You Wake Me Up Early In The

If You Tell Me Precisely What It Is A Machine Cannot Do, Then I Can Always Make A Machine Which Will Do Just That.

The Sciences Do Not Try To Explain, They Hardly Even Try To Interpret, They Mainly Make Models. By A Model Is Meant A Mathematical Construct Which, With The Addition Of Certain Verbal Interpretations, Describes Observed Phenomena. The Justification Of Such A Mathematical Construct Is Solely And Precisely That It Is Expected To Work-that Is, Correctly To Describe Phenomena From A Reasonably Wide Area.

The Most Vitally Characteristic Fact About Mathematics Is, In My Opinion, Its Quite Peculiar Relationship To The Natural Sciences, Or More Generally, To Any Science Which Interprets Experience On A Higher Than Purely Descriptive Level.

Neumann, To A Physicist Seeking Help With A Difficult Problem: Simple. This Can Be Solved By Using The Method Of Characteristics. Physicist: I'm Afraid I Don't Understand The Method Of Characteristics. Neumann: In Mathematics You Don't Understand Things. You Just Get Used To Them.

Any One Who Considers Arithmetical Methods Of Producing Random Digits Is, Of Course, In A State Of Sin. For, As Has Been Pointed Out Several Times, There Is No Such Thing As A Random Number - There Are Only Methods To Produce Random Numbers, And A Strict Arithmetic Procedure Of Course Is Not Such A Method.