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Hack 74. Live Life in the Fast Lane (You're Already In)

Hack 74. Live Life in the Fast Lane (You're Already In)

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Ourperceptualworldwhileonabusyhighwayorinatrafficjam

consistsofthebigtruckinfrontofus,thecarsweseetothe

rightandleftofus,andthepoorsapstuckbehindus.Tojudge

ourspeedoftravel,whilewedohaveaspeedometer,themost

compellingdatatendstobethecarsoneithersideofus.(Are

theypassingusorarewepassingthem?)

Trafficresearcherscallthetimeswhenyouarepassingother

carsskipsandthetimeswhenothercarsarepassingyouslips.

Recentresearchreferstoskipsaspassingepochsandslipsas

being-overtakenepochs.Itprobablydoesnotsurpriseyouthat

driversgreatlypreferpassingepochsoverbeing-overtaken

epochs.



Anepochisaperiodoftime.Drivers'liveswhiledrivinginheavytraffic

areessentiallydefinedbyseriesofepochsofveryshortduration.



Inadditiontolookingforfasterlanestomoveinto,drivershave

anothergoal,whichistokeeptheirownvehiclemovingas

quicklyaspossible,oratleastclosetotheirtargetspeed(which

mightbethespeedlimit,forexample).Ifthereareperceived

gapsbetweenthemselvesandthevehicleinfrontofthem,and

theyarenotcurrentlymovingattheirtargetspeed,driverswill

acceleratetoclosethegap.Itistheseburstsofacceleration

thataccountfortheskips(periodsofpassingothercars)and

slips(periodsofothercarspassingthem).Wearelikelyto

experiencemoreperiodsoftimewhenwearebeingpassed

thanperiodswhenwearedoingthepassing.Itisthisperceived

inequitythatcanresultindriversconcludingthattheyarein

theslowlane,evenifbothlanesareequallyslow.

Imaginetwolanesoftrafficsidebysidethataremovingatthe

sameaveragespeed.Gapsbetweencarsformrandomly;more

accurately,theyformsystematically,butbasedonarandom



startingconfiguration.Gapsarefilledastheyform,andwhen

gapsarefilled,carshaveaccelerated.



Averagespeedforalaneoftrafficcanbecalculatedasdistance

traveleddividedbyaperiodoftime.So,ifcarsintwolanescover

1,000yardsinfiveminutes,theybothhavethesameaveragespeedof

200yardsperminute,or6.8milesperhour.



Driversoncrowdedroadsoccasionallyhavegapstheyseekto

close,buttheyactuallyspendmuchmoretime(relatively

speaking)movingslowlyornotmovingatall.Duringthose

timesofslowmovement,which,ofcourse,takemoretime,

therewilloccasionallybecarsinotherlanesfillinggapsand

passingthedriversinthosetemporarilyslowlanes.

Asmeasuredbyepochs,foranyonedrivertherewillbemore

timespentbeingpassedthantherewillbetimespentdoingthe

passing.Thisisbecauseyoupasswhilemovingquicklyandyou

arepassedwhenyouaremovingslowly.Figure6-9paintsa

pictureofthisperception.



Figure6-9.Theperceptionoftimespentgetting

passed



Sittingstillwhilewatchingothercarsacceleratetofillgaps



createstheillusionthatourlaneismovingmoreslowly.



ProbabilityandTrafficPatterns

CanadianresearchersDonaldRedelmeierandRobertTobshirani,

whoconductedcomputersimulationstodeterminetheaccuracy

ofdriverperceptionsofotherlanes'speed,madesome

assumptionsabouttrafficpatternsthatwerebasedonthe

normaldistribution[Hack#23].

Tomirrortherealitythataparticularpatternofspacingona

crowdedhighwayhasseveralcauses(conditions,exitsand

entrances,andsoon),theyrandomlyassignedintervals

betweenmovingcarsbasedontwonormaldistributions:90

percentofintervalswereabouttwometersapart,giveortakea

10thofameter,while10percentoftheintervalswere100

metersapart,giveortake5meters.Atthestartofeachof

hundredsofsimulations,carswerecreatedandspaced

followingthisrandomizationplan.

Theresearcherscreateddatafortwolanesoftrafficmovingin

thesamedirectionatthesamespeed,fullofhundredsof

imaginaryvehicleswithtypicalaccelerationandbraking

capabilities.Theyprogrammedinasafedriverstrategyof

movingupwhentherewasspaceinalane,butnotgettingtoo

close.Theirsimulateddriverswerenotallowedtogettooclose

toanothervehicle'stailgate.Also,theywerenotallowedto

changelanes,whichmusthavebeenfrustratingforthelittle

computer-controlleddrivers.Noaccidentshere.



Intermsoftheaverageaccelerationandbrakingspeedfortheir

simulatedvehicles,RedelmeierandTibshiranichosetypicalstatistical

specifications(theabilitytogofrom0to63milesperhourin10

secondsandtheabilitytogofrom63milesperhourto0in5seconds),

whichhappentoprettymuchmatchaHondaAccord.



MakingWiseLane-ChangingDecisions

RedelmeierandTobshiranifoundthat13percentofthetime,

carsareeitherpassingorbeingpassed.Mostofthetime,cars

arerunningequaltoeachother.Whiletherewasabetter

chancethatanyparticulardriverwasbeingpassedthanthat

shewasdoingthepassing,whenshedidpasscars,shepassed

abunch.Themathworkedouttoadrawintermsofcars

passedandthenumberofcarsdoingthepassing.Thetotal

numberofcarsovertakenbyourdriverwasequaltothe

numberofcarsthatpassedher.

