Six Sources of Collapse: a Mathematician's Perspective on How Things Can Fall Apart in the Blink of an Eye PDF
Preview Six Sources of Collapse: a Mathematician's Perspective on How Things Can Fall Apart in the Blink of an Eye
i i “master” — 2012/10/11 — 22:40 — page i — #1 i i Six Sources of Collapse A Mathematician’s Perspective on How Things Can Fall Apart in the Blink of an Eye i i i i i i “master” — 2012/10/11 — 22:40 — page ii — #2 i i ThephotooftheTacomaNarrowsBridge onthecoverisusedcourtesyof UNIVERSITYOFWASHINGTONLIBRARIES SPECIALCOLLECTIONS Negativenumber:UW21418. c 2012bytheMathematicalAssociationofAmerica,Inc. (cid:13) LibraryofCongressCatalogCardNumber2012950085 PrinteditionISBN978-0-88385-579-9 ElectroniceditionISBN978-1-61444-514-2 PrintedintheUnitedStatesofAmerica CurrentPrinting(lastdigit): 10987654321 i i i i i i “master” — 2012/10/11 — 22:40 — page iii — #3 i i Six Sources of Collapse A Mathematician’s Perspective on How Things Can Fall Apart in the Blink of an Eye Charles R. Hadlock Bentley University PublishedandDistributedby TheMathematicalAssociationofAmerica i i i i i i “master” — 2012/10/11 — 22:40 — page iv — #4 i i CouncilonPublicationsandCommunications FrankFarris,Chair CommitteeonBooks GeraldBryce,Chair SpectrumEditorialBoard GeraldL.Alexanderson,Co-Editor JamesJ.Tattersall,Co-Editor RobertE.Bradley SusannaS.Epp RichardK.Guy KeithM.Kendig ShawneeL.McMurran JeffreyL.Nunemacher JeanJ.Pedersen KennethA.Ross MarvinSchaefer FranklinF.Sheehan i i i i i i “master” — 2012/10/11 — 22:40 — page v — #5 i i SPECTRUMSERIES TheSpectrumSeriesoftheMathematicalAssociationofAmericawassonamedtoreflect itspurpose:topublishabroadrangeofbooksincludingbiographies,accessibleexpositions of old or new mathematical ideas, reprintsand revisions of excellent out-of-printbooks, popular works, and other monographs of high interest that will appeal to a broad range of readers, includingstudents and teachers of mathematics, mathematical amateurs, and researchers. 777MathematicalConversationStarters,byJohndePillis 99PointsofIntersection:Examples—Pictures—Proofs,byHansWalser.Translatedfromtheoriginal GermanbyPeterHiltonandJeanPedersen AhaGotchaandAhaInsight,byMartinGardner AlltheMathThat’sFittoPrint,byKeithDevlin BeautifulMathematics,byMartinErickson CalculusandItsOrigins,byDavidPerkins CalculusGems:BriefLivesandMemorableMathematics,byGeorgeF.Simmons CarlFriedrichGauss:TitanofScience,byG.WaldoDunnington,withadditionalmaterialbyJeremy GrayandFritz-EgbertDohse TheChangingSpaceofGeometry,editedbyChrisPritchard Circles:AMathematicalView,byDanPedoe ComplexNumbersandGeometry,byLiang-shinHahn Cryptology,byAlbrechtBeutelspacher TheEarlyMathematicsofLeonhardEuler,byC.EdwardSandifer TheEdgeoftheUniverse:Celebrating10YearsofMathHorizons,editedbyDeannaHaunsperger andStephenKennedy EulerandModernScience,editedbyN. N. Bogolyubov,G. K. Mikhailov,andA. P.Yushkevich. TranslatedfromRussianbyRobertBurns. Eulerat300:AnAppreciation,editedbyRobertE.Bradley,LawrenceA.D’Antonio,andC.Edward Sandifer ExpeditionsinMathematics,editedbyTatianaShubin,DavidF.Hayes,andGeraldL.Alexanderson FiveHundredMathematicalChallenges,byEdwardJ.Barbeau,MurrayS.Klamkin,andWilliamO. J.Moser TheGeniusofEuler:ReflectionsonhisLifeandWork,editedbyWilliamDunham TheGoldenSection,byHansWalser.TranslatedfromtheoriginalGermanbyPeterHilton,withthe