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‘A paean to human potential … profoundly refreshing, energising explanations for why we do and think the way we do … Pinker writes like a dream’

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‘Eloquent in his defence of clear thinking . . . reason is a tool that human beings have to learn to use with care, something this book will help any reader to do’ Julian Baggini, Financial Times ‘Masterly . . . illuminating’ Raymond Tallis, TLS ‘In our uncertain age, which can so often feel so dark and disturbing, Steven Pinker has distinguished himself as a voice of positivity’ The New York Times ‘As with all of his books, this one, this one is erudite, lucid, funny, and dense with fascinating material . . . His characteristic brew of Yiddish jokes, brainy comics and incisive argumentation is a pleasure to read, even when the subjects are technical and mathematical. It’s no small achievement to make formal logic, game theory, statistics and Bayesian reasoning delightful topics full of charm and relevance’ Washington Post ‘An impassioned and zippy introduction to the tools of rational thought . . . Punchy, funny, and invigorating’ The Sunday Times ‘An engaging analysis of the highest of our faculties and perhaps (ironically) the least understood’ Wall Street Journal ‘Almost every sentence in Rationality is crisp and intelligible, which is quite a feat, given that explaining logic to humans is like teaching them Sanskrit’ New Statesman ‘Steven Pinker is among the best science writers in history, and with Rationality he applies his talents to one of the most important and misunderstood human abilities . . . If you’ve ever considered taking drugs to make yourself smarter, read Rationality instead’ Jonathan Haidt, co-author of The Coddling of the American Mind ‘Rationality is a terrific book, much-needed for our time. In addition to drawing together the tools for overcoming obstacles to rational thinking, Pinker breaks new ground with the evidence he provides linking rationality and moral progress’ Peter Singer, author of The Life You Can Save and The Most Good You Can Do

‘Pinker manages to be scrupulously rigorous yet steadily accessible and entertaining whether probing the rationality of Andrew Yang’s presidential platform, Dilbert cartoons, or Yiddish proverbs. The result is both a celebration of humans’ ability to make things better with careful thinking and a penetrating rebuke to muddleheadedness’ Publishers Weekly ‘A reader-friendly primer in better thinking through the cultivation of that rarest of rarities: a sound argument’ Kirkus Reviews

a b o u t t h e au t h or Steven Pinker is an experimental cognitive scientist. Currently Johnstone Professor of Psychology at Harvard, he has also taught at Stanford and MIT. He has won many prizes for his research, teaching, and his eleven books, including The Language Instinct, How the Mind Works, The Blank Slate, The Better Angels of Our Nature, and Enlightenment Now. He is a member of the National Academy of Sciences, a two-time Pulitzer Prize finalist, a Humanist of the Year, a recipient of nine honorary doctorates, one of Foreign Policy’s ‘World’s Top 100 Public Intellectuals’ and Time’s ‘100 Most Influential People in the World Today’.

st e v e n p i n ker A L S O BY S T E V E N P I N K E R

Language Learnability and Language Development

Rationality Learnability and Cognition

The Language Instinct What it Is, Why it Seems Scarce, How the Mind Works Why it Matters Words and Rules The Blank Slate The Stuff of Thought The Better Angels of Our Nature Language, Cognition, and Human Nature: Selected Articles The Sense of Style Enlightenment Now

E D I T E D BY S T E V E N P I N K E R

Visual Cognition Connections and Symbols (with Jacques Mehler) Lexical and Conceptual Semantics (with Beth Levin) The Best American Science and Nature Writing 2004

P EN GU I N B O O K S

P E N GUIN B O O KS UK | USA | Canada | Ireland | Australia India | New Zealand | South Africa Penguin Books is part of the Penguin Random House group of companies whose addresses can be found at global.penguinrandomhouse.com.

First published in the United States of America by Viking, an imprint of Penguin Random House LLC 2021 First published in Great Britain by Allen Lane 2021 First published in Penguin Books 2022 001 Copyright © Steven Pinker, 2021 Grateful acknowledgment is made for permission to reprint the following: Excerpt on page 55 from The Odyssey by Homer, translated by Emily Wilson.

Copyright © 2018 by Emily Wilson. Used by permission of W. W. Norton & Company, Inc. Charts rendered by Ilavenil Subbiah The moral right of the author has been asserted Printed and bound in Great Britain by Clays Ltd, Elcograf S.p.A. The authorized representative in the EEA is Penguin Random House Ireland, Morrison Chambers, 32 Nassau Street, Dublin D02 YH68 A CIP catalogue record for this book is available from the British Library ISBN: 978–0–141–98986–0 www.greenpenguin.co.uk Penguin Random House is committed to a sustainable future for our business, our readers and our planet. This book is made from Forest Stewardship Council® certified paper.

To R o s l y n Wi e s e n f e l d P i n k e r

What What is a isman, a man, If his If chief his chief good good andand market market of his of time his time Be but Be but to sleep to sleep andand feed? feed?

A beast, A beast, no more. no more.

SureSure he that he that made made us with us with suchsuch large large discourse, discourse, Looking Looking before before andand after, after, gavegave us not us not That That capability capability andand godlike godlike reason reason To fust To fust in us inunus’d. us unus’d.

— Hamlet — Hamlet

CO CN OTNETN ETNST S

Preface Preface

1. How 1. How Rational Rational an an Animal?

Animal?

xi

xi

1

1

2. Rationality 2. Rationality andand Irrationality Irrationality

35 35

3. Logic 3. Logic andand Critical Critical Thinking Thinking

73 73

4. Probability 4. Probability andand Randomness Randomness

111 111

5. Beliefs 5. Beliefs andand Evidence Evidence (Bayesian (Bayesian Reasoning) Reasoning)

149 149

6. Risk 6. Risk andand Reward Reward

(Rational (Rational Choice Choice andand Expected Expected Utility) Utility)

173 173

7. Hits 7. Hits andand False False Alarms Alarms

(Signal (Signal Detection Detection andand Statistical Statistical Decision Decision Theory) Theory)201 201

8. Self 8. Self andand Others Others (Game (Game Theory) Theory)

9. Correlation 9. Correlation andand Causation Causation

227 227 245 245

10.10.

What’s What’s Wrong Wrong with with People?

People?

11. Why 11. Why Rationality Rationality Matters Matters

283 283 319 319

Notes Notes

341 341

References References

361 361

Index Index of Biases of Biases andand Fallacies Fallacies

389 389

Index Index

391 391

P RPERFEAFC AE CE

RR

ationality ationality ought ought to be to the be the lodestar lodestar for for everything everything we we think think andand do. do.

(If you (If you disagree, disagree, are are youryour objections objections rational?) rational?)

Yet Yet in in an era an era blessed blessed withwith unprecedented unprecedented resources resources for for reasoning, reasoning,

the the public public sphere sphere is infested is infested withwith fakefake news, news, quack quack cures, cures, conspiracy conspiracy theories, theories, andand “post“posttruth” truth” rhetoric. rhetoric.

How How cancan we make we make sense sense of making of making sense— sense— andand its opposite? its opposite?

TheThe question question is urgent. is urgent.

In the In the third third decade decade of the of the third third millennium, millennium, we we faceface deadly deadly threats threats to our to our health, health, ourour democracy, democracy, andand the the livability livability of our of our planet. planet.

Though Though the the problems problems are are daunting, daunting, solutions solutions exist, exist, andand ourour species species has has the the intellectual intellectual wherewithal wherewithal to find to find them. them.

Yet Yet among among ourour fiercest fiercest problems problems today today is convincing is convincing people people to accept to accept the the solutions solutions when when we do we find do find them. them.

Commentaries Commentaries by the by the thousands thousands havehave lamented lamented ourour shortfall shortfall of of reason, reason, andand it’s become it’s become conventional conventional wisdom wisdom thatthat people people are are simply simply irrational. irrational.

In social In social science science andand the the media, media, the the human human being being is poris portrayed trayed as aas caveman a caveman out out of time, of time, poised poised to react to react to ato lion a lion in the in the grass grass

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withwith a suite a suite of biases, of biases, blind blind spots, spots, fallacies, fallacies, andand illusions. illusions.

(The (The WikiWikipedia pedia entry entry for for cognitive cognitive biases biases listslists almost almost twotwo hundred.) hundred.)

Yet Yet as aascognitive a cognitive scientist scientist I cannot I cannot accept accept the the cynical cynical viewview thatthat the the human human brain brain is a is basket a basket of delusions. of delusions.

HunterHuntergatherers— gatherers— ourour an- ancestors cestors andand contemporaries— contemporaries— are are not not nervous nervous rabbits rabbits but but cerebral cerebral problem problem solvers. solvers.

A list A list of the of the ways ways in which in which we’re we’re stupid stupid can’t can’t explain explain whywhy we’re we’re so smart: so smart: smart smart enough enough to have to have discovered discovered the the lawslaws of of nature, nature, transformed transformed the the planet, planet, lengthened lengthened andand enriched enriched ourour lives, lives, and,and, not not least, least, articulated articulated the the rules rules of rationality of rationality thatthat we we so often so often flout. flout.

To be To sure, be sure, I amI am among among the the firstfirst to insist to insist thatthat we can we can understand understand human human nature nature onlyonly by considering by considering the the mismatch mismatch between between the the en- environment vironment in which in which we we evolved evolved andand the the environment environment we we findfind our-ourselves selves in today. in today.

ButBut the the world world to which to which ourour minds minds are are adapted adapted is not is not justjust the the Pleistocene Pleistocene savannah. savannah.

It’s It’s anyany nonacademic, nonacademic, nontechnocratic nontechnocratic milieu— milieu— which which is tois say, to say, most most of human of human experience— experience— in which in which the the modern modern instruments instruments of rationality of rationality likelike statistical statistical formulas formulas andand datadatasetssets are are unavailable unavailable or inapplicable. or inapplicable.

As we As shall we shall see,see, when when people people are are given given problems problems thatthat are are closer closer to their to their lived lived reality reality andand framed framed in the in the ways ways in which in which theythey naturally naturally encounter encounter the the world, world, theythey are are not not as as witless witless as they as they appear. appear.

NotNot thatthat thisthis getsgets us off us off the the hook. hook.

Today Today we we do have do have refined refined instruments instruments of reason, of reason, andand we are we are bestbest off, off, as indias individuals viduals andand as aassociety, a society, when when we understand we understand andand apply apply them. them.

This This book book grew grew out out of aofcourse a course I taught I taught at Harvard at Harvard which which ex- explored plored the the nature nature of rationality of rationality andand the the puzzle puzzle of why of why it seems it seems to to be so be scarce. so scarce.

LikeLike many many psychologists, psychologists, I love I love to teach to teach the the arrestarresting,ing, Nobel Nobel Prize– Prize– winning winning discoveries discoveries of the of the infirmities infirmities thatthat afflict afflict human human reason, reason, andand consider consider them them to be to among be among the the deepest deepest giftsgifts to to knowledge knowledge thatthat ourour science science has has contributed. contributed.

AndAnd likelike many, many, I believe I believe thatthat the the benchmarks benchmarks of rationality of rationality thatthat people people so often so often fail fail to meato measuresure up to upshould to should be abegoal a goal of education of education andand popular popular science. science.

