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NEWTON INNOVATION AND CONTROVERSY

Peter Rowlands

University of Liverpool, UK

Published by

World Scientific Publishing Europe Ltd.

57 Shelton Street, Covent Garden, London WC2H 9HE

Head office: 5 Toh Tuck Link, Singapore 596224

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Library of Congress Cataloging-in-Publication Data

Names: Rowlands, Peter, author.

Title: Newton — innovation and controversy / by Peter Rowlands (University of Liverpool, UK).

Other titles: Newton — innovation and controversy

Description: Singapore ; Hackensack, NJ : World Scientific, [2017] | Includes bibliographical references and index.

Identifiers: LCCN 2017029435| ISBN 9781786344014 (hc ; alk. paper) | ISBN 1786344017 (hc ; alk. paper)

Subjects: LCSH: Newton, Isaac, 1642-1727.

Classification: LCC QC16.N7 R688 2017 | DDC 530.092 [B] --dc23

LC record available at https://lccn.loc.gov/2017029435

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Preface

Newton Innovation and Controversy completes the account of Newton’s scientific work begun in the two earlier books in the series: Newton and Modern Physics and Newton and the Great World System. The first of these emphasized the analytical approach to problems, largely developing from his optical work, where Newton had no simple way of applying mathematics to generate a series of results based on a generic underlying theory. The second was concerned with showing how the study of the planetary motions in terms of his new concept of universal gravity gave him just such an opportunity. The result was the greatest revolution in scientific history, with mathematical physics established as a universal subject, potentially capable of explaining any aspect of Nature from first principles.

To a large extent, it was the synthetic aspect of this development that most interested Newton’s contemporaries and immediate successors. That is, taking Newton’s analytically-derived fundamental principles as a given, the main object of physics became the explanation of as many physical phenomena, both celestial and terrestrial, as possible. Eventually, however, further breakthroughs required new fundamental principles, derived by the same kind of analytical reasoning as had been used originally by Newton.

The remarkable thing is that this seems to have most often occurred by a kind of attrition after exhausting the alternative possibilities rather than as a choice consciously made, while a study of Newton’s works shows that his own mental processes seem to have been pushing him in the direction of these developments. This suggests that a study of Newton’s work, in the dual context of both contemporary and subsequent developments, might provide insights into his extraordinary analytical thinking. In this capacity Newton seems to me to be absolutely singular. There have been other great mathematicians, other great mathematical physicists in the synthetic sense and other great experimentalists, but surely no analytical thinker who approaches anywhere near his level.

The aim of this three-volume study is to fully express the analytical power that made possible not only the great breakthroughs that were fully acknowledged by posterity, but also the ones that were suppressed or abandoned as a result of the controversies that such radical innovation necessarily generated. The value of this is found not only in the fuller picture it gives of Newton himself, but also in the possible leads it suggests for developing physics in the future. Physics is always in need of analytical inputs, never more so than at the present when we have models which have led to an incredible number of accurate experimental predictions, but no analytical insight as to why they are there. If we could understand the sources of such thinking in the practice of one of its greatest proponents, then we might be inspired to ﬁnding ways in which it could be emulated.

This is a study primarily of Newton’s physics, seen especially from an analytic perspective, but also in relation to how the combination of analytical and synthetic approaches could lead to an unstoppable combination given favourable circumstances. It naturally builds upon the work of many great Newton scholars, especially during the last fifty years, but I would like to think that the reader will find a considerable number of new insights and interpretations in the three books. Newton is so prolific and multifaceted that there is always a new twist or new angle even to a familiar story. I would also like to think that my experience as a physicist with a special interest in the foundations of the subject has been as valuable in this enterprise as my experience as a historian.

I don’t claim as much expertise in the non-scientific aspects of Newton’s career, treated in the seventh chapter of the present book, where I have clearly drawn on the research of a number of outstanding historians and scholars, but I certainly think that any picture of Newton would be incomplete without them. Even in these areas, however, there are manifestations of Newton’s analytical powers, sometimes leading to results as ‘valid’ as those in the more recognizably ‘scientific’ fields.

Like the other volumes in this series, this book has beneﬁted from the cooperation and support of many people, in particular Niccol´o Guicciardini for his profound comments and suggestions on the mathematical sections, Stephen Snobelen for providing funding for a conference in Halifax, Nova Scotia, and also Mike Houlden, Colin Pask, Mervyn Hobden, John Spencer and my wife Sydney.

Peter Rowlands Oliver Lodge Laboratory University of Liverpool

About the Author

Dr. Peter Rowlands obtained his BSc and PhD degrees from the University of Manchester, UK. He then spent some time working in industry and further education. He became a Research Fellow at the Department of Physics, University of Liverpool in 1987, and still works there. He has also been elected as Honorary Governor of Harris Manchester College, University of Oxford, a post he has held since 1993. Dr. Rowlands has published around 200 research papers and 12 books. Some of his recent works, published by World Scientific, include Zero to Infinity The Foundations of Physics (2007), The Foundations of Physical Law (2014), and How Schrödinger’s Cat Escaped the Box (2015). As a theoretical physicist, his research interests include, but are not limited to, foundations of physics, quantum mechanics, particle physics, and gravity. He has also done extensive work on the subjects of history and philosophy of science, and has published several books on these topics.

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4.4.CapillarityandtheForceofAttraction..............110

4.5.Newton’sInﬂuenceontheExplanationofMaterialStructure..115

5.4.ResistanceinFluids........................140

5.5.Vortices...............................159

InnovationandControversy

1.1.NewtonandControversy

Newtonwasoneofthemostsignificantinnovatorsinscientifichistory, particularlyfamousforhisworkinoptics,gravity,mathematicsand dynamics,thoughhealsocreatedsignificantideasinmanyotherareas. Muchofthisstillresonatestoday,buttherewasapricetopay.Controversy isaninevitableconsequenceofsettingout,asNewtondid,tochangethe entireintellectualmapoftheuniverse,perhapsevenofthehumanmind itself.Everythingthathepublishedwascontroversial;someofitstillis. Newton’sopticswasattackedfromtheinstanthisfirstpublishedpaper appearedin1672andhewasstilldefendingit50yearslaterwhenhis assistantJohnT.Desaguliersdemonstratedtherelevantexperimentstoa partyofFrenchvisitors.Newton’stheoryofuniversalgravitywasattacked from1687bysomeofEurope’sleadingintellectuals,includingHuygensand Leibniz,becauseitrigorouslyexcludedanyhypotheticalmechanism,and impliedthatforcescouldbetransmittedbetweenmaterialparticlesacross emptyspace.ThesameworkalsocausedfeudswithHookeandFlamsteed inEnglandoverdistributionofcreditandaccesstodata.1

ThedisputeswithHookeandFlamsteedhavebeendiscussedatlength bycommentatorsandusedasexamplesofNewton’squarrelsomenature, buttheyarenotthemostsignificantcontroversiesofhiscareer,asthey wereessentiallyonlypersonal.Muchmoresignificantwasanotherpersonal quarrel,againwithLeibniz,overtheinventionofthecalculus,asthisalso ledtoprofounddiscussionsconcerningthenatureofmathematicsandthe relativesignificanceoftheprocessesofanalysisandsynthesis.Thepersonal attackonNewtoninthiscaseandNewton’sresponsewerealsoparticularly significant,asdeprivingNewtonofcreditforhisinnovatorymathematics

1 See NewtonandtheGreatWorldSystem ,Chapters5and6.

wouldhavetakenfromhimtheonlysectionofhisworkthathadremained intrinsicallynoncontroversial,andconsequentlydamagedhiscredibilitywith respecttotherest.AtthesametimeLeibnizwascontrivingtosubvert aspectsofNewtoniandynamicsandgravitationaltheoryinanattemptat preservingtheCartesianworld-viewwhichNewtonhadsetouttoreplace. Theologywasanotherdrivingfactorinthissecondquarrel,thoughbased onlyonafewhintsthatNewtonhadincludedinhis Opticks and Principia Newton,however,avoidedanypersonalinvolvementintheargument,leaving SamuelClarke,hisfriendandtherectorofhislocalparish,tohandlethe dynamicalsubtleties.Togetherwithexperimentsonthermometry,published anonymouslyinalow-keymanner,thisultimatelyledinthedirectionofthe nineteenthcenturytheoryofthermodynamics.

Despitebeinginvolvedinsomanycontroversies,noonecouldhavebeen moreaversetothemthanNewtonorgoneoutofhiswaytopreventthem. Thoseheanticipatedhesetouttoavoideitherbynotpublishingpotentially oﬀendingmaterialorbypublishingitonlyinQueryformandtoningdown hislanguage.Heknewthathisviewsontheologyandchronologywere necessarilygoingtobecomediscordantinmatterswheretherewasahuge diversityofopinionsandnoexperimentalmethodtosupporttheideas. Hewiselyheldbackfrompublishingtheminhislifetimebutimmediate controversyeruptedinbothareasonposthumouspublicationofkeyworks. Infact,thechronologywasattackedferociouslyeveninhisownlifetime withasurreptitiouseditionofaFrenchtranslationofanabstract,which waspublishedonlysothatitcouldbeemphaticallyrefuted.2 Thissetthe toneforcommentsonNewton’schronologyalmostdowntothepresentday. Thetheologicalworkwaspublishedonlyinthecontextofthe Observations ontheProphecyofDanielandtheApocalypseofSt.John ,of1733,andthe TwoNotableCorruptions ,of1754,butitdidn’ttaketheeighteenthcentury divineslongtosuspectNewton’ssecretheterodoxy.Thecondemnationof this,however,wasoﬀsetbyapprovalofhispowerfulsupportfortheargument fromdesign.3

Evenwhenhesetouttosecurehisscientificlegacy,Newtondeliberately sacrificedlargesectionsofhiswork,includingthetheoryofmatterandthe electrifieduniverse,inorderthatthemoresecurelyestablishedpartswould notbechallenged.Heknewthathisviewsonthenatureofmatterandthe compositionofmaterialsubstanceswouldprovokeopposition,because,like

2 Abreg´edelachronologiedeM.leChevalierNewton ,Paris,1725.

3 Mandelbrote(2016).

hisgravitationaltheory,theyemptiedspaceandassumedforcesactingat adistance,sohedrewbackonnumerousoccasionsfrompublishingthem exceptinafewhintsinthe Opticks .Hepublishedsomematerialonfluidsin BookIIofthe Principia becausehewantedtounderstandtheaethereal fluidsthathemodifiedbutneverabandoned.Ultimately,thisbecame themostcriticizedpartofhisacceptedworkbecauseitwascompletely misinterpreted—essentiallyaserroneousCartesian-stylehypothesizing.He publishedonlyhintsofhisideasonchemistryandcohesionbecausethe formerwasbasedonproceduresthatcouldnotbedefendedastotally rational,andthelatterdependedagainonforcesactingatadistance whichhadgivenhimendlesstroublewithhistheoryofgravity.Unlike RobertBoyle,hewascarefulaboutneverpublishinganythingconnected withalchemy,anditwasnotuntilthenineteenthandtwentiethcenturies thatthisbecameoneofthemostcontroversialaspectsofhiscareer.Inall theseareasNewtonwasamajorinnovator,andthedegreeofcontroversyhis workgeneratedcanbetakenasameasureofitsoriginalityandsignificance.

