TheValueofSurpriseinScience*

StevenFrench,UniversityofLeeds

AliceMurphy,LMUMunich

ForthcominginErkenntnis

March2021version

AbstractScientificresultsareoftenpresentedas‘surprising’asifthatisagoodthing.Isit?Andifso,

why?Whatisthevalueofsurpriseinscience?Discussionsofsurpriseinsciencehavebeen

limited, but surprise has been used as a way of defending the epistemic privilege of

experiments over simulations. The argument is that while experiments can ‘confound’,

simulationscanmerelysurprise(Morgan2005).Ouraiminthispaperistoshowthatthe

discussion of surprise can be usefully extended to thought experiments and theoretical

derivations.Wearguethatinfocusingonthesefeaturesofscientificpractice,wecanseethat

thesurprise-confoundmentdistinctiondoesnotfullycapturesurpriseinscience.Wesetout

howthoughtexperimentsandtheoreticalderivationscanbringaboutsurprisesthatcanbe

disruptive inaproductiveway, andweendbyexploringhow this linkswith their future

fertility.

Introduction

Scientificresultsareoftenpresentedas‘surprising’,asifthatisagoodthing.Isit?Andif

so, why? What is the value of surprise in science? In addressing such questions

discussions have tended to focus on one of two features of scientific practice: novel

predictionsand their role in the realismdebate (seeHitchcockandSober2004); and

novel or surprising phenomena. In the former case, the surprise associatedwith the

noveltyisdefinitelyagoodthingasfarasthescientificrealistisconcerned,indicativeas

itisofthe‘mindindependent’natureoftherelevanttheory.However,weshallhavelittle

tosayaboutthathere.Inthelatter,thesurpriseisvaluedbecauseitsuggeststhat,given

thecontext,therelevantphenomenonisworthyoffurtherinvestigation.Anexamplehere

*Acknowledgments:We’dliketothankAaronMeskin,JuhaSaatsi,AdrianCurrie,attendeesattheHPSLeedsworkinprogressseminarandtheBristolphilosophyofscienceseminar,andtwoanonymousrefereesfortheirhelpfulcommentsonthispaper.

would be the fogging of Becquerel’s photographic plates, leading to the discovery of

spontaneousradioactivity.Anotherwouldbe thepolarizationof lightby IcelandSpar,

citedbyHacking,togetherwithothersurprisingopticalphenomenasuchasdiffraction,

dispersionandinterference,inhiswell-knowndefenceoftheprecedenceofobservation

overtheory(1983,p.156).However,thespecificsofsuchcasesarealsonotourfocus

here,althoughsuchnovelphenomenawillofferausefulfoiltoourconsiderations.

Ouraiminthispaperistwo-fold:first,weshallshowthatthediscussionofsurprisein

science canbeusefullyextended to include two further featuresof scientificpractice,

namely novel thought experiments and theoretical derivations. We focus on these

becausethoughtexperimentsarealsosaidtogeneratepredictionsandeven,inacertain

sense may be thought of as producing phenomena. More generally, both thought

experimentsandtheoreticalderivationscanbethoughtofasproducing‘outcomes’,just

ascomputersimulationsdo,yettherehasbeenconsiderablylessdiscussionofsurprise

in these cases. Given their central importance to science, there is obvious value in

extendingthediscussioninthisdirection.Furthermore,boththoughtexperimentsand

theoreticalderivationsofferanovelcontext inwhich todiscusssurpriseas theyboth

involve the imagination andmental representations and thereby raise the interesting

question,howcantheyorfeaturesassociatedwiththem,besurprisinginthatcase?We

shallcomebacktothisbelowbutthisthenrelatesdirectlytooursecondoverallaim.1

Thisistouseconsiderationofthesetwoscientificpracticestoputpressureonawell-

known distinction between ‘mere’ surprise and ‘confoundment’, with the former

associatedwiththeoutcomesofmodelsandcomputersimulations,andthelatterwith

novelphenomena(Morgan2005).Thedistinctionisexplicatedinthefollowingterms:a

phenomenonisconfounding,ratherthan‘merely’surprising,ifitis‘bothsurprisingand

unexplainable within the given realm of theory’ (2005, p. 324). Likewise, Ritson

emphasizes the disruptive nature of surprising results and states that ‘the kinds of

noveltyframedasmostvaluablearethosethatviolateexpectationsandaredifficultto

incorporateintoexistingstructuresofknowledge’(2020,p.1).

1We’dliketothankoneoftherefereesforpressingustobeclearerontheseissues.

The outcome of a computer simulation, say, is argued to be only ‘merely’ surprising

because it is ultimately explicable in terms of the theories in terms of which the

simulationwasconstructed.Anysurprise in thatcasemustpresumablybedue to the

scientist’scognitivelimitationswhenitcomestofollowingthestepsofthesimulation,

which may of course be complex. The core idea was captured by Wittgenstein who

dismissedthevalueofsurpriseindeductivecontexts:

"Thedemonstrationhasasurprisingresult!"--Ifyouaresurprised,thenyouhave

notunderstoodityet.Forsurpriseisnotlegitimatehere,asitiswiththeissueof

anexperiment.There--Ishouldliketosay--itispermissibletoyieldtoitscharm;

butnotwhenthesurprisecomestoyouattheendofachainofinference.Forhere

itisonlyasignthatunclarityorsomemisunderstandingstillreigns’(1978,111).