JustJust as as

p r epfraecfea c e

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citizens citizens should should grasp grasp the the basics basics of history, of history, science, science, andand the the written written word, word, theythey should should command command the the intellectual intellectual tools tools of sound of sound reasonreasoning.ing.

These These include include logic, logic, critical critical thinking, thinking, probability, probability, correlation correlation andand causation, causation, the the optimal optimal ways ways to adjust to adjust ourour beliefs beliefs andand commit commit to to decisions decisions withwith uncertain uncertain evidence, evidence, andand the the yardsticks yardsticks for for making making ra- rational tional choices choices alone alone andand withwith others. others.

These These tools tools of reasoning of reasoning are are indispensable indispensable in avoiding in avoiding follyfolly in our in our personal personal liveslives andand public public polipolicies.cies.

They They helphelp us calibrate us calibrate risky risky choices, choices, evaluate evaluate dubious dubious claims, claims, understand understand baffling baffling paradoxes, paradoxes, andand gaingain insight insight intointo life’slife’s vicissivicissitudes tudes andand tragedies. tragedies.

ButBut I knew I knew of no of no book book thatthat tried tried to explain to explain them them all. all.

TheThe other other inspiration inspiration for for thisthis book book waswas my my realization realization thatthat for for all its all fascination, its fascination, the the cognitive cognitive psychology psychology curriculum curriculum left left me me ill ill equipped equipped to answer to answer the the questions questions I was I was most most frequently frequently asked asked when when I told I told people people I was I was teaching teaching a course a course on rationality. on rationality.

Why Why do people do people believe believe thatthat Hillary Hillary Clinton Clinton ran ran a child a child sex sex ringring out out of aofpizzeria, a pizzeria, or or thatthat jet contrails jet contrails are are really really mindmindaltering altering drugs drugs dispersed dispersed by aby secret a secret government government program? program?

My My standard standard lecture lecture bullet bullet points points likelike “the“the gambler’s gambler’s fallacy” fallacy” andand “base“baseraterate neglect” neglect” offered offered little little insight insight intointo justjust the the enigmas enigmas thatthat are are making making human human irrationality irrationality so pressing so pressing an an issue issue today. today.

Those Those enigmas enigmas drew drew me me intointo newnew territories, territories, including including the the nature nature of rumor, of rumor, folkfolk wisdom, wisdom, andand conspiratorial conspiratorial thinking; thinking; the the contrast contrast between between rationality rationality within within an individual an individual andand in aincommua community;nity; andand the the distinction distinction between between twotwo modes modes of believing: of believing: the the reality reality mindset mindset andand the the mythology mythology mindset. mindset.

Finally, Finally, though though it may it may seem seem paradoxical paradoxical to lay to lay out out rational rational arguarguments ments for rationality for rationality itself, itself, it’s ait’s timely a timely assignment. assignment.

Some Some people people pur-pursue sue the the opposite opposite paradox, paradox, citing citing reasons reasons (presumably (presumably rational rational ones, ones, or why or why should should we we listen?) listen?) thatthat rationality rationality is overrated, is overrated, suchsuch as that as that logical logical personalities personalities are are joyless joyless andand repressed, repressed, analytical analytical thinking thinking must must be subordinated be subordinated to social to social justice, justice, andand a good a good heart heart andand reliable reliable

xiv xiv

p r epfraecfea c e

gut gut are are surer surer routes routes to wellto wellbeing being thanthan toughtoughminded minded logic logic andand ar- argument. gument.

Many Many act act as ifasrationality if rationality is obsolete— is obsolete— as ifasthe if the point point of of argumentation argumentation is tois discredit to discredit one’s one’s adversaries adversaries rather rather thanthan colleccollectively tively reason reason ourour wayway to the to the most most defensible defensible beliefs. beliefs.

In an In era an era in in which which rationality rationality seems seems both both more more threatened threatened andand more more essential essential thanthan ever, ever, Rationality Rationality is, above is, above all, all, an affirmation an affirmation of rationality. of rationality.

A major A major theme theme of this of this book book is that is that none none of us, of us, thinking thinking alone, alone, is is rational rational enough enough to consistently to consistently come come to sound to sound conclusions: conclusions: rationalrationality ity emerges emerges from from a community a community of reasoners of reasoners whowho spotspot eacheach other’s other’s fallacies. fallacies.

In that In that spirit spirit I thank I thank the the reasoners reasoners whowho made made thisthis book book more more rational. rational.

KenKen Binmore, Binmore, Rebecca Rebecca Newberger Newberger Goldstein, Goldstein, Gary Gary King, King, Jason Jason Nemirow, Nemirow, Roslyn Roslyn Pinker, Pinker, Keith Keith Stanovich, Stanovich, andand Martina Martina Wiese Wiese incisively incisively commented commented on the on the firstfirst draft. draft.

Charleen Charleen Adams, Adams, Robert Robert Au-Aumann, mann, Joshua Joshua Hartshorne, Hartshorne, Louis Louis Liebenberg, Liebenberg, Colin Colin McGinn, McGinn, Bar-Barbarabara Mellers, Mellers, Hugo Hugo Mercier, Mercier, Scott Scott Ogawa, Ogawa, Judea Judea Pearl, Pearl, David David Ropeik, Ropeik, Michael Michael Shermer, Shermer, Susanna Susanna Siegel, Siegel, Barbara Barbara Spellman, Spellman, Lawrence Lawrence Summers, Summers, Philip Philip Tetlock, Tetlock, andand Juliani Juliani Vidal Vidal reviewed reviewed chapters chapters in their in their areas areas of expertise. of expertise.

Many Many questions questions arose arose as Ias planned I planned andand wrote wrote the the book, book, andand theythey were were answered answered by by Daniel Daniel Dennett, Dennett, EmilyEmilyRose Rose Eastop, Eastop, Baruch Baruch Fischhoff, Fischhoff, ReidReid Hastie, Hastie, Nathan Nathan Kuncel, Kuncel, Ellen Ellen Langer, Langer, Jennifer Jennifer Lerner, Lerner, Beau Beau Lotto, Lotto, Daniel Daniel Loxton, Loxton, Gary Gary Marcus, Marcus, Philip Philip Maymin, Maymin, DonDon Moore, Moore, David David Myers, Myers, Robert Robert Proctor, Proctor, FredFred Shapiro, Shapiro, Mattie Mattie Toma, Toma, Jeffrey Jeffrey Watumull, Watumull, Jeremy Jeremy Wolfe, Wolfe, andand Steven Steven Zipperstein.

Zipperstein.

I counted I counted on on the the expert expert transcription, transcription, fact-factchecking, checking, andand reference reference hunting hunting

by Mila

by Mila Bertolo, Bertolo, Martina Martina Wiese, Wiese, andand KaiKai Sandbrink, Sandbrink, andand on on original original datadata analyses analyses by by Bertolo, Bertolo, Toma, Toma, andand Julian Julian De De Freitas.

Freitas.

AlsoAlso appreciated appreciated were were the the questions questions andand suggessuggestions tions from from the the students students andand teaching teaching staffstaff of General of General Education Education 1066: 1066: Rationality, Rationality, especially especially Mattie Mattie Toma Toma andand Jason Jason Nemirow.

Nemirow.

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Special Special thanks thanks go to gomy to my wisewise andand supportive supportive editor, editor, Wendy Wendy Wolf, Wolf, for working for working withwith me me on this on this book, book, ourour sixth; sixth; to Katya to Katya Rice, Rice, for copyfor copyediting editing ourour ninth; ninth; andand to my to my literary literary agent, agent, John John Brockman, Brockman, for for his his encouragement encouragement andand advice advice on our on our ninth. ninth.

I appreciate I appreciate as well as well the the sup-supportport overover many many years years from from Thomas Thomas Penn, Penn, PenPen Vogler, Vogler, andand Stefan Stefan McGrath McGrath of Penguin of Penguin UK.UK. Ilavenil Ilavenil Subbiah Subbiah once once again again designed designed the the graphics, graphics, andand I thank I thank her her for for her her work work andand her her encouragement. encouragement.

Rebecca Rebecca Newberger Newberger Goldstein Goldstein played played a special a special rolerole in the in the concepconceptiontion of this of this book, book, because because it isitshe is she whowho impressed impressed on me on me thatthat realism realism andand reason reason are are ideals ideals thatthat must must be singled be singled out out andand defended. defended.

Love Love andand gratitude gratitude go as gowell as well to the to the other other members members of my of my family: family: YaelYael andand Solly; Solly; Danielle; Danielle; Rob, Rob, Jack, Jack, andand David; David; Susan, Susan, Martin, Martin, Eva,Eva, Carl, Carl, andand Eric; Eric; andand my my mother, mother, Roslyn, Roslyn, to whom to whom thisthis book book is dedicated. is dedicated.

RR AA T ITO IO NN AA L ILTI T YY

1 H OW R AT I O N A L A N A N I M A L ?

Man is a rational animal. So at least we have been told.

Throughout a long life I have searched diligently for evidence in favor of this statement. So far, I have not had the good fortune to come across it.

— Bertrand Russell 1

He that can carp in the most eloquent or acute manner at the weakness of the human mind is held by his fellows as almost divine.

— Baruch Spinoza 2

H

omo sapiens means wise hominin, and in many ways we have earned the specific epithet of our Linnaean binomial. Our species has dated the origin of the universe, plumbed the

nature of matter and energy, decoded the secrets of life, unraveled the circuitry of consciousness, and chronicled our history and diversity. We have applied this knowledge to enhance our own flourishing, blunting the scourges that immiserated our ancestors for most of our existence. We have postponed our expected date with death

2

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r a triaotni ao lniatlyi t y

from from thirty thirty years years of age of age to more to more thanthan seventy seventy (eighty (eighty in developed in developed countries), countries), reduced reduced extreme extreme poverty poverty from from ninety ninety percent percent of humanof humanity to ityless to less thanthan nine, nine, slashed slashed the the rates rates of death of death from from warwar twentyfold twentyfold 3 3 Even Even when when the the ancient ancient bane bane of pesof pesandand from from famine famine a hundredfold. a hundredfold.

tilence tilence roserose up anew up anew in the in the twentytwentyfirstfirst century, century, we we identified identified the the cause cause within within days, days, sequenced sequenced its genome its genome within within weeks, weeks, andand adminisadministered tered vaccines vaccines within within a year, a year, keeping keeping its death its death toll toll to atofraction a fraction of of those those of historic of historic pandemics. pandemics.

TheThe cognitive cognitive wherewithal wherewithal to understand to understand the the world world andand bend bend it toit to ourour advantage advantage is not is not a trophy a trophy of Western of Western civilization; civilization; it’s it’s the the patripatrimony mony of our of our species. species.