assistanceofJeanPedersen. TheHarmonyoftheWorld:75YearsofMathematicsMagazine,editedbyGeraldL.Alexanderson withtheassistanceofPeterRoss AHistorianLooksBack:TheCalculusasAlgebraandSelectedWritings,byJudithGrabiner History of Mathematics: Highways and Byways, by Amy Dahan-Dalme´dico and Jeanne Peiffer, translatedbySanfordSegal HowEulerDidIt,byC.EdwardSandifer IntheDarkontheSunnySide:AMemoirofanOut-of-SightMathematician,byLarryBaggett IsMathematicsInevitable?AMiscellany,editedbyUnderwoodDudley IWanttoBeaMathematician,byPaulR.Halmos i i i i i i “master” — 2012/10/11 — 22:40 — page vi — #6 i i JourneyintoGeometries,byMartaSved JULIA:alifeinmathematics,byConstanceReid TheLighterSideofMathematics:ProceedingsoftheEuge`neStrensMemorialConferenceonRecre- ationalMathematics&ItsHistory,editedbyRichardK.GuyandRobertE.Woodrow LureoftheIntegers,byJoeRoberts MagicNumbersoftheProfessor,byOwenO’SheaandUnderwoodDudley MagicTricks,CardShuffling,andDynamicComputerMemories:TheMathematicsof thePerfect Shuffle,byS.BrentMorris MartinGardner’sMathematicalGames:TheentirecollectionofhisScientificAmericancolumns TheMathChatBook,byFrankMorgan MathematicalAdventuresfor StudentsandAmateurs,editedbyDavidHayesandTatianaShubin. WiththeassistanceofGeraldL.AlexandersonandPeterRoss MathematicalApocrypha,byStevenG.Krantz MathematicalApocryphaRedux,byStevenG.Krantz MathematicalCarnival,byMartinGardner MathematicalCirclesVolI:InMathematicalCirclesQuadrantsI,II,III,IV,byHowardW.Eves MathematicalCirclesVolII:MathematicalCirclesRevisitedandMathematicalCirclesSquared,by HowardW.Eves MathematicalCirclesVolIII: MathematicalCirclesAdieuandReturntoMathematicalCircles,by HowardW.Eves MathematicalCircus,byMartinGardner MathematicalCranks,byUnderwoodDudley MathematicalEvolutions,editedbyAbeShenitzerandJohnStillwell MathematicalFallacies,Flaws,andFlimflam,byEdwardJ.Barbeau MathematicalMagicShow,byMartinGardner MathematicalReminiscences,byHowardEves MathematicalTreks:FromSurrealNumberstoMagicCircles,byIvarsPeterson AMathematicianComesofAge,byStevenG.Krantz Mathematics:QueenandServantofScience,byE.T.Bell MathematicsinHistoricalContext,,byJeffSuzuki MemorabiliaMathematica,byRobertEdouardMoritz MusingsoftheMasters:AnAnthologyofMathematicalReflections,editedbyRaymondG.Ayoub NewMathematicalDiversions,byMartinGardner Non-EuclideanGeometry,byH.S.M.Coxeter NumericalMethodsThatWork,byFormanActon NumerologyorWhatPythagorasWrought,byUnderwoodDudley OutoftheMouthsofMathematicians,byRosemarySchmalz PenroseTilestoTrapdoorCiphers...andtheReturnofDr.Matrix,byMartinGardner Polyominoes,byGeorgeMartin PowerPlay,byEdwardJ.Barbeau ProofandOtherDilemmas:MathematicsandPhilosophy,editedbyBonnieGoldandRogerSimons TheRandomWalksofGeorgePo´lya,byGeraldL.Alexanderson RemarkableMathematicians,fromEulertovonNeumann,byIoanJames i i i i i i “master” — 2012/10/11 — 22:40 — page vii — #7 i i TheSearchforE.T.Bell,alsoknownasJohnTaine,byConstanceReid ShapingSpace,editedbyMarjorieSenechalandGeorgeFleck SherlockHolmesinBabylonandOtherTalesofMathematicalHistory,editedbyMarlowAnderson, VictorKatz,andRobinWilson SixSourcesofCollapse:AMathematician’sPerspectiveonHowThingsCanFallApartintheBlink ofanEye,byCharlesR.Hadlock Sophie’sDiary,SecondEdition,byDoraMusielak Student ResearchProjects in Calculus, by Marcus Cohen,Arthur