It Is A Common Observation That Those

Among The Minor, Yet Striking Characteristics Of Mathematics, May Be Mentioned The Fleshless And Skeletal Build Of Its Propositions; The Peculiar Difficulty, Complication, And Stress Of Its Reasonings; The Perfect Exactitude Of Its Results; Their Broad Universality; Their Practical Infallibility.

Looking Out Of My Window This Lovely Spring Morning I See An Azalea In Full Bloom. No, No! I Do Not See That; Though That Is The Only Way I Can Describe What I See. That Is A Proposition, A Sentence, A Fact; But What I Perceive Is Not Proposition, Sentence, Fact, But Only An Image Which I Make Intelligible In Part By Means Of A Statement Of Fact. This Statement Is Abstract; But What I See Is Concrete.

It Has Never Been In My Power To Study Anything, Mathematics, Ethics, Metaphysics, Gravitation, Thermodynamics, Optics, Chemistry, Comparative Anatomy, Astronomy, Psychology, Phonetics, Economics, The History Of Science, Whist, Men And Women, Wine, Metrology, Except As A Study Of Semeiotic .

Theoretically, I Grant You, There Is No Possibility Of Error In Necessary Reasoning. But To Speak Thus "theoretically," Is To Uselanguage In A Pickwickian Sense. In Practice, And In Fact, Mathematics Is Not Exempt From That Liability To Error That Affects Everything That Man Does.

It Is Not Too Much To Say That Next After The Passion To Learn There Is No Quality So Indispensable To The Successful Prosecutionof Science As Imagination. Find Me A People Whose Early Medicine Is Not Mixed Up With Magic And Incantations, And I Will Find You A People Devoid Of All Scientific Ability.