Here,surprisearisesbecauseofpeople’sepistemiclimitations;‘aproofistoolongtokeep

allitsstepsinmind,sosomethingislostfrompurview’(Simons,unpublished;seealso

French and Vickers 2011; French 2020). In such cases, then, the value of surprise is

consideredlessthanthatofconfoundment.

However,weshallarguethatthoughtexperimentsandtheoreticalderivationsmayalso

bedisruptiveofexpectationsandbedifficultto incorporate intoexistingstructuresof

knowledge. Following Currie (2018), we shall call this sense of surprise ‘productive

surprise’ and we suggest that it is more general than ‘confoundment’ whichmay be

retainedforsurpriseassociatedwithnovelphenomena.

WeshallbeginbyoutliningMorgan’sargumentsregardingtheepistemicprivilegingof

experimentsovercomputersimulationsandshallconsidertheminthecontextofthought

experimentsviatwomajorapproachesduetoBrownandNorton.Wedemonstratethat

thought experiments can surprise in a fruitful way, and that this cannot be

straightforwardlydismissedas‘mere’surprise.Thisthenleadsustotheconsiderationof

thenatureandroleofsurpriseinabroadertheoreticalcontextwhichweexplorethrough

theexampleofEinstein’sderivationofE=mc2.HereweshalldrawonMorgan’sclaimthat

aresultisconfoundingifitisinexplicablewithina‘givenrealmoftheory’andshallargue

that a lothingesonwhat countsas the ‘given realmof theory’.Again,witha suitable

choiceofthatrealm,weshallarguethatEinstein’sresultshouldberegardedassurprising

in aproductive senseandwe shall concludeby indicatinghowsuch surprises canbe

understoodasindicativeofacertain‘fertility’possessedbythetheoryconcernedandare

valuableinthatrespect.

1. MereSurpriseandConfoundment

Theuseofcomputersimulationstostudyarangeofcomplexphenomenaiswidespread

throughoutthesciences.Inphilosophyofscience,muchofthediscussionhasconcerned

how they compare with ordinary ‘physical’ experiments. Computer simulations have

beenreferredtoasvirtualexperiments,experiments insilico,orexperimentswithout

materiality.Andsomehaveclaimedthat ‘Simulationmodelling is justanother formof

experimentation’ (Norton and Suppe 2001, p. 92).2 But their status as genuinely

experimental has been contested as they do not intervene in the natural world and

instead, it has been claimed, study ‘hypotheticalworlds’ (Lenhard 2018).Oneway in

whichtherelationbetweenthesetwopracticeshasbeenexploredisthroughMorgan’s

(2005)distinctionbetweenmeresurpriseandconfoundment,originallypresentedvia

the comparison between modelling and experiment in economics. Boumans (2012),

Parke (2014), Currie (2018) and Beisbart (2018) have extended the discussion to

computersimulationsandtheiruseacrossscience.3

Althoughbothsimulationsandexperimentscanachievemeresurprise,onlythelatter,

Morgan argues, can achieve confoundment. This is articulated in terms of the key

differencesbetweentheobjectsofstudyinexperimentscomparedtothoseincomputer

simulations.Thus,Morganlinksthesurpriseargumenttoaclaimaboutthematerialityof

theformer.Bothsimulationsandexperimentsinvolvestudyingasystemthat“standsin”

2Arcangelihasarguedagainstwhatsheseesasthepervasive‘bias’fortheepistemologicalsuperiorityof‘real’experiments,ascomparedwiththoughtexperimentsand‘numerical’experiments(Arcangeli2018).Boydhasalsoarguedthatwhatmattersfortheepistemicutilityofempiricalresultsistheirprovenance(Boyd2018).Withauxiliaryinformationaboutdatagenerationprocessestakenintoaccountanotionof‘enrichedevidence’canbeelaboratedthatencompassessimulations.InthisregardwemightalsomentionDardashtiet.al.(2017)whoarguedthat‘analoguesimulations’mayplayaconfirmatoryroleinastrophysics,forexample.Thanksagaintooneoftherefereesforremindingusofthisfurtherliterature.3AquestiontoconsiderwouldbewhetherMorgan’sclaimsshouldbetakenasspecifictoeconomics,becauseofthecomplexityofpeopleandtheirbehaviour.Here,however,wefollowothersingeneralizingMorgan’sclaim:welosesomegeneralopennesstonaturewhenwesimulate.

forthesystemthatthescientistisultimatelyinterestedin.ButforMorgan,thereisacore

ontologicaldifference;theobjectinanexperimentreplicatespartoftheworlditstands

for (albeit in a way that is simpler tomanipulate), whereas the object of study in a

simulationonlyrepresentstheworldoutsideofthesimulation.4

This ontological difference then underpins that between confoundment and ‘mere’

surpriseviatheissueofcontrol:Asphysicalexperimentsaresaidtocaptureorreproduce

partsofthenaturalworld,theobjectinanexperimentisaversionoftheobjectinnature.

Thismeansscientistsarenotincompletecontroloftheexperiment’sresults.Whereasin

acomputersimulation,scientistsarestudyingsomethingartificialthattheyprogrammed

themselvesandoverwhichthey,ultimately,retaincontrol.

