Chance ... Must Be Something More Than

One Would Have To Have Completely Forgotten The History Of Science So As To Not Remember That The Desire To Know Nature Has Had The Most Constant And The Happiest Influence On The Development Of Mathematics.

If We Ought Not To Fear Mortal Truth, Still Less Should We Dread Scientific Truth. In The First Place It Can Not Conflict With Ethics? But If Science Is Feared, It Is Above All Because It Can Give No Happiness? Man, Then, Can Not Be Happy Through Science But Today He Can Much Less Be Happy Without It.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means. The Geometer Might Be Replaced By The "logic Piano" Imagined By Stanley Jevons; Or, If You Choose, A Machine Might Be Imagined Where The Assumptions Were Put In At One End, While The Theorems Came Out At The Other, Like The Legendary Chicago Machine Where The Pigs Go In Alive And Come Out Transformed Into Hams And Sausages. No More Than These Machines Need The Mathematician Know What He Does.

It May Happen That Small Differences In The Initial Conditions Produce Very Great Ones In The Final Phenomena. A Small Error In The Former Will Produce An Enormous Error In The Later. Prediction Becomes Impossible, And We Have The Fortuitous Phenomena.

Geometry Is Not True, It Is Advantageous.