TheThe SanSan of the of the Kalahari Kalahari Desert Desert in southern in southern Africa Africa are are oneone of the of the world’s world’s oldest oldest peoples, peoples, andand their their foraging foraging life-lifestyle, style, maintained maintained until until recently, recently, offers offers a glimpse a glimpse of the of the ways ways in which in which 4 4 HunterHuntergatherers gatherers don’t don’t justjust humans humans spent spent most most of their of their existence. existence.

chuck chuck spears spears at passing at passing animals animals or help or help themselves themselves to fruit to fruit andand nutsnuts 5 5 The The tracking tracking scientist scientist Louis Louis Liebenberg, Liebenberg, whowho growing growing around around them. them.

has has worked worked withwith the the SanSan for for decades, decades, has has described described howhow theythey oweowe 6 6 They They reason reason their their wayway from from their their survival survival to atoscientific a scientific mindset. mindset.

fragmentary fragmentary datadata to remote to remote conclusions conclusions withwith an intuitive an intuitive grasp grasp of of logic, logic, critical critical thinking, thinking, statistical statistical reasoning, reasoning, causal causal inference, inference, andand game game theory. theory.

TheThe SanSan engage engage in persistence in persistence hunting, hunting, which which putsputs to use to use ourour three three most most conspicuous conspicuous traits: traits: ourour twotwoleggedness, leggedness, which which enables enables us us to run to run efficiently; efficiently; ourour hairlessness, hairlessness, which which enables enables us to usdump to dump heatheat in in hot hot climates; climates; andand ourour big big heads, heads, which which enable enable us to usbe to rational. be rational.

TheThe SanSan deploy deploy thisthis rationality rationality to track to track the the fleeing fleeing animals animals from from their their hoofprints, hoofprints, effluvia, effluvia, andand other other spoor, spoor, pursuing pursuing them them until until theythey keelkeel 7 7 Sometimes Sometimes the the SanSan track track an an overover from from exhaustion exhaustion andand heatheat stroke. stroke.

animal animal along along oneone of its ofhabitual its habitual pathways, pathways, or, when or, when a trail a trail goesgoes cold, cold, by searching by searching in widening in widening circles circles around around the the last last known known prints. prints.

ButBut often often theythey track track them them by reasoning. by reasoning.

how h orwa triaotni ao ln aaln aann iamnai lm?a l ?

3

3

Hunters Hunters distinguish distinguish dozens dozens of species of species by the by the shapes shapes andand spacing spacing of their of their tracks, tracks, aided aided by their by their grasp grasp of cause of cause andand effect. effect.

They They maymay infer infer thatthat a deeply a deeply pointed pointed track track comes comes from from an agile an agile springbok, springbok, which which needs needs a good a good grip, grip, whereas whereas a flata flatfooted footed track track comes comes from from a a heavy heavy kudu, kudu, which which has has to support to support its weight. its weight.

They They cancan sex sex the the ani-animalsmals from from the the configuration configuration of their of their tracks tracks andand the the relative relative location location of their of their urine urine to their to their hindhind feetfeet andand droppings. droppings.

They They use use these these cat-categories egories to make to make syllogistic syllogistic deductions: deductions: steenbok steenbok andand duiker duiker cancan be be runrun down down in the in the rainy rainy season season because because the the wetwet sandsand forces forces open open their their hooves hooves andand stiffens stiffens their their joints; joints; kudu kudu andand eland eland cancan be run be run down down in in the the drydry season season because because theythey tiretire easily easily in loose in loose sand. sand.

It’s It’s the the drydry sea-seasonson andand the the animal animal thatthat left left these these tracks tracks is aiskudu; a kudu; therefore, therefore, thisthis animal animal cancan be run be run down. down.

TheThe SanSan don’t don’t justjust pigeonhole pigeonhole animals animals intointo categories categories but but make make finerfinergrained grained logical logical distinctions. distinctions.

They They tell tell individuals individuals apart apart within within a species a species by reading by reading their their hoofprints, hoofprints, looking looking for for telltale telltale nicks nicks andand variations. variations.

AndAnd theythey distinguish distinguish an individual’s an individual’s permanent permanent traits, traits, likelike its species its species andand sex,sex, from from transient transient conditions conditions likelike fatigue, fatigue, which which theythey infer infer from from signs signs of hoofof hoofdragging dragging andand stopping stopping to rest. to rest.

Defying Defying the the canard canard thatthat premodern premodern peoples peoples havehave no concept no concept of time, of time, theythey esti-estimate mate the the age age of an of animal an animal from from the the sizesize andand crispness crispness of its of hoofits hoofprints, prints, andand cancan datedate its spoor its spoor by the by the freshness freshness of tracks, of tracks, the the wetness wetness of saliva of saliva or droppings, or droppings, the the angle angle of the of the sunsun relative relative to ato shady a shady resting resting place, place, andand the the palimpsest palimpsest of superimposed of superimposed tracks tracks from from other other ani-animals. mals.

Persistence Persistence hunting hunting could could not not succeed succeed without without those those logical logical niceties. niceties.

A hunter A hunter can’t can’t track track justjust anyany gemsbok gemsbok from from among among the the many many thatthat havehave left left tracks, tracks, but but onlyonly the the oneone he has he has been been pursuing pursuing to to exhaustion. exhaustion.

TheThe SanSan alsoalso engage engage in critical in critical thinking. thinking.

They They know know not not to trust to trust their their firstfirst impressions, impressions, andand appreciate appreciate the the dangers dangers of seeing of seeing what what theythey want want to see. to see.

NorNor willwill theythey accept accept arguments arguments from from authority: authority: anyone, anyone,

4

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r a triaotni ao lniatlyi t y

including including a young a young upstart, upstart, maymay shoot shoot down down a conjecture a conjecture or come or come up up withwith his own his own until until a consensus a consensus emerges emerges from from the the disputation. disputation.

Though Though it’s mainly it’s mainly the the menmen whowho hunt, hunt, the the women women are are justjust as knowledgeable as knowledgeable at at interpreting interpreting spoor, spoor, andand Liebenberg Liebenberg reports reports thatthat oneone young young woman, woman, 8 8 !Nasi, !Nasi, “put“put the the menmen to shame.” to shame.”

TheThe SanSan adjust adjust their their credence credence in ainhypothesis a hypothesis according according to how to how diagnostic diagnostic the the evidence evidence is, ais, matter a matter of conditional of conditional probability. probability.

A porA porcupine cupine foot, foot, for for instance, instance, has has twotwo proximal proximal padspads while while a honey a honey bad-badger ger has has one,one, but but a padprint a padprint maymay fail fail to register to register on hard on hard ground. ground.

This This means means thatthat though though the the probability probability thatthat a track a track willwill havehave oneone padprint padprint given given thatthat it was it was made made by abyhoney a honey badger badger is high, is high, the the inverse inverse probaprobability, bility, thatthat a track a track waswas made made by abyhoney a honey badger badger given given thatthat it has it has oneone padprint, padprint, is lower is lower (since (since it could it could alsoalso be an be incomplete an incomplete porcupine porcupine track). track).

TheThe SanSan do not do not confuse confuse these these conditional conditional probabilities: probabilities: theythey know know thatthat since since twotwo padprints padprints could could onlyonly havehave been been left left by abyporcua porcupine, pine, the the probability probability of aofporcupine a porcupine given given twotwo padprints padprints is high. is high.

TheThe SanSan alsoalso calibrate calibrate their their credence credence in ain hypothesis a hypothesis according according to to its prior its prior plausibility. plausibility.

If tracks If tracks are are ambiguous, ambiguous, theythey willwill assume assume theythey come come from from a commonly a commonly occurring occurring species; species; onlyonly if the if the evidence evidence is is 9 As9 we As we definitive definitive willwill theythey conclude conclude thatthat theythey come come from from a rarer a rarer one.one.

shallshall see,see, thisthis is the is the essence essence of Bayesian of Bayesian reasoning. reasoning.

Another Another critical critical faculty faculty exercised exercised by the by the SanSan is distinguishing is distinguishing causation causation from from correlation. correlation.

Liebenberg Liebenberg recalls: recalls: “One “One tracker, tracker, Boroh// Boroh// xao,xao, toldtold me me thatthat when when the the [lark] [lark] sings, sings, it dries it dries out out the the soil,soil, making making the the roots roots good good to eat. to eat.

Afterwards, Afterwards, !Nate !Nate andand / Uase / Uase toldtold me me thatthat Boroh// Boroh// xao xao waswas wrong— wrong— it isitnot is not the the birdbird thatthat dries dries out out the the soil,soil, it isit is the the sun sun thatthat dries dries out out the the soil.soil.

TheThe birdbird is only is only telling telling them them thatthat the the soilsoil willwill drydry out out in the in the coming coming months months andand thatthat it isitthe is the timetime of the of the 10 10 yearyear when when the the roots roots are are good good to eat.” to eat.”

TheThe SanSan use use their their knowledge knowledge of the of the causal causal texture texture of their of their environenviron-

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ment ment not not justjust to understand to understand howhow it isitbut is but to imagine to imagine howhow it might it might be. be.

By playing By playing out out scenarios scenarios in their in their mind’s mind’s eye,eye, theythey cancan think think several several steps steps ahead ahead of the of the animals animals in their in their world world andand devise devise intricate intricate snares snares to to traptrap them. them.

OneOne endend of aofspringy a springy branch branch is anchored is anchored in the in the ground ground andand the the stickstick is bent is bent in half; in half; the the other other is tied is tied to atonoose a noose camouflaged camouflaged withwith twigs twigs andand sandsand andand heldheld in place in place by abytrigger. a trigger.

They They place place the the snares snares at the at the openings openings of barriers of barriers theythey havehave builtbuilt around around an antelope’s an antelope’s resting resting place, place, andand guide guide the the animal animal intointo the the deadly deadly spotspot withwith a hurdle a hurdle the the antelope antelope must must clear. clear.

Or they Or they lurelure an ostrich an ostrich to ato snare a snare by spotting by spotting its tracks its tracks under under a camelthorn a camelthorn treetree (whose (whose pods pods are are an ostrich an ostrich delicacy) delicacy) andand leaving leaving a conspicuous a conspicuous bone bone that’s that’s too too big big for for the the ostrich ostrich to swalto swallow,low, which which draws draws its attention its attention to atosmaller a smaller but but stillstill unswallowable unswallowable bone, bone, which which leads leads to ato still a still smaller smaller bone, bone, the the baitbait in the in the snare. snare.

Yet Yet for for all the all the deadly deadly effectiveness effectiveness of the of the San’s San’s technology, technology, theythey havehave survived survived in an inunforgiving an unforgiving desert desert for more for more thanthan a hundred a hundred thouthousandsand years years without without exterminating exterminating the the animals animals theythey depend depend on. on.

DurDuring ing a drought, a drought, theythey think think ahead ahead to what to what would would happen happen if they if they killed killed the the last last plant plant or animal or animal of its of kind, its kind, andand theythey spare spare the the members members 11 11 They They tailor tailor their their conservation conservation plans plans to to of the of the threatened threatened species. species.

the the different different vulnerabilities vulnerabilities of plants, of plants, which which cannot cannot migrate migrate but but re- recover cover quickly quickly when when the the rains rains return, return, andand animals, animals, which which cancan survive survive a drought a drought but but build build backback their their numbers numbers slowly. slowly.

AndAnd theythey enforce enforce these these conservation conservation efforts efforts against against the the constant constant temptation temptation of poachof poaching ing (everyone (everyone feeling feeling theythey should should exploit exploit the the scarce scarce species, species, because because if they if they don’t, don’t, everyone everyone elseelse will)will) withwith an extension an extension of the of the norms norms of of reciprocity reciprocity andand collective collective wellwellbeing being thatthat govern govern all their all their resources. resources.