To see this difference, consider surprise in simulations. Scientists are often ignorant

aboutcertainfeaturesoftheirsimulationsandeveniftheyknoweverythingaboutthe

startingassumptionoftheirmodelsandtherulesforhowthesystemwillchangeover

time, these can be very complex, and theywill not know all the consequences of the

conditionsthattheystartedwith.AsMorganhighlights,findingoutwhatfollowsfromthe

initialconditionsisthegoalofrunningthesimulation,andsometimeswhatfollowscan

beunexpected.However,shestates:‘Theconstraintsonthemodel’sbehaviourareset,

however opaque theymay be, by the scientist who built themodel so that however

unexpectedthemodeloutcomes,theycanbetracedbackto,andre-examinedintermsof,

themodel’(Morgan2005,p.325).Thus,asimulation’sresultcanbefullyexplainedbyits

designandimplementation,incorporatingtherelevanttheoreticalpresuppositions.Asa

consequence,itcannotconfound.

4 ForMorgan, this alone has epistemological implications: ‘we aremore justified in claiming to learnsomething about theworld from experiment because theworld and experiment share the same stuff’(2005,p.323,).Therearemanyissueswiththematerialityargument,includingproblemsestablishingwhat“materiallysimilar”actuallyconsistsin(Parke2014)andsomehavesuggesteditisrelevantsimilarity,notmaterial similarity, that is important (Parker 2009). Here, the materiality argument and the surpriseargumentwillbetreatedseparately(asinParke2014).Wetakeitthatwhatisrelevanttothesurpriseclaimisthatinanexperiment,wearestudyingamaterialsystem(notthatwearestudyingasystemthatismateriallysimilar).Thiswouldsuggestthatanaloguesimulationscouldalsoconfound.

Ontheotherhand,whenitcomestophysicalexperimentsthebehaviouroftheobject

underinvestigationisnotcompletelycontrolledbythedesignoftheexperiment,andso

genuinelynewphenomenacanemerge:

‘Such new behaviour patterns, ones that surprise and at first confound the

profession,areonlypossible ifexperimentsaresetupwithacertaindegreeof

freedom…[sothatits]behaviourisnottotallydeterminedbythetheoryinvolved,

norbytherulesoftheexperiment’(Morgan2005,p.324).

Thereis,then,thisimportantconditionof“noover-control”inthecaseofexperiments

thathavethepotentialtoconfoundratherthanmerelysurprise.Inconductingaphysical

experiment,ascientistsetsouttodiscoverhowasystemwillrespondtoanintervention.

Butifthesystemisover-controlled,thenthesystemwillnotbeabletoreactinthisway.

Instead,itsbehaviourisdictatedbythesetupand‘naturedoesn’thaveanythingtosay’

(Beisbert2018,p.187).ThisisincontrasttotheexampleofBecquerelandthefogged

photoplates.

To summariseMorgan’s argument: in a computer simulation, surprising results only

arise becausewe do not have epistemic access to all the consequences of ourmodel

before we run the simulation. But with an experiment, even within the setting of a

laboratorytherecanbe‘potentialforindependentaction’(2005,p.325).Andwhenthere

is,wecanbeconfrontedwithnewphenomenathatare‘unexplainablewithinthegiven

realmoftheory’(ibid,p.324).

Theepistemicvalueofconfoundmentliesinthefactthattherelevantphenomenacryout

forexplanation.Confoundingresultsarethusdisruptiveinaproductiveway:theyforce

ustothinkseriouslyaboutourexistingtheoriesandmotivatenewresearchinorderto

findawayofaccommodatingthesurprisingresults(againseealsoCurrie(2018)and

Ritson (2020)).Wewill now turn to the comparisons between thought experiments,

‘physical’experimentsandcomputersimulationsinordertoconsidertheextenttowhich

thefirstmaybesurprising.5

5Thereisanissuehere,raisedbyoneofthereferees,astowhethersurpriseshouldbeseenasapsychologicalnotionornot;thatis,isitafeelingwehave,orisitanobjectiverelationbetweensome

2. ThoughtExperiments,ExperimentsandComputerSimulations

Whatistherelationshipbetweenthoughtexperimentsand‘physical’experiments?Some

have taken the “experimental” aspect of thought experiments seriously, claiming that

thoughtexperimentsareexperimentsinthesamesenseaslab-basedexperimentsorare

on a continuumwith the latter (see Mach 1896, p. 453). In the design of a thought

experiment,certainfactorsareisolated,variablesarecontrolled,andirrelevantaspects

areidealisedaway.Thesevariablesarethenmanipulatedandtheexperimenter,albeitin

theirimagination,“observes”whatfollows.

SimilarlyforBrown(1986,2007),thatthoughtexperimentstakeplaceinthe“laboratory

ofthemind”doesnotentailthattheyarenotexperimentalinthesamesenseasthose

thattakeplaceinthephysical laboratory.Hearguesthatthoughtexperimentsinvolve

quasi-observationofwhatisessentiallyanabstractsetup;asystemisrepresentedand

thenobservedbythemind’seyeinawaythatisanalogoustoexperiments.6Incontrast,

othershavedrawnasharplinebetweenthoughtexperimentsand‘physical’experiments.

Forexample,forNorton(1991),thoughtexperimentsarejustarguments.Astheywork

byinferencesanddonotinvolveinteractingwith,manipulatingnorobservingthenatural

world,anysimilaritieswith‘physical’experimentsaresuperficial.Weshallreturntoboth

theseaccountsbelow.

