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JulesJ.Berman
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Abouttheauthor
JulesJ.Berman hasreceivedtwobaccalaureatedegrees fromMIT:oneinmathematicsandtheotherinearthand planetarysciences.HeholdsaPhDfromTempleUniversity andanMDfromtheUniversityofMiami.Hecompletedhis postdoctoralstudiesattheUSNationalInstitutesofHealth, andhisresidencyattheGeorgeWashingtonUniversity MedicalCenterinWashington,DC.Dr.Bermanservedas ChiefofAnatomicPathology,SurgicalPathology,andCytopathologyattheVeteransAdministrationMedicalCenterin Baltimore,Maryland,whereheheldjointappointmentsat theUniversityofMarylandMedicalCenterandattheJohns HopkinsMedicalInstitutions.In1998,hemovedtotheUS NationalInstitutesofHealthasMedicalOfficerandastheProgramDirectorfor PathologyInformaticsintheCancerDiagnosisProgramattheNationalCancerInstitute. Dr.BermanisapastpresidentoftheAssociationforPathologyInformaticsandthe2011 recipientoftheAssociation’sLifetimeAchievementAward.Hehasfirst-authoredmore than100journalarticlesandhaswritten20sciencebooks.BookswrittenbyDr.Berman, thatmayinterestreadersof ClassificationMadeRelevant, include
PerlProgrammingforMedicineandBiology,JonesandBartlett,2007
RubyProgrammingforMedicineandBiology,JonesandBartlett,2008
MethodsinMedicalInformatics:FundamentalsofHealthcareProgramminginPerl, Python,andRuby,CRCPress,2010
TaxonomicGuidetoInfectiousDiseases:UnderstandingtheBiologicClassesof PathogenicOrganisms,Elsevier,2012
PrinciplesofBigData:Preparing,Sharing,andAnalyzingComplexInformation, Elsevier,2013
DataSimplification:TamingInformationwithOpenSourceTools,Elsevier,2016
PrinciplesandPracticeofBigData:Preparing,Sharing,andAnalyzingComplex Information,SecondEdition,Elsevier,2018
Evolution’sClinicalGuidebook:TranslatingAncientGenesintoPrecisionMedicine, Elsevier,2019
TaxonomicGuidetoInfectiousDiseases:UnderstandingtheBiologicClassesof PathogenicOrganisms,SecondEdition,Elsevier,2019
LogicandCriticalThinkingintheBiomedicalSciences,VolumeI:DeductionsBased UponSimpleObservations,Elsevier,2020
LogicandCriticalThinkingintheBiomedicalSciences,VolumeII:DeductionsBased uponQuantitativeData,Elsevier,2020
Preface
Doesn’teveryonewanttheuniversetomakesense?Wouldn’titbegreatifwehumanshad arationalwayofrelatingeverythingwitheverythingelsesothatourworldmaybecomea bitlessconfusing?Asithappens,wehaveaniftylittledevicetodojustthat.Itiscalleda classification.Whilecatalogsandindexeshelpusorganizeitems,classificationsorganize relationshipsamongclasses.Itisthroughourunderstandingofclassrelationshipsthatwe begintounderstandourworld.In ClassificationMadeRelevant,wewillexplorethree majorthemes:
1. Thatbuildingclassificationsisoneofthemostintellectuallyrewardingpursuits availabletoseriousscientists.Wewillseethatthehistoryofscienceispunctuatedby momentsofintenseclaritywhenrelationshipsamongclassesaresuddenlyrevealed.
2. Thatthescienceofclassificationmustbelearned,justaswelearnanyotherscientific discipline.Manyofthedisastrousclassificationsforceduponscientistshavebeen producedbycluelessindividualswhoneglectedthefundamentalrulesofclassification construction.Wewilltakesomepleasureinreviewingsomeofthemostill-conceived classifications,alongwiththecommonerrorscommittedduringtheirconstruction.
3. Thatclassificationsaredevicesbywhichweorganizerelationshipsamongthingsand arenotjustameansbywhichwetidyupcollectionsofitemsbyinventingcategories. Muchofthebook’snarrativeisdrivenbythenotionthatclassificationsembodythe naturalorderoftheuniverse.Therelationshipsrevealedbyscientificclassifications leadustodiscoverhowtheworldoperates.Whenwevisitthegreatclassificationsof thenaturalworld,wecanbegintoappreciatetheunityofallthesciences.
Formostofus,thesubjectofclassificationhasnevergrabbedourfullattention.Wearenot preparedtobelievethatthescienceofclassificationisasubjectthatrequiresadisciplined andrigorouscourseofstudyorthatthereexistclassificationsthatplayanimportantrole inoureverydaylives.Inpointoffact,classificationsarevitaltoourexistence.Thisbook beginswithadiscussionofhowthehumanmindisconstantlysortingobjectsintoclasses, aswetrytoorganizeandsimplifyourenvironment.Whilewehumansarebusysorting orangesandapples,theuniverseispreoccupiedwithenforcingasetofnaturallawsthat allmaterialthingsandallforcesmustobey.Thesenaturallawsdeterminethekindsofparticles,atoms,molecules,andorganismsweseearoundusandhowtheyrelatetoone another.Whenweseehowthingscanbesortedintodefinedclassesthathaveexplicitrelationshipswithotherclasses,webegintheprocessofunderstandingouruniverse.The mannerinwhichwedefineclasses,theirproperties,andtheirrelationshipsisbestcodifiedwiththejudicioususeofasemanticlanguage.Doingsopermitscomputers,and
humans,toanalyzeclassificationsandtodrawnewinferencesabouthowourworld works.Noteverythinginourworldcanfitintoatraditionalclassification,andinsuch cases,weuseontologiestotieinformationandobjectstooneortoanotherofthenatural classifications.Wecanmodelclassificationsandontologiesinobject-orientedprogramminglanguages.Bydoingso,wecandrawnewinferencesfromthevastcollectionsofdata tiedtoclassifications.
