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The Extraordinary Fact Is That The First Idea I Had Which Motivated Me, That Worked, Is Conjecture, A Mathematical Idea Which May Or May Not Be True. And That Idea Is Still Unproven. It Is The Foundation, What Started Me And What Everybody Failed To **** Prove Has So Far Defeated The Greatest Efforts By Experts To Be Proven.

-Benoit Mandelbrot

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The Extraordinary Fact Is

Benoit Mandelbrot

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The Extraordinary Fact Is That The First Idea I Had Which Motivated Me, That Worked, Is Conjecture, A Mathematical Idea Which May Or May Not Be True. And That Idea Is Still Unproven. It Is The Foundation, What Started Me And What Everybody Failed To **** Prove Has So Far Defeated The Greatest Efforts By Experts To Be Proven.

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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.

Unfortunately, The World Has Not Been Designed For The Convenience Of Mathematicians.

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.

The Techniques I Developed For Studying Turbulence, Like Weather, Also Apply To The Stock Market

I Conceived And Developed A New Geometry Of Nature And Implemented Its Use In A Number Of Diverse Fields. It Describes Many Of The Irregular And Fragmented Patterns Around Us, And Leads To Full-fledged Theories, By Identifying A Family Of Shapes I Call Fractals.

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."

Many Painters Had A Clear Idea Of What Fractals Are. Take A French Classic Painter Named Poussin. Now, He Painted Beautiful Landscapes, Completely Artificial Ones, Imaginary Landscapes. And How Did He Choose Them? Well, He Had The Balance Of Trees, Of Lawns, Of Houses In The Distance. He Had A Balance Of Small Objects, Big Objects, Big Trees In Front And His Balance Of Objects At Every Scale Is What Gives To Poussin A Special Feeling.

I Was In An Industrial Laboratory Because Academia Found Me Unsuitable

If You Look At A Shape Like A Straight Line, What's Remarkable Is That If You Look At A Straight Line From Close By, From Far Away, It Is The Same; It Is A Straight Line.

The Rare Scholars Who Are Nomads-by-choice Are Essential To The Intellectual Welfare Of The Settled Disciplines.

The Extraordinary Fact Is That The First Idea I Had Which Motivated Me, That Worked, Is Conjecture, A Mathematical Idea Which May Or May Not Be True. And That Idea Is Still Unproven. It Is The Foundation, What Started Me And What Everybody Failed To **** Prove Has So Far Defeated The Greatest Efforts By Experts To Be Proven.

Engineering Is Too Important To Wait For Science.

When People Ask Me What's My Field? I Say, On One Hand, A Fractalist. Perhaps The Only One, The Only Full-time One.

The Most Complex Object In Mathematics, The Mandelbrot Set ... Is So Complex As To Be Uncontrollable By Mankind And Describable As 'chaos'.

Think Not Of What You See, But What It Took To Produce What You See.

Round About The Accredited And Orderly Facts Of Every Science There Ever Floats A Sort Of Dustcloud Of Exceptional Observations, Of Occurrences Minute And Irregular And Seldom Met With, Which It Always Proves More Easy To Ignore Than To Attend To.

I Went To The Computer And Tried To Experiment. I Introduced A Very High Level Of Experiment In Very Pure Mathematics.

Think Of Color, Pitch, Loudness, Heaviness, And Hotness. Each Is The Topic Of A Branch Of Physics

Everybody In Mathematics Had Given Up For 100 Years Or 200 Years The Idea That You Could From Pictures, From Looking At Pictures, Find New Ideas. That Was The Case Long Ago In The Middle Ages, In The Renaissance, In Later Periods, But Then Mathematicians Had Become Very Abstract.

Why Is Geometry Often Described As Cold And Dry? One Reason Lies In Its Inability To Describe The Shape Of A Cloud, A Mountain, A Coastline Or A Tree.

I Had Very, Very Little Training In Taking An Exam To Determine A Scientist's Life In France.

I Was Asking Questions Which Nobody Else Had Asked Before, Because Nobody Else Had Actually Looked At Certain Structures. Therefore, As I Will Tell, The Advent Of The Computer, Not As A Computer But As A Drawing Machine, Was For Me A Major Event In My Life. That's Why I Was Motivated To Participate In The Birth Of Computer Graphics, Because For Me Computer Graphics Was A Way Of Extending My Hand, Extending It And Being Able To Draw Things Which My Hand By Itself, And The Hands Of Nobody Else Before, Would Not Have Been Able To Represent.

Asking Questions

I Conceived, Developed And Applied In Many Areas A New Geometry Of Nature, Which Finds Order In Chaotic Shapes And Processes. It Grew Without A Name Until 1975, When I Coined A New Word To Denote It, Fractal Geometry, From The Latin Word For Irregular And Broken Up, Fractus. Today You Might Say That, Until Fractal Geometry Became Organized, My Life Had Followed A Fractal Orbit.

Humanity Has Known For A Long Time What Fractals Are. It Is A Very Strange Situation In Which An Idea Which Each Time I Look At All Documents Have Deeper And Deeper Roots, Never (how To Say It), Jelled.

For Much Of My Life There Was No Place Where The Things I Wanted To Investigate Were Of Interest To Anyone.

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Asking The Right Questions Is As Important As Answering Them

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Some Mathematicians Didn't Even Perceive Of The Possibility Of A Picture Being Helpful. To The Contrary, I Went Into An Orgy Of Looking At Pictures By The Hundreds; The Machines Became A Little Bit Better.

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An Extraordinary Amount Of Arrogance Is Present In Any Claim Of Having Been The First In Inventing Something.

Bottomless Wonders Spring From Simple Rules, Which Are Repeated Without End.

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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.

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Fractal Geometry Is Not Just A Chapter Of Mathematics, But One That Helps Everyman To See The Same World Differently.

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Being A Language, Mathematics May Be Used Not Only To Inform But Also, Among Other Things, To Seduce.

Order Doesn't Come By Itself.

My Fate Has Been That What I Undertook Was Fully Understood Only After The Fact.

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There Is A Saying That Every Nice Piece Of Work Needs The Right Person In The Right Place At The Right Time.

For Most Of My Life, One Of The Persons Most Baffled By My Own Work Was Myself.

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

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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.

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A Cloud Is Made Of Billows Upon Billows Upon Billows That Look Like Clouds. As You Come Closer To A Cloud You Don't Get Something Smooth, But Irregularities At A Smaller Scale.

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Pictures Were Completely Eliminated From Mathematics; In Particular When I Was Young This Happened In A Very Strong Fashion.

Self-similarity Is A Dull Subject Because You Are Used To Very Familiar Shapes. But That Is Not The Case. Now Many Shapes Which Are Self-similar Again, The Same Seen From Close By And Far Away, And Which Are Far From Being Straight Or Plane Or Solid.

One Couldn't Even Measure Roughness. So, By Luck, And By Reward For Persistence, I Did Found The Theory Of Roughness, Which Certainly I Didn't Expect And Expecting To Found One Would Have Been Pure Madness.

I Don't Seek Power And Do Not Run Around

A Fractal Is A Way Of Seeing Infinity.

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