It isItunthinkable is unthinkable for for a San a San hunter hunter not not to share to share meat meat withwith an emptyan emptyhanded handed bandmate, bandmate, or toorexclude to exclude a neighboring a neighboring band band driven driven from from their their droughtdroughtstricken stricken territory, territory, since since theythey know know thatthat memories memories are are longlong andand some some dayday fortunes fortunes maymay reverse. reverse.

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.. ..

.

TheThe sapience sapience of the of the SanSan makes makes the the puzzle puzzle of human of human rationality rationality acute. acute.

Despite Despite ourour ancient ancient capacity capacity for for reason, reason, today today we are we are flooded flooded withwith reminders reminders of the of the fallacies fallacies andand follies follies of our of our fellows. fellows.

People People gamgamble ble andand playplay the the lottery, lottery, where where theythey are are guaranteed guaranteed to lose, to lose, andand fail fail to invest to invest for for their their retirement, retirement, where where theythey are are guaranteed guaranteed to win. to win.

Three Three quarters quarters of Americans of Americans believe believe in at in least at least oneone phenomenon phenomenon thatthat defies defies the the lawslaws of science, of science, including including psychic psychic healing healing (55 percent), (55 percent), extrasensory extrasensory perception perception (41 (41 percent), percent), haunted haunted houses houses (37 (37 percent), percent), andand ghosts ghosts (32 (32 percent)— percent)— which which alsoalso means means thatthat some some people people believe believe 12 12 In soIn soin houses in houses haunted haunted by ghosts by ghosts without without believing believing in ghosts. in ghosts.

cialcial media, media, fakefake news news (such (such as Joe as Joe Biden Biden Calls Calls Trump Trump Supporters Supporters “Dregs “Dregs of Society” of Society” andand Florida Florida Man Man Arrested Arrested forfor TranquilTranquilizing izing andand Raping Raping Alligators Alligators in the in the Everglades) Everglades) is diffused is diffused far-fartherther andand faster faster thanthan the the truth, truth, andand humans humans are are more more likely likely to spread to spread 13 13 it than it than bots. bots.

It has It has become become commonplace commonplace to conclude to conclude thatthat humans humans are are simply simply irrational— irrational— more more Homer Homer Simpson Simpson thanthan Mr.Mr. Spock, Spock, more more Alfred Alfred E. E. Neuman Neuman thanthan John John vonvon Neumann.

Neumann.

And, And, the the cynics cynics continue, continue, what what elseelse would would youyou expect expect from from descendants descendants of hunterof huntergatherers gatherers whose whose minds minds were were selected selected to avoid to avoid becoming becoming lunch lunch for for leopards? leopards?

ButBut evo-evolutionary lutionary psychologists, psychologists, mindful mindful of the of the ingenuity ingenuity of foraging of foraging peo-peoples,ples, insist insist thatthat humans humans evolved evolved to occupy to occupy the the “cognitive “cognitive niche”: niche”: the the 14 14 ability ability to outsmart to outsmart nature nature withwith language, language, sociality, sociality, andand knowknowhow.how.

If contemporary If contemporary humans humans seem seem irrational, irrational, don’t don’t blame blame the the hunterhuntergatherers. gatherers.

How, How, then, then, cancan we understand we understand thisthis thing thing called called rationality rationality which which would would appear appear to be to our be our birthright birthright yet yet is soisfrequently so frequently andand flagrantly flagrantly flouted? flouted?

TheThe starting starting point point is tois appreciate to appreciate thatthat rationality rationality is not is not a a power power thatthat an agent an agent either either has has or doesn’t or doesn’t have, have, likelike Superman’s Superman’s X-ray X-ray

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vision. vision.

It isIta iskita of kitcognitive of cognitive tools tools thatthat cancan attain attain particular particular goals goals in in particular particular worlds. worlds.

To To understand understand what what rationality rationality is, why is, why it seems it seems scarce, scarce, andand whywhy it matters, it matters, we must we must begin begin withwith the the ground ground truths truths of of rationality rationality itself: itself: the the ways ways an intelligent an intelligent agent agent ought ought to reason, to reason, given given its goals its goals andand the the world world in which in which it lives. it lives.

These These “normative” “normative” models models come come from from logic, logic, philosophy, philosophy, mathematics, mathematics, andand artificial artificial intelligence, intelligence, andand theythey are are ourour bestbest understanding understanding of the of the “correct” “correct” solution solution to ato a problem problem andand howhow to find to find it. They it. They serve serve as an asaspiration an aspiration for those for those whowho want want to be to rational, be rational, which which should should mean mean everyone. everyone.

A major A major goalgoal of of thisthis book book is tois explain to explain the the most most widely widely applicable applicable normative normative tools tools of reason; of reason; theythey are are the the subjects subjects of chapters of chapters 3 to39.to 9.

Normative Normative models models alsoalso serve serve as benchmarks as benchmarks against against which which we can we can assess assess howhow human human schlemiels schlemiels do reason, do reason, the the subject subject matter matter of psyof psychology chology andand the the other other behavioral behavioral sciences. sciences.

TheThe many many ways ways in which in which ordinary ordinary people people fall fall short short of these of these benchmarks benchmarks havehave become become famous famous through through the the Nobel Nobel Prize– Prize– winning winning research research of Daniel of Daniel Kahneman, Kahneman, 15 15 Amos Amos Tversky, Tversky, andand other other psychologists psychologists andand behavioral behavioral economists. economists.

When When people’s people’s judgments judgments deviate deviate from from a normative a normative model, model, as they as they so often so often do, do, we we havehave a puzzle a puzzle to solve. to solve.

Sometimes Sometimes the the disparity disparity re- reveals veals a genuine a genuine irrationality: irrationality: the the human human brain brain cannot cannot cope cope withwith the the complexity complexity of aof problem, a problem, or itoris itsaddled is saddled withwith a bug a bug thatthat cussedly cussedly drives drives it toitthe to the wrong wrong answer answer timetime andand again. again.

ButBut in many in many cases cases there there is a is method a method to people’s to people’s madness. madness.

A probA problemlem maymay havehave been been presented presented to them to them in aindeceptive a deceptive format, format, andand when when it isittranslated is translated intointo a minda mindfriendlier friendlier guise, guise, theythey solve solve it. Or it. Or the the normative normative model model maymay itself itself be correct be correct onlyonly in ainparticular a particular envienvironment, ronment, andand people people accurately accurately sense sense thatthat theythey are are not not in that in that one,one, so the so the model model doesn’t doesn’t apply. apply.

Or Or the the model model maymay be designed be designed to bring to bring about about a certain a certain goal, goal, and,and, for for better better or worse, or worse, people people are are after after a difa different ferent one.one.

In the In the chapters chapters to come, to come, we will we will see see examples examples of all of these all these extenuating extenuating circumstances. circumstances.

TheThe penultimate penultimate chapter chapter willwill lay out lay out howhow

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some some of today’s of today’s florid florid outbursts outbursts of irrationality of irrationality maymay be understood be understood as the as the rational rational pursuit pursuit of goals of goals other other thanthan an objective an objective understandunderstanding ing of the of the world. world.

Though Though explanations explanations of irrationality of irrationality maymay absolve absolve people people of the of the charge charge of outright of outright stupidity, stupidity, to understand to understand is not is not to forgive. to forgive.

SomeSometimes times we can we can holdhold people people to atohigher a higher standard. standard.

They They cancan be taught be taught to spot to spot a deep a deep problem problem across across its superficial its superficial guises. guises.

They They cancan be be goaded goaded intointo applying applying their their bestbest habits habits of thinking of thinking outside outside their their comcomfortfort zones. zones.

AndAnd theythey cancan be inspired be inspired to set to set their their sights sights higher higher thanthan self-selfdefeating defeating or collectively or collectively destructive destructive goals. goals.

These, These, too,too, are are aspiaspirations rations of the of the book. book.

Since Since a recurring a recurring insight insight of the of the study study of judgment of judgment andand decision decision making making is that is that humans humans become become more more rational rational when when the the information information they’re they’re dealing dealing withwith is more is more vivid vivid andand relevant, relevant, let me let me turnturn to exto examples. amples.

Each Each of these of these classics— classics— from from math, math, logic, logic, probability, probability, andand forecasting— forecasting— exposes exposes a quirk a quirk in our in our reasoning reasoning andand willwill serve serve as aas a preview preview of the of the normative normative standards standards of rationality of rationality (and(and the the ways ways in in which which people people depart depart from from them) them) in the in the chapters chapters to come. to come.

Three Three Simple Simple Math Math Problems Problems Everyone Everyone remembers remembers being being tormented tormented in high in high school school by by algebra algebra problems problems about about where where the the train train thatthat left left Eastford Eastford traveling traveling westwest at 70 at 70 miles miles per per hour hour willwill meet meet the the train train thatthat left left Westford, Westford, 260260 miles miles away, away, traveling traveling easteast at 60 at miles 60 miles per per hour. hour.

These These three three are are simpler; simpler; youyou cancan do them do them in your in your head: head: • A• smartphone A smartphone andand a case a case costcost $110$110 in total. in total.

TheThe phone phone costs costs

$100 $100 more more thanthan the the case. case.

How How much much doesdoes the the casecase cost? cost?

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• It• takes It takes 8 printers 8 printers 8 minutes 8 minutes to print to print 8 brochures.

8 brochures.

How How longlong

would would it take it take 24 printers 24 printers to print to print 24 brochures?

24 brochures?

• On • On a field a field there there is aispatch a patch of weeds. of weeds.

Every Every dayday the the patch patch

doubles doubles in size. in size.

It takes It takes 30 days 30 days for for the the patch patch to cover to cover the the whole whole field. field.

How How longlong did did it take it take for for the the patch patch to cover to cover halfhalf the the field? field?

TheThe answer answer to the to the firstfirst problem problem is $5. is $5.

If you’re If you’re likelike most most people, people, youyou guessed guessed $10.$10.

ButBut if that if that were were right, right, the the phone phone would would costcost $110$110 ($100 ($100 more more thanthan the the case), case), andand the the totaltotal for for the the pairpair would would be $120. be $120.

TheThe answer answer to the to the second second question question is 8 isminutes.

8 minutes.

It takes It takes a printer a printer 8 minutes 8 minutes to print to print a brochure, a brochure, so as solong as long as there as there are are as many as many printprinters ers as there as there are are brochures brochures andand theythey are are working working simultaneously, simultaneously, the the timetime it takes it takes to print to print the the brochures brochures is the is the same. same.

TheThe answer answer to the to the third third problem problem is 29 is days.

29 days.

If the If the weed weed patch patch doubles doubles every every day,day, thenthen by working by working backwards backwards from from when when the the fieldfield waswas completely completely covered, covered, we may we may infer infer thatthat it was it was halfhalf covered covered the the dayday before. before.

TheThe economist economist Shane Shane Frederick Frederick gavegave these these questions questions (with (with differdifferent ent examples) examples) to thousands to thousands of university of university students. students.