Thefirstfivechaptersofthisbookaredevotedtothetheoryanddesignofclassifications. Chapter5,“TheClass-OrientedProgrammingParadigm,” explainshowcomputer scientistsmodelandanalyzeclassificationsandontologies.Althoughthechapteris intendedtobeaccessibletononprogrammers,itissimplyimpossibletotreatthetopic fairlywithoutincludingafewlinesofcode.Forthischapter,mostofthecodeisprovided asone-linersconsistingofonecommandwhoseresultingoutputcanbeexamined.In thosecases,noprogrammingknowledgeisrequired.Afewshortprogramsareprovided, butthesearenotcomputer-readyapplicationsandshouldnotbeusedassuch.These shortprogramsarewritteninPerl,Python,orRuby.Computerscientistscanadaptsnippetsofthiscodetoincludeintheirownsoftwareprogramsintheirpreferredprogramminglanguages.Nonprogrammerscanperusethecodeandseejusthoweasyitisto translateanalgorithmintosoftwarewritteninanypreferredcomputerlanguage.
Inthefinalthreechapters,wewillexaminethethreegreatclassificationsofthenatural world:“TheClassificationofLife,”“ThePeriodicTableoftheElements,”andthesymmetriesexemplifiedinthe“ClassificationTheoremofFiniteSimpleGroups.”Thesechapters arenotintendedtobeprimersforbiologists,chemists,orphysicists.Westudythegreat classificationssothatwecanseehowtheyweredevelopedandhowtheyhavebeenutilized.Inthefinalchapter,weshallseehowtheseclassifications,takentogether,encompassallofthesciences.
Whilecomposingthebook,Isettledonasetofconceptsandquestionsthatcanbe enjoyedbyanyonewithacollege-levelintroductiontoanyofthenaturalsciences.Torenderthetextaccessibletothewidestrangeofreaders,Ihavetriedtoeliminatedisciplinespecificjargon.Whenthetextbumpsupagainstanunavoidabletechnicalpointthat requiresexplanation,alinktoanappropriateglossaryitemisincluded.Theglossary providestermdefinitionsandoftenincludesanexpandeddiscussionoftheterm’srelevancetothechapter’stopics.Therearemorethan300glossarylinksincludedinthebook, andyouwillfindthemlistedatthebottomofparagraphs.Ifyouprefernottointerrupt yourreadingwithexcursionstotheglossary,youmayfinditrewardingtoperusethe chapterglossaries,afteryouhavereadthenarrativetext.
Sittinginclass
Section1.1.Sortingthingsout
Let’sbeginthisbookwithsomeprovocativeassertionsindireneedofproof.
1. Classificationsarethebestwaytoencapsulatetherelationshipsamongobjects.
2. Theuniverse,andmostthingsinit,canbereducedtoarelativelysmallnumberof classesofthings.
3. Theinheritanceofpropertiesthroughancestralclassesisoneofthestrongest intellectualtoolsavailabletoscientists.
4. “Triples”arethequantumofmeaningintheinformationworld.
5. Someitemscannotbesensiblyclassified,butallsuchobjectscanberepresented inalternatedatastructures,includingontologies;andultimatelylinkedtovalid classifications.
6. Modernobject-orientedprogrammingtechniquescanfullymodelclassifications andontologiesandpermitustoapplyalgorithmsthatdrawinferencesfrom classificationsandontologies.
7. Theassemblageofnaturalclassificationsisoneofmankind’sgreatestintellectual achievements.
8. Thenaturalsciences(i.e.,biology,chemistry,andphysics)obeyscientificlawsthat governouruniverse,andtheselawsarereflectedinclassifications.
9. Takentogether,threegreatclassifications(TheClassificationofLife,ThePeriodic TableoftheElements,andthesymmetriesexemplifiedbyTheClassificationTheorem
JamesJoyce
ofFiniteSimpleGroups)unifythenaturalsciencesandclarifytherelationships amongallmatterandforcesinouruniverse.
10. Futureadvancesinallofthescienceswilldependonourabilitytoenhanceexisting classifications.
[Glossary Meaning, Modeling, Naturalsciences, Ontology,Relationship, Triple]
Whenwereachtheendofthisbook,wewillhavereviewedabundantevidencesupportingeveryoneoftheseclaims.Toarriveatthatpoint,wewillneedtodiscusswhat itmeanstobeanobjectbelongingtoaclassthatbelongstoaclassification.
OurClassyUniverse
Despiteoursensethatanythingispossibleinthevastnessofspace,weseeanawfullot ofsamenessthroughouttheuniverse.Whereverweaimourtelescopes,weseegalaxies, mostofwhichareflatandspiral,manyhavingaboutthesamesize,andcomposedof thesameobjects:stars,planets,gas,dust,blackholes,andabundantnothingin between.Asmallsetofphysicallawsimposestabilityeverywhereatonce,andtheresult isthesomewhatrepetitiouscosmosthatweglimpseatnight(Fig.1.1).
FIG.1.1 Thevariousclassesofgalaxies.Woulditbeanover-simplificationtosuggestthattheyalllookmuch thesame? Source:U.S.NationalAeronauticsandSpaceAdministration.