Undercrowdeddrivingconditions,theotherlanewillseem

greenermuchofthetime.Therearesomewaystodealwith

themisperceptionandmakewiser(andstatisticallysafer)

drivingchoices:

Asalogicalscientist,youcanevaluateyourdrivingbythe

lengthofthejourney,notbywhetheryouwonorlostthe

trafficjamcompetition.Itshouldn'treallymatterifyou

thinkmorecarspassedyouthantheotherwayaround.

Keepthisotherlaneisbettermisperceptioninmindand

findbetterwaystojudgethespeedofotherlanes.Picka

uniquecarintheotherlane,andafterafewminutes

compareyourpositiontoit.Afterall,theresometimesare

fasterlanesthanothers;it'sjustthatyoucan'tlookat

passingcarsasthebestevidenceforspeed.

Onlargehighways,pickalanefartotheleftorrightof

upcomingexits,astrafficexitingandenteringtheroadis

themaincauseforslow-downsandspeed-ups.



Curbyouraggressivetendenciesinbothdrivingandincar

purchasing.Interestingly,thesimulationsshowedthat

aggressivedriving,suchasminimizingthestandard

followingdistancebetweenyouandanothervehicle,will

actuallyincreasetheamountoftimeyou'llnoticeothercars

passingyou.Also,fastercars(thosethatcanaccelerate

quickly)spendlesstimepassingbecausetheycandoit

quicker.So,yoursuper-poweredsportscarmightleadto

morefrustrationforyouoncrowdedhighways.

Thewisesttacticwhenitcomestodealingwiththelikely

misperceptionthattheotherlaneisfasterthanyoursmightbe

thesimplest.Justdon'tpayattentiontoit.Thesimulations

showthatifyoulookatotherlaneshalfasoften,you'llnotice

carspassingyouhalfasoften.

Isuppose,though,thatwedon'tneedastatisticalanalysisto

tellusthis.Insteadofthecarsbesideyou,paymoreattention

tothecarsbehindyou.You'rewayaheadofthemandthereare

thousandsofthem.You'vealreadywonthatgame.



SeeAlso

Redelmeier,D.A.andTibshirani,R.J.(1999)."Whycarsin

thenextlaneseemtogofaster."Nature,401,35.The

originalstudyreportingthismostrecenttrafficanalysis.

Redelmeier,D.A.andTibshirani,R.J.(2000)."Arethose

otherdriversreallygoingfaster?"Chance,13,3,8-14.A

moredetaileddescriptionofthefindingsreportedinthe

Naturearticle.







Hack75.SeekOutNewLifeandNew

Civilizations



Thesearchforextraterrestriallifeisaliveandwell.You

canusestatisticalsamplingandprobabilitytofocusthe

search.

Thescientificquesttomakecontactwithlifeonotherworlds

requiresthatdecisionsbemade.First,onemustdecideiflife

existsatallbeyondonourownplanet(mine'sEarth,what's

yours?).Second,onemustdeterminehowandwheretolook

forit.Youcanapplystatisticalprocedurestomakeboththese

decisions.



EstimatingtheNumberofSmartPlanets

In1961,FrankDrake,anastronomerwhowasinterestedin

lookingattheuniversefromafarbyreadingradiowaves(a

bunchofwhicharebouncingoffEarthallthetime),decidedto

estimatehowmanyothertechnologicallyadvancedcivilizations

probablyexist.

BeingalittleMilkyWay-centric,hewasmostinterestedin

determiningthenumberofadvancedworlds(planetswillingand

abletotalkwithus)thatarenearby,inourowngalaxy.Drake

suggestedthisequation:

Table6-23showsthemeaningsoftheabbreviationsinDrake's

equation.

TableDrakeequationcomponents



Term

R

Nh

Fl

Fi

Fc

L



Meaning

Rateatwhichnewstarsareproducedinthegalaxy(peryear)

Averagenumberofplanetsorbitingeachstarthatcansupportlife

Proportionofplanets(fromNh)onwhichlifedoesdevelop

Proportionofplanets(fromFl)onwhichintelligentlifedevelops

Proportionofplanets(fromFi)onwhichcivilizationsdevelop

Averagelifetime(inyears)ofcivilizations(fromFc)



Theformulaisreallynothingmorethanachainofprobabilities.

Thenumberofexpectedpositiveoutcomesisdeterminedby

multiplyingalltheseparatelikelihoodstogether.Thougha

simplerequationwithoutallthedifferentpermutationsofF

wouldworkjustaswell,thespecificdifferentcomponentswere

includedtohelpscientistsidentifytheimportantquestionsthat

neededtobeansweredtoestimatetheprobabilitythatweare

notalone.



ApplyingDrake'sEquation

Tocalculatearealisticnumberofplanetsinourgalaxythat

currentlyhaveintelligentlife,youhavetopluginsomerealistic

numbers.Also,weknowthatthecorrectanswer(thesolution)

mustbeatleast1,becausethereisintelligentlifeonEarth

(insertyourownjokehere),andmustbenomorethan

250,000,000,000(thenumberofstarsintheMilkyWay)times

theaveragenumberofplanetsaroundstarsthatcouldsupport

life.

Whentheequationwasfirstintroduced,onlyoneoftheterms

couldbeestimatedwithanyconsensusamongastronomers.R,

thenumberofnewstarsproducedinourgalaxyeachyear,is

believedtobeabout10.



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