Fermi and Experimental Simulation: The Real Scientific Hero of
R. A. Hettinga
Tue, 4 Mar 2003 10:14:31 -0500
<Merciless Nepotistic Plug>
Non-linearity itself aside (I think...), this kind of numerical experiment, by the way, is my *brother's* literal stock in trade, viz, <http:/www.numerex.com/>, or, more properly: <http://www.numerex.com/links.htm>
Now you know where all the brains went in my family. :-).
March 4, 2003
The Real Scientific Hero of 1953
By STEVEN STROGATZ
Last week newspapers and magazines devoted tens of thousands of words to the 50th anniversary of the discovery of the chemical structure of DNA. While James D. Watson and Francis Crick certainly deserved a good party, there was no mention of another scientific feat that also turned 50 this year - one whose ramifications may ultimately turn out to be as profound as those of the double helix.
In 1953, Enrico Fermi and two of his colleagues at Los Alamos Scientific Laboratory, John Pasta and Stanislaw Ulam, invented the concept of a "computer experiment." Suddenly the computer became a telescope for the mind, a way of exploring inaccessible processes like the collision of black holes or the frenzied dance of subatomic particles - phenomena that are too large or too fast to be visualized by traditional experiments, and too complex to be handled by pencil-and-paper mathematics. The computer experiment offered a third way of doing science. Over the past 50 years, it has helped scientists to see the invisible and imagine the inconceivable.
Fermi and his colleagues introduced this revolutionary approach to better understand entropy, the tendency of all systems to decay to states of ever greater disorder. To observe the predicted descent into chaos in unprecedented detail, Fermi and his team created a virtual world, a simulation taking place inside the circuits of an electronic behemoth known as Maniac, the most powerful supercomputer of its era. Their test problem involved a deliberately simplified model of a vibrating atomic lattice, consisting of 64 identical particles (representing atoms) linked end to end by springs (representing the chemical bonds between them).
This structure was akin to a guitar string, but with an unfamiliar feature: normally, a guitar string behaves "linearly" - pull it to the side and it pulls back, pull it twice as far and it pulls back twice as hard. Force and response are proportional. In the 300 years since Isaac Newton invented calculus, mathematicians and physicists had mastered the analysis of systems like that, where causes are strictly proportional to effects, and the whole is exactly equal to the sum of the parts.
But that's not how the bonds between real atoms behave. Twice the stretch does not produce exactly twice the force. Fermi suspected that this nonlinear character of chemical bonds might be the key to the inevitable increase of entropy. Unfortunately, it also made the mathematics impenetrable. A nonlinear system like this couldn't be analyzed by breaking it into pieces. Indeed, that's the hallmark of a nonlinear system: the parts don't add up to the whole. Understanding a system like this defied all known methods. It was a mathematical monster.
Undaunted, Fermi and his collaborators plucked their virtual string and let Maniac grind away, calculating hundreds of simultaneous interactions, updating all the forces and positions, marching the virtual string forward in time in a series of slow-motion snapshots. They expected to see its shape degenerate into a random vibration, the musical counterpart of which would be a meaningless hiss, like static on the radio.
What the computer revealed was astonishing. Instead of a hiss, the string played an eerie tune, almost like music from an alien civilization. Starting from a pure tone, it progressively added a series of overtones, replacing one with another, gradually changing the timbre. Then it suddenly reversed direction, deleting overtones in the opposite sequence, before finally returning almost precisely to the original tone. Even creepier, it repeated this strange melody again and again, indefinitely, but always with subtle variations on the theme.
Fermi loved this result - he referred to it affectionately as a "little discovery." He had never guessed that nonlinear systems could harbor such a penchant for order.
In the 50 years since this pioneering study, scientists and engineers have learned to harness nonlinear systems, making use of their capacity for self-organization. Lasers, now used everywhere from eye surgery to checkout scanners, rely on trillions of atoms emitting light waves in unison. Superconductors transmit electrical current without resistance, the byproduct of billions of pairs of electrons marching in lock step. The resulting technology has spawned the world's most sensitive detectors, used by doctors to pinpoint diseased tissues in the brains of epileptics without the need for invasive surgery, and by geologists to locate oil buried deep underground.
But perhaps the most important lesson of Fermi's study is how feeble even the best minds are at grasping the dynamics of large, nonlinear systems. Faced with a thicket of interlocking feedback loops, where everything affects everything else, our familiar ways of thinking fall apart. To solve the most important problems of our time, we're going to have to change the way we do science.
For example, cancer will not be cured by biologists working alone. Its solution will require a melding of both great discoveries of 1953. Many cancers, perhaps most of them, involve the derangement of biochemical networks that choreograph the activity of thousands of genes and proteins. As Fermi and his colleagues taught us, a complex system like this can't be understood merely by cataloging its parts and the rules governing their interactions. The nonlinear logic of cancer will be fathomed only through the collaborative efforts of molecular biologists - the heirs to Dr. Watson and Dr. Crick - and mathematicians who specialize in complex systems - the heirs to Fermi, Pasta and Ulam.
Can such an alliance take place? Well, it can if scientists embrace the example set by an unstoppable 86-year-old who, following his co-discovery of the double helix, became increasingly interested in computer simulations of complex systems in the brain.
Happy anniversary, Dr. Crick. And a toast to the memory of Enrico Fermi.
Steven Strogatz, professor of applied mathematics at Cornell, is author of "Sync: The Emerging Science of Spontaneous Order."
R. A. Hettinga <mailto: email@example.com>
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