Asithappens,theuniverseistrendingtowardanevenmoreblandandstableexistence. Theend-stageofstellarevolutionseemstobemainlylimitedtojustbrowndwarfs,white dwarfs,neutronstars,andblackholes [1].Whitedwarfsaretheend-stageobjectsformost main-sequencestarsandcanpersistforabout1035 years.Blackholes,anotherend-stage celestialobject,haveapredictedlifespanof1064 years.Asrelativelyshort-livedmainseriesstars,likeoursun,attaintheirvariousdestinies,theyleavebehindauniversefull ofdead-endobjects,predominantlywhitedwarfstars.TheMilkyWayisthoughttohave alreadyaccumulated10billionwhitedwarfs,andthenumberwillonlyincrease.Atsome pointinthefuture,illuminatedgalaxiessuchasourswillbegone,andtheuniversewillbe filledwithnearlyperpetualend-of-lifestars.
Whatistrueonthecosmologicalscaleisalsotrueontheatomicscale.Therearejust94 elementsthatoccurinnature.Afewdozenmorecanbecreatedartificially,buttheseare short-livedatomsthatdonotaccountformuchofwhatwefindinouruniverse.Ofthe matterthatwecanobserve,wenotethatHydrogen,thesmallestandsimplestofelements, accountsfor92%ofatomsinouruniverse.Helium,thesecondsmallestatom,accounts fornearlyeverythingelse.Theremaining92elementsmakedowithabout1%–2%ofmatter.Thereismuchlessatomicvarietythanwemightimagine.
Likewise,despitealargenumberoflivingspeciesonourplanet,theyareallvariations ofafewcommonthemesthatcanbeencapsulatedunderasimpleclassification,wherein therootorganism,andallofitsdescendants,arecarbon-basedandhaveanucleicacid genome.ThisbringstomindwhatIrefertoastheFirstLawofClassification,namely, “Inaworldwhereanythingcanhappen,relativelylittledoes.”[Glossary Organism, Species]
Thereisareasonthattheuniverseisstableandfilledwithobjectshavinglimitedlifestyleoptions.Putsimply,systemsthatareunstableceasetoexist;thatiswhatitmeansto beunstable.Iftherewerenosetofphysicallawsthatapplyeverywhereintheuniverse, throughouttime,thentheuniversewouldbechaotic.Wewouldhavemattersuddenly droppingoutofexistence,orpoppingupagaininstrangeanddistantlocations.Wewould nothaverepeatablechemicalreactions.AnexperimentonTuesdaywouldyieldadifferent outcomethanthesameexperimentperformedonWednesday;andthatisassumingthat wewouldhaveaTuesday,andaWednesday,andanexperiment.Orwemighthavenothing thatwerecognizeasmatterandenergy.Theentireuniversemightsimplyvanish,inabang orawhimper.
[Glossary System]
WedonotknowtheconditionsofexistenceatthemomentoftheBigBang.Wecan claimthattheBigBangwasagrossviolationoftheconservationlawsformatterand energy,anassertionthatwouldsuggestthatourbeginningswerenotnearlyasstable andnon-chaoticaswhatweseetoday.IlyaPrigoginedescribedmathematicallyhowa stablesystemmightarisefromachaoticsysteminhistheoryofdissipativestructures, forwhichhewasawardedthe1977NobelPrizeinchemistry [2].
StevenWolfram,amathematicianandapioneerincomputerscience,conducteda fascinatingsetofcomputersimulationsemployingsimpleautomatathatgenerated graphicoutputsconsistingofcollectionsofblocksemanatingfromapoint.Theautomatamade“decisions”suchasputablockontop,putablockontheleftside,makeblock black,makeblockwhite.Anelementofrandomnesswasintroducedatvariouspointsin thealgorithmsthatcontrolledtheautomata [3].Withoutgoingintoadetaileddescriptionoftheirimplementations,wecansimplyacknowledgethatwewouldexpectthe graphicoutputsoftheautomatatoberandomandunpredictableandthatwewouldcertainlynotexpecttoseearatherfixedsetofrecurringpatternsintheoutput.Regardlessof preconceptions,Wolframfoundthattheout putsindeedhadrecurringpatternsandthat hecouldassignthesepatternstoclasses [3].Afterhechoseclassesforthepatterns,he foundadditionalpropertiesoftheoutputthatcharacterizedtheclasses.Regardingthose classes,andtheirproperties,hewrote,“ButwhenIstudiedmoredetailedpropertiesof cellularautomata,whatIfoundwasthatmost ofthesepropertieswerecloselycorrelated withtheclassesthatIhadalreadyidentified.Indeed,intryingtopredictdetailedpropertiesofaparticularcellularautomaton,itwasoftenenoughjusttoknowwhatclassthe cellularautomatonwasin.”Helikenedtheprocessoffindingclassesandpropertiesto buildinganaturalclassificationofchemicalsubstancesorlivingorganisms.Thiswasa remarkableoutcomeforasetofcomputersimulationsthatshouldhavebeenrandom, formless,andchaotic.
Thetopicofthespontaneousgenerationoforderfromchaosisbestlefttothemathematiciansandthemetaphysicians.Let’ssimplifythesituationbyagreeingthatstablesystems,bydefinition,persistlongerthanunstablesystems,wecanexpectthatstable systemswilleventuallyreplaceunstable,chaoticsystems.Indeed,wefindourselvesgovernedbystableuniversallaws,appliedtoasmallassortmentofelementaryparticles.All theforcesthatcontrolthebehaviorofmatteractinahomogeneousspace-timecontinuum.Wecanthankoursimple,andnon-chaoticuniverseforthebirthofaworldwherethe nightskyiseverywherefilledwithtwinklingstars,andwehumanscansleepknowingthat thesunalsorises.
