Mach Boltzmann

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Brit. 7. Phil. Sci. 36 (I985), 299-329 Printed in Great Britain 299

DiscussionsAN HISTORICAL NOTE ON ERNST MACH

A number of philosophers ncluding Peter Clark [I976] & [I982]) andPaulFeyerabendI980] in thisjournalandLarryLaudanI976] and MichaelGardner I979] elsewherehave triedto suggestthat perhapsErnst Mach'soppositionto atomsand Ludwig Boltzmann'skinetic theoryof gaseswasscientificand justified.Much as I respectMach's independent udgmentand expeciallyhis warningsaboutexcessive dealisationn physics I cannotagree.As anhistorianof science, authorof a biographyof Mach [I972], andasco-editorof forthcomingvolumes on the correspondence espectivelyofMach andhis principalmethodological ritic Ludwig BoltzmannI do notbelievethatthe attempt o whitewashMach'spositionon atomismwill standup. It is understandablehat philosophersmaybe reluctant o believethatphilosophicalviews, assumptions,or prejudicescan stand in the way ofscientificprogress,but sometimesthe evidenceis too strong to be easilyarguedor willed away.PerhapsMach's oppositionto 'billiardball'atoms shouldhave includedsupportfor atoms as changing,perishable corpuscles' uch as Boltzmannstrongly advocated,but it never did. And perhapsMach'soppositiontoBoltzmann'skinetictheory shouldhave been groundedon real technicaldifficultiessuch as whatClarkcalls 'the problemof the anomalous pecificheat ratios'or real defectsin his use of idealisedmolecularmodels ratherthanseeminglyautomatic ejectionof anythingand everythingbasedontheatomictheory,but it never did. Inprinciple Mach was remarkablyolerant.He allowed hat the atomictheorymight have'provisional alue' n scienceand were there no need to reconcile the philosophicalassumptionsofpsychologywith thoseof physics,he would haveno objection o physicistscontinuingto use the atomic theory.But in practice he was adamant.Hemade no use of the atomic theory in his own scientificwork duringhismatureyears,not evenconcerning hockwaveswhere he theorymight havebeen useful.In my [I972] book on Mach I failed to mention the many technicalobjectionsto Boltzmann'skinetic theory which accompanied he manyphilosophical ttacksby Mach,Ostwald,andtheirfollowers.My reasonwasthat virtuallyall of the technicalobjectionswere highlymathematical ndmost appeared n English ournals,and therewas and is no evidencewhichhas been made availableto me that Mach had ever read the technicalobjections or was even aware of them. His criticisms of Boltzmann'sstatisticalinterpetationof the second law of thermodynamicswas quite


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300 3fohnBlachmoreindependentof scientific objections,apart from the largelyphilosophicalreversibilityand recurrenceobjectionsof Loschmidt and Zermelo. Topartly comperusate or my 'oversight' the forthcoming edition ofBoltzmann'scorrespondencewill include the technical objections byCulverwell,Bryan, Burburry,Watson, and others including Boltzmannhimself whichoriginallyappearedas letters to the editor in Natureduringthe middle I890S.PerhapsMach was too clever to be a 'simple-mindedpositivist'as PaulFeyerabend upposes.1Perhapsno philosopher s literallysimpleminded,but his reductionof the physicalworld to sensationsand his beliefthat allrealknowledges scientificwas surelypositivisticas it was understoodat thetime, and he did sharethe simplemindedopposition o atoms whichmanypositivists held. His reasons were -not primarly physical; they werephilosophical,f one may labeltheopinionsof a posititivistasphilosophical.What were Mach's philosophicalobjections?Peter Clarksupposes thathis opposition to use of the atomic theory was based on his notion of'Denkokonomie' s if one should alwayspick the simplest heory n scienceand is if one could imagine a simpler approach han atomism. Mach'soppositionto the realityof 'billiardball'atoms (a very differentquestion)was that as eternal and unchanging substances' hey were metaphysicaland ncapablenprinciple f beingobserved.On the otherhand, t isnot clearwhy he seemed unable to appreciate hatby the late nineteenthcentury alargenumberof physicistsand chemistswere already hinkingof atoms interms of divisible and transientcorpuscles which were not necessarilysubject to Mach's philosophicalobjections.(His partialparalysis n I898andwithdrawal romuniversity ife in I 90 I naturallydid not helphim keepup with the latest opinions n physics, but his fairlyrapidreturn o writingandpublishingwouldsuggest hatheshouldhaveknownwhatwasgoing on.His strong nterest n Einstein'sspecial heoryof relativityduring 909 andI9I0 wouldindicatehe was still capableof followingrecentdevelopments.)There is a belatedly published story by Ludwig Boltzmann's lastassistant,StefanMeyer I950] which I include n my biography[I972], pp.3I9-23) thatMach changedhis mindabout atom-s fter lookingthroughaspinthariscope nd observing he scintillations,but since Mach wrote andpublishedattackson the reality of atoms as late as I9I0, if there was aconversion t presumablymust have been after that year, that is, betweenI 9 I 0 andhisdeath n I 9 I 6. The quotationagainst he realityof atoms s to befound in a 'Kampfschrift' gainstMaxPlanckand assortedcritics [I9I0]& [I9I9], pp. I0-I I)The resultsof the atomictheory can be just asmanifoldand useful if one is not insuch a hurry to treat atoms as realities.Therefore all honor to the beliefs ofphysicists But I myself cannot make this particular belief my own (trans.Blackmore,I972], p. 32I).1 Note from Paul Feyerabend, ostmarked January 984.