1.2.NewtonandhisModernCritics

MuchofthecriticismofNewton—bothpersonalityandwork—ismodern inorigin.Newton,wehavesaid,isseenbymanyasthegreatestscientist whoeverlived.4 Acolossalfigure,atoweringintellect—thesuperlatives donotdojusticetothisextraordinaryindividual,whoremainsmassively influentialnearlythreehundredyearsafterhisdeath.Yettherehasalways beenacriticalundercurrent.Ofcourse,likeeveryoneelse,Newtonhadflaws, bothasamanandasascientist,but,forreasonsthathavelittletodowith establishinghistoricaltruth,heseemstohavebeensingledoutforsome fairlyintensivenegativecriticismoverthelastfiftyyears.Wehearthathe wasamagus,abelieverinalchemyandmillennialprophecies,notatall therationalscientistofpopularlegend.Hewasunsociable,nevermarried, quarrelledwithlotsofpeople,ruthlesslypersecutedenemiesofthestate, wasbipolar,autistic,obsessive,abnormal,hadadisturbedchildhood,was apuritananddogmatic,andrepresentedtheworstaspectsofmonolithic science.Herefusedtopublishhismathematicalwork,wasunfairtoHooke, Leibniz,Flamsteedandothers,gotinvolvedinbitterprioritydisputes,

4 IliffeandSmith(2016),forexample,rankhim‘amongthetoptwoorthreegreatest theoreticalscientistsever’(withMaxwellandEinstein),amongthetoptwomathematicians (withGauss),and‘inthefirstrankofexperimentalists’,withnooneelsefiguringinmore thanoneofthesecategories(15).Hewas,inparticular,‘anextraordinaryproblem-solver, asgood,itwouldappear,ashumanityhaseverproduced’(30).

repressedBritishmathematics,andhadanegativeinﬂuenceinsupporting thecorpusculartheoryoflight.Hiscelestialmechanicsleftalottobeworked outbyhissuccessors,hismechanicshadtobetranslatedintotheproper algebraicform.

Inadditiontheterm‘Newtonian’isregularlyusedastheexpressionfor theorieswhichhavenecessarilybeensupersededbymoremodernthinking, forexample,byrelativitytheory,quantumtheory,orthetheoryofchaotic systems.Conventionalphilosophyhasneverratedhisworkinthatﬁeld, whilesomeauthoritiesclaimthathewasnotparticularlysuccessfulasan economistattheMint.Inscience,hepushedhisdatabeyondthelimits towhichitcouldgo,andleftalotofhisworkinarathersketchyform, aswellasbeingwrongonnumerousoccasions.Therewasalsothedesire foramoremodernhero,soEinsteinolatryappearedintheearlytwentieth centurytoreplacetheNewtonolatryoftheprevioustwohundredyears,amid claimsthatNewton’smostimportantworkhadbeensupersededbyspecial relativity,generalrelativityandquantummechanics.

Clearlysomeoftheiconoclasmissimplyanoverreactiontoearlier hyperbole.Butmanyofthecommentsmadeaboutboththemanandhis workaremassivelywideofthemark.Assumptionshavebeenmadeon theflimsiestofevidenceorlackofit,nottomentiontheprejudicesof thewriterandthedesiretoproduceasensationalistslant.Speculations byoneauthor,thatNewtondestroyedHooke’sportraitorthathemade upthestoryofbeinginspiredbythefallofanapple,become‘facts’in another.Mostofthejudgementsofthemanstemfromasingleworkby FrankE.Manual,which,thoughbrilliantlywritten,isneverthelessbasedon thepseudoscientificpremisesofFreudianpsychoanalysis.5 Also,thoughmuch brilliantworkhasbeendoneonthesciencebyseriousstudentsofthesources, othershaveallowedsuperficialinvestigationstocolourtheirassessments.In fact,muchofNewton’sworkisverydifficultandeventhebest-informed scholarscanbewrongoncrucialpoints.Inaddition,mathematicaland physicalresearchershavebeenslowinusingtheirspecialknowledgetoadd theirperspective.

Whilemakingcriticalcommentswheretheyareappropriate,Iwill notbefollowingthisline.Astudyofthesourcesshowsrepeatedlythat Newtonisadiﬃcultauthorwhodemandscloseattention,andcannotbe

5 Manuel(1968).Togiveanideaofthelevelofabsurditytowhichthiscanlead,wemay quote,asGleickdoes(2003,240),Manuel’squestion:‘Intheactoffornicationbetween hisfriendHalifaxandhisniecewasNewtonvicariouslyhavingcarnalintercoursewithhis mother?’(1968,262).

understoodonasuperficialreading.Wenowknow,justtotakeafew randomexamples,thathisalchemicalresearcheswereaworkofscience andnotanoccultstudy,mergingintochemistry(andevenhighenergy physics);thathewasanimportantphilosopher,acapableeconomist,that evenhismorebizarreinterestsyieldedsomevalidresults;thatanumber ofsignificantmathematicalresultspreviouslyconsideredfaultyareinfact correct;andthathisabstractmathematicalmodels(forexample,thatof gasesinthesecondbookofthe Principia )shouldnotbeconfusedwith physicalonesandarecompletelycorrectintheirownterms.Inaddition, theproblemwiththe‘replacement’ofNewtonasall-conqueringherowith Einstein,isthatitdoesn’tquitefitthefactsoftwentiethcenturyscience. Thoughrelativityreceivedmostpublicattention,partlyforextra-scientific reasons,quantummechanicswasreallythegreatrevolutionoftheperiod, thoughitarrivedwithoutanyofthemediacircusattendingtheearlier theory.Generalrelativity,amuchmorespecialisedandrestrictedtheory, doesn’thavethesamestatus,forallitsculturalcachet,andtalkofthetwo theoriesasthe‘twinpillars’ofmodernphysicalthought.Einsteincametoo earlytobeareallysignificantcontributortoquantummechanics.Thehero cannotbetotallyalignedwiththeheroicstory.Einstein’sworkisofgreat significance,butthissignificancedoesnotlieinbeingopposedtothework ofhispredecessor.

Thespecialandgeneraltheoriesofrelativityledtoavastnumberof superficialcommentsaboutNewtoniantheory.Theword‘Newtonian’,aswe haveseen,isoftenusedtomeansomethingotherthanwhatwasbeingdone intherevolutionaryperiodofthetwentiethcentury.‘Non-Newtonian’is usedforrelativisticversusnonrelativistic,quantumversusclassical,chaotic versusstandarddeterministic,butnoneofthemoderndevelopmentsis actuallynon-Newtonianinthesenseimplied.If‘Newtonian’means,asit should,pertainingtoNewton’sownideas,wefindthatnoneofthemodern theoriesisoutsidehisinterestsandnonereallycontradictshisvision.We needtorecallthatalotofthe‘Newtonianideasoverthrown’aspectofearly twentiethcenturyphilosophywaspoliticalratherthanscientific.Peoplefelt thatthereoughttobeaspiritofrevolutionaboutinaperiodthatdefined itselfbytheword‘modern’,andthemodernistrevolutionwouldnotbejust anotherstageinhumanhistorybutatrulydefiningmomentwhichcould not,bydefinition,besuperseded.Westillhaven’teradicatedthatmodeof thinkingdespiteitsmanydisastrousconsequences.Despiteamassoftruly greatscholarship,alotofwhatwassaidaboutNewtonandNewtonian scienceinthetwentiethcenturywasbasedonfallacy.ThomasKuhnsaw scienceasbeingcreatedbyrevolutionsseparatedbylongperiodsofstasis

or‘normal’science;Poppersawscienceasdefinedbypotentialfalsification.6 BothattemptedtofitNewtoninthispicture,buthisworkdoesnotfit wellwiththem.Theideathatasingleexperimentalresultcandecideon philosophicalissues,orchangeanentirephilosophy,isafantasy.Itisalso dangeroustoassumethatcurrentwaysofthinkingareintrinsicallysuperior toearlieronesbeforeafundamentalbasisisestablishedforphysics.

1.3.AnEarlyControversy

Thefirstandinmanywaysthemostsignificantcontemporarycontroversy came,in1672,withNewton’sfirstpaperonoptics,containinghisnewtheory ofcolour.7 Forarelativelyunknownindividualtodevelopanextended scientifictheorybasedonworkdoneoveraperiodoftimeusinganew methodologyisdangerous,becauseitrequiresgoingthroughtheinitialstages toreachtheresultsofrealimportance.InthecaseofNewton,itmeant alsohavinghisexperimentalexpertise.Themuch-laudedsystemof‘peer review’isoftenuselessinthesecases,especiallywherethenewmethodology requiresinductiveorrecursivethought,becausethesheernoveltyofthe conceptsmeansthatnoreferencecanbefoundwithinexistingknowledge forcomparison.Infact,thehistoryofphysicsduringthelastcenturyshows thatmanyofthemostimportantdiscoveriesmadeduringtheperiodhada difficulttimeinmakingitthroughthesystemorbeingacceptedafterthey had,andwecanonlyimaginewhattheblindfaithinsuchanarbitrary processasreviewingbyafewindividuals,withalltheproblemsposed bytheirprejudices,ignorance,self-interest,andsheerlackofimagination, hascostusinlostopportunities.Science,likeeveryotherfieldofhuman endeavour,isdominatedbypowerstructures.Theonlydifferenceisthat sciencestillseemstooperateunderthedelusionthatthepowerstructures arebenign.