Section1.2.Thingsandtheirparts
Thingyness
Ithasalwaysstruckmeasamusingthatinfictionalencounterswithalienlifeforms, authorstypicallycreateaclassificationofalienbeingshavinga1:1correspondencewith analogoushumanbeings:here’sthealiencity,here’sanalienhouse,here’sasmallalien baby,here’sanalienmilitarygeneralpreparingforwar.Mostsciencefictionmoviesdepict aliensasbeingmuchmoresimilartohumansthanhumansaretotheotherterrestriallife formswithwhomwecohabit.Sadly,ourmostinventiveauthorsseemincapableof
imagininganunfamiliarformofexistence,evenwhenit’sallmake-believe.Ofcourse, thereareexceptions.
HereisashortexcerptfromC.S.Lewis’classicnovel Perelandra,whereinhisfictional character,ElwinRansom,arrivesonVenus.
Hisfirstimpressionwasofnothingmoredefinitethanofsomethingslanted-as thoughhewaslookingataphotographwhichhadbeentakenwhenthecamera wasnotheldlevel.Andeventhislastedonlyforaninstant.Theslantwasreplaced byadifferentslant.
In Perelandra,theworldisatfirstperceivedtobeformless.Thetravelercannotdistinguish onethingfromanother.Eventually,theworldcomesintofocus,andallthe“things”on Perelandraaresortedout.C.S.Lewisremindsusthattheuniverseisameaninglessvision untilthemindfindsawaytosortrealityintorecognizablegroupsofthings.
In Perelandra,thetravelerexperiencesabriefperiodofdisorientationuponhisarrival inanalienland.Inthesciencefictionnovel Solaris,writtenbyStanislawLem,astronauts visitastrangeplanetthatdefieshumanunderstanding.Anenigmaticplanetcomestothe attentionofearthscientistswhofindthatitserraticpaththroughspaceseemstodefythe lawsofgravity.Whenthesurfaceoftheplanetisobservedfromanorbitingsciencestation, largeartifactsmimickinghumanforms,areseentoassembleanddisassemble.Soon,the residentsofthesciencestationarevisitedbyapparitionsthathavetheappearanceof familiarhumans. Solaris exploresthereactionofthescientiststotheinscrutableemanationsoftheplanet,butthedevelopingmysteriesareneversolved.Asthebookends,the scientistsslowlylapseintovariousformsofhighlypersonalizedinsanity.
Sciencefictionoftenseemsfar-fetched,butitalwaysaimstorevealbasictruthsabout thehumancondition.Thefactofthematteristhatweoftenfailtoperceivethethingsthat shareourreality.Afavoriteexample,fromtherealmofarcheology,involvesthemysteryof theMayanglyphs.Wehaveallseenimagesofthesebeautifulandornatestonecarvings. Forgottenbyhistoryfornearly700years,earlytwentieth-centuryarcheologistsuncovered theseMayanartifactsandattemptedtofathomtheirmeaning.EricThompson(1898–1975)stoodasthepremierMayanistauthorityfromthe1930sthroughthe1960s.After trying,andfailing,todeciphertheglyphs,heconcludedthattheyrepresentedmystic, ornatesymbols;notlanguage.Theglyphs,accordingtoThompson,wereunworthyoffurtherstudy.Thompsonwasveneratedtosuchanextentthat,throughouthislongtenureof influence,workintheareaofglyphtranslationwassuspended.WhenThompson’sinfluencefinallywaned,anewgroupofMayanistscameforward,hopingtomindmeaningin theenigmaticglyphs.ThesenewMayanists,undeterredbynaysayers,learnedthatthe glyphsweremoreorlessstraightforwardrepresentationsoftheMayanlanguage,much asitisspokentodaybyMayanswhoweretaughttheirnativespeech.Breakingthecode involvedlearningsomesymbologyandmasteringtheproperwayofmovingfromone symboltothenext,throughthetext [4] (Fig.1.2).
Theearlyarcheologistsfailedtoperceivetheglyphsasthe“things”thattheywere.The issueofproperlyperceivingthethingsinourenvironmentisaseriousissueamongphilosophers.Let’slookatafew“thingy”problemssothatwecanappreciatetheirrelevance tothegeneraltopicofclassification.
Whenwelookataboyonhisbicycle,wetendtothinkoftwospecificitems:theboy, andthebike.Wedon’tusuallythinkofacompositeitem(i.e.,aboy-bikechimera),probablybecauseweknowwhatitmeanstobeaboy,andweknowthatwhenaboysitsatopa bike,hedoesnotsuddenlytransformintoacompositestructure.MydogBailey,onthe otherhand,hasanentirelydifferentwayofassessingthesituation.Whenheseesaboy ridingabike,heisconvincedthatheisseeingacreaturethatisneitherboynorbike, butahorriblechimerathatmustbeattackedanddestroyed.Mindyou,Baileyloveschildrenandisindifferenttobicycles,buthebearsadeephatredofthecreaturethatemerges whenitengulfsboyandbike.
