Six Sources of Collapse

222 Pages·2012·4.791 MB·English

by  Charles R. Hadlock

Six Sources of Collapse
A Mathematician’s Perspective on How
Things Can Fall Apart in the Blink of an Eye
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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
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HowEulerDidIt,byC.EdwardSandifer
IntheDarkontheSunnySide:AMemoirofanOut-of-SightMathematician,byLarryBaggett
IsMathematicsInevitable?AMiscellany,editedbyUnderwoodDudley
IWanttoBeaMathematician,byPaulR.Halmos
JourneyintoGeometries,byMartaSved
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TheLighterSideofMathematics:ProceedingsoftheEuge`neStrensMemorialConferenceonRecre-
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OutoftheMouthsofMathematicians,byRosemarySchmalz
PenroseTilestoTrapdoorCiphers...andtheReturnofDr.Matrix,byMartinGardner
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PowerPlay,byEdwardJ.Barbeau
ProofandOtherDilemmas:MathematicsandPhilosophy,editedbyBonnieGoldandRogerSimons
TheRandomWalksofGeorgePo´lya,byGeraldL.Alexanderson
RemarkableMathematicians,fromEulertovonNeumann,byIoanJames
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ShapingSpace,editedbyMarjorieSenechalandGeorgeFleck
SherlockHolmesinBabylonandOtherTalesofMathematicalHistory,editedbyMarlowAnderson,
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SixSourcesofCollapse:AMathematician’sPerspectiveonHowThingsCanFallApartintheBlink
ofanEye,byCharlesR.Hadlock
Sophie’sDiary,SecondEdition,byDoraMusielak
Student ResearchProjects in Calculus, by Marcus Cohen,Arthur Knoebel, EdwardD. Gaughan,
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Symmetry,byHansWalser.TranslatedfromtheoriginalGermanbyPeterHilton,withtheassistance
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Thisbookis dedicatedtomy grandchildren,
— Charles, Rob, Ben, Kent, Catherine, McKenzie, andForrest —
inthehopethattheyandtheirpeerswillsuccessfully exert intellect,
compassion, andleadership intakingonthenew challenges of
collapsethatwill surely confronttheirgeneration.
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
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