Newton’scareershowsthatitisnotacompletelynewproblem,for adisastrouspeerreviewofthisfirstpublishedpapernearlystoppedhis scientificcareerinitstracks.Theveryseriousquarrelwhichfollowedhis disclosureofthecompositenatureofwhitelightsawNewtonrangedagainst Hooke,Huygens,PardiesandawholehostofEnglishJesuits,andonlyended whenNewtonterminatedthecorrespondenceinafitofrage.Essentially,the critiquesofHookeandtheothersinvolved,notonlytherejectionofhis supposed‘hypotheses’,butalsohisembryonicuniversalmethod.Onlyhis

6 Kuhn(1962);Popper(1963).

7 See NewtonandModernPhysics and NewtonandtheGreatWorldSystem fordetails.

‘impact’inventionofthereﬂectingtelescopesurvivedtheonslaught.8 This episodehastobetakenasthesourceformanyofhissubsequentactions, andthelaterprioritybattlesshouldalsobeseeninthislight.

Theoriginoftheproblemwasadifferenceinmethodology.Newton believedthatcertainconcepts,suchasrefrangibility,couldbederived byabstractionfromempiricalphenomenaandthenusedwithoutfurther referencetomechanisticmodels.Inthishewascorrect,andsuchthinking becametheroutetomakingphysicsthekeytouniversaltruth,ratherthan anempiricalstudyaimedatthekindofimmediatepracticalutilitythat seemstohavebeenthemainobjectiveoftheearlyfellowshipoftheRoyal Society.Newton’smethodallowedhimtoassumepropertieslikeperiodicity andcorpuscularity,andlaterpolarisability,toexistasabstractconcepts, withoutrequiringamodel.He did devisemodelsonoccasions,buttheywere nevertheprimarypurposeofhisscientificinvestigations,andtheyoften representedhisleastsuccessfuleffortsatexplanation.However,thinking intheabstractstyleappearstobeverydifferentfromthedefaultmode normallyassumedbyhumankind,andNewton’scontemporariessimplydid notseethepoint.Manylaterwritershavenotseenthepointeither,even tothepresentday.Newton’sabstractmethodologyhasneverbeenfully appreciatedeitherbeforeorsince.But,simplybyaprocessofattrition andnaturalselection,itultimatelybecametheclassicmethodforcreating generalsolutionsofwideapplicabilityratherthanforsolvingeachproblem asaspecificinstanceasitarose.

Theopticalcontroversy,ofcourse,occurredrightatthebeginningof Newton’scareer,longbeforehehadworkedouthowtoreformulatethe wholeofphysicsandmanyyearsbeforehehadformulatedhismostpowerful abstractconceptsorhadsystematisedhispractices,butitcameabout becauseNewtonhad,almostinadvertently,introducedamethodwhich camenaturallytohimbutwhichwasincomprehensibletomostofhis contemporaries.ForNewton,allthatwasnecessarytomakesenseofhis experimentswastoacceptthefactthatlightrayswhichproducedsensations ofdiﬀerentcolourswerediﬀerentintheabstractandmathematically

8 Forthebenefitofreadersinfuturetimes,inadditiontoitsuseasanindexof theperceivedimportanceofvariousscientificjournals,‘impact’wasanarbitraryand undefinableparameterinventedbyearlytwenty-firstcenturypoliticiansintheUKto measurethesupposedvalueofresearchfundedbytax-payers,andwaslargelyaimedat identifyingprojectswhichseeminglyprovidedanimmediatereturnoninvestment,despite theoverwhelmingevidencethatsuchreturnsnearlyalwaysresultedfromdiscoveriesthat couldnothavebeenpredicted—aclassiccaseofamisunderstandingofthescientific processthroughalackofknowledgeofscientifichistory.

measurablepropertyofrefrangibility,thequalitydefinedassin i/sin r in Descartes’lawofrefraction.Thiswastruewhatevermechanicalhypothesis wasusedtoexplainthefact,ifanywerenecessaryatall,andhewouldrather jettisoneverythingthanconcedethisfundamentaltruth.Themethodhewas intheprocessofdiscoveringmatteredmoretohimthananyofthespecific conclusionsituncovered.So,althoughitwashisrejectionofthehypothetical methodwhichhadtriggeredthelongseriesofopticalcontroversies,and, althoughherealisedthathypotheseshadaroletoplayinscientifictheorising, mostnotablywhenhewrotehis HypothesisExplainingthePropertiesof Light in1675,hewasnotpreparedtoconcedethathypothesesshouldtake precedencewhenamoresecureabstracttruthhadbeenestablished. 9

Theexperimentsreportedin1672requiredaveryhighdegreeof experimentaltechnique,whichNewtonwasforcedtospelloutindetail insubsequentrepliesinthe PhilosophicalTransactions tocriticismsby theJesuitsofLiège.10 Newtontookagreatdealoftroubletosecurethe rightkindofprismsandevenconstructedhisownwater-filledones.A skilledexperimenterlikeHookecouldreproducetheexperimentalresults afteranumberoftrials,butanamateursuchasAnthonyLucascouldnot. Approachingtheworkwithapreconceivedattitudewaslikelytoleadtoa negativeoutcome.Evenafterthemaincontroversyhaddieddown,when Newtonrefusedtoprolongthecorrespondence,continentalCartesians,such asEdméMariottecontinuedtopublishpaperssayingthatboththeory andexperimentswerewrong,11 andthisbecameperfectammunitionfor aconvincedCartesiansuchasLeibniz,whoseattackonNewton,though largelycovert,wasmountedsimultaneouslyonallpossiblefronts:dynamics, gravity,opticsandmetaphysics,aswellasmathematics.

Newtonianopticsonlybecameacceptedafteritsauthorbecamecelebratedforhisworkincelestialdynamics,andthenbynomeansimmediately.

9 InadraftQueryNewtonmakesclearthathisearlyworkinopticshadledtoseemingly irreducibleabstractorsemi-abstractideaswhichincluded‘theoriginaldifferencesofthe raysoflightinrespectofrefrangibilityreflexibility&colour&theiralternatefitsofeasy reflexion&easytransmission&thepropertiesofbodiesbothopake&pellucidonwhich theircoloursdepend&thesediscoverysbeingprovedmaybeassumedasPrinciplesin theMethodofCompositionforexplainingthephænomenaarisingfromthem’(CULAdd. 3970.3,f.242r ,NP).

10 Linus(3);Gascoignes(1);Lucas(1).Schaﬀer(1989)hasalengthydiscussionofthe controversiesinrelationtothedetailedclaimsoftheexperimentsandtheexperimental techniquesused.Newton,likeFaradayafterhim,wasanexperimenterwholeftnothingto chance,workingthroughmanypossiblevariationsonhisexperimentstoclosedownevery possibleloophole(Shapiro,2002,230).

11 Mariotte(1681).

The Opticks wasnotpublisheduntilthe Principia hadbeeninprintfor 17years.Hookehadconcededthatsomeoftheexperimentswerecorrect asearlyas1675,buttheexactconditionsspeciﬁedbyNewtonwerenot alwayseasytomatch,socontroversypersistedandDesagulierswasstill doingNewtoniandemonstrationexperimentstoprovetheirvalidityaslate as1722.12 Theimmediateandcomprehensiverejectionoftheearlypaper ontheanalysisofwhitelightbecameafactofgreatimportancetotheway Newtonsubsequentlychosetopresenthiswork.Hewasalreadyinclined toshunpublicity,eitherbecauseofhisnaturaltemperament,orbecause hewantedtoavoiddrawingattentiontohismoreesotericandclandestine investigations;buthenowbecameevenmorecautiousandsecretiveabout hisideas.

WhetherornotFrankManuel’srepresentationofNewtonasamanwith aMessianiccomplexisagenuinerepresentationofhischaracter,13 itseemsto beanaccuraterepresentationofthepositioninwhichhenowfoundhimself. Asatheologian,Newtonwascomfortablewithamind-setbasedonarticlesof faith.Heprobablyalsoknewthathehadspecialpowersinuncoveringtruths inaholisticway,whichcouldseemalmostlikedivinerevelation.Whathe couldn’texplainwashowhehadarrivedathisabstractandgeneralising ideas.Inthisposition,ascientisthastofindastrategywhichwillconvince peoplewhoworkinanentirelydifferentway.Tosaythattheideasonly havetobeacceptedtobecomeobviouswon’tconvincepeoplewhowantto knowwhytheyshouldtaketheinitialstepofacceptingtheminthefirst place,especiallyifitmeansjettisoningtheirownpettheories.Thisiswhy manyideasthatinretrospectseemobvioushavebeenmetwithhostility atthetime.Newtonhadastrategy.Hedecidedtopresenthisconclusions asthe direct resultsofthekindofexperimentalinquiriespopularwithhis mechanically-mindedcontemporaries.Howcouldthisfail?Heproduceda powerfully-arguedcaseinhisbrilliantreporton‘ANewTheoryofLight andColours’;14 buthisstrategystillfailed—becausehisthenmorepowerful opponentsalreadyhadmodel-dependenttheoriesavailablewhichtheycould modifytoaccommodateanynewsetofdata.