FiveFive out out of six of got six got 16 16 Yet Yet at least at least oneone of them of them wrong; wrong; oneone in three in three got got them them all wrong. all wrong.

eacheach question question has has a simple a simple answer answer thatthat almost almost everyone everyone understands understands when when it’s pointed it’s pointed out.out.

TheThe problem problem is that is that people’s people’s heads heads are are turned turned by superficial by superficial features features of the of the problem problem which which theythey mistakenly mistakenly think think are are relevant relevant to the to the answer, answer, suchsuch as the as the round round numbers numbers 100100 andand 10 in 10 in the the firstfirst problem problem andand the the factfact thatthat the the number number of printers of printers is the is the same same as the as the number number of minutes of minutes in the in the second. second.

Frederick Frederick callscalls his his low-lowtechtech battery battery the the Cognitive Cognitive Reflection Reflection Test, Test, andand suggests suggests thatthat it exposes it exposes a cleavage a cleavage between between twotwo cognitive cognitive systems, systems, laterlater made made famous famous

by Kahneman

by Kahneman (his(his sometime sometime coauthor) coauthor)

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in the in the 20112011 bestseller bestseller Thinking, Thinking, FastFast andand Slow.

Slow.

System System 1 operates 1 operates rap-rapidlyidly andand effortlessly, effortlessly, andand it seduces it seduces us with us with the the wrong wrong answers; answers; Sys-Systemtem 2 requires 2 requires concentration, concentration, motivation, motivation, andand the the application application of of learned learned rules, rules, andand it allows it allows us to usgrasp to grasp the the right right ones. ones.

No No oneone thinks thinks these these are are literally literally twotwo anatomical anatomical systems systems in the in the brain; brain; theythey are are twotwo modes modes of operation of operation which which cut cut across across many many brain brain structures. structures.

System System 1 1 means means snapsnap judgments; judgments; System System 2 means 2 means thinking thinking twice. twice.

TheThe lesson lesson of the of the Cognitive Cognitive Reflection Reflection TestTest is that is that blunders blunders of of 17 17 reasoning reasoning maymay come come from from thoughtlessness thoughtlessness rather rather thanthan ineptitude. ineptitude.

Even Even students students at the at the mathmathproud proud Massachusetts Massachusetts Institute Institute of Techof Technology nology averaged averaged onlyonly twotwo out out of three of three correct. correct.

Performance Performance doesdoes correlate correlate withwith math math skill, skill, as you’d as you’d expect, expect, but but it also it also correlates correlates withwith patience. patience.

People People whowho describe describe themselves themselves as not as not impulsive, impulsive, andand whowho would would rather rather waitwait for for a larger a larger payment payment in ain month a month thanthan get get a smaller a smaller 18 18 oneone right right away, away, are are lessless likely likely to fall to fall intointo the the traps. traps.

TheThe firstfirst twotwo items items feelfeel likelike trick trick questions. questions.

That That is because is because theythey givegive details details which, which, in the in the backbackand-andforth forth of conversation, of conversation, would would be be relevant relevant to what to what the the speaker speaker is asking, is asking, but but in these in these examples examples are are de- designed signed to lead to lead the the hearer hearer astray. astray.

(People (People do better do better when when the the smartsmartphone phone costs, costs, say,say, $73$73 more more thanthan the the casecase andand the the combination combination costs costs 19 19 But But of course of course realreal life life is also is also baited baited withwith garden garden paths paths andand $89.) $89.)

siren siren songs songs thatthat lurelure us from us from good good decisions, decisions, andand resisting resisting them them is a is a partpart of being of being rational. rational.

People People whowho fall fall for for the the alluring alluring but but wrong wrong answers answers on the on the Cognitive Cognitive Reflection Reflection TestTest appear appear to be to less be less rational rational in other in other ways, ways, suchsuch as turning as turning down down lucrative lucrative offers offers thatthat require require a bita bit of waiting of waiting or aorbita of bitrisk. of risk.

AndAnd the the third third problem, problem, the the oneone withwith the the weed weed patch, patch, is not is not a trick a trick question question but but tapstaps a real a real cognitive cognitive infirmity. infirmity.

Human Human intuition intuition doesn’t doesn’t grasp grasp exponential exponential (geometric) (geometric) growth, growth, namely namely something something thatthat risesrises at aatrising a rising rate,rate, proportional proportional to how to how large large it already it already is, such is, such as comas compound pound interest, interest, economic economic growth, growth, andand the the spread spread of aofcontagious a contagious

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20 20 disease. disease.

People People mistake mistake it for it for steady steady creep creep or slight or slight acceleration, acceleration,

andand their their imaginations imaginations don’t don’t keepkeep up with up with the the relentless relentless doubling. doubling.

If you If you deposit deposit $400 $400 a month a month intointo a retirement a retirement account account thatthat earns earns 10 10 percent percent annually, annually, howhow big big willwill youryour nestnest eggegg be after be after forty forty years? years?

Many Many people people guess guess around around $200,000, $200,000, which which is what is what youyou get get by mulby multiplying tiplying 400400 by 12 by by 12 110% by 110% by 40. by 40.

Some Some know know thatthat thatthat can’t can’t be be right right andand adjust adjust their their guess guess upward, upward, but but never never enough. enough.

Almost Almost no no oneone getsgets the the correct correct answer: answer: $2.5$2.5 million. million.

People People withwith a shaky a shaky grasp grasp of exponential of exponential growth growth havehave been been found found to save to save lessless for for retirement retirement 21 21 andand to take to take on more on more creditcreditcardcard debt, debt, twotwo roads roads to penury. to penury.

A failure A failure to visualize to visualize exponential exponential blastoff blastoff cancan traptrap experts experts as as well— well— eveneven experts experts in cognitive in cognitive biases. biases.

When When CovidCovid19 arrived 19 arrived in the in the United United States States andand Europe Europe in February in February 2020, 2020, several several social social scientists scientists (including (including twotwo heroes heroes of this of this book, book, though though not not Kahneman Kahneman himself) himself) opined opined thatthat people people were were irrationally irrationally panicking panicking because because theythey hadhad readread about about a gruesome a gruesome casecase or two or two andand got got carried carried away away by the by the “availability “availability bias” bias” andand “probability “probability neglect.” neglect.”

TheThe objective objective riskrisk at the at the time, time, theythey noted, noted, waswas lower lower thanthan thatthat of the of the flu or flustrep or strep throat, throat, which which everyone everyone 22 22 The The fallacy fallacy of the of the fallacy fallacy scolds scolds waswas to underestito underestiaccepts accepts calmly. calmly.

mate mate the the accelerating accelerating raterate at which at which a disease a disease as contagious as contagious as Covid as Covid cancan spread, spread, withwith eacheach patient patient not not onlyonly infecting infecting newnew onesones but but turnturning ing eacheach of them of them intointo an infector. an infector.

TheThe single single confirmed confirmed American American death death on March on March 1 grew 1 grew in successive in successive weeks weeks to 2,to6,2,40, 6, 40, 264,264, 901,901, andand 1,729 1,729 deaths deaths per per day,day, adding adding up to upmore to more thanthan 100,000 100,000 deaths deaths

by June

by June 23 1 and 1 and soonsoon making making it the it the most most lethal lethal hazard hazard in the in the country. country.

Of23 course Of course

the the authors authors of these of these obscure obscure op-opeds eds cannot cannot be blamed be blamed for for the the insouinsouciance ciance which which lulled lulled so many so many leaders leaders andand citizens citizens intointo dangerous dangerous comcomplacency, placency, but but their their comments comments show show howhow deeply deeply rooted rooted cognitive cognitive biases biases cancan be. be.

Why Why do people do people misunderestimate misunderestimate exponential exponential growth, growth, as George as George W. W. Bush Bush might might havehave put put it? In it?the In the great great tradition tradition of the of the physician physician in in

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the the Molière Molière playplay whowho explained explained thatthat opium opium makes makes people people sleepy sleepy be- because cause of its of dormitive its dormitive power, power, social social scientists scientists attribute attribute the the errors errors to an to “exponential an “exponential growth growth bias.” bias.”

LessLess circularly, circularly, we we might might point point to to the the ephemerality ephemerality of exponential of exponential processes processes in natural in natural environments environments (prior (prior to historical to historical innovations innovations likelike economic economic growth growth andand compound compound interest). interest).

Things Things thatthat can’t can’t go on go forever on forever don’t, don’t, andand organisms organisms cancan multiply multiply onlyonly to the to the point point where where theythey deplete, deplete, foul,foul, or saturate or saturate their their environments, environments, bending bending the the exponential exponential curve curve intointo an S. an This S. This in- includes cludes pandemics, pandemics, which which peter peter out out once once enough enough susceptible susceptible hosts hosts in in the the herdherd are are killed killed or develop or develop immunity. immunity.

A Simple A Simple Logic Logic Problem Problem If anything If anything lies lies at the at the corecore of rationality, of rationality, it must it must surely surely be logic. be logic.

TheThe prototype prototype of aofrational a rational inference inference is the is the syllogism syllogism “If “If P then P then Q. Q. P. There P. There fore,fore, Q.”Q.” Consider Consider a simple a simple example. example.

Suppose Suppose the the coinage coinage of aofcountry a country has has a portrait a portrait of one of one of its of emiits eminentnent sovereigns sovereigns on one on one sideside andand a specimen a specimen of its of magnificent its magnificent fauna fauna on the on the other. other.

Now Now consider consider a simple a simple if-then if-then rule:rule: “If a“If coin a coin has has a king a king on one on one side,side, thenthen it has it has a bird a bird on the on the other.” other.”

Here Here are are fourfour coins, coins, Which Which of the of the coins coins do do displaying displaying a king, a king, a queen, a queen, a moose, a moose, andand a duck. a duck. youyou havehave to turn to turn overover to determine to determine whether whether the the rulerule has has been been violated? violated?

If you’re If you’re likelike most most people, people, youyou saidsaid “the“the king” king” or “the or “the kingking andand the the duck.” duck.”

TheThe correct correct answer answer is “the is “the kingking andand the the moose.” moose.”

Why? Why?

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Everyone Everyone agrees agrees youyou havehave to turn to turn overover the the king, king, because because if you if you failed failed to find to find a bird a bird on on the the reverse reverse it would it would violate violate the the rulerule in so in many so many words. words.

Most Most people people know know there’s there’s no point no point in turning in turning overover the the queen, queen, because because the the rulerule sayssays “If king, “If king, thenthen bird”; bird”; it says it says nothing nothing about about coins coins withwith a queen. a queen.

Many Many say say youyou should should turnturn overover the the duck, duck, but but when when youyou think think about about it, that it, that coincoin is irrelevant. is irrelevant.

TheThe rulerule is “If is king, “If king, thenthen bird,” bird,” not not “If “If bird, bird, thenthen king”: king”: if the if the duck duck shared shared the the coincoin withwith a queen, a queen, nothing nothing would would be amiss. be amiss.

ButBut nownow consider consider the the moose. moose.

If you If you turned turned thatthat coincoin overover andand found found a king a king on the on the obverse, obverse, the the rulerule “If “If king, king, thenthen bird” bird” would would havehave been been transgressed. transgressed.

TheThe answer, answer, then, then, is “the is “the kingking andand the the moose.” moose.”

