James Gleick

Chaos: Making a New Science


Normal big physics:

False assumption: complex behavior ===> complex causes.

Traditional anomalies for normal physics:

1970s New paradigm.

Emergence from across disciplines.

New techniques: Computer simulation and graphics

New language: fractals, lyopunov exponents, etc.

New vision:

Shifted focus:

Revolution complete:

Writing history: 20th c. = Relativity, Quantum, Chaos.

1. The Butterfly Effect

Physics: slide rule forecasts for spacecraft, comets, planets.

Meteorology: same idea, but more variables. Waited for computer.

Von Neumann: built a computer at the Institute for Advanced Study, Princeton.

Saw weather modelling as ideal task.

1950-60s: John Von Neumann saw critical points of instability of weather systems as an opportunity for control: cloud seeding. Tremendous optimism.

Didn't expect instability at every point.

Achilles' heel: need predictions to know where you are forcing the weather to.

Tacit assumption of prediction: given approximate initial conditions, you can get approximate state of a deterministic system later.

Works for comets and spacecraft. Less in economics. Less in weather prediction.

1980s: huge supercomputer weather modelling industry. Practice spread to economic forecasting.

Model parameters tinkered when strange predictions come out (sound familiar?)

Never able to predict more than three days.

Weather states represented by sixty mile grid pattern. Dust devils missed by grid can cascade into squalls, eddies, hurricanes.

Philosopher/Physicist Henri Poincare clearly made these observations about the mathematics of the Newtonian 3-body problem at the turn of the century. The mathematician Birkhoff learned it from Poincare. Edward Lorenz heard lectures by Birkhoff at MIT.

Edward Lorenz:

Butterfly effect:

Computer weather simulation on tube computer in office.

Output oscillating, semi-periodic graphs of pressure, wind direction, etc.

One day re-ran a simulation with a slightly truncated decimal expansion of initial condition.

.506127 vs. .506

Truncation same as small puff of wind on a global scale.

Started similar and quickly grew completely different.

Discovery: long-run weather prediction is doomed.

Von Neumann's control program is blind: can't predict where you are moving the weather to.

Problem is not randomness but deterministic geometry mimicking randomness.

Linked unpredictabilitiy to aperiodicity: if small perturbations didn't become big, then passing nearby to a previously visited state would result in predictable near-cycle. So aperiodicity is linked to unpredictability.

Sought aperiodic variation of weather model and found it. Colleagues astonished that twelve equations could produce both.

Simplified system to 3 nonlinear equations.

Usually linear equations are studied, since they are solvable and solutions can be superimposed (Notice tacit textbook influence in paradigm. Recall Kuhn's discussion of tacit knowledge).

Nonlinearity arises from "accidents" that Galileo taught us to leave out: e.g., friction.

Friction depends on speed, speed depends on friction. "Rules change as you play the game".

Fluid mechanics: Navier-Stokes equataions. Nonlinear. Von Neumann: mathematical difficulties must be expected.

Lorenz' 3-equation model: arises from convection.

Convection cells.

Water wheel model: friction pivot, leaky buckets, variable water spigot.

Models disk rotataing in magnetic field. Historically known that such disks periodically reverse themselves.

Application to earth's magnetic field, which inexplicably reverses.

Lorenz attractor: plot of trajectory of system in 3-space.

Complex behavior contrary to physicist's intuitions about such simple equations.

Science highly compartmentalized. Too much to read in each discipline. Nobody in biology, ecomomics, etc. saw Lorenz's paper in Journal of the Atmospheric Sciences.

Some questions:

  1. What possibility was not on the table for physicists?
  2. Why not? Do science textbooks teach more than they intend? What does this say about Kuhn's concept of the tacit knowledge of a paradigm?
  3. Was there a crisis here? What was Lorenz's role in the "revolution"?
  4. How well does Lorenz fit Kuhn's profile of an extraordinary scientist?
  5. Was was discovered? Did it contradict anything in classical physics? How then was it new?
  6. Is Gleick pushing the Kuhn wagon too hard?
  7. Why would anybody want to?