ThestrengthofNewton’sinductivemethodinproducingpowerfulresults ofgreatgeneralityhadputhiminavulnerableposition.Theprocessby whichhegainedhisgreatestinsightswasinexplicable—itdoesn’tfollow theusualrulesofdeductivelogic,anditcouldnotbeduplicatedbyan

12 Desaguliers(1722).

13 Manuel(1968).

14 ‘ANewTheory’, Corr. 1:92–102.

iterativechainofreason.Sohewasunabletoexplainthesourceofhis superiorinsightstothesatisfactionofotherphilosophers,andtheyweren’t willingtoconcedethattheyshouldusehisstartingpoint.Hewasonlyable toconvincethemofhissuperiorityatalaterdatebysheermathematical power.Thelongdrawnoutbattleoverhisearlyworkonoptics,soobviousto him,incomprehensibletohiscontemporariesintheabstractformhestated it,eventuallytriedhispatiencebeyondendurance.Itwasaharshlesson foraresearcheratthebeginningofhiscareer.Foralongtime,hemadean eﬀorttotrytoaccommodatehisvisiontoencompassotherpeople’stheories, ideasandquestions,andweseethisinpoliteandcourteousletterstomany correspondents—forexample,MichaelDary,FrancisNorth,WilliamBriggs andJohnHarington,andperhapsJoshuaMaddock.15 Intheend,however, theendlesscriticismoftheexperimentsonwhichhebasedhistheorytookits toll,andhefounditimpossibletotoleratethesheerrefusalofcorrespondents toseethefactthattohimwasblindinglyobviousbutcouldnotbederived fromanythingelse:nomatterwhathypothesisexplainedthenatureoflight, itwascomposedofrays‘diﬀerentlyrefrangible’.‘ThisIbelieve’,hewrote, ‘hathseemedthemostParadoxicallofallmyassertions,&metwiththe mostuniversall&obstinatePrejudice.Buttomeitappearsasinfallibly true&certaine,asitcanseemextravaganttoothers’.16

Fromalatervantagepoint,weseethatNewton’stheoryoflightwould havebeencompletelyobvious onceaccepted andthenapowerfulsource ofnewdevelopment.However,toacceptsuchatheory,hiscontemporaries wouldhavehadtoadoptanewtypeofthinking,beyondthattowhichthey hadbecomeaccustomed.Thesamepatternhasrepeateditselfmanytimes sinceinthehistoryofphysics.Thoughnatureisgroundedinideasthat arefundamentallysimple,thissimplicityisofanabstractkindandvery differentfromthesupposed‘simplicity’of‘concrete’everydayexperience, whichisactuallycomplex.Toadoptnature’smodeofsimplicityisavery difficultexercise,becauseitrunscountertonormalhumanexperience.So, simpleand‘obvious’factsareveryhardwonandalwaysstronglyresisted. Evennow,thescientificcommunityhasneverbeenfullywonovertothefact thatsimplicityandtheconcreteareatoppositepolesofhumanexperience, andithascertainlyneverfullyaccepteditsconsequences.‘Fundamental’

15 NewtontoDary,6October1674, Corr. I,319–320,and22January1675, Corr. I,332–333;toNorth,21April1677, Corr. II,205–207;toMaddock,7February1679, Corr. II, 287–288;toBriggs,20June1682, Corr. II,377–378,and12September1682, Corr. II, 381–385;toHarington,30May1698, Corr. IV,274–375.

16 NewtontoOldenburg,5December1674, Corr. I,328.

theoriesarestillbeingputforwardinastylewhichisincompatiblewith producinglastingresults.Thediﬃcultyisincreasedbecausemostofphysics actuallyconcernstheconcreteandcomplex;onlythefundamentalsare simple,andmostphysicistshavenooccasiontoconcernthemselveswith these.Becauseconcretemodelsworksowellinotherareasofphysics,the tendencytodescribefundamentalsusingthemcanbealmostirresistible,but longexperienceofthefailureofthisstrategysuggeststhatsomeaspectsof physicscanneverbeexpressedinthisway.

1.4.GravityEstablishedasaUniversalTheory

Itmayhavebeentheearliercriticismsengenderedbyhisopticalwork whichmadeNewtoncomposethe Principia verylargelyinthegeometrical styleratherthaninthemuchmorerevolutionaryanalytic.Hadheused revolutionarymathematicsalongsiderevolutionaryphysicshisworkwould havehadmuchlessimmediateimpact.Hewasdeterminedthatthistimehe wouldnotfailinhispublicmessage.Evenafterhegainedfameastheauthor ofthe Principia,theexperienceovertheopticalpaperhadaprofoundeﬀect onhim.Itiswellknownthathefeltobligedtooverstatetheaccuracyofhis workinanumberofspeciﬁcinstances,inordertoavoidgivingammunition tothecontinentalCartesians,whosubjectedhisworkinallareastoa never-endingbarrageofhostilecriticism.Leibniz,themostprominentofthe Cartesians,concedednothingtoNewtoninphysics,recognisingonlythat hehadmadeadvancesinmathematics.Eventhere,hethoughtnothingof appropriatingNewtonianresultsinthephysicalapplicationofmathematics ifhecouldprovidethemwithaCartesianinterpretationwhichwould underminetheonegivenbyNewtoninthe Principia.Theprioritybattle overthecalculustookplaceinthecontextofamuchmoreextensiveall-out warconcerningthefundamentalsofmetaphysicsandnaturalphilosophy.

Gravitywasaparticularproblem.Howcouldoneinvokeaforceof gravity,hisopponentsargued,ifonehadnophysicalexplanationforit? Newtonwouldhavenoneofthiskindofargument.Thephysicalexplanation, ifanyexisted,hadnobearingontheexistenceofthegravitationalforce: ‘ButhithertoIhavenotbeenabletodiscoverthecauseofthoseproperties ofgravityfromphænomena,andIfeignnohypotheses;forwhateverisnot deducedfromthephænomenaistobecalledanhypothesis;andhypotheses, whethermetaphysicalorphysical,whetherofoccultqualitiesormechanical, havenoplaceinexperimentalphilosophy’.17 ‘Gravitymustbecausedbyan

17 GeneralScholium(withtheusualamendmentof‘frame’to‘feign’).

agentactingconstantlyaccordingtocertainlaws,butwhetherthisagent bematerialorimmaterialisaquestion,Ihavelefttotheconsiderationof myreaders’.18 ‘Andtousitisenoughthatgravitydoesreallyexist,andact accordingtothelawswhichwehaveexplained,andabundantlyservesto accountforallthemotionsofthecelestialbodies,andofoursea’.19

Thecatastrophicfailureoftheembryonicpeerreviewsystemin1672 meantthatthetrulyrevolutionarynatureofNewton’sworkwasnot understood,and,toalargeextent,itwasonlyvaguelyapprehendedlong afterwards.Hispowerfulmethodologywasneverfullyaccepted,evenbythe peoplewhoapprovedofitsresults.Thereseemstohavebeentworeasonsfor this.TheﬁrstwasthatNewtonwasapowerfulanalyst.Theabilitytothink inthiswayseemstobeextremelyuncommon,andtheabilitytorecognize suchthinkingdoesnotseemtobeparticularlywidespreadeither.TheGreeks probablyproducedonlytwogenuinelyanalyticalthinkers—Parmenides andZeno—bothgreatlymisunderstoodbytheircontemporariesandeven downtothisday.ThesecondwasthatNewtonwasprimarilyatheologian, andhiscontemporariesknewit.AshehimselfwrotetoBentleyafterhe hadpublishedthe Principia :‘WhenIwrotemytreatiseaboutourSysteme IhadaneyeuponsuchPrinciplesasmightworkwithconsideringmenfor thebeliefeofaDeity&nothingcanrejoycememorethentoﬁnditusefull forthatpurpose’.20 Newtonhadintroducedorreintroducedawholeseries oftheologicalconceptsintophysics,justwhenitwasestablishingitselfasa modern,‘secular’subject,basedongoodmaterialistprinciples.

ThoughitwascertainlytruethatNewtonhadderivedhistheorydirectly fromexperiments,itwasalsotruethatthiswasonlypossiblebecausehehad introducedintoscienceanewandnon-mechanisticstyleofthinkingwhich hadmoreincommonwithlatemediaevalmodesofthoughtthananything fashionableinhisday.Hiscontemporariesrejectedhisabstractionsbecause theythoughtthathewasnotbeing‘modern’.Themechanisticstyle—the inventionofmechanistichypothesesormechanicalmodels—wasmodern; abstractcategorieswere‘occult’,andhadbeenbanishedbyDescartes,once andforall,fromthestudyofnature.But,asNewtonprotestedforthebeneﬁt ofLeibniz:

TotellusthateverySpeciesofThingsisendow’dwithanoccultspeciﬁck QualitybywhichitactsandproducesmanifestEﬀects,istotellusnothing:

18 NewtontoBentley,25February1693; Corr. III,253–356,254,Cohen, PapersandLetters, 302–303.

19 GeneralScholium.

20 NewtontoBentley,10December1692; Corr. III,233.

buttoderivetwoorthreegeneralPrinciplesofMotionfromPhænomena, andafterwardstotellushowthePropertiesandActionsofallcorporeal ThingsfollowfromthosemanifestPrinciples,wouldbeaverygreatstepin Philosophy,thoughtheCausesofthosePrincipleswerenotyetdiscover’d: AndthereforeIscruplenottoproposethePrinciplesofMotionabovemention’d,theybeingofverygeneralextent,andleavetheirCausestobe foundout.21

Perhapssigniﬁcantly,heusedhisopponents’ownfavouritemetaphorof clockworktoillustratehispoint,remindingthemthatthegravitythatdrove clockworkwasjustasmuchamysteryasthegravitythatdrovetheworld system:

...certainlyGodcouldcreatePlanetsthatshouldmoveroundofthemselveswithoutanyothercausethengravity...Andtounderstandthis withoutknowingthecauseofgravity,isasgoodaprogressinphilosophy astounderstandtheframeofaclock&thedependanceofyewheelsupon oneanotherwithoutknowingthecauseofthegravityoftheweightwhich movesthemachineisinthephilosophyofclockwork...

Andthereforeifanymanshouldsaythatbodiesattractoneanotherby apowerwhosecauseisunknowntousorbyapowerseatedintheframe ofnaturebythewillofGod,orbyapowerseatedinasubstanceinwhich bodiesmove&ﬂotewithoutresistance&whichhasthereforenovisinertiæ butactsbyotherlawsthenthosethataremechanical:Iknownotwhyhe shouldbesaidtointroducemiracles&occultqualities&ﬁctionsintoye world... 22

Thereweremanyotherthingsthatcouldnotbeexplainedmechanically, yettheywereacceptedbythemechanistsandnotconsideredoccult:

Thesameoughttobesaidofhardness.Sothengravityandhardnessmust goforoccultqualitysunlesstheybeexplainedmechanically.Andwhymay notthesamebesaidofthevisinertiæ&theextensiontheduration& mobilityofbodies,&yetnomaneverattemptedtoexplainthesequalities mechanically,ortookthemformiraclesorsupernaturalthingsorﬁctions oroccultqualities.Theyarethenaturalrealreasonablemanifestqualities ofallbodiesseatedinthembythewillofGodfromthebeginningofthe creation&perfectlyuncapableofbeingexplainedmechanically,&somay bethehardnessofprimitiveparticlesofbodies.23

21 Q31.

22 Draftlettertoeditorof MemoirsofLiterature,after5May1712; Corr. V,298–300, quoting300.Theeditorsofthe Correspondence saythatthis‘isanearlyappearance’of ‘anon-Cartesianaether,hereinvokedasamereconjecture’( op.cit.,301).

