its mountains, cities, trees, and butterflies. There should also be regions where histories are somewhat different from ours, with all possible variations. For example, some readers will be pleased to know that there are infinitely many O-regions where Al Gore is the President of the United States.

In this astonishing world view, our Earth and our civilization are anything but unique. Instead, countless identical civilizations are scattered across the infinite expanse of the cosmos. With humankind reduced to absolute cosmic insignificance, our descent from the center of the world, a process begun by Copernicus, is now complete.


In 1981, Alan Guth made what some considered at the time to be the most important contribution to cosmology in a generation: the theory of inflation. In Guth's model, the very early universe underwent a period of rapid expansion; this accounts for, among other puzzles in big-bang theory, the present-day universe's puzzling homogeneity.

Today, more than 25 years later, Guth's inflationary model still holds sway, as other cosmologists have moved the theory in new directions, i.e. chaotic inflation, eternal inflation, brane inflation, among others.

The implications of inflation are particularly important in the context of the landscape of string theory. One of the leading researchers studying how inflationary cosmology evolves through the landscape is Alex Vilenkin, a theoretical physicist at Tufts who has been working in the field of cosmology for 25 years and is a pioneer in introducing the ideas of eternal inflation and quantum creation of the universe from nothing. Here he sets forth his ideas of how the set of theories which began with Guth's inflationary scenario are playing out.



ALEXANDER VILENKIN is Professor of Physics and Director of the Institute of Cosmology at Tufts University. A theoretical physicist who has been working in the field of cosmology for 25 years, Vilenkin has written over 150 papers and is responsible for introducing the ideas of eternal inflation and quantum creation of the universe from nothing.

Alexander Vilenkin's Edge Bio Page



Theoretical physicists working in the rarefied field of loop quantum gravity have developed a way to describe elementary particles as merely tangles in space. If they are right, it could be the most profound scientific generalisation of all time, in which everything in the universe emerges from a simple network of relationships, with no fundamental building blocks at all. — New Scientist, Editorial [12 August 06]

About a decade ago, in my book The Third Culture (1995), Lee Smolin's chapter ("A Theory of the Whole Universe") began with the following comments:

"What is space and what is time? This is what the problem of quantum gravity is about. In general relativity, Einstein gave us not only a theory of gravity but a theory of what space and time are — a theory that overthrew the previous Newtonian conception of space and time. The problem of quantum gravity is how to combine the understanding of space and time we have from relativity theory with the quantum theory, which also tells us something essential and deep about nature. If we can do this, we'll discover a single unified theory of physics that will apply to all phenomena, from the very smallest scales to the universe itself. This theory will, we're quite sure, require us to conceive of space and time in new ways that take us beyond even what relativity theory has taught us.

"But, beyond even this, a quantum theory of gravity must be a theory of cosmology. As such, it must also tell us how to describe the whole universe from the point of view of observers who live in it — for by definition there are no observers outside the universe. This leads directly to the main issues we're now struggling with, because it seems very difficult to understand how quantum theory could be extended from a description of atoms and molecules to a theory of the whole universe. As Bohr and Heisenberg taught us, quantum theory seems to make sense only when it's understood to be the description of something small and isolated from its observer — the observer is outside of it. For this reason, the merging of quantum theory and relativity into a single theory must also affect our understanding of the quantum theory. More generally, to solve the problem of quantum gravity we'll have to invent a good answer to the question: How can we, as observers who live inside the universe, construct a complete and objective description of it?"

Discover Magazine had run a cover story proclaiming Smolin "The New Einstein". It may have impressed the general reader, but not mainstream physicists. As cosmologist Alan Guth, father of the inflationary theory of the Universe, noted in The Third Culture:

"The relativity physicists belong to a small club. It's a club that has yet to convince the majority of the community that the approach they're pursuing is the right one. Certainly Smolin is welcome to come and give seminars, and at major conferences he and his colleagues are invited to speak. The physics community is interested in hearing what they have to say. But the majority looks to the superstring approach to answer essentially the same questions."

Also weighing in was particle physicist and Nobel Laureate Murray Gell-Mann:

"Smolin? Oh, is he that young guy with those crazy ideas? He may not be wrong!"