Knoebel, EdwardD. Gaughan, DouglasS.Kurtz,andDavidPengelley Symmetry,byHansWalser.TranslatedfromtheoriginalGermanbyPeterHilton,withtheassistance ofJeanPedersen. TheTrisectors,byUnderwoodDudley TwentyYearsBeforetheBlackboard,byMichaelStuebenwithDianeSandford WhoGaveYoutheEpsilon?andOtherTalesofMathematicalHistory,editedbyMarlowAnderson, VictorKatz,andRobinWilson TheWordsofMathematics,byStevenSchwartzman MAAServiceCenter P.O.Box91112 Washington,DC20090-1112 1-800-331-1MAA FAX:1-301-206-9789 i i i i i i “master” — 2012/10/11 — 22:40 — page viii — #8 i i Thisbookis dedicatedtomy grandchildren, — Charles, Rob, Ben, Kent, Catherine, McKenzie, andForrest — inthehopethattheyandtheirpeerswillsuccessfully exert intellect, compassion, andleadership intakingonthenew challenges of collapsethatwill surely confronttheirgeneration. i i i i i i “master” — 2012/10/11 — 22:40 — page ix — #9 i i Preface The worldisafascinatingcombinationoffragilityandresilience.Inthemidstofterrible warsandatrocitiesandcountriesbeingtornapart,wealsosee imagesofchildrenplaying soccer in the street and youngcouples startingfutures together at weddingcelebrations. The signs ofpast collapses are all aroundus, butwe keep buildingnew lives, structures, andinstitutionstotaketheirplace. Thisisabookaboutcollapse.It’sintendedtohelpsomeofusmanagecollapsealittle better, promotingit when we want toand protectingourselves from itwhen we need to. The first stepis tounderstanditbetter, usingdifferenttoolsand differentpointsofview. Much of thisbook isabout historyand experience — the anatomies of past collapses in many different subject areas from finance to fighter jets, networks to nanostructures. In surveying these diverse cases, we find extraordinary commonalities. The same kinds of dynamicsoccuroverandoveragain. Letmeexplainwhymybackgroundasamathematiciangivesmeaparticularperspec- tiveonthissubject.Somepeoplethinkthatmathisallaboutsolvingequations,butthey’re deadwrong.Mathismuchmoreaboutidentifyingcommonfeaturesanddescribingthem inawaythatcapturestheiressence. Mathematicalsymbolsandequationsare basicallya languagethathelpstoclearawaysomeofthedetailsowecanfocusonthosefundamental underlyingfeatures or principles. No matter what your math background, whether quite modest(say,comfortwiththeequationsandgraphsofhighschoolpre-calculus)orhighly advanced, I think you will be interested to see how using the mathematical language of probabilities, game theory, dynamical systems, networks, and related fields helps to or- ganize ouraccumulated experience aboutreal worldcollapses. Thiscan bringintomuch sharper focus the pointsof vulnerabilityin the systems of the present and future. That’s howwecanbridgethegap,forexample,fromtheamazingexperimentofbiologicalevo- lutiontothe designoforganizations,or fromthe movements of a past civilizationto the layoutoffireexits. You can read this book looking for only what I have described above, skimming or skippingtherest.You’llfindthediscussionoffamouscollapseeventsinlanguageIthink you will readily understand: what really happened at Chernobyl, why did the mortgage market crash, what was that “flash crash” you heard about, how could a falling branch knockoutpowertoalmosttheentireNortheast,andmore.Thisisseriousmaterialandthe ix i i i i
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