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An HistoricalNoteonErnstMach 30IThe only evidence I have been able to find from Mach'spublishedorunpublishedwritingsthat he had begun to have second-thoughtsaboutatomsseemsto surface n his last 'Notizbuch'from I9I0 to I9I4. On page37 he writeswith a shaky eft hand,presumablyduringI9I I:

Atomebewegensichim RaumundZeit.Wasist RaumundZeit?Raum st vonderMaterieabstrahiert, on derAusdehnungderMaterie.Zeitvon derVeraenderungderMaterie.Andpage I32, most likelyfrom I9I4 in anextremely aintandshaky efthand.(Hewasseventy-sixyearsoldandhisparalysiswouldstillnot lethimwritewith his righthand):

Atomenichtoccult?1II

Concerningkinetictheory,it may be well to keep in mind that there is adifferencebetweenatomistswhoobjectedto one ormoretechnicalaspectsof Boltzmann'swork(suchasvirtuallyallof the contributorso the kineticdiscussionin the British Isles) but who in generalfavouredthe kinetictheoryandanti-atomistswhoopposed hekinetic heory nprinciplesuchasMach,Ostwald,andtheirfollowers).Also, it mightbehelpfulto rememberthat especially on the Continentphysicistswith a strong knowledgeofmathematicswere still rarebirds. (Even the extensiveinterestin kinetictheoryin EnglandandIreland,whichpresumablyhadbeenstimulatedbyMaxwell,was led primarilyby mathematicianswith an interest n physicsratherthan by professionalphysicists,though Lord Kelvin would be anexception.)MostContinentalphysicists suchasMach)wereexperimental-istswhodidnotfeelcompetent ohandlecomplexmathematics.Theycouldcarefullyfollow neither the technical argumentsof Boltzmannnor hiscritics.To justify this weakness t was natural o appealboth to a formofthermodynamiceductionismandto positivistarguments hatthe purposeof sciencewas merely to discoverrelationsbetweenphysicalappearancesandto remindeachotherthatatomsandmoleculeswerestillunobservable(thoughLoschmidtandKelvinhadcalculatedheapproximateizeof somemolecules namannerconsistentwithAvogadro'sawasearlyasthemiddleI 860sandbythe I 8gosnewelements o fill in theperiodicchartwerebeingdiscoveredalmosteveryyear).Mach'sNotizbucherarelocated n the Ernst-Mach-Institut,Eckerstrasse , Freiburg mBreisgau.Therearesixty-five n number romthe I860S until I9I4. They includedraftsofpapers,diagrams, omments,addresses, ists of namesto sendpreprintsandbooksto, butafterMach'spartialparalysisn I898 theremarks reshorterand ncreasinglymoredifficulttoread.Mach ypedhiscorrespondencefter 898 andhecontinued osendandreceivemanylettersafter 9 I4 until hisdeath woyears ater.Noneofhis Notizbucher ndveryfewof theletterswrittenby him havebeenpublished,but FriedrichStadlerhasprepareda bookofessayswhichincludesthe entiretyof the lastNotizbuchas an appendix.The bookwill bepublished n Viennaandshouldappearn I986.