A decade later, Smolin's ideas are beginning to get traction.New Scientist has published a cover story [12 August 06] reporting on the work on "Braids" and Loop Quantum Gravity by Smolin, Carlo Rovelli, Sundance Bilson-Thompson, and Fotini Markopoulou. An accompanying editorial proclaims that "it could be the most profound scientific generalisation of all time."

Is it time to overthrow decades of work on string theory? The jury is out on the ideas generated by Smolin and his colleagues, but the question is now being asked by more than a few physicists.




I invited a group of cosmologists, experimentalists, theorists, and particle physicists. Stephen Hawking came. We had three Nobel laureates: Gerard 't Hooft, David Gross, Frank Wilczek; well-known cosmologists and physicists such as Jim Peebles at Princeton, Alan Guth at MIT, Kip Thorne at Caltech, Lisa Randall at Harvard; experimentalists, such as Barry Barish of LIGO, the gravitational wave observatory; we had observational cosmologists, people looking at the cosmic microwave background; we had Maria Spiropulu from CERN, who's working on the Large Hadron Collider—which, a decade ago, people wouldn't have thought it was a probe of gravity, but now due to recent work in the possibility of extra dimensions it might be.



Physicist/cosmologist Lawrence Krauss, who recently was featured on Edge("How Do You Fed-ex the Pope?"), recently convened a physics conference on St. Thomas, which included an all-star cast of cutting-edge theorists and physicists.


Stephen Hawking, David Gross, Kip Thorne, Lisa Randall


Lawrence Krauss and Stephen Hawking on the way to Atlantis Submarine


Frank Wilczek, Betsy Devine, and Alan Guth


Krauss scuba diving to meet Atlantis Submarine

The topic of the meeting was "Confronting Gravity." Krauss intended to have "a meeting where people would look forward to the key issues facing fundamental physics and cosmology". They could meet, discuss, relax on the beach, and take a trip to the nearby private island retreat of the science philanthropist Jeffrey Epstein, who funded the event.

For Krauss, what came out of the conference was the over-riding issue that "there appears to be energy of empty space that isn't zero! This flies in the face of all conventional wisdom in theoretical particle physics. It is the most profound shift in thinking, perhaps the most profound puzzle, in the latter half of the 20th century. And it may be the first half of the 21st century, or maybe go all the way to the 22nd century. Because, unfortunately, I happen to think we won't be able to rely on experiment to resolve this problem."

"It's not clear to me", he says, "that the landscape idea will be anything but impotent. Ultimately it might lead to interesting suggestions about things, but real progress will occur when we actually have new ideas. If string theory is the right direction, and I'm willing to argue that it might be, even if there's just no evidence that it is right now, then a new idea that tells us a fundamental principle for how to turn that formalism to a theory will give us a direction that will turn into something fruitful. Right now we're floundering. We're floundering, in a lot of different areas."

Other physicists, whether present at the conference or not, will no doubt feel diiferently. Edge looks forward to their comments.


LAWRENCE M. KRAUSS, a physicist/cosmologist, is the Ambrose Swasey Professor of Physics and chairman of the Physics Department of Case Western Reserve University. He is the author of The Fifth Essence, Quintessence, Fear of Physics, The Physics of Star Trek, Beyond Star Trek, Atom, and Hiding in the Mirror.




...there is a deep relation between Einstein's notion that everything is just a network of relations and Darwin's notion because what is an ecological community but a network of individuals and species in relationship which evolve?  There's no need in the modern way of talking about biology for any absolute concepts for any things that were always true and will always be true.


Last year Edge received an invitation from Juan Insua, Director of Kosmopolis, a traditional literary festival in Barcelona, to stage an event at Kosmopolis 05 as part of an overall program "that ranges from the lasting light of Cervantes to the (ambiguous) crisis of the book format, from a literary mapping of Barcelona's Raval district to the dilemma raised by the influence of the Internet in the kitchen of writing, from the emergence of a new third culture humanism to the diverse practices that position literature at the core of urban creativity."

