The Extraordinary Fact Is That The First

I've Been A Professor Of Mathematics At Harvard And At Yale. At Yale For A Long Time. But I'm Not A Mathematician Only. I'm A Professor Of Physics, Of Economics, A Long List. Each Element Of This List Is Normal. The Combination Of These Elements Is Very Rare At Best.

Regular Geometry, The Geometry Of Euclid, Is Concerned With Shapes Which Are Smooth, Except Perhaps For Corners And Lines, Special Lines Which Are Singularities, But Some Shapes In Nature Are So Complicated That They Are Equally Complicated At The Big Scale And Come Closer And Closer And They Don't Become Any Less Complicated.

The Mandelbrot Set Is The Most Complex Mathematical Object Known To Mankind.

Beautiful, Damn Hard, Increasingly Useful. That's Fractals.

If You Look At Coastlines, If You Look At That Them From Far Away, From An Airplane, Well, You Don't See Details, You See A Certain Complication. When You Come Closer, The Complication Becomes More Local, But Again Continues. And Come Closer And Closer And Closer, The Coastline Becomes Longer And Longer And Longer Because It Has More Detail Entering In.