On On average, average, onlyonly 10 percent 10 percent of people of people make make those those picks. picks.

TheThe Wason Wason selection selection tasktask (named (named after after its creator, its creator, the the cognitive cognitive psychologist psychologist Peter Peter Wason) Wason) has has been been administered administered withwith various various “If P “If P thenthen Q” Q” rules rules for for sixtysixtyfivefive years. years.

(The (The original original version version usedused cards cards withwith a letter a letter on one on one sideside andand a number a number on the on the other other andand a rule a rule likelike “If “If there there is aisDa on D one on one side,side, there there is ais3 aon3 the on the other.”) other.”)

Time Time andand again again people people turnturn overover the the P, or P, the or the P and P and the the Q, and Q, and fail fail to turn to turn 24 It’s It’s not not thatthat they’re they’re incapable incapable of understanding of understanding the the overover the the not-notQ.24Q.

right right answer. answer.

As with As with the the Cognitive Cognitive Reflection Reflection Test, Test, as soon as soon as itasisit is explained explained to them to them theythey slapslap themselves themselves on the on the forehead forehead andand accept accept 25 But But their their unreflective unreflective intuition, intuition, left left to its toown its own devices, devices, failsfails to do to do it.25it.

the the logic. logic.

What What doesdoes thisthis tell tell us about us about human human rationality? rationality?

A common A common explaexplanation nation is that is that it reveals it reveals ourour confirmation confirmation bias:bias: the the badbad habit habit of seeking of seeking evidence evidence thatthat ratifies ratifies a belief a belief andand being being incurious incurious about about evidence evidence 26 People People think think thatthat dreams dreams are are omens omens because because thatthat might might falsify falsify it.26it.

theythey recall recall the the timetime when when theythey dreamt dreamt a relative a relative hadhad a mishap a mishap andand she she did,did, but but theythey forget forget about about all the all the times times when when a relative a relative waswas finefine after after theythey dreamt dreamt she she hadhad a mishap. a mishap.

Or Or theythey think think immigrants immigrants comcommitmit a lota of lotcrime of crime because because theythey readread in the in the news news about about an immigrant an immigrant

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whowho robbed robbed a store, a store, but but don’t don’t think think about about the the larger larger number number of stores of stores robbed robbed by nativeby nativeborn born citizens. citizens.

Confirmation Confirmation biasbias is a iscommon a common diagnosis diagnosis for for human human follyfolly andand a a target target for for enhancing enhancing rationality. rationality.

Francis Francis Bacon Bacon (1561– (1561– 1626), 1626), often often credited credited withwith developing developing the the scientific scientific method, method, wrote wrote of aofman a man whowho waswas taken taken to atochurch a church andand shown shown a painting a painting of sailors of sailors whowho hadhad es- escaped caped a shipwreck a shipwreck thanks thanks to their to their holyholy vows. vows.

“Aye,” “Aye,” he remarked, he remarked, 27 27 “but“but where where are are theythey painted painted thatthat were were drowned drowned after after their their vows?” vows?”

He He observed, observed, “Such “Such is the is the wayway of all of superstitions, all superstitions, whether whether in astrolin astrology,ogy, dreams, dreams, omens, omens, divine divine judgments, judgments, or the or the like;like; wherein wherein men, men, hav-having ing a delight a delight in such in such vanities, vanities, mark mark the the events events where where theythey are are fulfilled, fulfilled, but but where where theythey fail,fail, although although thisthis happened happened much much oftener, oftener, neglect neglect 28 28 Echoing Echoing a famous a famous argument argument by the by the philosopher philosopher andand passpass them them by.”by.”

KarlKarl Popper, Popper, most most scientists scientists today today insist insist thatthat the the dividing dividing lineline be- between tween science science andand pseudoscience pseudoscience is whether is whether advocates advocates of aofhypotha hypothesisesis deliberately deliberately search search for for evidence evidence thatthat could could falsify falsify it and it and accept accept 29 29 the the hypothesis hypothesis onlyonly if itifsurvives. it survives.

How How cancan humans humans make make it through it through the the dayday withwith an inability an inability to to apply apply the the most most elementary elementary rulerule of logic? of logic?

PartPart of the of the answer answer is that is that 30 30 It doesn’t It doesn’t ask ask people people to to the the selection selection tasktask is aispeculiar a peculiar challenge. challenge.

apply apply the the syllogism syllogism to make to make a useful a useful deduction deduction (“Here’s (“Here’s a coin a coin withwith a king; a king; what’s what’s on the on the other other side?”) side?”) or to ortest to test the the rulerule in general in general (“Is(“Is the the rulerule truetrue of the of the country’s country’s coinage?”). coinage?”).

It asks It asks whether whether the the rulerule applies applies specifically specifically to each to each of aofhandful a handful of items of items before before them them on the on the table. table.

TheThe other other partpart of the of the answer answer is that is that people people do do apply apply logic logic when when the the rulerule involves involves the the shoulds shoulds andand shouldn’ts shouldn’ts of human of human life life rather rather thanthan arbitrary arbitrary symbols symbols andand tokens. tokens.

Suppose Suppose the the PostPost Office Office sellssells fiftyfiftycentcent stamps stamps for for thirdthirdclassclass mailmail but but requires requires ten-tendollar dollar stamps stamps for for Express Express Mail.

Mail.

That That is, propis, properlyerly addressed addressed mailmail must must follow follow the the rulerule “If a“If letter a letter is labeled is labeled Express Express Mail, Mail, it must it must havehave a tena tendollar dollar stamp.” stamp.”

Suppose Suppose the the label label andand the the

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stamp stamp don’t don’t fit on fit the on the same same sideside of the of the envelope, envelope, so asopostal a postal worker worker has has to turn to turn envelopes envelopes overover to check to check to see to see if the if the sender sender has has followed followed the the rule.rule.

Here Here are are fourfour envelopes. envelopes.

Imagine Imagine thatthat youyou are are a postal a postal worker. worker.

Which Which onesones do you do you havehave to turn to turn over? over?

džƉƌĞƐƐ džƉƌĞƐƐ

ϯƌĚ ĐůĂƐƐ ϯƌĚ ĐůĂƐƐ

ϱϬൔϱϬൔ

ΨϭϬΨϭϬ

TheThe correct correct answer answer once once again again is Pisand P and not-notQ, namely Q, namely the the Ex-Express press envelope envelope andand the the oneone withwith the the fiftyfiftycentcent stamp. stamp.

Though Though the the problem problem is logically is logically equivalent equivalent to the to the fourfourcoincoin problem, problem, thisthis timetime almost almost everyone everyone getsgets it right. it right.

TheThe content content of aoflogical a logical problem problem mat-mat31 31 When When an ifanthen if-then rulerule implements implements a contract a contract involving involving permispermisters.ters.

sions sions andand duties— duties— “If you “If you enjoy enjoy a benefit, a benefit, youyou must must paypay a cost”— a cost”— thenthen a violation a violation of the of the rulerule (take (take the the benefit, benefit, don’t don’t paypay the the cost) cost) is equivais equivalentlent to cheating, to cheating, andand people people intuitively intuitively know know what what it takes it takes to catch to catch a a cheater. cheater.

They They don’t don’t check check up on up people on people whowho aren’t aren’t enjoying enjoying the the ben-benefit efit or people or people whowho havehave paidpaid a cost, a cost, neither neither of whom of whom could could be trying be trying to get to get away away withwith something. something.

Cognitive Cognitive psychologists psychologists debate debate exactly exactly what what kinds kinds of content of content temporarily temporarily turnturn people people intointo logicians. logicians.

They They can’t can’t be just be just anyany con-concrete crete scenarios, scenarios, but but must must embody embody the the kinds kinds of logical of logical challenges challenges thatthat we became we became attuned attuned to astowe as developed we developed intointo adults adults andand perhaps perhaps when when we we evolved evolved intointo humans. humans.

Monitoring Monitoring a privilege a privilege or duty or duty is one is one of of these these logiclogicunlocking unlocking themes; themes; monitoring monitoring danger danger is another. is another.

People People know know thatthat to verify to verify compliance compliance withwith the the precaution precaution “If “If youyou rideride a a bicycle, bicycle, thenthen youyou must must wear wear a helmet,” a helmet,” theythey havehave to check to check thatthat a child a child on aonbicycle a bicycle is wearing is wearing a helmet a helmet andand thatthat a child a child without without a helmet a helmet doesdoes not not get get ontoonto a bicycle. a bicycle.

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Now, Now, a mind a mind thatthat cancan falsify falsify a conditional a conditional rulerule when when the the violations violations are are tantamount tantamount to cheating to cheating or danger or danger is not is not exactly exactly a logical a logical mind. mind.

Logic, Logic, by definition, by definition, is about is about the the form form of statements, of statements, not not their their content: content: howhow Ps and Ps and Qs Qs are are connected connected by if, by then, if, then, and,and, or, or, not,not, some, some, andand all,all, regardless regardless of what of what the the Ps and Ps and Qs Qs stand stand for. for.

Logic Logic is a iscrowning a crowning achievement achievement of human of human knowledge. knowledge.

It organizes It organizes ourour reasoning reasoning withwith unfamiliar unfamiliar or abstract or abstract subject subject matter, matter, suchsuch as the as the lawslaws of government of government andand science, science, andand when when implemented implemented in silicon in silicon it turns it turns inert inert matter matter intointo thinking thinking machines. machines.

ButBut what what the the untutored untutored human human mind mind commands commands is is not not a generala generalpurpose, purpose, contentcontentfreefree tool,tool, withwith formulas formulas likelike “[If“[If P P then then Q] is Q]equivalent is equivalent to notto not[P and [P and notnot Q],”Q],” intointo which which anyany P and P and Q can Q can be plugged. be plugged.

It commands It commands a seta set of more of more specialized specialized tools tools thatthat bakebake together together the the content content relevant relevant to the to the problem problem withwith the the rules rules of of logic logic (without (without those those rules, rules, the the tools tools wouldn’t wouldn’t work). work).

It isn’t It isn’t easyeasy for for people people to extricate to extricate the the rules rules andand wield wield them them in novel, in novel, abstract, abstract, or or apparently apparently meaningless meaningless problems. problems.

That’s That’s what what education education andand other other rationalityrationalityenhancing enhancing institutions institutions are are for. for.

They They augment augment the the ecological ecological rationality rationality we are we are born born andand grow grow up with— up with— ourour horse horse sense, sense, ourour street street smarts— smarts— withwith the the broaderbroaderspectrum spectrum andand more more potent potent tools tools of reasonof reason32 32 ing ing perfected perfected by our by our bestbest thinkers thinkers overover the the millennia. millennia.

A Simple A Simple Probability Probability Problem Problem OneOne of the of the most most famous famous television television game game shows shows from from the the heyday heyday of of the the genre genre from from the the 1950s 1950s to the to the 1980s 1980s waswas Let’sLet’s Make Make a Deal. a Deal.

Its host, Its host, Monty Monty Hall, Hall, achieved achieved a second a second kindkind of fame of fame when when a dilemma a dilemma in in 33 33 probability probability theory, theory, loosely loosely based based on the on the show, show, waswas named named after after him.him.

A contestant A contestant is faced is faced withwith three three doors. doors.