23 ibid

AsNewtonwroteinalettertoCotes:‘...Experimentalphilosophyproceeds onlyuponphenomenaanddeducesgeneralpropositionsfromthemonlyby induction.Andsuchistheproofofmutualattraction.Andthearguments fortheimpenetrability,mobilityandforceofallbodiesandforthelawsof motionarenobetter...’24

SamuelClarkeexpressedtheNewtonianpositioninanotherletterto Leibniz:

Thatanybodyshouldattractanotherwithoutanyintermediatemeans,is indeednotamiracle,butacontradiction:for’tissupposingsomethingto actwhereitisnot.Butthemeansbywhichtwobodiesattracteachother, maybeinvisibleandintangible,andofadiﬀerentnaturefrommechanism; andyet,actingregularlyandconstantly,maywellbecallednatural;being muchlesswonderfulthananimalmotion,whichisneveryetcalledamiracle. Ifthewordnatural forces ,meansheremechanical;thenallanimals,and evenmen,areasmeremachinesasaclock.Butiftheworddoesnotmean, mechanicalforces;thengravitationmaybeaﬀectedbyregularandnatural powers,thoughtheybenotmechanical.25

Newtonwasaccusedinhisowndayof not beingamechanist—ofbelieving in‘occult’or‘magical’qualities,andhisthoughtsonthemicrophysicsof matter,nottomentionhisworkinalchemy,suggestthathewasinno senseabelieverinaclockworkuniverse.Ultimatecausesforhimwerenot mechanical.Paradoxically,Newton’stheologicalconcernsmadehimamore modernthinkerthanthemechanistsofhisowndayandofours.

ThoughNewtonusedrationalthinking,hewasnotarationalist.Hedid notbelievethatfundamentaltruthscouldbediscoveredbyreason.Also,it wouldhavebeenunthinkableforNewtontohavecreatedanimageofGod asa‘watchmaker’,asisoftenalleged.Thephrasecomesfromaletterby Leibniz,whointerpretsapassagefromQuery31assuggestingthatGod hadactuallytointerferefromtimetotimewiththemotionsofplanets andcometstokeepthemintheirorbits.26 ButClarkerepliedtothis,most certainlywithNewton’sapproval:‘Thenotionoftheworld’sbeingagreat machine,goingonwithouttheinterpositionofGod,asaclockcontinues togowithouttheassistanceofaclockmaker;isthenotionofmaterialism andfate,andtends(underpretenceofmakingGoda supra-mundane

24 NewtontoCotes,31May1713; Corr. V,400.

25 Clarke,FourthReplytoLeibniz,26June1716;Alexander(1956,53).

26 LeibniztoPrincessCaroline,November1715;Alexander(1956,11).

intelligence )toexcludeprovidenceandGod’sgovernmentinrealityoutof theworld’.27

Theclockworkuniverseidea,ofcourse,longpredatedtheseventeenth century,andhasnothingtodowiththeintroductionoftheNewtonian system.NicholasOresme,forexample,wasalreadyusingthemetaphor asearlyasthefourteenthcentury,thatperiodwhenmechanicalclocksof thehighestquality,andoftenofgreatsophistication,firstbegantobe constructed.Aversionofitisfoundevenearlierinthatgreatthirteenth centurytextbook,the DeSphaera ofSacrobosco.28 Bytheseventeenth century,ithadbecomeasmuchapartofgeneralcultureasitwasofscience. WhileKepler,Boyleandothersusedtheideaintheirscientificworks,soalso didpoetssuchasFrancisQuarlesandThomasTraherne.29 Newtonwas,in thissense—andasonotheroccasions—beingaccusedofbeingoutofline withthegeneralconsensus;hisideasdid not fitinwithclockworkregularity, andhemadenoattempttoclaimthattheydid.

ForNewton,ashestatedexplicitlyinhisworks,Godwasa‘governor’ (παντoκρατoρ,intheGeneralScholium),whomovedeverythingbyhisWill alone.30 DavidGregoryrecordedinamemorandumof21December1705: ‘Theplaintruthis,thathebelievesGodtobeomnipresentintheliteral sense...WhatcausedidtheAncientsassignofGravity.Hebelievesthat theyreckonedGodthecauseofit,nothingels,thatisnobodybeingthe cause;sinceeverybodyisheavy’.31

Newtonknewthattheworldwouldnotinstantlyrecognisethemeaning ofthe Principia .Thebattlesovertheinventionofthecalculuswerepart ofamuchbiggerstruggleovertheexplanationofthegreatworldsystem, andwinningonebattlewasanecessarypreludetowinningtheother.That Newtonultimatelysucceededishistory,butitwasnotinevitable.Had anyoneelsesolvedtheproblemofplanetarymotions—andseveralpeople

27 Clarke,FirstReplytoLeibniz,26November1715;Alexander(1956),Smith(2007)states thattheclockworkaspect(acommonenoughmetaphorelsewhere)isnowhereapparentin the Principia,andappearstohavebeengraftedontotheunderstandingoftheNewtonian systembyLaplace.

28 Oresme(1968,289);Sacrobosco(1949).

29 KeplertoJ.G.HerwartvonHohenburg,16February1605,quotedKoestler(1967),IV, 331:‘Myaimistoshowthattheheavenlymachineisnotakindofdivine,livebeing, butakindofclockwork,insofarasnearlyallthemanifoldmotionsarecausedbyamost simple,magnetic,andmaterialforce,justasallmotionsoftheclockarecausedbya simpleweight.AndIalsoshowhowthesephysicalcausesaretobegivennumericaland geometricalexpression’.Boyle(1690);Quarles(1624);Traherne(1675).

30 Q31.

31 DavidGregory,memorandum,21December1705;Hiscock(1937,30).

cameclose—theNewtonianuniversalmethod,whichwasamuchmore signiﬁcantinnovation,mightneverhaveseenthelightofday.Theearly versionofNewton’smethodhadalreadybeenuniversallyrejectedin1672, whenhehadappliedittooptics,andtheunderlyingphilosophyofthe Principia wasagainopposedonalmostallsides;onlythemathematical resultswereaccepted,andthatpartofthephilosophytheynecessarily carriedwiththem,butthewholebasisonwhichtheywereconstructedwas considered‘unphysical’and‘occult’.Thestoryofmodernphysicsis,from onepointofview,thegradualcomingtotermswiththeNewtonianlegacy.

AnalysisandSynthesis

2.1.NewtonandLeibniz

ThecontroversythatinevitablyfollowedonfromNewton’sradically innovativeworkinopticaltheoryandgravityalsoengulfedhislessproblematicworkinmathematics,thoughhereitbecameapersonalbattleto securehistitletotheauthorshipoftheonlypartofhisworkthatremained uncontestedonintrinsicgrounds.ThemerelistingofNewton’sdiscoveriesin mathematicsshowshowpowerfulthetoolkitwasthatwasavailabletohimin hisworkinphysics.1 Wealsoknowthathemadegooduseofitintheyearsto come.However,theattacksthatweremadeonhisopticsonlyconﬁrmedhis naturalreluctancetolayhimselfopentopublicdispute,and,thoughhewas persuadedtosendhisearlytractoncalculus Deanalysi,tothemathematical impresario,JohnCollins,inLondon,hecouldnotbepersuadedtopublish hismathematicalworkintheRoyalSociety’s PhilosophicalTransactions. Ultimately,thisledtothemostnotoriousofhismajordisputeswithhis contemporaries,theargumentwithLeibnizoverpriorityintheinventionof thecalculusasageneralmethod.

ThequarrelwithLeibnizwasoneofakindthathasaffectedscience atfrequentintervalsdowntothepresentday.Universallydeploredby theworthyhistorianswhoconsiderscienceapurelyobjectivesearchfor truth,theprioritydisputeisunlikelytodisappearinwhatwillalways beacompetitiveenterprisebetweenindividualsorgroupsofindividuals. Inaddition,thoughthedisputebetweenNewtonandLeibnizwasmainly abouttheinventionofthecalculus,italsospilledoverintootherthings. Bothmenwereoutsiders,obligedtoforcetheirwayintothescientific establishment,andnevercompletelysecureintheirpositions.Bothwere highlyoriginalthinkers,withwideinterests,eachdetermined,fordifferent

1 Thisisdiscussedindetailin NewtonandtheGreatWorldSystem,Chapter2.

18 Newton—InnovationandControversy reasons,tobenumberone.Leibniz,muchmorethanNewton,wasanurbane andsophisticatedtypeofperson,whohasalwayshadhissupporters.But hecould,nevertheless,alsobevainandarrogant,andamasterofsubtle duplicity.2 Itwasprobablyinevitablethattwosuchtalentedandegotistical menwouldbecomemajorrivals,butitmayhavebeenthesupportersrather thantheprincipalswhoturnedtherivalryintoanopenconﬂict.

Inaddition,prioritywaspossiblylessimportanttotheparticipants, atleasttoNewton,than credibility.Newtonseemstohavebeenstrangely unconcernedaboutclaimingpriorityinmanycaseswhereitwouldhavebeen relativelyeasyforhimtodoso.Hegenerallyciteshisearlierworkonthe basisof towhomitwascommunicated and when,ratherthanwhenitwas actuallydiscovered.Hisgreatestanxietywasthepossibilityofbeingaccused ofplagiarismandsonotbeingregardedasacrediblewitness.Theuseof anencryptedanagraminhiscorrespondencewithLeibnizmayhavebeen intendedtopreventthekindofretrospectiveclaimonhismostimportant ideasthathehaddiscoveredwasinevitableinanycorrespondencewith RobertHooke.