Something radically new is in the air: new ways of understanding physical systems, new focuses that lead to our questioning of many of our foundations. A realistic biology of the mind, advances in physics, information technology, genetics, neurobiology, engineering, the chemistry of materials: all are questions of capital importance with respect to what it means to be human.

Charles Darwin's ideas on evolution through natural selection are central to many of these scientific advances. Lee Smolin, a theoretical physicist, Marc D. Hauser, a cognitive neuroscientist, and Robert Trivers, an evolutionary biologist, travelled to Barcelona last October to explain how the common thread of Darwinian evolution has led them to new advances in their respective fields.

The evening was presented by Eduard Punset, host of the internationally-viewed Spanish-language science television program Redes, and a best-selling author in Spain. A Redes television program based on the event was broadcast throughout Spain and Latin America.

The house was packed. The Barcelona press was present (see El PaisLa VanguardiaEl PaisEl Mundo, and a cover story in "Culturas", the magazine fo La Vanguardia).

Back to Event page




Einstein's derivation of E = mc² was wholly mathematical. I know his derivation, as does just about anyone who has taken a course in modern physics. Nevertheless, I consider my understanding of a result incomplete if I rely solely on the math. Instead, I've found that thorough understanding requires a mental image - an analogy or a story - that may sacrifice some precision but captures the essence of the result.

Here's a story for E = mc². Two equally strong and skilled jousters, riding identical horses and gripping identical (blunt) lances, head toward each other at an identical speed. As they pass, each thrusts his lance across his breastplate toward his opponent, slamming blunt end into blunt end. Because they're equally matched, neither lance pushes farther than the other, and so the referee calls it a draw.

This story contains the essence of Einstein's discovery. Let me explain.

BRIAN GREENE, a professor of physics and mathematics at Columbia, is the author of The Elegant Universe and The Fabric of the Cosmos.

Brian Greene's Edge Bio page 



If I had the opportunity to meet the assumed designer, I'd ask what, to me, is the most important question of them all: ''Mr. Designer, who designed you?"

If the designer answers that it doesn't know, that perhaps it was also designed, we fall into an endless regression, straight back to the problem of the first cause, the one that needs no cause. At this point the mask tumbles and we finally discover the true identity of the IDists' Designer. We should capitalize the word, as this is how we are taught to refer to God.

MARCELO GLEISER, a professor of physics and astronomy at Dartmouth College, is the author of The Prophet and the Astronomer: A Scientific Journey to the End of Time.

Marcelo Gleiser's Edge Bio Page



I doubt that pure philosophical discourse can get us anywhere. Maybe phenomenological narrative backed by psychological and anthropological investigations can shed some light on the nature of Mathematical Truth.

As to Beauty in mathematics and the sciences, here speaks Sophocles' eyewitness in Antigone:

     "..... Why should I make it soft for you with tales to prove myself a liar? Truth is Right."

Einstein & Gödel, Princeton, 1950s (Photo by Oskar Morgenstern, IAS Archives)

A true Realist, a true Platonist will not stoop to choose between Beauty and Truth, he will have the tenacity to stick it through until Truth is caught shining in her own Beauty. Sure there are messy proofs, we have to bushwhack trough a wilderness of ad hoc arguments, tours de force, combinatorial jungles, false starts and the temptations of definitions ever so slightly off target. Eventually, maybe not in our own lifetime, a good proof, a clear and beautiful proof will be honed out.

VDS Self-Portrait

That, I think, is the belief of the true Platonist. What Gödel and Einstein were doing when walking together over the Institute's grounds may have been just that; bush whacking, comparing mental notes and encouraging each other not to give up while getting all scratched and discouraged. Yet finding solace in speaking to each other in their mother tongue about their deepest concerns, and the state of the cosmos, the world, the weather and their households to


Verena Huber-Dyson, a Swiss national born in Naples in 1923, was educated in Athens before returning to Zurich to study mathematics (with minors in physics and philosophy), obtaining her PhD under Andreas Speiser in 1947. She moved to the United States in 1948, and happened to be in exactly the right field, the right place, and the right time to witness her two particular areas of interest — group theory and formal logic — have an unexpected impact (via particle physics and digital computing) on the real world.

