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The Last Level Of Metaphor In The Alice Books Is This: That Life, Viewed Rationally And Without Illusion, Appears To Be A Nonsense Tale Told By An Idiot Mathematician. At The Heart Of Things Science Finds Only A Mad, Never-ending Quadrille Of Mock Turtle Waves And Gryphon Particles. For A Moment The Waves And Particles Dance In Grotesque, Inconceivably Complex Patterns Capable Of Reflecting On Their Own Absurdity.

-Martin Gardner

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The Last Level Of

Martin Gardner

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The Last Level Of Metaphor In The Alice Books Is This: That Life, Viewed Rationally And Without Illusion, Appears To Be A Nonsense Tale Told By An Idiot Mathematician. At The Heart Of Things Science Finds Only A Mad, Never-ending Quadrille Of Mock Turtle Waves And Gryphon Particles. For A Moment The Waves And Particles Dance In Grotesque, Inconceivably Complex Patterns Capable Of Reflecting On Their Own Absurdity.

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Biographical History, As Taught In Our Public Schools, Is Still Largely A History Of Boneheads; Ridiculous Kings And Queens, Paranoid Political Leaders, Compulsive Voyagers, Ignorant General The Flotsam And Jetsam Of Historical Currents. The Men Who Radically Altered History, The Great Scientists And Mathematicians, Are Seldom Mentioned, If At All.

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The Universe Is Almost Like A Huge Magic Trick And Scientists Are Trying To Figure Out How It Does What It Does.

The Last Level Of Metaphor In The Alice Books Is This: That Life, Viewed Rationally And Without Illusion, Appears To Be A Nonsense Tale Told By An Idiot Mathematician.

The Sudden Hunch, The Creative Leap Of Mind That "sees" In A Flash How To Solve A Problem In A Simple Way, Is Something Quite Different From General Intelligence.

Wouldn't The Sentence 'i Want To Put A Hyphen Between The Words Fish And And And And And Chips In My Fish-and-chips Sign' Have Been Clearer If Quotation Marks Had Been Placed Before Fish, And Between Fish And And, And And And And, And And And And, And And And And, And And And And, And And And Chips, As Well As After Chips?

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Let The Bible Be The Bible. It's Not About Science. It's Not Accurate History. It Is A Grab Bag Of Religious Fantasies Written By Many Authors. Some Of Its Myths, Like The Star Of Bethlehem, Are Very Beautiful. Others Are Dull And Ugly. Some Express Lofty Ideals, Such As The Parables Of Jesus. Others Are Morally Disgusting.

Consider A Cow. A Cow Doesn't Have The Problem-solving Skill Of A Chimpanzee, Which Has Discovered How To Get Termites Out Of The Ground By Putting A Stick Into A Hole. Evolution Has Developed The Brain's Ability To Solve Puzzles, And At The Same Time Has Produced In Our Brain A Pleasure Of Solving Problems.

When Reputable Scientists Correct Flaws In An Experiment That Produced Fantastic Results, Then Fail To Get Those Results When They Repeat The Test With Flaws Corrected, They Withdraw Their Original Claims. They Do Not Defend Them By Arguing Irrelevantly That The Failed Replication Was Successful In Some Other Way, Or By Making Intemperate Attacks On Whomever Dares To Criticize Their Competence.

As Far As I Know, Clifford Pickover Is The First Mathematician To Write A Book About Areas Where Math And Theology Overlap. Are There Mathematical Proofs Of God? Who Are The Great Mathematicians Who Believed In A Deity? Does Numerology Lead Anywhere When Applied To Sacred Literature? Pickover Covers These And Many Other Off-trail Topics With His Usual Verve, Humor, And Clarity. And Along The Way The Reader Will Learn A Great Deal Of Serious Mathematics.

Speaking About Symmetry, Look Out Our Window, And You May See A Cardinal Attacking Its Reflection In The Window. The Cardinal Is The Only Bird We Have Who Often Does This. If It Has A Nest Nearby, The Cardinal Thinks There Is Another Cardinal Trying To Invade Its Territory. It Never Realizes It Is Attacking Its Own Reflection. Cardinals Don't Know Much About Mirror Symmetry!

It Is Part Of The Pholosophic Dullness Of Our Time That There Are Millions Of Rational Monsters Walking About On Their Hind Legs, Observing The World Through Pairs Of Flexible Little Lenses, Periodically Supplying Themselves With Energy By Pushing Organic Substances Through Holes In Their Faces, Who See Nothing Fabulous Whatever About Themselves.