There is debate, then, around the relationship between thought experiments and

experiments,muchofwhichiscentredaroundthequestionwhethertheformershould

beclassedwiththelatterorheldasdistinct.Thismakescomputersimulationsahelpful

pointofcomparisonwhenthinkingabouttheepistemologyofthoughtexperimentsgiven

backgroundcommitments,outstandingproblemsandlivemethodologicaloptions?Ourresponseisthatitinvolvesboth:aswetrytoarticulatehere,thesurpriseassociatedwithcertainthoughtexperimentsandtheoreticalderivationsisindicativeoftheirsignificanceandarisesinaspecificcontextthatinvolvesbackgroundcommitmentsetc.butofcourseitmanifests,inboththescientistandtheiraudience,asaspecificfeeling.SeeCurrie(2018)foranaccountofsurpriseasan“epistemicgood”inscience,ratherthanjustapsychologicalfeature.6 Morespecifically,this—thephenomenon,i.e.whatisobservedintheexperiment—iswhatBrownwouldlabelthe“narrow”senseofa(thought)experiment.Experimentsinthebroadsense‘includesthewholethingfromtheoryandbackgroundassumptionstothefinalresult’(2007,158).

that(aswesaw)thereisalsodebateregardingwhethertheycanbeexperimentalinsome

sense. In light of these comparisons, we can now think about Morgan’s surprise-

confoundment distinction in the context of thought experiments. Here we are less

interestedintheidentityquestion—arethoughtexperimentsorcomputersimulations

experiments?Instead,weshallfocusontheissueofprivilegingexperimentsinvirtueof

theircapacitytoconfoundratherthan‘merely’surprise.7

3. SurpriseinThoughtExperiments

WhatdoesMorgan’sdistinctionbetweensurpriseandconfoundmentmeanforthought

experiments?Ononehand,weclearlyknowofexamplesof thoughtexperiments that

haveproducedunexpectedandsignificantoutcomes.TakeEinstein’schasingabeamof

lightexamplewhichexposesthesurprisingtensionsbetweenNewtonianmechanicsand

Maxwell’sequations.Ontheotherhand,thoughtexperiments,likecomputersimulations,

donotinvolveinteractionwiththeworld.Soshouldthesurprisethatarisesfromthought

experiments be dismissed as a less valuable kind as Morgan suggests in the case of

computersimulations?Weshallshowthat,dependingontheaccountofwhatathought

experimentis,therearealternativeviewsastohowtheycansurprise,andwhetherthey

canconfound.WeshallfirstexaminetheissuefromtheperspectiveofBrown’splatonist

view,beforeturningtoNorton’saccount.Wethensuggestanalternativepositionwhich

attendstotherolethattheimaginationplaysinthoughtexperimentsthatdemonstrates

howtheycanbringaboutproductivesurprisesinadistinctiveway.

a) Brown’sView:ThoughtExperimentsandPlatonism

Brownarguesthatthereisasetofthoughtexperimentsthatprovideknowledgeofthe

worldthrough“transcendingempiricism”;theyallowusaccesstothelawsofnaturethat

existasrelationsholdingbetweenuniversals,suchasmass,spinetc.,thataretakentobe

platonicentities.BrownpresentsGalileo’sfamousthoughtexperimentagainstAristotle

7SeeSorensen(1992),Bokulich(2001)andStuart(2016)forfurtherdiscussionsontherelationsbetweenthoughtexperimentsandexperiments.Whilesuchviewsalsohaveimplicationsfortheepistemicstatusofthoughtexperiments,wedonotdiscussthemheregiventhattheydonotfocusonsurprise.

as an illustrative example. This underminesAristotle’s theory that heavier bodies fall

fasterthanlighterones.Galileoasksustoimagineattachingtwoballstogether,aheavy

one and a light one, and dropping them from the leaning tower of Pisa. What does

Aristotle’stheorypredict?Boththatthecombinedbodieswillfallfasterthantheheavier

ballonitsown,asthecombinedobjectisheavier,andthatthecombinedobjectwillfall

slower,asthelighterballisinclinedtofallslowerandso,willdragtheheavierbodyback.

Fromthis,Galileoproposesanewtheory;allobjectsmadeofthesamematerialfallatthe

samespeed.

Brownstatesthathere,‘wehaveatransitionfromonetheorytoanotherwhichisquite

remarkable.Therehasbeennonewempiricalevidence.Theoldtheorywasrationally

believedbeforethethoughtexperiment,butwasshowntobeabsurdbyit.Thethought

experimentestablishedrationalbeliefinanewtheory’(1986,p.10).ForBrown,thisisa

prioriknowledge;thebeliefinGalileo’stheoryisnotbasedonnewempiricaldataand

importantly,neitherisitlogicallyderivablefromolddata(weshallreturntothisbelow

whenwediscussNorton’sview).