Thebasicfactsarenowwellknown.Althoughsomeindividualcases thatwecannowdesignateasdiﬀerentiationandintegration(thenknown asthemethodsoftangentsandquadrature)hadbeenknownpreviously,no generalmethodhadbeendevised,inparticularthefactthatthemethods wereinverseoperations,beforeNewtoninventedhisversionofthecalculus between1664and1666,andwrotehisﬁrsttractonit, Toresolveproblems bymotion,inthelatteryear.3 Itwasfollowedrapidlybyanumberof others,including Deanalysi,writtenin1669,4 andthemorealgorithmicallystructured Demethodis,writtenin1670–1671.5 Leibniz’sinventioncame

2 RichardC.Brown(2012),118,saysofhisearlycorrespondencethat‘onedetectsafeeling thathepromisedmorethanheactuallyhadachieved,sincehisannouncementsofgrandiose discoveriesoftenevaporateduponinspection.Thereiscertainlysometimesatoneof boastfulnessinLeibniz’scorrespondencethatcontrastsunfavourablywiththebusinesslike directnessofNewton’.Leibnizwasalsoamasterattheartofostentatiouslypraisinghis rivalsinpublicwhileattackingtheminprivateorcondemningtheminanonymousreviews.

3 MP I,400–448.Theearliermethodsoftangentsandquadraturewerealsoconceived almostexclusivelyingeometricterms,diﬀeringsigniﬁcantlyinstructurefromthecalculus methodswhichfollowed.Though,withhindsight,wecanseethattheindividualresults wereequivalenttosomeofthoselaterachievedbycalculusmethods,thecalculuswasby nomeansaninevitableconsequencewaitingtohappen.Brown(2012)discussesthisin relationtomathematicianslikeBarrowandtheearlyLeibniz.

4 MP II,206–247.

5 MP III,322–353.Guicciardini(2009a)considersthisasNewton’s‘masterpiece’in algebraiccalculus(179,341,368).

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Hibernal. Wintry, brumal, arctic, glacial, frigid.

A. Summery, balmy, zephyrous, halcyon, tropical.

Hide. Conceal, secrete, mask, dissemble, protect, store, disguise, screen, cover, burrow, ensconce; suppress, shelter, withhold, cloak, veil, bury, inter, entomb, overwhelm.

A. Expose, disclose, discover, exhume, show, tell, raise, reveal, unveil, unmask, uncover, exhibit, confess, betray, avow, divulge, disinter, make known, lay bare, lay open, publish, advertise, manifest, promulgate, admit; strip.

Hideous. Frightful, dreadful, appalling, horrible, ghastly, terrible, horrid, grim, shocking, grisly; unshapely, ugly, monstrous.

A. Graceful, beautiful, attractive, captivating.

High. Prominent, superior, distinguished, preëminent; dignified, great, admirable; recondite, abstruse, occult, profound, dark, obscure, transcendental; proud, haughty, arrogant, supercilious, lordly; boastful, ostentatious, bragging, vainglorious; despotic, domineering, overbearing, tyrannical; turbulent, violent, strong, tumultuous, boisterous; extreme; complete, full; dear; shrill, acute, sharp, high-pitched; northerly, southerly; early, primeval; capital, principal; strong-flavored; noble, exalted, steep, tall, towering, uplifted, elevated, eminent, lofty.

A. Low, base, degraded, inferior, mean, short, stunted, depressed, dwarfed, ignoble.

Hinder. Delay, embarrass, oppose, prevent, stay, stop, retard, hamper, impede, baffle, encumber, check, bar, clog, counteract, frustrate, foil, interrupt, obstruct, resist, thwart, block, balk, debar.

A. Quicken, hasten, speed, accelerate, expedite, enable, facilitate, promote.

Hinge. Turn, depend, hang, be dependent; move, work, rotate, circulate.

A. Halt, jar, grate, precipitate, abrade; give, fail.

Hire. Engage, commission, rent, employ; bribe, buy up; lease, let.

A. Buy, purchase.

History. Annals, chronicle, recital, memoir, narrative, record, register, story, account, archives, narration, muniment, memorial, autobiography, biography.

A. Fiction, fable.

Hit. Strike; reach, attain, win, secure, gain; suit, accord with; clash, collide; succeed, be successful; chance, hazard, touch, mistake.

A. Fail, err, miss, mischance, swerve, deflect, overshoot.

Hitch. Catch, get stuck or impeded; go by jerks; fasten, unite, connect, tie, attach; bar, stick, stickle, jam.

A. Run, glide, slide, rotate, flow, continue.

Hoard. Store, deposit, save, garner, husband, hive, accumulate, amass, treasure.

A. Waste, squander, dissipate, scatter.

Hoarse. Husky, raucous; grating, rough, harsh, low, guttural, gruff.

A. Melodious, rich, mellow, sweet, mellifluous.

Hoary. Hoar, white, gray, silvery, frosty.

A. Dark, raven, jet, black.

Hoax. Deceive, cheat, impose upon; befool, bamboozle, trick, dupe.

A. Guide, enlighten, inform, undeceive, direct, regulate, correct.

Hobby. Nag, hobby-horse; pursuit, whim, amusement, specialty, idiosyncrasy.

A. Nuisance, horror, aversion, incubus, bugbear, scarecrow.

Hold. Possess, retain, have, occupy; clasp, grasp, clutch, clinch; restrain, confine, imprison, detain; bind, fasten, unite, connect; stop, stay, arrest, suspend, withhold; support, maintain, sustain, continue, prosecute; embrace, entertain, cherish; heed, regard, consider, notice, judge, esteem, count, reckon, deem; contain, admit; celebrate, solemnize; assemble, convene; cohere, adhere,

cling, stick, cleave; be firm, be fast, persist, last, endure; be derived; think, be of opinion, believe; stand, be true.

A. Drop, surrender, fail, abandon, desert, release, forego, vacate, concede, break, cease; speed, accelerate; give, dispense; disperse.

Hollow, a. Empty, void, vacant, vacuous, cavernous; insincere, false, faithless, hypocritical, treacherous, deceitful, false-hearted, pharisaical; artificial, concave, insubstantial, flimsy, transparent, senseless, unsound; deep, low, rumbling.

A. Full, solid, firm, sincere, well-stored, strong, true, sound, genuine, substantial.

Holy. Hallowed, sacred, consecrated, blessed, devoted, set apart; righteous, saintly, spiritual, devout, saintlike, godly, religious, heavenly-minded, pious, pure; reverend, sanctified, divine.

A. Cursed, polluted, unsanctified, unconsecrated, unhallowed, wicked, worldly, abominable, common, impure, unholy, secular, profane, evil.

Homage. Fealty, allegiance, devotion, loyalty, fidelity; reverence, obeisance, respect, deference, duty, service, honor; worship, adoration; affiance, submission, veneration.

A. Treason, rebellion, defiance, insubordination, disaffection.

Home. Habitation, hearth, residence, house, abode, dwelling, domicil, fireside, hearthstone, ingleside.

Homely. Domestic, homelike; plain, coarse, uncomely, inelegant, homespun; rather ugly.

A. Handsome, beautiful, courtly, refined, elegant.

Honest. Honorable, fair, open, straightforward, equitable; upright, virtuous, conscientious, just, true, faithful, trusty, reliable, trustworthy; genuine, thorough; decent, reputable, respectable, creditable, suitable, proper; chaste; truthful, ingenuous, sincere, frank, unreserved, candid, good.

A. Lying, unscrupulous, mendacious, untrue, deceitful, dishonest, false, hypocritical, fraudulent, disingenuous, perfidious, faithless, treacherous, unfaithful, traitorous; dishonorable, improper, wrong, insincere, vicious.

Honesty. Integrity, uprightness, probity, justice, fairness, equity, honor, fidelity, faithfulness; truth, truthfulness, veracity; genuineness, thoroughness; chastity, virtue; sincerity, candor, frankness, openness, unreserve, ingenuousness; straightforwardness, rectitude.

A. Insincerity, trickery, dishonesty, guile, fraud, deception, unfairness, chicanery.

Honor. Veneration, reverence, respect, homage, deference, civility; dignity, elevation, distinction; majesty; reputation, repute, fame, esteem, credit, glory, consideration; integrity, probity, rectitude; pride, nobility, eminence, high-mindedness, spirit, self-respect, grandeur, renown.

A. Contempt, irreverence, disrespect, slight, obscurity, demoralization, degradation, debasement, disgrace, cowardice, infamy, dishonor.

Honorable. Honest, upright, high-minded, illustrious, noble, great, just, fair, trustworthy, conscientious, virtuous, estimable, reputable, right, proper, creditable, equitable.

A. Dishonorable, dishonest, false, treacherous.

Honorary. Unofficial, nominal, gratuitous, titular, unremunerative.

A. Professional, official, remunerative, jurisdictional.

Hoot. Shout; cry like an owl; denounce, hiss, execrate, cry down, decry, sibilate.

A. Salute, welcome, cheer, honor, acclaim, eulogize.

Hope. Trust, confidence, faith, reliance; expectancy, expectation, possibility; dependence; anticipation, prospect, longing, vision, desire.

A. Despair, despondency, distrust, abandonment, disbelief, abjuration.

Horizontal. Plain, flat, level, even, plane.

A. Vertical, inclined, uneven, slanting, sloping, hilly, broken, irregular, rough, rolling, rugged.

Horrible. Horrid, frightful, terrible, terrific, alarming, dire, portentous, appalling, horrific, horrifying, formidable, awful,

harrowing, dreadful, hideous, fearful; abominable, ghastly, detestable, hateful, direful.

A. Lovely, desirable, enjoyable, attractive, beautiful, fair, pleasant, amiable.

Horror. Fright, alarm, dread, fear, consternation, terror, affright, dismay, panic; abomination, abhorrence, detestation, disgust, hatred, shuddering, antipathy; shrinking.

A. Love, attraction, enticement, allurement.

Horse. Steed, charger, stallion, gelding, mare, colt, pony, nag, courser, barb, filly, palfrey; cavalry, horsemen; stand, support, frame.

Hospitable. Generous, liberal, bountiful, open, kind, unconstrained, unreserved, receptive, large-minded; sociable, neighborly, charitable.

A. Unsociable, exclusive, retired, recluse, unneighborly, churlish.

Host. Entertainer; innkeeper, landlord; army, legion; multitude, horde, throng, number, assemblage.

