TheCalculusofHappiness the Calculus of Happiness How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love Oscar E. Fernandez Princeton University Press Princeton and Oxford Copyright(cid:1)c 2017byPrincetonUniversityPress PublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540 IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock, OxfordshireOX201TR press.princeton.edu JacketartcourtesyofShutterstock AllRightsReserved ISBN978-0-691-16863-0 LibraryofCongressCataloging-in-PublicationData Names:Fernandez,OscarE.(OscarEdward) Title:Thecalculusofhappiness:howamathematicalapproachtolifeaddsuptohealth, wealth,andlove/OscarE.Fernandez. Description:Princeton:PrincetonUniversityPress,[2017]|Includesbibliographical referencesandindex. Identifiers:LCCN2016044257|ISBN9780691168630(hardcover:alk.paper) Subjects:LCSH:Mathematics–Popularworks. Classification:LCCQA93.F4672017|DDC650.101/51–dc23LCrecordavailableat https://lccn.loc.gov/2016044257 BritishLibraryCataloging-in-PublicationDataisavailable ThisbookhasbeencomposedinMinionPro Printedonacid-freepaper.∞ TypesetbyNovaTechsetPvtLtd,Bangalore,India PrintedintheUnitedStatesofAmerica 1 3 5 7 9 10 8 6 4 2 ToEmilia Onedaywhenyoucanreadthis Sabrásqueestabapensandoenti Andwhenthatdaycomes Búscameydameunbesoyunabrazo Becausethere’snobettergift Queunahijalepuededarasupapá. Contents Preface ix MathTopicsCoveredbyChapter xiii PartI: AHealthierYouIsJustaFewEquationsAway 1 CHAPTER1 HowManyCaloriesShouldYouEatEachDay? 3 1.1 TheLinearFunctionsHiddeninYourDiet 4 1.2 TheMathematicsofMetabolism 8 1.3 BurnThoseCalories!WorkThoseQuads! 11 1.4 TheCaloriesRequiredtoDigestFood 14 CHAPTER2 LiveLonger(andBeHealthier)byEatingthe RightFoods 20 2.1 AGameofMacronutrientMusicalChairs 20 2.2 HowtoEatMoreandBeHealthier:EnergyDensity 29 2.3 LiveLong(er)andProsperwiththeWaist-HeightRatio 34 PartII: AMathematician’sGuidetoManagingYourMoney 41 CHAPTER3 DissectingYourMonthlyBudget 43 3.1 TheReturnoftheKing(theLinearFunction) 44 3.2 ToExpenses,andBeyond! 49 3.3 HowManyYearsWillItTakeYoutoReachFinancial Independence? 62 CHAPTER4 HowtoBeatWallStreetatItsOwnGame 69 4.1 HowtoMake15%aYear,Guaranteed 70 4.2 TheSafestInvestments 71 4.3 QuantifyingInvestmentRiskandReturn 73 4.4 Stocks,Bonds,andthe“All-Weather”Portfolio 77 viii • Contents PartIII: LookingforLove?ThereMayBeanEquationforThat 87 CHAPTER5 Finding“The1” 89 5.1 WhattheSearchforAliensCanTeachYouaboutFinding YourSoulmate 89 5.2 WhyHiringaSecretaryIsLikeDating 92 5.3 TheStableMatchingProblem 97 CHAPTER6 LivingHappilyEverAfterwith“The1” 103 6.1 YourRelationshipasaDynamicalSystem 104 6.2 NeedHelpMakingaJointDecision?There’sanEquation forThat 108 6.3 HowPsychologistsUseMathtoPredictDivorce 113 Epilogue 118 Acknowledgments 120 AppendixA:BackgroundContent 121 Appendix1 123 Appendix2 128 Appendix3 130 Appendix4 141 Appendix5 143 Appendix6 144 Bibliography 151 Index 157 Preface NUMBERS—THEY’RE EVERYWHERE.Theydescribethepricesyoupay for things, the calories you consume each day, and even your dating life (How many people have you dated? How long did those rela- tionships last?). What you may not have realized is that many of the numbers we care about—like the answers to the aforementioned questions—are the outputs of various inputs. (Example: the calories you consume in a day—the output number—depends on the calories of the individual foods eaten—the inputs.) When thought of this way, an intriguing question emerges: can we use mathematics to improve ourlives? This book is dedicated to answering that question for three aspects oflifewethinkaboutconstantly:health,wealth,andlove.Fortunately, many of the input-output relationships in that trio are described by functions, special types of equations well-understood by mathemati- cians. I’ll guide you through the formulas behind health, wealth, and loveinthechaptersthatfollow.We’llseethattheyarisequitenaturally from careful observations about our everyday experiences, and we’ll learnhowtoextractvaluableandpowerfulinsightsfromthem.Here’s asamplingoftheresultstogiveyouasenseofwhatImean. • Chapter 1: A research-backed equation that determines how many calories you should eat each day given certain inputs, including age andweight. • Chapter2:Aresearch-baseddietthatcanloweryourbadcholesterol, raise your good cholesterol, decrease your risk for developing heart diseaseanddiabetes,andhelpyouloseweight. • Chapter2:Aresearch-backedequationthatestimateshowmanyyears offuturelifeyou’relosing(andthentellsyouhowtogetthemback).