IfyoubelievethatmydogBaileylackscommonsense,youmightwanttoreconsider afterreadingthenextexample.Humansneverconsiderthemselvescompositeitems.We aresoaccustomedtothinkingofourselvesassingularentitiesthatwehaveinventedthe word“I”asashortandconvenientwayofreferringtoourselves,withoutbotheringtostate ourfullnames.Irefertomyselfas“I”,andyourefertoyourselfas“I”andwebothseem
FIG.1.2 Mayanglyphs,displayedinPalenqueMuseum,Chiapas,Mexico.Earlyinthe20thcentury,prevailingwisdom heldthattheseglyphswerepurelydecorative,withnosemblancetolanguage. Source:Wikipedia,andenteredinto thepublicdomainbyitsauthor,Kwamikagami.
satisfiedwiththat.Whathappenswhenanindividualbecomespregnant?Doessuchan individualbecometwoindividuals,ordoesitbecomeacompositecreature?
Let’ssteparoundthespecialcaseofpregnancy,andjustfocusonthework-a-day humanbeing.Mostofthecellsinahumanarediploidcells,andthesecellsconstitute ourso-called“soma”;thebrains,organs,muscle,bone,andconnectivetissuethatwalk andtalkandwatchtelevision.Thesomalivesforsomeperiodbeforesuccumbingtoinevitablebutunscheduleddeath.Asidefromthesoma,eachofuscontainsaspecializedpopulationofcellshavingitsspecializedgenome,itsownsetofbiologicalattributes,andthe capacityforimmortality.Thesearethehaploidcells(i.e.,gametes)thatmatureasoocytes (eggs)inthefemaleandasspermcellsinmales.Thespermcellsarecapableoflivingoutsidethebodyandfusingwithoocytesobtainedfromanotherindividual.Theresulting zygotecanmultiplyanddevelopintoanotherorganismalsocomposedofamixtureof diploidsomaticcells(doomedtodeath)andhaploidcells(potentiallyimmortalized throughtheprocessofconception).Arewehumanstwocreaturesinone:thediploid somaticorganismandthehaploidgerminativeorganism?Thisisatoughquestion,but perhapswecanshedsomelightontheanswerbyreferringtotheplantkingdom.Some plantsundergoalternatinggenerationsinwhichahaploidorganism(gametophyte)producesadiploidorganism(sporophyte),whichproducesahaploidorganism,whichproducesadiploidorganism,andsoon.Thehaploidorganismcontainsgametesthat differentiatetoformthestructuralcelltypesofthegametophyticplant.Thesporophyte containsdiploidcellsthatdifferentiatetoformthesomaofthesporophyticplant.The gametophyteandthesporophytearetwoseparateplants,distinguishablefromeach other.Knowingthistobetrue,woulditbefar-fetchedtoimaginethatthegametesand thesomaofthehumanspeciesare,infact,twoverydifferentorganismsthathappen tosharethesamephysicalspace,mostofthetime?(Fig.1.3).
FIG.1.3 Thelifecycleofplantsalternatesbetweenahaploidorganism(onecompletesetofchromosomesineachcell) andadiploidorganism(twocompletesetsofchromosomesineachcell). Source:Wikipedia,andenteredintothe publicdomainbyitsauthor,PeterCoxhead.
Let’slookatanotherexamplewherewemightmisinterpret“thingyness.”Twopatients areseenbyanoncologist(i.e.,aphysicianspecializingincancer).Bothofthemhappento haveamassintheircolon,andbothofthemhavebeengiventhesamediagnosis:“adenocarcinomaofthecolon”.Eachpatienthastheirindividualanduniquegenome,which, foreachpatient,isthesamegenomecontainedinthecellpopulationthatgivesriseto theirrespectiveadenocarcinomas.Inbothcases,thetumorgenomecontinuously mutates,producingagrowththatisdifferentfromthegenomeofthepatientinwhich itarisesandthatisdifferentfromthegenomeoftheadenocarcinomafoundintheother patient.Thebiologyofeachofthetwotumorsisunique,andtheclinicaloutcomeofthe twopatientsareunlikelytobeequivalent.Thisbeingthecase,whywouldwegivethe samename,“adenocarcinoma”,tothetwobiologicallyandgeneticallydifferenttumors? Asithappens,weassignthetwotumorsthesamenamebecausebothtumorsarosefrom thesametypeofcellinthesameanatomictissue.Physiciansbuiltaclassificationofneoplasmsbasedonthetumor’scelltypeoforigin;acellthatdoesnotpersistinthedeveloped tumor.Foravarietyofreasons,thiskindofindirectapproachto“thingyness”seemsto workforus;atleastforthemoment.
Let’sexamineonemoreperplexingaspectof“thingyness”;theissueofthe“new thing”.Whatdowemeanwhenwerefertoan ewthing?Isanewthingsomethingthat comesintoexistenceatonce,withoutpre-existenceinformorsubstance;orisanew thingjustanoldthingthathasbeenmodi fiedinsomeway?Anewdayisjustanold daythathascompletedonemorerevolution.Anewsnowstormisjusttheconvergence ofpre-existingweatherfronts.Anewsandwichisjusttheassemblageofoldingredients thatwerelayingaroundthekitchen.Today’ssquirrelisjusttheresultofsomecombinationofcellulardeath,cellrenewal,andcellmaintenanceoccurringinapopulationof billionsofcellsthatconstitutedyesterday’ssquirrel.Anewbabyisjusttheresultof thefusionoftwooldgermcells.Howdowecreateaclassificationofdiscreteitems,when weseemtoliveinauniversewhereineverythingdevelopsovertime,frompre-existing matterandenergy?