The High Number From The Middle East Is Only Coincidence, He Said. It Is No Particular Choice On Our Part, ... We Accept Visa Trainees From Those Countries. We'd Accept Them From Other Countries, Too, But We Don't Get Their Applications.

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One Day, When I Was Doing Well In Class And Had Finished My Lessons, I Was Sitting There Trying To Analyze The Game Of Tic-tac-toe... The Teacher Came Along And Snatched My Papers On Which I Had Been Doodling... She Did Not Realize That Analyzing Tic-tac-toe Can Lead Into Dozens Of Non-trivial Mathematical Questions.

Although Lewis Carroll Thought Of The Hunting Of The Snark As A Nonsense Ballad For Children, It Is Hard To Imagine - In Fact One Shudders To Imagine - A Child Of Today Reading And Enjoying It.

The Greatest Scandal Of The Century In American Psychiatry ... Is The Growing Mania Among Thousands Of Inept Therapists, Family Counselors, And Social Workers For Arousing False Memories Of Childhoood Sexual Abuse.

Mathematics Is Not Only Real, But It Is The Only Reality.

Modern Science Should Indeed Arouse In All Of Us A Humility Before The Immensity Of The Unexplored And A Tolerance For Crazy Hypotheses.

If God Creates A World Of Particles And Waves, Dancing In Obedience To Mathematical And Physical Laws, Who Are We To Say That He Cannot Make Use Of Those Laws To Cover The Surface Of A Small Planet With Living Creatures?

One Would Be Hard Put To Find A Set Of Whole Numbers With A More Fascinating History And More Elegant Properties Surrounded By Greater Depths Of Mystery--and More Totally Useless--than The Perfect Numbers.

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Indeed, There Is Something To Be Said For The Old Math When Taught By A Poorly Trained Teacher. He Can, At Least, Get Across The Fundamental Rules Of Calculation Without Too Much Confusion. The Same Teacher Trying To Teach New Math Is Apt To Get Across Nothing At All.

[t]he More The Public Is Confused, The Easier It Falls Prey To Doctrines Of Pseudo-science Which May At Some Future Date Recieve The Backing Of Politically Powerful Groups [...]a Renaissance Of German Quasi-science Paralleled The Rise Of Hitler.

Mathematics Is Not Only Real, But It Is The Only Reality. That Is That Entire Universe Is Made Of Matter, Obviously. And Matter Is Made Of Particles. It's Made Of Electrons And Neutrons And Protons. So The Entire Universe Is Made Out Of Particles. Now What Are The Particles Made Out Of They're Not Made Out Of Anything. The Only Thing You Can Say About The Reality Of An Electron Is To Cite Its Mathematical Properties. So There's A Sense In Which Matter Has Completely Dissolved And What Is Left Is Just A Mathematical Structure.

A Surprising Proportion Of Mathematicians Are Accomplished Musicians. Is It Because Music And Mathematics Share Patterns That Are Beautiful?

Mathemagical Mathematics Combines The Beauty Of Mathematical Structure With The Entertainment Value Of A Trick.

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If You Ask Me To Tell You Anything About The Nature Of What Lies Beyond The Phaneron… My Answer Is “how Should I Know?”… I Am Not Dismayed By Ultimate Mysteries… I Can No More Grasp What Is Behind Such Questions As My Cat Can Understand What Is Behind The Clatter I Make While I Type This Paragraph.

If Present Trends Continue, Our Country May Soon Find Itself Far Behind Many Other Nations In Both Science And Technology Nations Where, If You Inform Strangers That You Are A Mathematician, They Respond With Admiration And Not By Telling You How Much They Hated Math In School, And How They Sure Could Use You To Balance Their Checkbooks.

If All Sentient Beings In The Universe Disappeared, There Would Remain A Sense In Which Mathematical Objects And Theorems Would Continue To Exist Even Though There Would Be No One Around To Write Or Talk About Them. Huge Prime Numbers Would Continue To Be Prime, Even If No One Had Proved Them Prime.

There Are, And Always Have Been, Destructive Pseudo-scientific Notions Linked To Race And Religion; These Are The Most Widespread And Damaging. Hopefully, Educated People Can Succeed In Shedding Light Into These Areas Of Prejudice And Ignorance, For As Voltaire Once Said: "men Will Commit Atrocities As Long As They Believe Absurdities."

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