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

Science Would Be Ruined If (like Sports) It Were To Put Competition Above Everything Else, And If It Were To Clarify The Rules Of Competition By Withdrawing Entirely Into Narrowly Defined Specialties. The Rare Scholars Who Are Nomads-by-choice Are Essential To The Intellectual Welfare Of The Settled Disciplines.

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 Beauty Of What I Happened By Extraordinary Chance To Put Together Is That Nobody Would Have Believed That This Is Possible, And Certainly I Didn't Expect That It Was Possible. I Just Moved From Step To Step To Step.

In Mathematics And Science Definition Are Simple, But Bare-bones. Until You Get To A Problem Which You Understand It Takes Hundreds And Hundreds Of Pages And Years And Years Of Learning.

I Claim That Many Patterns Of Nature Are So Irregular And Fragmented, That, Compared With Euclid - A Term Used In This Work To Denote All Of Standard Geometry - Nature Exhibits Not Simply A Higher Degree But An Altogether Different Level Of Complexity ... The Existence Of These Patterns Challenges Us To Study These Forms That Euclid Leaves Aside As Being "formless," To Investigate The Morphology Of The "amorphous."