Thingynessisthefirst,andmostcrucial,step-inclassification.Whenweassignthings toclasses,weneedtodistinguishonethingfromanother,ataskthatisnotaseasyasit sounds.Ourchoiceof“things”tobeincludedinclassificationislargelyareflectionofour perceptionsofreality.Hence,every“thing”isjustanotherhypotheticalinourstruggleto buildaclassification.[Glossary Gamete, Germcell, Germcellline, Germline, Haploid, Haploidorganisms]
Afterwe’vechosenourthings,ournexttaskistotacklethedilemmaof“parthood”.Specifically,ifathingisacompositeofparts,andthepartsare“things”intheirownright,then howshalltheclassificationdealwiththerelationshipsthatexistbetweenthingsandtheir parts?Whathappenswhenathing’spartisalsoapartofsomeotherthing,belongingto anotherclassofthings?
Occasionally,Iamaskedtodeliveralectureonthetopicofclassification.Earlyinmy talk,Ialwaysaskthegroupthefollowingquestion.“Isalegasubclassofhumans?”.With veryfewexceptions,theanswertheytellmeis,“Ofcourse.Allhumansarebornwithlegs, soalegisanintegralpartofahuman,andthereforealegisasubclassofhumans.”I alwaysrespondthatsubclasseshavethedefiningpropertiesoftheirsuper-classes.A subclassofahumanwouldneedtobeatypeofhuman;justastheclasscontaining thehumanspecies(i.e.,ClassHomo)wouldneedtobeatypeofprimate(i.e.,asubclass ofClassPrimate).Alegisnotatypeofhuman,andthereforealegisnotasubclassof humans.
Partshaveaspecialrelationshiptotheir“wholes”.Thewordtodescribethisrelationshipisoftenreferredtoas“parthood.”Mereology,fromtheGreekroottranslatedasthe studyofparts,isthefielddevotedtoparthood [5].Foranyonewhomightthinkthat theconceptofparthoodistrivialandobvious,considerthefollowingquestions:
-Isanembryoapartofthewomanwhocarriesitinherwomb?
-Isanembryoapartofthedevelopedhumanwhodoesnotyetexistatthetimethatthe embryoexists?
-Isanacornapartofanoaktreeintowhichitwilldevelop?
-Isanacornattachedtoabranchofanoaktreepartofthattree?
-Isanacornthathasfallentothegroundapartoftheoaktreefromwhichitdropped?
-Isacaterpillarapartofthebutterflyintowhichitwilldevelop?
-Iscollectedgarbageapartofthegarbagetruckinwhichithasbeencollected?
-IsUraniumapartoftheLeadintowhichitwilleventuallytransmute?
-Isastairwellpartofamanfallingdownastairwell?
-Isalivepersonapartofthedeadpersonheorshewillbecome?
-Isaprecancerapartofcancerintowhichitmayeventuallydevelop?
-Isatitaniumhipapartofahumanwhohashadahipreplacement?
-Isacellfromahumanliverpartofahuman?
-Isatissueculturepreparedfromhumanlivercellspartofahuman?
-Ismidnightapartofyesterdayortoday?
-Isapairofshoespartofanyonespecificitemofapparel?
-Arethewordsyouarecurrentlyreadingapartoftheauthorwhowrotethewords?
[Glossary Precancer]
Thelistgoesonandon.Weallhaveourperceptionsoftherelationshipsbetween acornsandoaktreesandlivepersonsanddeadpersons,buttheseperceptionswillvary frompersontoperson,anditislikelythatnoneofourperceptionsquitedojusticetothe mereologists’philosophyof“parthood.”In “Chapter3.OntologiesandSemantics”wewill discusssomeoftheformalwaysinwhichwecandescribetherelationsbetweenthings, parts,andclasses.
Section1.3.Relationships,classes,andproperties
Objectsarerelatedtooneanotherwhenthereissomefundamentalordefiningprinciple thatappliestothemmutuallyandwhich,ideally,helpsustobetterunderstandtheir nature.Forexample,whenwesaythatforceismasstimesacceleration,wearedescribing arelationshipbetweenforceandanacceleratingmass.Theequivalence,doesnottellus whatforceis,anditdoesnottelluswhatmassis,butitdescribeshowmass,force,and accelerationrelatetooneanother,anditbringsusalittleclosertoanunderstandingof theirfundamentalnatures.
PossiblythemostelegantrelationshipknownisexpressedbytheEuleridentity (Fig.1.4).
TheEulerIdentity,whichrelates7fundamentalmathematicalconceptsinasingleassertion.
IntheequationfortheEulerIdentity,5universalconstantsand2fundamentalsymbols ofmathematicsarerelatedtooneanother,inasinglemathematicalassertion,aslisted:
Thenumber0,theadditiveidentity.
Thenumber1,themultiplicativeidentity.
Thenumberpi(pi ¼ 3.141 ),thefundamentalcircleconstant.
Thenumbere(e ¼ 2.718…),a.k.a.Euler’snumber,occurswidelyinmathematical analysis.
Thenumberi,theimaginaryunitofthecomplexnumbers.
Theidentitysymbol“¼”andtheadditivesymbol,“+”.