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302 ffohnBlackworeTherecan belittle question hatmorephysicistsatleast nCentralEuropewerefamiliarwith Mach'santi-atomistic ookssuchas Erhaltung erArbeit

[I 872], Die Mechanik 883], and Principiender WarmelehreI 896] thanwithtechnicalobjections o Boltzmann'skinetic heorypublishedabroadnEnglish.As alreadymentioned,semi-philosophical bjections,whichstillinterestmanypeople includingSir Karl Popper [I974], such as those ofLoschrnidt nreversibility f motion[ 876] and Zermelo n hisextensionofNietzsche's 'eternalrecurrence'speculation I896] were widely known.It was Boltzmann'sanswerswhich were not sufficientlycirculatedorcomprehended(and even today his notorious 'H-theorem' can seemmindboggling).Mach's anti-atomismand oppositionto a mechanical explanation'ofthermodynamics, owever,preceded oththe argumentsof Boltzmannandthoseof his criticsand at leastonthe Continenthelpedto disposephysicistsandmany chemistsagainstBoltzmann'sworkbeforethey hadeven read t.Machstoppedusing theatomic heory n hiswork n I 863 andattackedt inI 872.Boltzmannbeganpublishing n the late I 860S, replied o Loschmidt'sobjectionsin the middle I870S, becamewell-knownfor his ideas in theI880S, and was stronglycriticizedon mathematical,physical,and philo-sophicalgroundsduringthe I 8gos.WilhelmOstwald,a co-founderof physicalchemistryandlong the mostinfluentialman in the discipline with his efficient laboratoryand vastnumbersof students, freely admittedthat Mach among the living andRobert Mayer among the dead had influencedhis thinking the most(Ostwald, [I90I]). Ostwald'santi-atomismbecameconspicuousin I892when he publisheda chemistrytextbookwith no reference o atoms.Hisattemptto substituteenergyequationsfor everythingatomisticprovokedBoltzmannandthe mathematicianFelix Klein into a devestatingreplyatLubeckduringa scientific onferencen I 895,but theinfluenceof MachandOstwaldwas so great by then thatmost physicistsand many chemistsinGermany, Austria, and France still seemed to oppose Boltzmann.Continuumphysicsappearedo be the waveof thefuture,eitherOstwald's'energeticism',Mach's 'physicalphenomenology',or Lorentz's 'electro-magneticworld-view'.Atomismseemed dead apartfrom the continuingdiscoveries fRamsayandRayleighandJ.J. Thomson'sapparent iscoveryof somethingwhich wassoon calledan 'electron'.As for the technicalobjectionsto Boltzmann'swork which weremuchdiscussed n I 895 and I 896 in England,whiletheyseemedto fit in withthegeneralopposition o dis-continuityphysicsat the timeand theanticipationthat the triumph of continuum physics was at hand, should not beovervalued,particularlyby us who have the benefit of hindsight.As JohnNyhof has pointedout in his still unpublisheddoctoraldissertationI98I]technicalobjections uchas thoseaboutanomalous pecificheatratioswerescarcely atal,as seems ratherevidentfromthe fact that both PlanckandEinsteinfrom I900 on acceptedand usedBoltzmann'smajor deas, thatis,


