"Nancy Kress - Feigenbaum Number" - читать интересную книгу автора (Kress Nancy)

She was the only person I'd ever seen who came close to matching what she should have
been.
"This is the latest batch of phase space diagrams," Fran said. "The computer just finished
them -- I haven't even, printed them, yet."
I crouched beside her to peer at the terminal.
"Don't look any more disorganized to me than the last bunch."
"Nor to me, either, unfortunately. Same old, same old." She laughed: in chaos theory, there
is no same old, same old. The phase space diagrams were infinitely complex, never repeating,
without control.
But not completely. The control was there, not readily visible, a key we just didn't
recognize with the mathematics we had. Yet.
An ideal no one had seen.
"I keep thinking that your young mind will pick up something I've missed," Fran said. "I'll
make you a copy of these. Plus, Pyotr Solenski has published some new work in Berlin that I
think you should take a look at. I downloaded it from the net and e-mailed you."
I nodded, but didn't answer. For the first time today, calm flowed through me, soothing me.
Calm.
Rightness.
Numbers.
Fran had done good, if undistinguished, work in pure mathematics all her life. For the last
few years she -- and I, as her graduate student -- had worked in the precise and austere
world of iterated function theory, where the result of a given equation is recycled as the
starting value of the next repetition of the same equation. If you do that, the results are
predictable: the sequences will converge on a given set of numbers. No matter what initial
value you plug into the equation, with enough iterations you end up at the same figures,
called attractors. Every equation can generate a set of attractors, which iterations converge
on like homing pigeons flying back to their nests.
Until you raise the value plugged into the equation past a point called the Feigenbaum
number. Then the sequences produced lose all regularity. You can no longer find any pattern.
Attractors disappear. The behavior of even fairly simple equations becomes chaotic. The
pigeons fly randomly, blind and lost.
Or do they?
Fran -- like dozens of other pure mathematicians around the world -- looked at all that
chaos, and sorted through it, and thought she glimpsed an order to the pigeons' flight. A
chaotic order, a controlled randomness. We'd been looking at nonlinear differential equations,
and at their attractors, which cause iterated values not to converge but to diverge. States
which start out only infinitesimally separated go on to diverge more and more and more ... and
more, moving toward some hidden values called, aptly enough, strange attractors. Pigeons
from the same nest are drawn, through seeming chaos, to points we can identify but not
prove the existence of.
Fran and I had a tentative set of equations for those idealized points.
Only tentative. Something wasn't right. We'd overlooked something, something neither of
us could see. It was there -- I knew it -- but we couldn't see it. When we did, we'd have
proof that any physical system showing an ultra dependence on initial conditions must have a
strange attractor buried somewhere in its structure. The implications would be profound -- for
chaos mathematics, for fluid mechanics, for weather control.
 For me.
I loved looking for that equation. Sometimes I thought I could glimpse it, behind the work
we were doing, almost visible to me. But not often. And the truth I hadn't told Fran, couldn't
tell her, was that I didn't need to find it, not in the way she did. She was driven by the finest