Behind Behind oneone of them of them is a is sleek a sleek newnew car.car.

Behind Behind the the other other twotwo are are goats. goats.

TheThe contestant contestant picks picks a door, a door, say say Door Door 1. To 1. To build build suspense, suspense, Monty Monty opens opens oneone of the of the other other twotwo

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doors, doors, say say Door Door 3, revealing 3, revealing a goat. a goat.

To To build build the the suspense suspense stillstill fur-further,ther, he gives he gives the the contestant contestant an opportunity an opportunity either either to stick to stick withwith their their original original choice choice or to orswitch to switch to the to the unopened unopened door. door.

YouYou are are the the con-contestant. testant.

What What should should youyou do?do?

34 34 They They figure figure thatthat since since the the car car waswas placed placed Almost Almost everyone everyone stays. stays.

behind behind oneone of the of the three three doors doors at random, at random, andand Door Door 3 has 3 has been been elimeliminated, inated, there there is now is now a fiftya fiftyfiftyfifty chance chance eacheach thatthat the the car car willwill be bebe behindhind Door Door 1 or1Door or Door 2. Though 2. Though there’s there’s no harm no harm in switching, in switching, theythey think, think, there’s there’s no benefit no benefit either. either.

So they So they stickstick withwith their their firstfirst choice choice out out of inertia, of inertia, pride, pride, or anticipation or anticipation thatthat their their regret regret after after an unlucky an unlucky switch switch would would be more be more intense intense thanthan their their delight delight after after a lucky a lucky one.one.

TheThe Monty Monty HallHall dilemma dilemma became became famous famous in 1990 in 1990 when when it was it was presented presented in the in the “Ask“Ask Marilyn” Marilyn” column column in Parade, in Parade, a magazine a magazine in- in35 35 serted serted in the in the Sunday Sunday edition edition of hundreds of hundreds of American of American newspapers. newspapers.

TheThe columnist columnist waswas Marilyn Marilyn vos vos Savant, Savant, known known at the at the timetime as “the as “the world’s world’s smartest smartest woman” woman” because because of her of her entry entry in the in the Guinness Guinness BookBook of of World World Records Records for the for the highest highest score score on an onintelligence an intelligence test.test.

VosVos Savant Savant wrote wrote thatthat youyou should should switch: switch: the the oddsodds of the of the car car being being behind behind Door Door 2 2 are are twotwo in three, in three, compared compared withwith oneone in three in three for for Door Door 1. The 1. The col-column umn drew drew ten ten thousand thousand letters, letters, a thousand a thousand of them of them from from PhDs, PhDs, mainly mainly in mathematics in mathematics andand statistics, statistics, most most of whom of whom saidsaid she she waswas wrong. wrong.

Here Here are are some some examples: examples: YouYou blewblew it, and it, and youyou blewblew it big! it big!

Since Since youyou seem seem to have to have dif-difficulty ficulty grasping grasping the the basic basic principle principle at work at work here, here, I’ll explain.

I’ll explain.

After After the the hosthost reveals reveals a goat, a goat, youyou nownow havehave a onea onein-two in-two chance chance of being of being correct. correct.

Whether Whether youyou change change youryour selection selection or not, or not, the the oddsodds are the are the same. same.

There There is enough is enough mathematical mathematical illiteracy illiteracy in this in this country, country, andand we don’t we don’t needneed the the world’s world’s highhighest IQ est propagating IQ propagating more. more.

Shame!

Shame!

— Scott — Scott Smith, Smith, PhD, PhD, University University of Florida of Florida

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I amI am suresure youyou willwill receive receive many many letters letters on this on this topic topic from from highhigh school school andand college college students. students.

Perhaps Perhaps youyou should should keepkeep a a few few addresses addresses for help for help withwith future future columns. columns.

— W. — Robert W. Robert Smith, Smith, PhD, PhD, Georgia Georgia State State University University

Maybe Maybe women women looklook at math at math problems problems differently differently thanthan men. men.

36 36 — Don — Don Edwards, Edwards, Sunriver, Sunriver, Oregon Oregon

Among Among the the objectors objectors waswas PaulPaul Erdös Erdös (1913– (1913– 1996), 1996), the the renowned renowned mathematician mathematician whowho waswas so prolific so prolific thatthat many many academics academics boast boast of of their their “Erdös “Erdös number,” number,” the the length length of the of the shortest shortest chain chain of coauthorof coauthor37 37 ships ships linking linking them them to the to the great great theoretician. theoretician.

ButBut the the mansplaining mansplaining mathematicians mathematicians were were wrong wrong andand the the world’s world’s smartest smartest woman woman waswas right. right.

YouYou should should switch. switch.

It’s It’s not not thatthat hardhard to to see see why.why.

There There are are three three possibilities possibilities for for where where the the car car could could havehave been been placed. placed.

Let’s Let’s consider consider eacheach door door andand count count up the up the number number of of times times out out of the of the three three thatthat youyou would would winwin withwith eacheach strategy. strategy.

YouYou picked picked Door Door 1, but 1, but of course of course that’s that’s justjust a label; a label; as long as long as Monty as Monty fol-followslows the the rulerule “Open “Open an unselected an unselected door door withwith a goat; a goat; if both if both havehave goats, goats, pickpick oneone at random,” at random,” the the odds odds come come out out the the same same whichever whichever door door youyou picked. picked.

Suppose Suppose youryour strategy strategy is “Stay” is “Stay” (left(left column column in the in the figure). figure).

If the If the car car is behind is behind Door Door 1 (top 1 (top left),left), youyou win.win.

(It doesn’t (It doesn’t matter matter which which of of the the other other doors doors Monty Monty opened, opened, because because you’re you’re not not switching switching to eito either.) ther.)

If the If the car car is behind is behind Door Door 2 (middle 2 (middle left),left), youyou lose.lose.

If the If the car car is is behind behind Door Door 3 (bottom 3 (bottom left),left), youyou lose.lose.

So the So the odds odds of winning of winning withwith the the “Stay” “Stay” strategy strategy are are oneone in three. in three.

Now Now suppose suppose youryour strategy strategy is “Switch” is “Switch” (right (right column). column).

If the If the car car is behind is behind Door Door 1, you 1, you lose.lose.

If the If the car car is behind is behind Door Door 2, Monty 2, Monty would would havehave opened opened Door Door 3, so3,you so you would would switch switch to Door to Door 2 and 2 and win.win.

If the If the car car is behind is behind Door Door 3, he 3, would he would havehave opened opened Door Door 2, so 2, you so you would would

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switch switch to Door to Door 3 and 3 and win.win.

TheThe odds odds of winning of winning withwith the the “Switch” “Switch” strategy strategy are are twotwo in three, in three, double double the the odds odds of staying. of staying.

38 38 Even Even if you if you don’t don’t work work through through the the logilogiIt’s It’s not not rocket rocket surgery. surgery.

cal cal possibilities, possibilities, youyou could could playplay a few a few rounds rounds yourself yourself withwith cutouts cutouts andand toystoys andand tot tot up the up the outcomes, outcomes, as Hall as Hall himself himself did did to convince to convince a a 39 39 Or Or youyou skeptical skeptical journalist. journalist.

(Nowadays, (Nowadays, youyou cancan playplay it online.) it online.)

could could pursue pursue the the intuition intuition “Monty “Monty knows knows the the answer answer andand gavegave me me a a clue;clue; it would it would be foolish be foolish not not to act to act on it.” on it.”

Why Why did did the the mathematimathematicians, cians, professors, professors, andand other other bigshots bigshots get get it soitwrong? so wrong?

Certainly Certainly there there were were failures failures of critical of critical thinking thinking coming coming from from sexism, sexism, ad hominem ad hominem biases, biases, andand professional professional jealousy. jealousy.

VosVos Savant Savant is is

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an attractive an attractive andand stylish stylish woman woman withwith no initials no initials after after her her name name whowho wrote wrote for for a recipea recipeandand gossipgossipfilled filled rag rag andand bantered bantered on lateon latenight night 40 40 SheShe defied defied the the stereotype stereotype of aofmathematician, a mathematician, andand her her talktalk shows. shows.

celebrity celebrity andand bragging bragging rights rights from from Guinness Guinness made made her her a big a big fat target fat target for for a takedown. a takedown.

ButBut partpart of the of the problem problem is the is the problem problem itself. itself.

LikeLike the the teasers teasers in in the the Cognitive Cognitive Reflection Reflection andand Wason Wason selection selection tests, tests, something something about about the the Monty Monty HallHall dilemma dilemma is designed is designed to bring to bring out out the the stupid stupid in in ourour System System 1. But 1. But in this in this casecase System System 2 is2not is not much much brighter. brighter.

Many Many people people can’t can’t swallow swallow the the correct correct explanation explanation eveneven when when it’s it’s pointed pointed out out to them. to them.

This This included included Erdös, Erdös, who, who, violating violating the the soulsoul of aof matha mathematician, ematician, waswas convinced convinced onlyonly when when he saw he saw the the game game repeatedly repeatedly sim-sim41 41 Many Many persist persist eveneven when when theythey see see it simulated it simulated andand eveneven when when ulated. ulated.

theythey repeatedly repeatedly playplay for for money. money.

What’s What’s the the mismatch mismatch between between ourour intuitions intuitions andand the the lawslaws of chance? of chance?

A clue A clue comes comes from from the the overconfident overconfident justifications justifications thatthat the the knowknowit-alls it-alls offered offered for for their their blunders, blunders, sometimes sometimes thoughtlessly thoughtlessly carried carried overover from from other other probability probability puzzles. puzzles.

Many Many people people insist insist thatthat eacheach of of the the unknown unknown alternatives alternatives (in (in thisthis case, case, the the unopened unopened doors) doors) must must havehave an equal an equal probability. probability.

That That is true is true of symmetrical of symmetrical gambling gambling toystoys likelike the the faces faces of aof coin a coin or sides or sides of aof die, a die, andand it isita is reasonable a reasonable starting starting point point when when youyou know know absolutely absolutely nothing nothing about about the the alternatives. alternatives.

ButBut it isitnot is not a law a law of nature. of nature.

Many Many visualize visualize the the causal causal chain. chain.

TheThe car car andand goats goats were were placed placed prior prior to the to the reveal, reveal, andand opening opening a door a door can’t can’t move move them them around around after after the the fact.fact.

Pointing Pointing out out the the independence independence of causal of causal mechanisms mechanisms is ais a common common wayway to debunk to debunk other other illusions illusions suchsuch as the as the gambler’s gambler’s fallacy, fallacy, in which in which people people misguidedly misguidedly think think thatthat after after a run a run of reds of reds the the nextnext spinspin of the of the roulette roulette wheel wheel willwill turnturn up black, up black, when when in fact in fact the the wheel wheel has has no memory, no memory, so every so every spinspin is independent. is independent.

As one As one of vos of vos Savant’s Savant’s correspondents correspondents mansplained, mansplained, “Picture “Picture a race a race withwith three three horses, horses, eacheach

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having having an equal an equal chance chance of winning. of winning.

If horse If horse #3 drops #3 drops deaddead 50 feet 50 feet intointo the the race, race, the the chances chances for for eacheach of the of the remaining remaining twotwo horses horses are are no longer no longer oneone in three in three but but rather rather are are nownow oneone in two.” in two.”

