James Gleick

Chaos: Making a New Science


Chapter 4. A Geometry of Nature

Benoit Mandelbrot (1960s). Contributed ideas on fractional dimension.

Born in Warsaw 1924. Lithuanian Jewish family.

Father clothing wholesaler, mother dentist.

Moved to Paris in 1936 (!!!)

Uncle Szolem Mandelborjt, mathematician in Paris, founter of Bourbaki.

Apprentice toolmaker.

Sporadic education.

Liberation of Paris.

Passed month-long oral and written exam for elite Ecole Normale and Ecole Polytechnique. Relied on geometrical intuition to solve analytical problems. Didn't fit Bourbaki mold.

Acquired knowledge of history of math and science.

Mathematical linguistics: Distribution of words in texts.

Investigations into game theory.

Economics: scaling regularities in economies of large and small cities.

At IBM: study of distribution of noise in telephone lines.

Study of water level of Nile river. Quantity can change discretely, but trends can be extended through time (Cantor-like behavior)

Classical geomterty: too smooth to capture nature. Infinitely embedded pits and roughtness are the essence of nature, rather than accidents to be ignored (note figure/ground issue again).

Coastline study:

Chkristopher Scholz, Lamont-Doherty Geophysical Observatory.

Anatomy:

Mandelbrot finds fame:

Self-similarity

Remained for physics to turn chaos into a science. Fractal geometry is an effect, not a cause and scientists want to know why.