A. Handful, sprinkling, group, knot, corps, section; guest, traveler, boarder, lodger.

Hostage. Sponsor, bail, surety.

A. Dictator, conqueror.

Hostile. Inimical, unfriendly; adverse, opposite, contrary, repugnant, opposing, opposed.

A. Friendly, kindly, amicable, neighborly, cordial, congenial.

Hostility. Enmity, animosity, hatred, unfriendliness, ill will; opposition, repugnance, variance, contrariety.

A. Companionship, congeniality, sympathy, harmony, fellow-feeling, concord, alliance, kindliness, friendship.

Hot. Burning, fiery, scalding, heated, very warm; irascible, impetuous, excitable, passionate, hasty, furious, violent; ardent, fervent, vehement, eager, glowing, animated, fervid; biting, pungent, sharp, acrid, peppery, stinging, piquant, high-flavored; choleric.

A. Cold, frigid, cool, arctic, chilled, chilly, boreal, bleak, wintry, frosty, icy; apathetic, unresponsive, unfeeling, stoical, passionless, uninspiring, dull, dead, indifferent, unconcerned.

Huge. Immense, enormous, colossal, vast, bulky, stupendous, gigantic, elephantine, Herculean, Cyclopean, large, great, monstrous, prodigious.

A. Petty, pigmy, puny, undersized, small, minute.

Human. Cosmical, ethnical, anthropological, rational, civilized.

A. Inhuman, beastly, irrational, animal, brutish.

Humane. Kind, benevolent, benignant, accommodating, tender, compassionate, charitable, sympathetic, gentle, clement, kindhearted; tender-hearted; elevating, refining, cultivating, rational, spiritual, humanizing; benign, merciful, gracious, pitying, human, forgiving.

A. Barbarous; inhuman, unkind, cruel, unmerciful.

Humanity. Mankind; benevolence, kindness, philanthropy, tenderness, sympathy, charity, humaneness, good nature; human spirit, rationality, reason, culture; man, compassion, sensibility.

A. Unkindness, cruelty, inhumanity, irrationality, bestiality, barbarity.

Humanize. Soften, make humane; civilize, cultivate, refine, polish, improve, enlighten, reclaim, educate; ameliorate, christianize.

A. Barbarize, degrade, debase, brutalize, depress.

Humble. Meek, modest, unassuming, unobtrusive, lowly, unpretending, submissive, small, poor, low; obscure.

A. High, lofty, assuming, pretentious, proud, boastful, arrogant, eminent.

Humid. Damp, wet, moist, vaporous, dank, spongy.

A. Dry, arid, moistureless, parched.

Humor, n. Disposition, temper, bent, propensity, bias, predilection; mood, frame of mind, fancy, caprice, whim, freak, vagary, crotchet; pleasantry, fun, jocularity, wit, facetiousness.

A. Nature, personality, mind, purpose, will, seriousness.

Humorous. Facetious, jocular, jocose, funny, comical, sportive, comic, ludicrous, pleasant, witty.

A. Grave, serious, sober, matter-of-fact, solemn, sad.

Hurry, n. Flutter, flurry, precipitation, confusion, bluster, bustle, agitation, perturbation; haste, despatch, celerity, expedition, quickness, promptness.

A. Slowness; composure.

Hurry, v. Haste, hasten, move quickly; urge, speed, expedite, despatch, accelerate.

A. Delay, retard, slow down; loiter, saunter, move slowly.

Hurt, n. Damage, harm, injury, mischief, disadvantage, detriment, wound.

A. Benefit, pleasure.

Hurt, v. Injure, harm, damage, impair, mar; pain, wound; grieve, afflict, bruise.

A. Heal, soothe, console, repair, benefit, compensate, reinstate.

Hurtful. Harmful, injurious, mischievous, detrimental, deleterious, disadvantageous, baneful, noxious, prejudicial, pernicious, baleful.

A. Helpful, beneficial, advantageous, wholesome, salubrious, good, sanative, remedial.

Hybrid. Mixed, impure, mongrel, mule, half-breed.

A. Pure, unmixed, thoroughbred.

Hypocrisy. Formalism, Pharisaism, cant, pietism, sanctimoniousness, assumed piety; deceit, deception, dissimulation, false profession, imposture; sanctimony, pretense, sham, affectation.

A. Sincerity, transparency, truth, honesty, genuineness, candor, frankness, openness, ingenuousness, truthfulness.

Hypocrite. Deceiver, impostor, pretender, cheat, dissembler; Pharisee, formalist.

A. Saint, believer, Christian; dupe, bigot, fanatic, simpleton.

Hypocritical. Canting, Pharisaical, sanctimonious; insincere, dissembling, false, hollow, faithless, deceitful, unctuous, smug, smooth, mincing.

A. Candid, truthful, sincere, plain-spoken, transparent, genuine.

Hypothesis. Scheme, speculation, system, supposition, conjecture, guess, surmise, theory.

A. Certainty, demonstration, evidence, fact, proof, discovery.

IIdea. Concept, conception, impression, judgment, plan, opinion, purpose, conceit, design, fancy, pattern, thought, theory, belief, image, imagination, notion, supposition, ideal, apprehension, fantasy, model, sentiment, archetype; doctrine, understanding; fiction.

A. Object, form, subject; substance, fact, actuality, reality.

Ideal, n. Idea, archetype, original, model, standard, prototype.

A. Fact, performance, reality, practice, act, accomplishment, achievement, action, realization, attainment, development, doing, incarnation, embodiment, execution.

Ideal, a. Mental, conceptional, intellectual, notional, creative, spiritual, poetical, supposititious, unreal, fictitious, imaginary, fanciful, imaginative, chimerical.

A. Physical, material, visible, tangible, historical, substantial, real, actual, palpable.

Ideality. Imagination, conception, invention, fancy, creativeness, genius.

A. Imitation, uninventiveness, copyism, unimaginativeness; literality.

Identical. Same, selfsame, not different; particular.

A. Different, separate, contrary.

Identify. Prove identical, make identical, confound; unite, integrate, incorporate, recognize, verify.

A. Divide, disunite, confound, confuse, overlook, mistake.

Identity. Sameness, unity, oneness, union, personality, individuality, convertibility.

A. Difference, separateness, distinctness, contrariety, plurality.

Idiocy. Imbecility; foolishness, fatuity, irrationality; aberration, insanity; stupidity, folly, senselessness, incapacity.

A. Intelligence, sagacity, wisdom, capacity, brilliancy, astuteness, acuteness, sense, common sense, soundness; sanity, judgment.

Idiom. Specialty, phrase, turn, peculiarity, characteristic.

A. Barbarism, solecism.

Idiosyncrasy. Peculiarity, idiocrasy; constitution, temperament, specialty, characteristic, individuality, singularity, eccentricity.

A. Community, universality, generality.

Idiot. Fool, natural, imbecile.

A. Sage, authority, luminary.

Idle. Unbusied, unused, leisure; useless, ineffectual, fruitless, bootless, unavailing, vain, abortive, futile; trifling, trivial, unimportant, trashy, foolish, unprofitable; waste, empty; indolent, inert, lazy, slothful, unoccupied, vacant, inactive, sluggish, unemployed.

A. Active, busy, diligent, industrious, employed, working; occupied; tilled; filled, populated; assiduous.

Idolize. Deify; adore, worship, reverence, venerate.

A. Loathe, abominate, execrate, abhor.

Ignoble. Plebeian, vulgar, untitled, baseborn, low, mean, rustic, peasant; worthless, insignificant, contemptible; dishonorable, disgraceful, inferior, unworthy; humble.

A. Honorable, eminent, exalted, noble, lordly, illustrious, grand, notable.

Ignominious. Dishonorable, infamous, disgraceful, shameful, scandalous, disreputable, opprobrious; despicable, base, deserving ignominy, contemptible.

A. Honorable, creditable, reputable, estimable, worthy.

Ignominy. Dishonor, disgrace, discredit, shame, infamy, disrepute, contempt, obloquy, opprobrium, scandal, abasement, odium; reprobation, reproach.

A. Credit, honor, reputation, glory, luster, distinction, renown.

Ignoramus. Smatterer, novice, wiseacre, dunce, simpleton, dullard, greenhorn, numskull.

A. Savant, sage, luminary.

Ignorance. Illiteracy, stupidity, nescience, blindness, darkness.

A. Knowledge, wisdom, sense, learning, erudition.

Ignorant. Illiterate, unlearned, unlettered, unskilled, untaught, untutored, uneducated, ill-informed, uninstructed, uninformed.

A. Educated, learned, instructed, sage, wise, skilled, cultured, trained, well-informed, cultivated.

Ignore. Disregard, neglect, overlook, not recognize; set aside, reject; disown, repudiate.

A. Own, notice, recognize, mark, visit, avow, claim.

Ill, n. Wickedness, depravity, evil; misfortune, calamity, affliction, misery, harm, pain.

A. Good, blessing, fortune; righteousness, integrity, honor.

Ill, a. Bad, evil, unfortunate, unfavorable; wicked, wrong, iniquitous, naughty; sick, ailing, diseased, disordered, poorly, indisposed; cross, crabbed, surly, peevish, hateful, malicious; illfavored, ugly.

A. Well, strong, good, vigorous, healthy, robust, hearty, hale.

Ill-bred. Impolite, uncivil, uncourteous, uncourtly, uncouth, unpolished, rude, ill-behaved, ill-mannered.

A. Polite, well-behaved, civil, refined, courteous.

Illuminate. Light, illumine, illume; enlighten, make wise, instruct, inspire; emblazon, irradiate.

A. Darken, obscure, bedim, mislead, delude.

Illusion. Delusion, hallucination, deception, error, fallacy, mockery, fantasy, phantasm, chimera; dream, vision, myth.

A. Body, substance, form, reality, actuality, essence.

Illusive. Delusive, deceptive, deceitful, fallacious; visionary, unreal, disappointing, fugitive, erroneous, false, imaginary, illusory, chimerical.

A. Substantial, real, true, satisfactory, solid, permanent.

Illustrate. Elucidate, explain, exemplify, make clear; interpret, demonstrate, represent, embody, paint, image; adorn with pictures.

A. Obscure, misinterpret, confuse, mystify, darken, misrepresent.

Illustrious. Glorious, splendid, brilliant, bright, radiant; famous, famed, noted, renowned, distinguished, celebrated, eminent, signal, remarkable, conspicuous; deathless, noble.

