Information Processing

The evening began ominously. Dyson had a stomach bug -- he declined to eat anything at dinner, and made several emergency trips to the bathroom. After dinner he fell asleep on a couch in the physics building. Facing a packed auditorium, with people sitting in the aisles and filling an adjoining overflow room with video monitor, the other organizers and I decided that we'd offer Freeman the chance to call the whole thing off when we woke him up. Luckily for everyone, he felt much better after the nap, and was obviously energized by the large and enthusiastic crowd. After we finished the Q&A, he turned to me and said "Well, your questions cured my bug!"

The questions we asked are listed below. You'll have to wait to watch the video in order to hear the answers!

[Video. Transcript.]

CAMBRIDGE

You write that scientists come in two varieties: hedgehogs and foxes. Foxes know many tricks, hedgehogs only one. Which kind of scientist makes the most important discoveries?

Of course, molecular biology was being born at that moment. But you advised Francis Crick, while he was still a physicist, that moving into biology might be premature. He didn’t take your advice did he, and a few years later he helped discern the structure of DNA? Mistake on your part?


MOVE TO AMERICA

You wrote that since childhood, some part of you had always known that the “Americans held the future in their hands and that the smart thing for me to do would be to join them.” Was that why you made your home in America? Do Americans still hold the future in their hands.

In the 50s, many people were fascinated with the potential of nuclear energy. Admiral Lewis L. Strauss, then Chairman of the U.S. Atomic Energy Commission, when he said: "It is not too much to expect that our children will enjoy electrical energy in their homes too cheap to meter." Did you share this excitement?

There were plans to build a nuclear airplane that would fly for a year at a time and you got involved with a nuclear rocket project-- the Orion Project. Tell us about that.

Weren’t you involved in the project’s demise—the test ban treaty?


THE SCIENTIFIC PROCESS

Now about the nature of science. You write, “Science is an art form and not a philosophical method. The great advances in science usually result from new tool rather than from new doctrines.” Could you elaborate?

Physics leads to some pretty weird places. You were at Princeton when Everett proposed his "Many Worlds" interpretation of quantum mechanics. Could you describe the reaction to his ideas then (including your own), and your present opinion?

It’s been said that Quantum Electrodynamics or QED is the most successful theory science has ever produced, having been verified in some cases to an accuracy of 12 decimal places. It was worked out by two geniuses, Feynman and Schwinger, but their theories looked totally at odds—one used diagrams the other formal analysis. In perhaps your most celebrated piece of physics, you showed they were equivalent. I’m curious, did Feynman and Schwinger grasp immediately what you had done?

You write, “Heretics who question the dogmas are needed... I am proud to be a heretic. The world always needs heretics to challenge the prevailing orthodoxies.” Do we need more heretics today?


WILD IDEAS

From science fact to science fiction. Your speculations about the future of humanity include the Dyson tree and the Dyson sphere. A Dyson tree is a genetically engineered plant capable of growing on a comet. You think comets are promising places for life..how so?

You've proposed that genetic engineering might be used for many purposes, from green energy to adapting humans for life in space…even to people growing their own dogs. Please tell us more.

What about engineering ourselves for greater intelligence; could that be the next leap forward in human evolution?


SCIENCE AND CULTURE

Jacques Hadamard said “It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others. ” Have scientists and mathematicians seized or squandered opportunities to learn from others in different disciplines?

To what extent should the public's view influence the path of science?

As a great observer of science, you’ve seen how science can evoke excessive hype and fear….has the negative public reaction to things like nuclear energy, GMOs, nanotechnology…has this surprised you?


SCIENCE AND RELIGION

Science and religion. There are scientists, like NIH chief Francis Collins, who believe in God and think religion is compatible with science. There are scientists, who are what you call passionate atheists—Hardy, Erdos, Dawkins, who think religion is a massive irrational distraction. You say that religion must be explored from the inside and those atheists, even very smart philosophers like Dan Dennett, will never understand it. How so?


In 2000, you were awarded the Templeton Prize for Progress in Religion. You wrote, "I am neither a saint nor a theologian. To me, good works are more important than theology." What did you mean?


WRAP UP

We’ve spoken about science and religion, let’s end talking about technology. You write, “Technology is a gift of God. After the gift of life, it is perhaps the greatest of God's gifts. It is the mother of civilizations, of arts and of sciences.” In your lifetime, those gifts include biotechnology, computers, and the Internet. What gifts might lie in our future?

What would you be working on today if you were 25 years old?

I will report the answers to some of my dinner questions. About Dirac and the path integral, Dyson thought that Feynman's story was probably true -- Dirac did not know that the quantum amplitude and the exponential of the action were more than "analogous" (indeed, they are proportional) until after Feynman had worked it out. It was also Feynman who had the idea of the sum over classical paths. In Dirac's paper the exponential of the action might have been a quantum operator, like the time evolution operator, which is the exponential of the Hamiltonian.

In Dirac's paper he writes that the quantum amplitude and e^{iS} are "analogous". Later Feynman asked him directly about it (according to Feynman):

F: Did you know they are proportional?

D: Are they?

F: Yes.

D: Oh, that's interesting.

I also asked about the infamous night with Feynman in the hotel in Oklahoma, and Dyson confirmed the accuracy of Feynman's recollection :-)

I think this web cartoon by Abstruse Goose is hilarious! (Thanks to DB for sending it to me :-)

Who is the artist? I did a quick search and didn't find anything -- is he/she deliberately anonymous (other than the Chinese characters on the upper left)?

For the perplexed: see earlier post path integrals.

I've finished lecturing on renormalization of QED, and am now covering path integrals. Feynman, following an earlier observation of Dirac, showed that the quantum amplitude for a particle to propagate from A to B is given by the sum over all possible paths connecting A to B, weighted by i times the classical action of each path:

Amplitude = Sum e^{i S[path]}

This yields a very intuitive formulation of quantum mechanics and quantum field theory. Mathematicians don't like the Feynman path integral (merely a heuristic used by physicists!). Due to its highly oscillatory integrand, little has been rigorously established about its properties or even its existence. Under better control is the related Wiener integral (an imaginary time Feynman integral or Euclidean path integral), which takes the form (S is real):

Sum e^{- S}

It didn't take long for physicists on Wall St. to realize that options pricing theory can be completely recast in path integral language. The Euclidean path integral for a free particle describes Brownian motion (a random walk). Interpret the location of the particle (in 1 spatial dimension - cake!) as the log of the price of a security, and you are off to the races! In the path integral language we value a derivative contract as the payoff averaged over all future paths. (We can only do this if the derivative can be perfectly hedged at all times, so risk preferences do not enter, but that is a subtlety.)

I derived a closed form expression using the free particle propagator and delta function potentials for the value of any possible exotic path-dependent option. At the time, this was quite novel, as such contracts were usually priced using Monte Carlo simulations. (If you look hard enough you can find an MIT Sloan school report with all the details :-) Soon after, I was offered a job in the equity derivatives group at Morgan Stanley. Being young and idealistic (dumb and naive), I decided it was better to be a postdoc at Harvard than a future multi-millionaire (although now that I think about it I did have a faculty offer at Yale by that time). A reporter from CNBC interviewed me as one of the rare "rocket scientists" who turned down Wall St. (They had no shortage of interviews with the other type :-) The camera man even shot some footage of me walking into Lyman Lab with my crummy backpack full of physics books.