Clearly, Clearly, he he concluded, concluded, it would it would not not make make sense sense to switch to switch one’s one’s bet bet from from horse horse #1 #1 to horse to horse #2. #2.

ButBut thisthis is not is not howhow the the problem problem works. works.

Imagine Imagine thatthat after after youyou place place youryour bet bet on #1, on #1, GodGod announces, announces, “It’s“It’s not not going going to to He He could could havehave warned warned against against be horse be horse #3; no #3; comment no comment on horse on horse #1.”#1.”

42 In42 In horse horse #2 but #2 but didn’t. didn’t.

Switching Switching youryour bet bet doesn’t doesn’t sound sound so crazy. so crazy.

Let’sLet’s Make Make a Deal, a Deal, Monty Monty HallHall is God. is God. TheThe godlike godlike hosthost reminds reminds us how us how exotic exotic the the Monty Monty HallHall problem problem is. It is.requires It requires an omniscient an omniscient being being whowho defies defies the the usual usual goalgoal of aof a conversation— conversation— to share to share what what the the hearer hearer needs needs to know to know (in this (in this case, case, which which door door hides hides the the car)— car)— andand instead instead pursues pursues the the goalgoal of enhancof enhanc43 43 And And unlike unlike the the world, world, whose whose clues clues ing ing suspense suspense among among third third parties. parties.

are are indifferent indifferent to our to our sleuthing, sleuthing, Monty Monty Almighty Almighty knows knows the the truth truth andand knows knows ourour choice choice andand picks picks his his revelation revelation accordingly. accordingly.

People’s People’s insensitivity insensitivity to this to this lucrative lucrative but but esoteric esoteric information information pinpoints pinpoints the the cognitive cognitive weakness weakness at the at the heart heart of the of the puzzle: puzzle: we conwe confusefuse probability probability withwith propensity. propensity.

A propensity A propensity is the is the disposition disposition of an of an object object to act to in actcertain in certain ways. ways.

Intuitions Intuitions about about propensities propensities are are a major a major partpart of our of our mental mental models models of the of the world. world.

People People sense sense thatthat bentbent branches branches tendtend to spring to spring back, back, thatthat kudu kudu maymay tiretire easily, easily, thatthat porcupines porcupines usu-usuallyally leave leave tracks tracks withwith twotwo padprints. padprints.

A propensity A propensity cannot cannot be perbe perceived ceived directly directly (either (either the the branch branch sprang sprang backback or itordidn’t), it didn’t), but but it can it can be inferred be inferred by scrutinizing by scrutinizing the the physical physical makeup makeup of an of object an object andand working working through through the the lawslaws of cause of cause andand effect. effect.

A drier A drier branch branch maymay snap, snap, a kudu a kudu has has more more stamina stamina in the in the rainy rainy season, season, a porcupine a porcupine has has twotwo proximal proximal padspads which which leave leave padprints padprints when when the the ground ground is soft is soft but but not not necessarily necessarily when when it isithard. is hard.

ButBut probability probability is different; is different; it isita isconceptual a conceptual tooltool invented invented in the in the 44 44 TheThe word word has has several several meanings, meanings, but but the the oneone seventeenth seventeenth century. century.

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thatthat matters matters in making in making risky risky decisions decisions is the is the strength strength of one’s of one’s belief belief in an in unknown an unknown statestate of affairs. of affairs.

AnyAny scrap scrap of evidence of evidence thatthat alters alters ourour confidence confidence in an inoutcome an outcome willwill change change its probability its probability andand the the rational rational wayway to act to upon act upon it. The it. The dependence dependence of probability of probability on ethereal on ethereal knowlknowledge edge rather rather thanthan justjust physical physical makeup makeup helps helps explain explain whywhy people people fail fail at the at the dilemma. dilemma.

They They intuit intuit the the propensities propensities for for the the car car to have to have ended ended up behind up behind the the different different doors, doors, andand theythey know know thatthat opening opening a a door door could could not not havehave changed changed those those propensities. propensities.

ButBut probabilities probabilities are are not not about about the the world; world; they’re they’re about about ourour ignorance ignorance of the of the world. world.

New New information information reduces reduces ourour ignorance ignorance andand changes changes the the probabilprobability. ity.

If that If that sounds sounds mystical mystical or paradoxical, or paradoxical, think think about about the the probability probability thatthat a coin a coin I just I just flipped flipped landed landed heads. heads.

ForFor you,you, it’s .5. it’s For .5. For me,me, it’s 1 it’s 1 (I peeked).

(I peeked).

Same Same event, event, different different knowledge, knowledge, different different probability. probability.

In In the the Monty Monty HallHall dilemma, dilemma, newnew information information is provided is provided by the by the all- allseeing seeing host. host.

OneOne implication implication is that is that when when the the reduction reduction of ignorance of ignorance granted granted by the by the hosthost is more is more transparently transparently connected connected to the to the physical physical circumcircumstances, stances, the the solution solution to the to the problem problem becomes becomes intuitive. intuitive.

VosVos Savant Savant invited invited her her readers readers to imagine to imagine a variation a variation of the of the game game show show with, with, say,say, 45 45 You You pickpick one.one.

Monty Monty reveals reveals a goat a goat behind behind 998998 of of a thousand a thousand doors. doors.

the the others. others.

Would Would youyou switch switch to the to the door door he left he left closed? closed?

This This timetime it it seems seems clear clear thatthat Monty’s Monty’s choice choice conveys conveys actionable actionable information. information.

OneOne cancan visualize visualize himhim scanning scanning the the doors doors for for the the car car as he as decides he decides which which oneone not not to open, to open, andand the the closed closed door door is a issign a sign of his of his having having spotted spotted the the car car andand hence hence a spoor a spoor of the of the car car itself. itself.

A Simple A Simple Forecasting Forecasting Problem Problem Once Once we get we get intointo the the habit habit of assigning of assigning numbers numbers to unknown to unknown events, events, we can we can quantify quantify ourour intuitions intuitions about about the the future. future.

Forecasting Forecasting events events

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is big is big business. business.

It informs It informs policy, policy, investment, investment, riskrisk management, management, andand ordinary ordinary curiosity curiosity about about what what lies lies in store in store for for the the world. world.

Consider Consider eacheach of the of the following following events, events, andand write write down down youryour estimate estimate of the of the likelihood likelihood thatthat it will it will taketake place place in the in the coming coming decade. decade.

Many Many of them of them are are pretty pretty unlikely, unlikely, so let’s so let’s make make finer finer distinctions distinctions at the at the lower lower endend of the of the scale scale andand pickpick oneone of the of the following following probabilities probabilities for for each: each: lessless thanthan .01 .01 percent, percent, .1 percent, .1 percent, .5 percent, .5 percent, 1 percent, 1 percent, 2 percent, 2 percent, 5 per5 percent, cent, 10 percent, 10 percent, 25 percent, 25 percent, andand 50 percent 50 percent or more. or more.

1. Saudi 1. Saudi Arabia Arabia develops develops a nuclear a nuclear weapon. weapon.

2. Nicolás 2. Nicolás Maduro Maduro resigns resigns as president as president of Venezuela. of Venezuela.

3. Russia 3. Russia has has a female a female president. president.

4. The 4. The world world suffers suffers a new a new andand eveneven more more lethal lethal pandemic pandemic thanthan CovidCovid19. 19.

5. Vladimir 5. Vladimir Putin Putin is constitutionally is constitutionally prevented prevented from from running running for another for another term term as president as president of Russia of Russia andand his wife his wife takes takes his his place place on the on the ballot, ballot, allowing allowing himhim to run to run the the country country from from the the sidelines. sidelines.

6. Massive 6. Massive strikes strikes andand riotsriots force force Nicolás Nicolás Maduro Maduro to resign to resign as as president president of Venezuela. of Venezuela.

7. A7.respiratory A respiratory virus virus jumps jumps from from batsbats to humans to humans in China in China andand starts starts a new a new andand eveneven more more lethal lethal pandemic pandemic thanthan CovidCovid19. 19.

8. After 8. After IranIran develops develops a nuclear a nuclear weapon weapon andand teststests it initan in unan underground derground explosion, explosion, Saudi Saudi Arabia Arabia develops develops its own its own nuclear nuclear weapon weapon in response. in response.

I presented I presented items items likelike these these to several to several hundred hundred respondents respondents in ain a survey. survey.

On On average, average, people people thought thought it was it was likelier likelier thatthat Putin’s Putin’s wifewife would would be president be president of Russia of Russia thanthan thatthat a woman a woman would would be president. be president.

They They thought thought it was it was likelier likelier thatthat strikes strikes would would force force Maduro Maduro to reto resignsign thanthan thatthat he would he would resign. resign.

They They thought thought Saudi Saudi Arabia Arabia waswas more more

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r a triaotni ao lniatlyi t y

likely likely to develop to develop a nuclear a nuclear weapon weapon in response in response to an to Iranian an Iranian bomb bomb thanthan it was it was to develop to develop a nuclear a nuclear weapon. weapon.

AndAnd theythey thought thought it was it was likelier likelier thatthat Chinese Chinese batsbats would would startstart a pandemic a pandemic thanthan thatthat there there 46 46 would would be abepandemic. a pandemic.

YouYou probably probably agree agree withwith at least at least oneone of these of these comparisons; comparisons; 86 86 percent percent of the of the participants participants whowho rated rated all the all the items items did.did.

If so, If you so, you vio-violated lated an elementary an elementary law law of probability, of probability, the the conjunction conjunction rule:rule: the the probprobability ability of aof conjunction a conjunction of events of events (A and (A and B) must B) must be less be less thanthan or equal or equal to the to the probability probability of either of either of the of the events events (A, (A, or B). or The B). The probability probability of of picking picking an evenan evennumbered numbered spade spade out out of aofdeck a deck of cards, of cards, for for example example (even (even andand spade), spade), has has to be to less be less thanthan the the probability probability of picking of picking a a spade, spade, because because some some spades spades are are not not eveneven numbers. numbers.

In each In each pairpair of world of world events, events, the the second second scenario scenario is a isconjunction a conjunction of events, of events, oneone of which of which is the is the event event in the in the firstfirst scenario. scenario.

ForFor example, example, “Iran “Iran teststests a nuclear a nuclear weapon weapon andand Saudi Saudi Arabia Arabia develops develops a nuclear a nuclear weapon” weapon” is a is conjunction a conjunction thatthat embraces embraces “Saudi “Saudi Arabia Arabia develops develops a nua nuclear clear weapon” weapon” andand must must havehave a smaller a smaller chance chance of happening, of happening, since since there there are are other other scenarios scenarios in which in which the the Saudis Saudis might might go nuclear go nuclear (to (to counter counter Israel, Israel, to flaunt to flaunt hegemony hegemony overover the the Persian Persian Gulf, Gulf, andand so on). so on).

By the By the same same logic, logic, Maduro Maduro resigning resigning the the presidency presidency has has to be to more be more likely likely thanthan Maduro Maduro resigning resigning the the presidency presidency after after a series a series of strikes. of strikes.

What What are are people people thinking? thinking?

A class A class of events of events described described by aby single a single