A. Ignominious, disgraceful, infamous, inglorious, disreputable.

Ill will. Malevolence, unkindness, malice, enmity, hatred, hate, rancor, envy, grudge, uncharitableness, ill nature; antipathy, dislike, aversion.

A. Good will, benevolence, beneficence.

Im- or In-. This prefix, which is regularly in-, and which becomes il- before l, ir- before r, and im- before a labial, means in, into, on, or among, or denotes the negative not, or, occasionally, has a simple intensive meaning. Such words as begin with this prefix without modification of the combined meaning of the prefix and root word, will be easily derived from the antonyms and synonyms of the root words. Others of more derived meaning are found here.

Image. Statue; idol, object of worship; likeness, effigy, figure, resemblance, similitude, representation, picture; trope, metaphor; idea, copy, conception, fiction, shadow, vision.

A. Person, original, substance, subject, object, reality, truth, verity.

Imagery. Phantasm, phantom, vision, dream; tropes, figures of speech, poetry, fancy, illustration, metaphor, similitude.

A. Prose, statement, fact.

Imagination. Conception, invention, ideality, fancy, fantasy, creative power; esemplastic faculty; idea, notion; contrivance, scheme, device, plot; illusion.

Imaginative. Inventive, creative, plastic, poetical, esemplastic, poetic; conceptive, romantic, ideal, original.

A. Unimaginative, unpoetical, prosaic, unromantic, literal, uninventive, matter-of-fact.

Imagine. Conceive, think, image, fancy, picture; devise, contrive, frame, project, invent, create, mold; suppose, assume; deem, apprehend, believe; surmise, understand, fabricate, presume.

A. Represent, exhibit, depict, prove, demonstrate, verify, substantiate.

Imbecile, a. Weak, feeble, helpless, infirm, decrepit; foolish, witless, idiotic, driveling, fatuous.

A. Shrewd, clever, sagacious.

Imbecility. Weakness, debility, feebleness, infirmity, helplessness; foolishness, childishness, idiocy, fatuity, dotage, senility.

A. Strength, energy, virility, vigor, power.

Imbibe. Absorb, take in, suck in, swallow up; receive, gather, gain, acquire, get, pick up; assimilate, learn.

A. Discard, reject, renounce, disavow, abjure, repudiate.

Imitate. Copy, follow, pattern after; mimic, ape, mock, impersonate, take off; burlesque, travesty, parody; represent, resemble, portray, depict, repeat, counterfeit.

A. Misrepresent, caricature, alter, vary, distort, remodel, differentiate, dissimilate, modify.

Imitative. Imitating, copying, mimicking, aping, apish, caricaturing, unoriginal, servile.

A. Original, creative, inventive.

Immaculate. Spotless, unspotted, stainless, unsullied, unsoiled, untainted, unblemished, untarnished, clean, pure, undefiled; innocent, guiltless, sinless, faultless, fair, holy, saintly; virgin, unpolluted.

A. Impure, corrupt, sinful, contaminated, defiled, polluted, tainted, spotted.

Immanent. Intrinsic, inherent, internal, indwelling; empirical; innate, subjective, congenital, ingrained, natural, implicit.

A. Emanant, transitive, developed, projective, exsilient, phenomenal, explicit, accidental, transcendental, transeunt.

Immaterial. Incorporeal, unbodied, unfleshly, spiritual, supersensible; unimportant, insignificant, unessential, nonessential, trivial, trifling.

A. Material, physical, important, corporeal, essential.

Immature. Unripe, crude, raw, green, unformed, unprepared, imperfect, rudimentary, unfinished; premature, hasty, unseasonable, untimely; undeveloped.

A. Ripe, complete, developed, mature, finished.

Immeasurable. Illimitable, unbounded, boundless, limitless, measureless, immense, infinite; vast, unfathomable.

A. Finite, limited, circumscribed, restricted, shallow, bounded.

Immediate. Proximate, close, near, next; direct, unmediated; instantaneous, instant, present; contiguous.

A. Distant, remote, mediate, future.

Immediately. Presently, this instant, straightway, directly, forthwith, at once, now, right off, instantly, without delay.

A. Hereafter, by-and-by, after a while, sometime.

Immemorial. Olden, ancient, hoary, archaic, primitive, remote, time-honored, primordial.

A. Recent, modern, late, fresh, upstart.

Immerse. Dip, plunge, submerge, sink, douse, duck, bury; soak, steep, macerate, drown, inundate, overwhelm.

A. Dry, drain, parch, ventilate, air, ground, strand.

Immigration. Migration, colonization, settlement.

A. Exodus, emigration.

Imminent. Impending, hovering, threatening.

A. Improbable, doubtful, unexpected, unlikely, contingent, chimerical, problematical; warded, staved, escaped.

Immunity. Freedom, exemption, release, exoneration; prerogative, privilege, right, liberty, charter, franchise; dispensation.

A. Liability, obligation, jurisdiction, impost, amenability, burden.

Imp. Sprite, hobgoblin, demon, devil, flibbertigibbet, scamp, brat.

A. Cherub, angel.

Impact. Impulse, shock, impression, stroke; collision, contact, striking, impinging; application.

A. Isolation, separation, interval, removal, avoidance, noncontact, shave.

Impair. Deteriorate, vitiate, injure, harm, make worse; lessen, diminish, decrease; enervate, weaken, enfeeble; reduce, damage.

A. Enhance, improve, repair, augment, better, increase.

Impassioned. Passionate, vehement, impetuous, animated, exciting, glowing, intense, fervid, fervent, warm, ardent, zealous; spirited.

A. Cool, impassive, unimpassioned, apathetic, indifferent. Impatience. Uneasiness, disquietude, restlessness; haste, vehemence, eagerness, precipitation, impetuosity; heat, violence of temper, irritability, irritableness.

A. Patience, calmness, endurance, composure, leniency, submission, forbearance, long-suffering.

Impediment. Bar, hindrance, obstacle, obstruction, difficulty, clog, encumbrance, stumbling-block, check.

A. Assistance, aid, benefit, help, relief, succor, advantage; aidance, support, furtherance.

Imperative. Commanding, authoritative, peremptory; binding, obligatory; urgent, irresistible, dictatorial, inexorable, compulsory.

A. Indulgent, lenient, supplicatory, mild, optional, discretional, entreative.

Imperial. Belonging to an empire, kingly, regal, sovereign, royal; majestic, grand, magnificent, exalted, great, noble, supreme, consummate, superb.

A. Ignoble, servile, slavish, beggarly, mean, paltry. Imperious. Magisterial, dictatorial, despotic, domineering, tyrannical, overbearing, lordly, haughty, arrogant, authoritative, exacting.

A. Yielding, compliant, submissive, gentle, mild, docile, ductile.

Impetuous. Fierce, vehement, violent, furious, passionate, precipitate, hasty, headlong, over-zealous, reckless, rash, excitable.

A. Careful, slow, deliberate, thoughtful, reflective, leisurely. Implement. Utensil, tool, appliance, instrument.

A. Labor, work, science, art, agriculture, manufacture.

Implicate. Entangle, enfold, involve, connect, associate, compromise, charge, incriminate.

A. Disconnect, extricate, acquit, dissociate.

Implication. Entanglement, involution; inference, conclusion; intricacy, complication; concealment, latency; allusion, insinuation, innuendo, adumbration.

A. Arrangement, system, orderliness; manifestation, expression, exposition, demonstration, production.

Implicit. Understood, implied, inferred, tacit; unreserved, unhesitating, firm, steadfast, unshaken, undoubting; involved.

A. Expressed, explicit, developed, stated, plain, specific, unambiguous.

Imply. Involve, import, include, signify, mean, indicate, suggest, hint, denote.

A. Express, declare, state, pronounce.

Import, n. Meaning, sense, purport, drift, signification, gist, spirit, bearing, tenor, intention.

A. Statement, proceeding.

Import, v. Bring into; purport, denote, imply, betoken, signify, mean; concern, be of significance to; introduce.

A. Export, banish, exile, send abroad.

Importance. Consequence, moment, weight, significance, momentousness, import, concern; avail; self-importance, pomposity.

A. Nothingness, insignificance, unimportance, immateriality.

Important. Grave, weighty, momentous, serious, material, significant; influential, prominent, pompous, self-important, consequential; expressive, leading, main, relevant, considerable, essential, great, dignified.

A. Insignificant, trivial, inconsiderable, irrelevant, secondary, petty, mean, uninfluential, minor, unimportant.

Importunate. Urgent, pertinacious, pressing, teasing, busy, solicitous, overurgent, overentreative.

A. Modest, diffident, self-reliant, self-respecting.

Importune. Urge, entreat, press, solicit, dun, beset, pester, tease, worry, trouble.

A. Surrender, sacrifice, abandon; grant, bestow.

Impose. Put, set, lay, place; appoint, enjoin, prescribe; obtrude, palm off, pass; inflict, subject.

A. Remove, disburden, unload, free; hold up, arrest, disclose.

Imposing. Stately, august, majestic, grand, noble, commanding, impressive; striking, effective, dignified.

A. Petty, undignified, unimposing, insignificant, paltry, puny.

Imposition. Imposing, putting, placing, laying; burden, levy, tax, constraint, oppression, injunction; deception, fraud, artifice, trickery, imposture, cheating; presumption, exaction, encroachment.

A. Sanction, warrant, authority; truth, verity, fact, certainty, verification, genuineness, authenticity, honesty.

Impost. Tax, duty, custom, excise, levy, toll, tribute, rate; imposition.

A. Revenue, proceeds, exemption, immunity.

Impostor. Deceiver, pretender, cheat, hypocrite, knave, charlatan, mountebank, rogue, Pharisee, trickster, dissembler.

A. Guide, enlightener, detector, undeceiver.

Imposture. Cheat, trick, deception, imposition, fraud, ruse, delusion, dodge, artifice, wile, deceit, stratagem, hoax.

A. Truth, fact, verity, reality.

Impotence. Disability, incapacity, incompetence, powerlessness, weakness, inefficiency, infirmity, frailty, imbecility, inability, incapability, helplessness, disqualification.

A. Capacity, vigor, qualification, ability.