...And, on an entertaining side-note, Clifford Pickover often posts "shiver in awe" tweets about mathematical factoids that are astounding to learn of. And this one just about did make me shiver in awe:
"The string 62644957128 occurs at position 62644957128 in the decimal digits of Pi. tinyurl.com/blrm9ar " WHOOOOA!!
"Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born" --Jonathan Coulton
If the life of Benoit Mandelbrot interests you then a new book coming out shortly will be of note, a posthumous autobiography, entitled "The Fractalist." [Mandelbrot died just 2 years ago this month.]
I haven't read it, but from what I can tell, if you're interested primarily in the details of Mandelbrot's mathematical contributions this volume may not be a good choice, but if you're interested in his life this is a definite read:
"It was the winter of 1961. When he made this discovery, Mandelbrot was at IBM, studying income distribution patterns between the rich and poor. The Harvard economics department invited him to speak about his work. He walked into the office of his host that day to a surprise. On the chalk-board was a figure with a convex shape that opened to the right. He immediately turned to Professor Hendrik Houthhakker and asked why his diagram was already drawn. Houthhakker was perplexed: ‘These are graphs of cotton prices.’
"The puzzling similarity in pattern between income distribution and cotton prices got Mandelbrot thinking. Was it pure coincidence that the two were spitting images of one another, or was there a deeper truth in the strange connection between the two pictures? And so it was that Mandelbrot was propelled into investigating the mysteries of finance."
and it concludes this way:
"These models, Mandelbrot’s body of work suggests, have caused us to misperceive risk in a dangerous way. His work is a potential explanation to unusual market volatility: it suggests that our notions of ‘usual’ might be incorrect. There are academics who have taken up the baton from Mandelbrot, who died last October. These scholars work to build fractal descriptions of markets, models that take into account the Levy distribution. It remains to be seen how long it will take Wall Street to begin using these Levy-based models."
His name will forever leave its stamp on mathematics. In memory, I'll just re-post the 3rd post I ever ran on this blog, one of the many tributes to his Mandelbrot Set that can be found on the Web:
YouTube video of Mandelbrot Set with Jonathan Coulton's lyrics below:
lyrics:
Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born
His disdain for pure mathematics and his unique geometrical insights
Left him well equipped to face those demons down
He saw that infinite complexity could be described by simple rules
He used his giant brain to turn the game around
And he looked below the storm and saw a vision in his head
A bulbous pointy form
He picked his pencil up and he wrote his secret down
Take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Mandelbrot's in heaven, at least he will be when he's dead
Right now he's still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home
Just take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Go on change the world in a tiny way
Come on change the world in a tiny way
