1-Murphys-Law

Unit2Murphy’sLawTEACHER:Goodafternoon,everyone.Morethan200yearsago,theScottishpoetRobertBurnssaidthat“thebestlaidplansofmiceandmenoftengoawry.”I’msureweallhavefirsthandexperiencewithwhatBurnsmeans;nomatterhowcarefullyweplanaprojectandnomatterhowcarefullywetryto,uh,anticipateproblems,we’relikelyto,uhencountersomethingunexpectedandunwelcomethatwillthrowourplanoffcourse.Well,classtodaywe’llbelookingathowplanscangorightorwrong..,and,uh,howwecanmakesenseofthis.AreyouallfamiliarwithMurphy’sLaw?Well,accordingtoMurphy’sLaw,anythingthatcangowrongwillgowrong.Sowe’llbelookingateverydayexamplesofMurphy’sLawuh,thingslikewhytoastfallsbuttered-sidedown,whyitalwaysseemslikewechooseslowlinesatthesupermarket,andwhyitissodifficulttowinwhenwegamble.Asyoumayknow,wenowhavemanydifferentversionsofMurphy’sLaw,andtodayI’dliketolookatthesciencebehindthreeofthem.I’lltrytoshowyouthatsomethingswhichhavehappenedtoyou,andwhichyoumayhavethoughtweresimplybadluck,hadnothingtodowithluckatall.WhatI’msayingisthattherearesomeverygoodscientificreasonsformanyofthethingsthathappentous,andwe’renotvictimsofbadluckasoftenaswemightthink.Whenweconsidersomebasicscienceandprobabilitytheory,wecanmoreclearlyunderstandwhysome“bad”thingshappenthewaytheydo.Allright.Let’sbeginwithaverycommonplacesituation.Let’ssayyou’vejustgottenup.You’restillsleepy,andyoumakeyourwaytothebreakfasttable.Inyourhalf-awakestate,youaccidentallyhityourpieceoftoast,whichhasbutterononeside.Thetoastbeginstofalltothefloor.Nowwhatarethechancesthatyou’llbeluckyandthetoastwilllandbuttered-sideup?Well,thetoasthasonlytwosides,somostpeoplethinkthattheanswerisfifty-fifty.Fiftypercent.Right?Doyouthinkthatthere’sa50percentchancethatthetoastwilllandwiththebuttered-sideup?STUDENT1:Well,thissoundslikeatrickyquestion,but,uh,yeah.Logically,50percentsoundsaboutright.TEACHER:Yes,50percentdoesseemright,but,inthiscase,Murphy’sLawofFallingToastsays:“Toastwhichfallsfromatablewilllandbuttered-sidedown.”Actually,theprobabilityofthishappeningisextremelyhigh.It’scloseto100percent.Now,here’swhy.Whensomethinglikeapieceoftoastfallsfromatable,itsbehaviorisnotrandom.Therateofspiniscontrolledbythelawsofphysics.Thisistheproblem.Therateofspin,thatis,howfastthetoastspins,istoolowforthetoasttomakeacompleterevolution.It’stooslowtoturncompletelyaroundandhitthefloorbuttered-sideup.Therateofspinisdeterminedbytheforceofgravity(Theforceofgravityistheforceexertedbythegravitationalfieldofamassiveobjectonanybodywithinthevicinityofitssurface.).Soinaveryrealsense,thelawsofphysics,andspecificallytherateofspin,makesurethatourtoastlandsbuttered-sidedownalmostallthetime.Sothepointisthatsimpleprobabilitiesforexample,theprobabilitythattoasthasafifty-fiftychanceoflandingbuttered-sideupcanbegreatlyaffectedbyothermorefundamentalfactors,suchasthelawsofphysics.So,inthiscase,webelievethatwehavebadluckbecausewedon’tunderstandthatthenaturallawsofphysicsareineffect.Thetoastshouldlandbuttered-sidedown.OK?Let’slookatthenextpoint.Nowwecometooneofmymostfrustratingsituationsinlife,thesupermarketline.Inthiscase,Murphy’sLawofSupermarketLinessays:“Thelinenexttoyouwillmovefasterthanyours.”Noweverybodywantstogetintothefastestlinewhentheygotothesupermarket,right?OK,solet’ssaythatyou’reatyourlocalsupermarketandtherearefivelines,buteachofthefivelineslooksprettymuchequalinlength.Now,ofcourse,youwanttotrytoanticipatewhichoneofthefivelineswillmovethefastest.Well,thisiswheresimpleprobabilitytheoryentersthepicture.Thechancesthatyouhavechosenthefastestofthefivelines,isonedividedbythenumberoflines,whichisfiveinthiscase.Somathematically,theformulaisonedividedbyNwhereNisthetotalnumberoflines.Sointhisexample,onedividedbyfivegivesus,what?STUDENT2:Onedividedbyfiveisone-fifthor...uh...20percent.TEACHER:Right.Twentypercent.There’sonlya20percentchancethatwehavechosenthefastestofthefivelines.Nowevenifwereducethattothreelines,ourlineandthelinesoneachsideofus,thechanceswe’vechosenthefastestlinearestillonlywhat?STUDENT2:Uh,33percent.Oneoutofthree.TEACHER:Sure.Onedividedbythreeis33percent,soit’snotjustyourimaginationthatonelinenearyoualmostalwaysmovesfasterthanyours.Simpleprobabilitytheoryshowsthattheodds(probabilities)areagainstyou.Ifthereareverymanylines,thechancesthatyou’llchoosethefastestonearequitelow.So,yousee,ithaslittletodowithluck,butweperceivethatitdoes.Allright.Nowlet’slookatafinalsituationthatshowshowwecommonlymisunderstandthelawsofprobability.We’vecometoMurphy’sLawofGamblingthatsayssimply:“Youwilllose.”Nowinthecaseofthesupermarketlinesthatwe’vejusttalkedabout,probabilitytheoryappliedverynicely.Andactually,aswegothroughlife,mostthingsarefairlypredictablebecausetheyfollowthebasiclawsofprobability.Weatherisanexample.Let’ssaythatit’sbeenrainingforaweek,andafriendsaystoyou“Ithinkit’sgoingtobesunnytomorrow.”Isthatanunreasonablestatement?Well,no.Cloudsmove,andtheyareoflimitedsize,soifit’sbeenrainingforaweek,it’slikelythattherainandcloudswillendsoon.Inotherwords,thenextsunnydayismorelikelytooccuraftertheseventhdayofrainthanafterthefirst,becausethestormfronthas’whatiscalleda