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An HistoricalNoteorlErnstMach 303well beforesuch technical objections had been met. Had Continentalphysicists been aware of Lakatos's theory of 'degeneratingresearchprogrammes'hey might have labeledBoltzmann'skinetictheorywith theexpression,but theywouldhave beenas wrongthenas PeterClarkappearsto be in his [I976] paper.When the continuumeuphoriahad died down(largelyas a result of Planck'squantumtheoryand Einstein'stheoryonBrownianmotion) and it becameclearthatatomswerehereto stay,the tideunderstandably egan to turnagainstthe anti-atomismof both MachandOstwalduntilOstwaldhimselfrecantedn I908 andperhapsMachin I9I4.To be sure,not all of Boltzmann'sworkhas beenretainedand therearestill occasionalcritics,but in termsof the largerpicturehe has contributedso much of value to modern physics, and by no means least to theunderstanding f Planck and Einsteinthemselvesthat to complainaboutdifficultiesn retaining heentirecorpusofhis labourwouldbe like rejectingKepler'sdiscoveriesor importancebecauseof his occasionalmysticism,technicaloversights,or his 'fourth aw'.As for Mach'sspecificobjections o Boltsmann's tatisticalnterpretationof the secondlaw, theredon'tseemto be anyexceptopposition o anythingwhichseemsto presuppose he realityof atomsanda distrustof whatMachtermed 'Lottospiel'or in Englishbingo. In point of fact, Mach was notpersuadedhatthesecond awwas essentiallydifferent romthe first.He didrepeatLoschmidt'sobjectionthat if all mechanicalmotionwas reversibleandentropywas not, then if the second awwas validsomethingwaswrongwith traditional mechanics. But he never seems to have replied toBoltzmann'sstatisticalinterpretationof the second law as an answertoLoschmidt,at least not in amathematicalmanner.Indeed,apart roma fewisolateddisparaging emarkshe did his best to ignore the entire kineticormechanicaldevelopment fter he discoveryof the first aw.In fact,when hepublishedhis Warmelehren I896 (largely o counterBoltzmann'sLubecktriumphoverOstwald he previousyear)hisbookwas severelycriticised orjust this failing.J. E. Trevor,who likedMach'sotherbooks,couldnot helpmentioning n his review I897]:Mach's treatmentof the early history of the ltheoryof heat, say of the periodprecedingGibbsarousesonlyadmiration, ut the remainder f thebookhas by farneitherthe same completenessnor the same finish.Horstmannss racticalappli-cation of thermodynamicmethod to chemical action is neglected, Massieu'scharacteristicunctions,Helmholtz's heoryof free energyand its application,V.Oettingen'santitheticdevelopments ndthe magnificentworkof Gibbs areall butlittle more thancited. This is indefensible,especiallysince the authorbringshistreatment o far downinto the presentas to touchupon the recentdiscussionon'energetics'.Then again,the assemblageof both new andreprintedphilosophicalsketchesat theclose, instructive s theyare, s verydisconnected;hebookasa wholeis neithera collectionof scientificpapersnor a well-rounded ritical reatiseon itssubject, we get the impression hat a splendidwork,partially inishedhas beendumpeduponthe market n companywith the materials or its completion.

In short, Mach's opposition to both the reality of atoms and to


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An HistoricalNote on ErnstMach 305'The hypothesis of evolution in the atom or transformation f its substance,coupledwith the supposition hat energyemittedby the radium s takenout of thestore in the atom seems to me to be utterly mpossible . .'

JOHN BLACKMOREKirchberg m Wechsel,LowerAustriaREFERENCESBLACKMORE,. T. [I972]: ErnstMach-His Life, Work& Influence. niversity of CaliforniaPress.CLARK, . [I 976]: 'Atomism versus Thermodynamics', in Method ndAppraisaln thePhysical

Science, d. C. Howson, pp. 4I-I05. Cambridge University Press.CLARK,P. [I982]: 'Matter, Motion & Irreversibility' (Review of S. G. Brush The Kind ofMotionWe Call Heat) British3rournalforhePhilosophy f Science, 3, pp. I65-86.FEYERABEND,. [I980]: 'Zahar on Mach, Einstein and Modern Science', British3tournalforhePhilosophy f S;cience,I, pp. 273-82.GARDNER,M. [I979]: 'Realism and Instrumentalism in Igth Century Atomism', Philosophy fScience, 6, pp. I-34.LAUDAN,L. [I976]: 'The Methodological Foundation of Mach's Anti-Atomism and TheirHistorical Roots', in Motionand TimeSpaceandMatter,ed. P. K. Machamer and R. G.Turnbull, pp. 390-4I7. Ohio State Universtiy Press.MACH, E. [I896]: Die Principiender Warmelehre-historisch-kritischntwickelt. . AuflageI923. Verlag von Johann Ambrosius Barth.

MACH, E. [I9I0]: 'Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre undihre Aufnahme durch die Zwitgenossen' Physikalische eitschrift,I, pp. 599-606.MACH, E. [I9I9]: Die Leitgedankenmeinernaturwissenschaftlichenrkenntnislehrend iAreAufnahme urchdie Zeitgenossen.innlicheElemente nd naturwissenschaftlicheegriffe.Verlag von Johann Ambrosius Barth.MEYER, . [ 950]: ' Die Vorgeschichte der Grundung und das erste Jahrzehnt des Institutes furRadiumforschung' Sitzangsberichteer &)sterreichischenkademie er Wissenschaft,59,PP- 5o.NYHOF,J. [I98I]: Instrumentalismnd Beyond,Doctoral Dissertation, University of Otago,Dunedin, New Zealand.OSTWALD,W. [I90I]: VorlesungenberNaturphilosophie.. Auflage, I902, p. 4. Verlag vonJohann Ambrosius Barth.