WehavealreadyseenthatBrowntakestheanalogybetweenthoughtexperimentsand

physicalexperimentsseriously.Andjustasthelattermayconfoundus,somaytheformer

onthisviewsincethisclassofthoughtexperimentsmayproduceresultsthatcannotbe

tracedbacktoorexplainedintermsoftheinitialconditionsofthethoughtexperiment,

andtheseresultsmaybeinexplicableintermsofthe‘giventheory’.Thus,forBrown,the

insightswegainfromplatonicthoughtexperimentsarenotsimplyamatterof‘seeingold

empiricaldata inanewway’ (ibid.,p.11)butrather, involvegenuinediscovery.Here,

then, we see how thought experiments may confound, at least on a ‘platonic’

interpretation.Ofcourse,thatinterpretationcomeswithacertainontologicalcostand

onemightprefertoavoidthatbyadoptingamoreminimalistapproachtowhichweshall

nowturn.

b) Norton’sView:ThoughtExperimentsareArguments

This alternative view takes thought experiments to be arguments. In answering the

questionofhowtheycanhavenovelempiricalimportNortonclaimsthatthereis‘only

onenon-controversialsourcefromwhichthisinformationcancome:itiselicitedfrom

informationwealreadyhavebyanidentifiableargument…Thealternativetothisviewis

tosupposethatthoughtexperimentsprovidesomenewandevenmysteriousrouteto

knowledgeofthephysicalworld’(1991,p.129).

Norton’sviewmaybeseparatedintotwoclaims.Thefirstisareconstructionthesis:The

epistemicpowerofathoughtexperimentisthatofitsreconstructedargumentform.The

secondclaimisabouttheperformanceofathoughtexperiment:theconductofathought

experimentjustisthatofanargument.

Revisiting Galileo’s thought experiment, it can be reconstructed as an argument

(uncoveringaninconsistencyinAristotle’sphysics)asfollows:

(i) Naturalspeedisdirectlyproportionaltoweight

(ii) Weightisadditive

(iii) Naturalspeedismediative

From(ii)and(iii),wegetthenegationof(i)8

BeisbartandNorton(2012)andBeisbart (2012)claimthatcomputersimulationsare

alsoarguments.The thought is thatcomputersimulationsraiseaparallel issue to the

abovequestion:howdotheyprovideknowledgeaboutareal-worldtargetwithoutany

observation of that target? Their answer is that thought experiments and computer

simulations provide knowledge in the sameway: we build what we know into their

construction,thatis,thedescriptionofthethoughtexperimentortheassumptionsofthe

computersimulation,andthisknowledgeisthentransformedthroughalogicalprocess.

Thus, computer simulations can also be reconstructed into arguments, and their

epistemic force is not thereby lost. And further, that ‘the reconstructing argument is

executedwhenacomputersimulation iscarriedout’ (Beisbart2012,p.419-420).We

shallnotconsiderfurtherthisviewherebutwewillcomebacktosomeoftheworriesof

theargumentviewwhenappliedtothoughtexperiments.

8 Norton’s reconstruction is limited to the “destructive” part of Galileo’s thought experiment and does not include the step that is central to Brown’s platonism view, i.e. the introduction of the new theory that all bodies fall at the same speed. This is because, Norton argues, the move involves a problematic assumption, namely that the ‘speed of fall of bodies depends only on their weights’ (1996, 342).

Now, on this view of thought experiments, do they ‘merely’ surprise or can they

confound?BeisbartandNortondonotdenythatwegainnewknowledgefromthought

experiments(andcomputersimulations)as‘theresultsinferredwerenotknownprior

toinvestigations’(2012,p.409).However,theydrawadistinctionbetween‘discovery’,

as in thecaseofphysicalexperimentsand ‘inferring’as inthesecases,wherethought

experimentscanbearticulated in termsof inferencesdrawn fromwhat is implicit. In

Galileo’s thoughtexperiment, the contradiction inAristotelianphysicswasalready, in

somesense“there”;thethoughtexperimentquaargumentsimplyexposedit.

However,reductioargumentssuchasthisarepragmaticallyawkwardinthatthereader

isinvitedtoassumethatwhichissubsequentlyshowntobefalse.Ifwetakethisinitial

assumptionorpremise,thatis,(i)intheabovereconstruction,asthe‘giventheory’inthe

characterisationofconfoundment,thenofcoursetheconclusion,thatthe‘giventheory’

isfalse,cannotbeexplainedintermsofthatverytheory(atleastnotonmostaccountsof

explanation).However, if the ‘given theory’ is expanded to include theargument as a

whole,thenclearlytheconclusionisexplicable–we’vejustgivenanargumentforit!In

terms of this ‘argumentative’ characterisation, then, thought experiments such as

Galileo’smaysurprisebuttheydonotconfound.

HerewerecallWittgenstein’sdismissalofthevalueofsurpriseindeductivecontextson

thegroundsthatthecauseofthesurprisehastodowithscientists’cognitivelimitations.

Ifweweretofollowthisline,alongwithNorton’spresentationofthoughtexperiments

asarguments,thentheremightseemtobelittleofanyinteresttosayaboutsurprisein

this context.9 However, it is important to note that Norton’s reconstructions are not

limitedtodeductivearguments;theycanalsoincludeinductivesteps,asintheexample

ofEinstein’selevator10;‘thecaseistypicalandwillholdforallobservablephenomena’

9FrenchandVickers(2011)introducethistounderminePopper’sviewthatsurprisemotivatesarealistview of theories. Again, we come back to connections between surprise in theories and thoughtexperimentsinsection4.10Einsteinimaginedsomeoneperformingexperiments,suchasthrowingaballandobservingitstrajectory,inanelevatorthatwasacceleratingupwards.Herealisedthattheobservationsmadewouldbeexactlyasiftheelevatorwereinagravitationalfield,concludingthattheprincipleofrelativityshouldbeextendedtoincludeacceleratingframesofreference.ThisthoughtexperimentthusplayedafundamentalroleinthedevelopmentoftheGeneralTheoryofRelativity.Whatitbringsintothelightistheequivalencebetweeninertial and gravitational mass which had been noted by Newton but which Einstein elevated into afundamentalprinciple.