She considers herself an Intuitionist, and this prompts the question she is asking herself:

"When I think with what a sure touch Bernoulli, Euler and their contemporaries summed infinite series without having a precise definition of convergence, which only came over a century later with Weierstrass and Cauchy, I am starting to wonder whether we are not witnessing a typical evolutionary phenomenon here.

"I don't think any contemporary analyst (Walter Hayman, Wolfgang Fuchs, Lars Ahlfors etc) would nowadays have that skill although they have other, more precise reasons for seeing that a series converges and more sophisticated and powerful methods for summing them.

"I am thinking both of the way our appendix has become obsolete, and of how some aborigines in central Australia are still able to hear what is happening at distances farther than we can perceive noises.

"So I wonder whether it might not be possible that mathematical intuition is regressing (atrophying by disuse) just as the discipline is evolving and so much can be accomplished without that extra fine sense — a phenomenon now due to the IT escalation, but already started with the surge of precision via formalization and mathematical logic."

Some of what follows is a challenge for the layperson...a rewarding challenge. "People are not prepared to roll up their sleeves and do some hard thinking and figuring," Huber-Dyson says, "and read a book with a a pad of paper and a few sharp pencils on the side, or their laptop in action. Reminds me of some of my colleagues, who said 'Oh it's brilliant, but soooo dense'. But to make up for that I had a few students who thrived on my dense cooking."


VERENA HUBER-DYSON is emeritus professor of the Philosophy department of the University of Calgary, Alberta Canada, where she taught graduate courses on the Foundations of Mathematics, the Philosophy and Methodology of the sciences.

Before the Vietnam war she was an associate professor in the Mathematics department of the University of Illinois. She taught in the Mathematics department at the University of California in Berkeley. She is the author or a monograph, Gödel's theorems: a workbook on formalization, which is based on her experience of teaching graduate courses and seminars on mathematical logic, formalization and its limitations to mathematics, philosophy and interdisciplinary students at the Universities of Calgary, Zürich and Monash.

She lives in Berkeley, California.




A recent, important turn in my life occurred when I realized that something that I have long been stating in footnotes should be put on the marquee. I have engaged myself, without realizing it, in undertaking a theory of roughness. Think of color, pitch, heaviness, and hotness. Each is the topic of a branch of physics. Chemistry is filled with acids, sugars, and alcohols; all are concepts derived from sensory perceptions. Roughness is just as important as all those other raw sensations, but was not studied for its own sake.

Introduction by John Brockman

During the 1980s Benoit Mandelbrot accepted my invitation to give a talk before The Reality Club. The evening was the toughest ticket in the 10 year history of live Reality Club events during that decade: it seemed like every artist in New York had heard about it and wanted to attend. It was an exciting, magical evening. I've stayed in touch with Mandelbrot and shared an occasional meal with him every few years, always interested in what he has to say. Recently, we got together prior to his 80th birthday.

Mandelbrot is best known as the founder of fractal geometry which impacts mathematics, diverse sciences, and arts, and is best appreciated as being the first broad attempt to investigate quantitatively the ubiquitous notion of roughness.

And he continues to push the envelope with his theory of roughness. "There is a joke that your hammer will always find nails to hit," he says. "I find that perfectly acceptable. The hammer I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at least some roughness everywhere."

"My book, The Fractal Geometry of Nature," he says, reproduced Hokusai's print of the Great Wave, the famous picture with Mt. Fuji in the background, and also mentioned other unrecognized examples of fractality in art and engineering. Initially, I viewed them as amusing but not essential. But I soon changed my mind.

"Innumerable readers made me aware of something strange. They made me look around and recognize fractals in the works of artists since time immemorial. I now collect such works. An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role had remained unrecognized and waited for me to be uncovered."


BENOIT MANDELBROT is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T.J. Watson Research Center. His books include The Fractal Geometry of Nature; Fractals and Scaling in Finance); and (with Richard L. Hudson) The (mis)Behavior of Markets.

Benoit Mandelbrot's Edge Bio Page 


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