[EAS]New Kind of Science
pjk at design.eng.yale.edu
Wed Mar 5 22:48:06 EST 2003
Mail*Link¨ SMTP New Kind of Science
Dear Colleagues -
This NYT item courtesy of my colleague Nathan Price. As you will be
aware, with the publication of his book "A New Kind of Science,"
Stephen Wolfram, of Mathematica fame, is advocating a new kind of
science, not in mathematically closed-form but based on the
automata-like behaviors of simple computer programs.
If you happen to be in Boston on March 17th, Wolfram is talking
about his work at Boston Univ., George Sherman Union, Metcalf Hall,
775 Commonwealth Ave. @ 7pm <www.bu.edu/mathfn/NKS>. I wonder how
we'll be looking back at this 50 years from now.
The Real Scientific Hero of 1953
March 4, 2003
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
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
Steven Strogatz, professor of applied mathematics at
Cornell, is author of "Sync: The Emerging Science of
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