(1991,p.137).11Andso,Norton’sviewofthoughtexperimentsallowforstepsthatare

ampliative;theygobeyondwhatisstatedinthepremises.12Thesameholdstooforhis

and Beisbert’s account of computer simulations, these can also transform the

assumptionsinthemodelinawaythatpreservestheprobabilityoftruth(2012,p.411).

Nevertheless,onNortonandBeisbart’sview,theinformationwegainthroughdeductive

and inductive inferences does not constitute genuine discovery as in the case of

experiments(2012,409).AndBeisbart(2012,2018)hasexplicitlyendorsedMorgan’s

accountwhendiscussingtheepistemicstatusofsimulations,offeringtheexampleofthe

Michaelson-Morleyexperiment (1887) thatundermined theview that theearthhasa

non-zerovelocitywithrespecttotheether.AsBeisbartargues, thisexperiment ‘hasa

complicated set-up, and a number of assumptions are needed to interpret its data as

having implications about the ether. But this does not imply what the result of the

experimentis’.Ifinstead,asimulationwasused,itwouldnothaveconfoundedasthere

wouldbeanassumptionregardingtheearth’svelocitywithrespecttotheetherinthe

simulation’sprogramming(Beisbart2018,12).13

Despitethis,Currie(2018)andParke(2014)giveexamplesofsimulationsthatproduce

results that go against expectations and ‘promote changes to, or re-examinations of,

explanatoryresourcespertainingtothetarget’(Currie2018,p.654).14Wehaveindicated

11Norton’snotionoflogicalreasoninginthoughtexperimentshasexpandedovertheyearstoincludestepsbeyonddeductionandinductiontoinformalinferencesandreasoningfromanalogy.Thishasbeentakentorendertheargumentaccount‘vacuouslytrue’(Brendel2018,p.287).12Thisampliativefeaturemaysuggestthatinductioncanleadtodiscoveriesorgeneratesurprisesbeyond‘meresurprise’,anditwouldbeinterestingtothinkmoreaboutthisinthecontextofanargumentviewofthoughtexperiments.However,considerenumerativeinductionforexample:afterobservingmanywhiteswansundervariousconditions,ithardlyseemssurprisingthatthenextswanIseeiswhite.Perhapsthenitistheuniversalgeneralisation‘Allswansarewhite’thatismeanttocomeasasurprise,butagaingiventhatthiswouldhavebeenformulatedafterobservingnumerousswansundervariedconditions,thatseemsimplausible.Whatmightseemasurpriseisifthegeneralisationholds,unfalsified,evenwhenthefieldisgreatlyenlarged(toincludeAustralia,say)butthenonemightexpectthatfeelingofsurprisetodissipateasscientistsofferanexplanationastowhythegeneralisationhastohold,forfundamentalbiologicalreasons.Again,wearegratefultoarefereeforraisingthisissue.13Further,wecanconsidercasesofthoughtexperimentsthatmaybringaboutmeresurprise(inthesenseofanunexpectedconsequence)butdonotconfound.Oneexample,discussedbyBokulich(2001),istherocketsandthreadthoughtexperiment,whichdrawsoutaphysicalimplicationofspecialrelativity(belowweshallconsideranimplicationofthetheorythatweclaimcanberegardedasproductiveinawaythatsuggeststhedistinctionbetween‘mere’surpriseandconfoundmentistoocoarse-grained).14 Importantly,theyeachgiveexamplesofsimulationswhich,theyargue,canconfoundinMorgan’ssense.ParkepresentstheexampleoftheABMSugarscapewhichhad“hiddenfeatures”thatwererevealedinthesimulation(2014,531).Currieoutlinesasimulationofsauropods’gait.Theresultwas

above how the issue of whether thought experiments confound, rather than merely

surprise,maydependonhowtheyarecharacterised.However,what is crucial is that

evenwhenpresentedintheformofanargument,theycanbedisruptiveinthesenseof

forcing us to re-evaluate our existing theories. Indeed, for many such thought

experimentsthisistheirprincipalroleanditisobviouslythecaseinthereconstruction

ofGalileo’sthoughtexperiment,where,althoughtherearenonewempiricaldiscoveries

beingmade,thescenarioweareaskedtoimagineexposesacontradictioninAristotelian

physicsandsubsequentlypromptsthedevelopmentofanewtheory.15Takentogether,

theseconclusionsputpressureonMorgan’sclaimthatthedifferentsourcesofsurprise

impacttheepistemicstatusofthefeatureunderconsideration.

