Just As Houses Are Made

All Great Progress Takes Place When Two Sciences Come Together, And When Their Resemblance Proclaims Itself, Despite The Apparent Disparity Of Their Substance.

I Then Began To Study Arithmetical Questions Without Any Great Apparent Result, And Without Suspecting That They Could Have The Least Connexion With My Previous Researches. Disgusted At My Want Of Success, I Went Away To Spend A Few Days At The Seaside, And Thought Of Entirely Different Things. One Day, As I Was Walking On The Cliff, The Idea Came To Me, Again With The Same Characteristics Of Conciseness, Suddenness, And Immediate Certainty, That Arithmetical Transformations Of Indefinite Ternary Quadratic Forms Are Identical With Those Of Non-euclidian Geometry.

To Invent Is To Discern, To Choose.

Geometry Is Not True, It Is Advantageous.

So Is Not Mathematical Analysis Then Not Just A Vain Game Of The Mind? To The Physicist It Can Only Give A Convenient Language; But Isn't That A Mediocre Service, Which After All We Could Have Done Without; And, It Is Not Even To Be Feared That This Artificial Language Be A Veil, Interposed Between Reality And The Physicist's Eye? Far From That, Without This Language Most Of The Initimate Analogies Of Things Would Forever Have Remained Unknown To Us; And We Would Never Have Had Knowledge Of The Internal Harmony Of The World, Which Is, As We Shall See, The Only True Objective Reality.