POPPER, . R. [I 974]: 'Autobiography of Karl Popper', in ThePhilosophy f KarlPopper,d. P.A. Schilpp, pp. I56-67. Later published as UnendedQuest I976]. Fifth Impression[I980]. Fontana/Collins.TRAVERS,M. [I9SI]: Sir WilliamRamsay,p. Z5I-2. London.TREVOR, . E. [I897]: 3tournal f PhysicalChemistry,, p. 43I.

SOME RECENT OBJECTIONS TO THEBAYESIAN THEORY OF SUPPORTBayesianism today makes a serious claim to be regarded as the logic ofscientific inference (one of its very obvious strengths is that it adjudicatesboth statistical and non-statistical inference in a uniform way, for example).

My thanks to Stephen Brush for his acute comments which have contributed significantly tothe revision of this historical note.

An HistoricalNote on ErnstMach 305'The hypothesis of evolution in the atom or transformation f its substance,coupledwith the supposition hat energyemittedby the radium s takenout of thestore in the atom seems to me to be utterly mpossible . .'

JOHN BLACKMOREKirchberg m Wechsel,LowerAustriaREFERENCESBLACKMORE,. T. [I972]: ErnstMach-His Life, Work& Influence. niversity of CaliforniaPress.CLARK, . [I 976]: 'Atomism versus Thermodynamics', in Method ndAppraisaln thePhysical

Science, d. C. Howson, pp. 4I-I05. Cambridge University Press.CLARK,P. [I982]: 'Matter, Motion & Irreversibility' (Review of S. G. Brush The Kind ofMotionWe Call Heat) British3rournalforhePhilosophy f Science, 3, pp. I65-86.FEYERABEND,. [I980]: 'Zahar on Mach, Einstein and Modern Science', British3tournalforhePhilosophy f S;cience,I, pp. 273-82.GARDNER,M. [I979]: 'Realism and Instrumentalism in Igth Century Atomism', Philosophy fScience, 6, pp. I-34.LAUDAN,L. [I976]: 'The Methodological Foundation of Mach's Anti-Atomism and TheirHistorical Roots', in Motionand TimeSpaceandMatter,ed. P. K. Machamer and R. G.Turnbull, pp. 390-4I7. Ohio State Universtiy Press.MACH, E. [I896]: Die Principiender Warmelehre-historisch-kritischntwickelt. . AuflageI923. Verlag von Johann Ambrosius Barth.

MACH, E. [I9I0]: 'Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre undihre Aufnahme durch die Zwitgenossen' Physikalische eitschrift,I, pp. 599-606.MACH, E. [I9I9]: Die Leitgedankenmeinernaturwissenschaftlichenrkenntnislehrend iAreAufnahme urchdie Zeitgenossen.innlicheElemente nd naturwissenschaftlicheegriffe.Verlag von Johann Ambrosius Barth.MEYER, . [ 950]: ' Die Vorgeschichte der Grundung und das erste Jahrzehnt des Institutes furRadiumforschung' Sitzangsberichteer &)sterreichischenkademie er Wissenschaft,59,PP- 5o.NYHOF,J. [I98I]: Instrumentalismnd Beyond,Doctoral Dissertation, University of Otago,Dunedin, New Zealand.OSTWALD,W. [I90I]: VorlesungenberNaturphilosophie.. Auflage, I902, p. 4. Verlag vonJohann Ambrosius Barth.

POPPER, . R. [I 974]: 'Autobiography of Karl Popper', in ThePhilosophy f KarlPopper,d. P.A. Schilpp, pp. I56-67. Later published as UnendedQuest I976]. Fifth Impression[I980]. Fontana/Collins.TRAVERS,M. [I9SI]: Sir WilliamRamsay,p. Z5I-2. London.TREVOR, . E. [I897]: 3tournal f PhysicalChemistry,, p. 43I.

SOME RECENT OBJECTIONS TO THEBAYESIAN THEORY OF SUPPORTBayesianism today makes a serious claim to be regarded as the logic ofscientific inference (one of its very obvious strengths is that it adjudicatesboth statistical and non-statistical inference in a uniform way, for example).

My thanks to Stephen Brush for his acute comments which have contributed significantly tothe revision of this historical note.

Mach Boltzmann

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