Havingsaidthat,weagreethatthereisadifferencebetweenthoughtexperimentsand

computersimulationsontheonehand,andexperimentsontheother,inthatthesurprise

arises inadifferentway.So,topursuethecomparisonfurther,werecall thatphysical

experimentscanresultinnewempiricalresultsthatmayforceustoreviseourtheoretical

knowledge. Simulationsdiffer in thatdesigning and running a simulation is away ‘of

fillingout,makingexplicit,andprobingourtheoretical,conceptualandempiricalideas’

(Currie2018,p.656).Thisisstillawayofgeneratingknowledge(andcanbringabout

productivesurprises) butunliketheexperimentcase, itdoesnotinvolvethis ‘contact

withnewempiricalresults’(ibid).Likewise,thoughtexperimentsprobeourtheoretical,

conceptual and empirical ideas. However, there are important differences between

thought experiments and computer simulationswhich illustrate how they probe this

knowledgeindifferentways.Andthishasimplicationsforhowtheformerbringabout

productivesurprises.

c) Thoughtexperimentsandtheimagination

In order to explore those differences, let us begin with the view that computer

simulations are simply more complex thought experiments. Di Paolo et al (2000)

unexpectedandpromptedtheinvestigatorstoreflectontheexplanatoryresourcesofthetarget(2018,654).15AccordingtoFeyerabend(1975,pp.73ff;seealsoArthur1999,pp.220-227)Galileoofferedanew‘naturalinterpretation’ofthephenomenonallowinghimtobringtheCopernicanviewintoconsonancewiththefactsthatapparentlyrefutedit.

characterise simulations as ‘opaque’ thought experiments, and Lenhard (2018) has

arguedthatduetotheircomplexityandopacity,theformeraremorelikelytosurprise

thanthelatter.16

Althoughitmayseemthatsimulationsaremoretransparentinthattheyworkbyalarge

numberofsimplesteps,whatLenhardmeansisthatthoughtexperiments‘havetomeet

high standards of intelligibility, because the whole process takes place in cognition’

whereas in a computer simulation, ‘it is the multitude of interrelated steps that can

rendertheoverallprocessopaque’(2018,p.485).Ifwetakehimtomeanmeresurprise,

asopposedtoconfoundment,thenhisclaimisthatwearemorelikelytogetsurprising

behaviours (someofwhichmaybeproductive) fromcomputersimulations than from

thoughtexperiments,asthelatterare“transparent”inawaythattheformerarenot.17

However, characterising computer simulations as more complex or opaque thought

experiments misses something important about the latter. Firstly, part of what is

surprisingaboutthoughtexperimentsistheirsimplicity.Thereissomethingsurprising

inGalileo’s thought experiment that it had such significance in thehistoryof science,

despite being a simple imagined scenario, involving the behaviour of bodies being

dropped from a tower.18 We shall come back to this in the context of theoretical

derivations.

Secondly,wecansee,byattendingtotheroleofimagination,thatthoughtexperiments

canbringaboutsurpriseinadistinctiveway.Itjustisnotobviouslythecasethatwehave

clearaccess toour imaginingsand theconnectionsbetween them,andhence thought

experiments cannotbe characterisedas straightforwardlyas thisviewpresupposes.19

16StuartandNersessian(2019)alsodiscussthedifferentwaysinwhichscientistscanlackaccesstotheircomputermodel,andtheyarguethatvisualisationscanbecreatedtoreduceepistemicopacity.17SeeLehnard(2019)forhismoredetailedviewonsurpriseinsimulations. 18Ofcourse,thesurprisegeneratedbysuchthoughtexperimentsmayvaryaccordingtotherelevantscientific(andperhapsmorebroadly,social)context.Havingsaidthat,itisoftendifficulttodiscoverhowsurprisedscientists–muchless,generalreaders–wereuponbeingpresentedwithone,particularlyinearliercenturies,giventhatthisreactionwastypicallynotrecorded(foranexampleofamodernexpressionofsurpriseovercertainfeaturesoftheoreticalphysics,seePeierls1979).Again,ourthankstooneoftherefereesforremindingusofthisissue.19TheWittgensteiniandismissalofsurpriseindeductionscanbelinkedtohisclaimthattheimaginationcannotprovideuswithnewinformationbecauseitissubjecttothewill(whereas‘real’objectsarenot)(1980,§80).Similarly,Whitestates‘onecan’tbesurprisedbythefeaturesofwhatoneimagines,sinceoneputthemthere’(1992,92).Stock(2007)andTodd(2020)haveofferedadetailedresponsetosuch

Thus, returning to Galileo’s thought experiment, Gendler has argued that, contra to

Norton’s account, it is not straightforward to conclude that Aristotelian physics is

inconsistent, since it is unclear whether all the propositions in the reconstructed

argumentformoughttobeconsideredpartofAristotle’stheory.Inparticular,ithasbeen

askedwhyweshouldconsider(iii)aspartofthetheory—thatnaturalspeedismediative,

ormorespecificallythat ‘NaturalspeedisapropertysuchthatifabodyAhasnatural

speed1,andabodyBhasnaturalspeed2,thenaturalspeedofthecombinedbodyA-B

willfallbetween1and2’(1998,p.404).Withoutthisassumption,theinconsistencyclaim

isunfounded.

