It Is The Simple Hypotheses Of Which

A Reality Completely Independent Of The Spirit That Conceives It, Sees It, Or Feels It, Is An Impossibility. A World So External As That, Even If It Existed, Would Be Forever Inaccessible To Us.

Pure Logic Could Never Lead Us To Anything But Tautologies; It Can Create Nothing New; Not From It Alone Can Any Science Issue.

Mathematics Has A Threefold Purpose. It Must Provide An Instrument For The Study Of Nature. But This Is Not All: It Has A Philosophical Purpose, And, I Daresay, An Aesthetic Purpose.

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.

Astronomy Is Useful Because It Raises Us Above Ourselves; It Is Useful Because It Is Grand; .... It Shows Us How Small Is Man's Body, How Great His Mind, Since His Intelligence Can Embrace The Whole Of This Dazzling Immensity, Where His Body Is Only An Obscure Point, And Enjoy Its Silent Harmony.