Itisthroughrelationshipsthatweunderstandourworld,butthoserelationshipscannot befullyappreciatedwithoutsomeintellectualeffort.Thestoryistoldofthestatistician whowasusingtheGaussiandistributiontodescribeapopulationtrend.Afriendwith noknowledgeofmathslookedovertheshoulderofthestatisticianandinquiredthemeaningoftheodd-lookingsymbolforpi.Thestatisticiansaid,“That’spi,theratioofacircle’s circumferencetoitsdiameter.”Hisfriendsaid,“Surelyyoujest.Youcan’texpectmeto believethatapopulationtrendcanhaveanyrelationshiptothecircumferenceofa circle!” [6]
Theconceptsof“relationship”and“similarity”areoftenmistakenforoneanother.To betterunderstandthedifference,considerthefollowing.Whenyoulookupattheclouds, youmayseetheshapeofalion.Thecloudhasatail,likealion’stale,andafluffyhead,like alion’smane.Withalittleimagination,themouthofthelionseemstoroardownfromthe sky.Youhavesucceededinfindingsimilaritiesbetweenthecloudandalion.Whenyou lookatacloudandyouimagineateakettleproducingaheadofsteam,andyourecognize thatthephysicalforcesthatcreateacloudfromtheocean’swatervaporandthephysical forcesthatproducesteamfromthewaterinaheatedkettlearethesame,thenyouhave foundarelationship.
FIG.1.4
Scientificlawsareclassifyingrulesbecausetheystatetherelationshipsamongclasses ofthings.Becausetheyapplyeverywhereandatanytime,theyarethestrictestofallrelationships.Whendifferenttypesofthingsobeythesamescientificlaws,wecaninferthat thosethingsmustberelatedtooneanother.Inthenextchapter,wewillseethatclassificationsaretheembodimentofthenaturallawsthatrelateclassesofthings.[Glossary Universallawsversusclasslaws]
Nowthatwehaverepeatedlyreferredtotheconceptofaclass,weshouldstopa momentandgive“class”aproperdefinition.
Aclassisdefinedbythefollowingproperties:
1. Classescontainuniqueandidentifiableobjects(zeroormoreofthem)
Uniquenessandidentifiabilityarecloselyrelatedconcepts.Whenafactory’sproduction lineproducesthesamepart,thousandsoftimesinaday,itmaystampauniquenumber oneachpart.Itistheassignmentofapermanentandimmutableidentifyingnumberthat makeseachpartunique.Whenwehaveidentifiableitems,wecanobserveandrecord data(e.g.,measurements)fortheitem.Atanylatertime,wecanusetheuniqueidentifier oftheitemtoretrieveitsdata.Computerscientistsworkwithso-calleddataobjects.These areuniquelyidentifiedconstructionsthatcanbeassignedtoaclass.Eachdataobjecthas accesstoallofthemethodsoftheirassignedclass.Dataobjects,asthenamesuggests, oftencontaindatathatcanbeaccessedandmodified.Theymayhaveavarietyofmethods thatarespecificforthemselves(i.e.,instancemethods).Adataobjectshouldcontainselfdescriptivedata(i.e.,dataaboutitself,includingitsuniqueidentifier).[Glossary Data object, Instance, Mutability,Uniqueidentifier]
Theobjectsbelongingtoaclassareoftenreferredtoasinstancesorasmembers.Inthe ClassificationofLife,objectsheldwithinaclassarethenamesofspecies,andthenamesof speciesareunique.Everyspeciesisassignedtoadirectparentclass,whichbiologistsrefer toasthegenus(Latinfortypeorrace)ofthespecies.Inthebinomialsystemofbiological classification,therearetwopartstoeveryspeciesname.Thefirstpartofthespeciesname isitsgenus,equivalenttoaperson’ssurname(familyname).Thenameofthegenusis alwayscapitalized.Thesecondpartofthebinomialisthespecies-specificname,equivalenttoaperson’sgivenname,andisnevercapitalized.Forexample, Homosapiens isour binomialspeciesname,with“Homo”beingthenameofourgenusorfamily,and“sapiens” beingourspecies-specificname.
Aclassmaycontainasfewaszeroobjects.Aslongasalltherequisiteclassproperties aresatisfied,wehaveaclass.Theremaybesomeadvantagetohavingclassmethodswithoutobjectsifthosemethodscanbeinheritedbyotherclassesorutilizedbyobjectsthat maynotbelongtoanyclass.Asingletonclassisaclassthatcontainsexactlyonenamed object.AgoodexampleofasingletonclassisthegenusClassHomo.Thereisonlyone extantobjectbelongingtoClassHomo,and H.sapiens isourname.Computerscientists usesingletonclassestopermitonespecificobjecttoexecuteallofthemethodsavailable toaclass.Weshalllearnmoreabouttheseconceptsin“Chapter5.TheClass-Oriented ProgrammingParadigm.”[Glossary Singletonclass, Singletonmethod]
2. Classeshaveadefinition(i.e.,theclassdefinition)tellinguswhatobjectsbelongto theclassandwhatobjectsdonotbelongtotheclass.
Classdefinitionsareprovidedinplainwrittenlanguageandaretypicallycollectedindocumentsknownasschemas.
3. Theclassmayhaveclassmethodsassociatedwithitthatcanbeusedbyevery memberoftheclass
Classmethodscantaketheformofdescriptorsoralgorithmsthatapplyexclusivelyto membersoftheclass,includingdescendantsubclassesoftheclass.Methodsavailable toallthemembersofaclassthatarenotexclusivetotheclassanditsdescendantsubclassesmayalsobeprovided,butsuchmethodsarenotreferredtoasclassmethods.This isanothertopicthatwewillsavefor Chapter5.
