MANDELBROT... THE FIRST AND GREATEST CHAOTICIAN OF OUR TIME!!!

I. Life Overview

A. Born in Warsaw in 1924 to Lithuanian Jewish Family

B. Moved to Paris, France in 1936

C. Received no elementary education

D. Enrolled in prestigious colleges/academies in France

1. Uncle Szolem Mandelbrot was member of "Bourbaki" (French Mathematicians) and helped nephew along.

E. Never understood Algebra, solved problems by "picturing" them in his mind

F. Condemned Euclidean Geometry because it only had 3 dimensions, none of which were reality. (earned doctorate in Math)

G. Left Bourbaki and pursued radical views, led to America. (Yorktown Heights, NY; IBM research center)

H. became expert at:

1. linguistics 2. game theories 3. aeronautics

4. engineering 5. economics 6. physiology

7. geography 8. astronomy 9. physics

I. First mathematician with access to high-speed computers

II. Fractals, Chaos, and the Fourth dimension

A. First stumbled across it in economics. (See below)

B. Said "Aha!" There is a pattern in the irregularity of economics (if you look hard enough)

C. Used computers to calculate z - > z² + c (Mandelbrot Set) GREATEST discovery in 20th century mathematics? Based on dynamic calculations based on the constant feedback of complex numbers with zero as the starting point. By hand, this equation generates a totally random and meaningless set of numbers. Computers can make the billions of computations quickly and represent them graphically on a 2d plane (the screen) to show what you see. If you magnify far enough, you will see even more mandelbrot sets. Magnify more, and you'll see more (etc. for infinity)

D. Fourth dimension

E. IMPORTANT QUOTE: KEY TO ENTIRE IDEA--- "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

F. ONLY dimension capable of describing the chaotic forms of the real world

G. Fractal = from Latin "fractus" meaning to create irregular fragments (self- contained chance)

H. "Just so every snow flake falling from the same cloud at the same time under identical conditions is still unique, different from all of the rest. This is only possible because of the infinity which lies in the fourth dimension and the interplay of chance-the unpredictable chaos.

I. Cantor's Dust = fractal between 0 and the first dimension

1. draw a line, erase the middle third

2. two lines now, erase the middle third of each

3. three lines now, erase the middle third of each

4. continue forever (yeah, right)

5. Created in early 1900's by George Cantor, avoided as a "useless monstrosity" until Mandelbrot revealed the fourth dimension.

6. numerical value = .63

7. result is between points and line (0 and 1d)

J. IBM had errors in data transfers that seemed totally random: Mandelbrot found a pattern in the fourth dimension (more specifically, between 0 and the first dimension) and found it to correspond to Cantor's Dust. SOLVED THE PROBLEM!

K. Sierpiniski Gasket (Waclaw Sierpiniski)

1. between first and second dimensions (line and plane)

2. numerical value = 1.58

3. take equilateral triangle, remove central upside down triangle

4. repeat forever in each resulting triangle

5. result is more than a line... more than a plane!

L. Fractals exist everywhere (clouds, lightning, trees, blood vessels, galaxies, mountains, bushes, ferns, etc.)