4. Anobjectthatisamemberofaclasscannotbelongtoanyotherclass
Asalogicalcorollary,aclassdefinitioncannotbewrittentoincludeobjectsthatlogically belongtootherclasses.Thiscorollaryistrueb ecauseotherwise,classdefinitionswould conflictwithoneanother.Asasimpleexample,supposeIdefineaclassofobjectswhose height,infeet,isexactlydivisibleby2.We’llcallthisClassEven_height.Thisclasswould includeobjectsofheight2ft,4ft,6ft,andsoon.Atfirstglance,thiswouldseemtobea properclass.Ithasadefinitionthatinclud esmembersandthatexcludesnon-members (e.g.,objectswhoseheightinfeetisanoddnumber).ClassEven_heightmayhaveits classmethods.Forexample,aninclusionmethodmightconsistofsomethinglike, “Addtheheightofanytwoclassobjectstoyieldanallowableheightofanotherclass object.”ClassEven_heightseemstobeshapingupasalegitimateclass.Now supposeIinventaclasscalle dClassSpheres.Spherescancomeinanyheight,including heightsthatareexactlydivisibleby2,andthiswouldimplythatmembersofClassSphere arealsomembersofClassEven_height.Thissituationisstrictlyforbiddeninsofarasa classdefinitionmustbewrittentoexcludeobjectsbelongingtootherclasses.Hence,the existenceofClassSphereconflictswithCla ssEven_height.Oneoftheseclasses,andpossiblybothofthem,mustnotbepermittedtoexist.Ifwegivethematteralittlethought, wemayrealizethatlotsofcompletelyunrelatedobjectscanhaveallmannerofheight, evenoroddandthatcreatingaClassEven_heightisasillyidea.Aswebegintoseethat wehavecreatedanillegitimateclass,wegetour firstinklingthatcreatingaclassification canbedifficult.
5. Aclassisitselfanidentifiableobjectandmaybelongtoaclass(i.e.,maybeasubclass ofanotherclass).
Atfirstblush,wemightthinkthatclasses,beingnothingmorethanabstractionsthathold realobjects,cannotbeconsideredarealobjectinneedofidentification.Therefore,we mightinferthatclassesandtheirsubclassesareallabstractions,andtheonlyrealitems aretheobjectsinsertedinclassesandsubclasses.Thisisabadwayofthinking,onseveral
counts.First,aclassiscomposedofrealobjects,andsomethingcomposedofrealobjects is,logically,arealobject.Secondly,classesareuniqueandcanbesensiblyprovidedwitha uniqueidentifier.Whenwereach“Chapter5.TheClass-OrientedProgrammingParadigm,”wewillseehowusefulitistoknowthateveryclassisitselfadataobjectbelonging toClass(theclassofclassesandconsequentlytheclassiestofclasses).[Glossary Child class, Parentclass, Subclass, Superclass]
Nowthatwehaveadefinitionof“class,”canwebegintoinventclasses,andcanwe assignobjectstoourinventedclasses?Yes,butweneedtoproceedcarefully,soasnot torepeatcommonmistakes.Forexample,whenIwasachild,Ilearnedthattherewere flowers,andtrees,andbushes;leadingmetobelievethatthesewerethethreemajorclassesofplants.Allplants,Iimagined,fellintooneofthesethreeclasses.Ofcourse,this pseudo-classificationwasnothingmorethanacategorizationofplantsintothreemorphologicallydistinctivegroupsthatcouldbeappreciatedbyschool-agechildrenwithout reallydelvingverydeeplyintobotanicalscience.
Sophisticatedstudents,whomayhavetakenacourseinbotanyoragriculture,know thatplantscannotbesensiblydividedintoflowers,trees,andbushes.Treesandbushes aresimplyfeaturesofspeciesbelongingtovariousclassesofplants.Amongbotanists, thereisnoClassTree,andthereisnoClassBush.Asfortheflowers,thereisaclassfor thefloweringseedplants(ClassAngiospermae)andanotherclassofseedplantsthat donotflower(ClassGymnospermae).BoththeAngiospermsandGymnospermscontain speciesthatgrowliketreesandbushes.Hadbotanistscreatedaclassjustfortrees,we wouldhavebeeninalotoftroublesincewewouldhavefoundtreespeciesamongclasses ofplantsthatdifferedfromoneanotherinalmosteveryregardandhavingnoclasspropertiesincommon.Wewouldalsofindtreesandtheircloserelativesthatcangrowas bushesorasdemurelilypads.Inpointoffact,allofthetreesinClassAngiospermae aretypesoffloweringplants.Wesaythataplantisatreeifithappenstolooktalland wistfulandifithasatrunkfromwhichbranchesorleafyclustersemanate;butthese arejusttraits,notclass-definingproperties(Fig.1.5).[Glossary Non-quantitativetrait, Quantitativetrait]
Aclassisacollectionofthingsthatshareoneormorepropertiesthatdistinguishthe membersoftheclassfrommembersofotherclasses.Whencreatingclassifications,the mostcommonmistakeistoassignclassstatustoaproperty.Whenapropertyisinappropriatelyassignedasaclass,thentheentireclassificationisruined.Hence,itisimportant tobeveryclearonthedifferencebetweenthesetwoconceptsandtounderstandwhyitis humannaturetoconfuseonewiththeother.Aclassisaholderofrelatedobjects(e.g., items,records,categorizedthings).Apropertyisafeatureortraitthatcanbeassigned toanitem(Fig.1.6).
Muchofourconfusioncomesfromthewaythatweareraisedtothinkandspeakabout therelationshipsbetweenobjectsandproperties.Wesay“Heishungry,”usingatermof equality,“is”,todescribetherelationshipbetween“He”and“hungry”.Technically,the sentence,“Heishungry”assertsthat“He”and“hungry”areequivalentobjects.Wenever bothertosay“Hehashunger,”butotherlanguagesaremorefastidious.AGermanmight