Asaresult,therearevariouslogicallypossiblewaysoutfortheAristotelian.Forexample,

theycanask—arethebodiesthataretiedtogetheroneobjectortwo?Ifoneobject,then

itwillfallatthespeedthatisproportionaltothecombinedweight.20Gendlercontends

that thethoughtexperiment is indispensableandcannotbereconstructed inNorton’s

sensewithoutlosingitsdemonstrativeforce.21Thissuggeststhattheimaginationallows

kinds of jumps that cannot be accommodated within the framework of more formal

reasoning.22Understandingthoughtexperimentsasargumentsthusfailstofullycapture

theirpotentialtoproductivelysurprise,afeaturethatcharacterizes,atleastinpart,their

roleinscientificpractice.23

Our conclusion, then, is that thought experiments open up space for a discussion of

surprise that is more nuanced than a classification into either ‘mere’ surprise or

claims,andseealsoKind(2018)andEgeland(2019)fordiscussionsofhowwecangainnewinformationfromtheimagination.20Indeed,ithasbeenarguedthatanAristoteliancouldhavechosenthisoption—thereisnocommitmentatthistimeonthisissue(seeVickers(2013,p.196)). 21ForGendler,Galileo’srejectionoftheAristotelianview,andthe“blocking”oftheAristotelian“waysout”(whenthethoughtexperimentispresentedinitsnon-argumentform)isjustifiedbecauseittapsintoourpreviouslyunarticulatedknowledgeoftheworld(1998,407).Inthissense,heraccountdeniestheclaimthatimaginingsaresolelyconstitutedbythepersonwhoisimagining(whichwaskeytoWittgenstein’sscepticism)sincethebackgroundbeliefsthatcontributetotheimaginingcomefromtheimaginer’sexperienceoftheworld,ratherthansolelyfromtheimaginerthemselves.Stock(2007)alsodiscusseshowimaginingsarepartlyinformedbybeliefsabouttheworld.22Itisoftenhighlightedthattheimaginationhastobeappropriatelyconstrainedifitistoprovideinsightsabouttheworld.Whatweemphasisehereisnotthattheimaginationistotallyunconstrainedwhenitisfruitfulinscience,butratherthatitcanallowforreasoningthatislessrestrictivethanthatinargumentsorcomputersimulations(seealsoStuart,2020).23Focusingonimaginationallowsustocapturethissenseofsurprisewithoutcommittingtoaplatonicviewofthoughtexperiments.

confoundment.Certainly,theproductivenatureofthesurprisetheyengendersuggests

thattheformerlabelisinadequate,whereastherequirementofinexplicabilityinterms

ofthe‘giventheory’associatedwiththelatterclearlyneedstobehandledcarefully.With

thatinmind,letusnowturntoafurtherscientificarenainwhichsurprisecanarise,that

oftheoreticalderivations.

4. TheoreticalSurprise

ConsiderEinstein’sderivationofE=mc2whichPoppersubsequentlydeclaredmusthave

comeasasurprisetohim(1978,p.162).24Herethesurpriseisnotthatassociatedwith

discoveringthatapredictionturnsouttobecorrect;thatis,itisnotthekindofsurprise

associatedwithnovelpredictions.Rather,thesurpriseisassociatedwiththetheoretical

derivationitself,priortoanyconfirmationofatheoreticalprediction,whichinthiscase

hadtodowiththediscoveryofnuclearfission.ForPopper, theepistemicvalueofthe

surpriseinthiscaseseemstohavebeenthesameasthatofBecquerelbeingsurprisedat

hisphotographicplatesbeingfogged.25Thatis,justas‘material’realitymaysurpriseus,

socantheories, leadingPoppertofamouslylocatetheminhisWorldThree,or, ‘…the

worldofintelligibles,or…theworldoftheoriesinthemselves,andtheirlogicalrelations

…’(Popper1972,p.154).

Ifwetakethese‘intelligibles’asabstractentities,insomesense(seeFrench2020,Ch.5)

wecandrawaclearcomparisonwithBrown’sviewofthoughtexperiments,asdiscussed

above.Indeed,Popperinsiststhattheorieshaveapropertythatonlyexistingthingscould

have:thiselementofsurprise.Hetakesthistobeamarkoftherealityofsomething:just

as physical objects surprise us aswe discovermore about them, so too do scientific

theories.

24Ithasbeenquestionedwhetherthisissuchanappositeexample,given,ithasbeenclaimed,thattheexactmeaningofthisequationiscontentious.Whetherornotthatisthecase(andwethinknot),thisisaclearlysignificantresultaboutwhichsurprisehasbeenexpressedandwhichalsoexemplifiescertainfeaturesthatwewishtofocusonhere. 25BedessemandRuphy(2019)givetheBecquerelcaseasanexampleof‘scientificunpredictability’,inthesense of ‘the occurrence of unexpected results in the course of the inquiry that open up new lines ofresearchanddiscoveries.’(ibid.,p.3).Ofcourse,Becquerelwasalready‘primed’,asitwere,tomakesuchadiscovery,givenhisinterestinphosphorescenceandfollowingthediscoveryofx-raysbyRöntgen.

Onecouldmaintainthatthisisacaseof‘mere’surpriseandinsist,alongWittgensteinian

lines,thatthereasonswhypeoplearesurprisedbysuchtheoreticalimplicationsliein

theircognitivelimitations.Inotherwords,ifEinsteinwassurpriseditwasonlybecause

notevenhewaslogicallyomniscient.However,eventhisdoesnotmeanthatithasno

epistemicvirtueaswesawinthecaseofregardingthoughtexperimentsasarguments.

Beforeweconsiderthatpoint,itisworthnoting,however,thattheWittgensteinianline

appearstofalterinthiscase,simplybecauseEinstein’sproofisfamouslynotthatlong,

withtheentirepaperrunningforonlythreepages.

Einstein begins bynoting that ‘[t]he results of the previous investigation [namely his

papersettingoutthebasisofSpecialRelativity]leadtoaveryinterestingconclusion…’,

anopeningsentencethatmayindeedindicatehissurpriseattheresult.Hetheninvokes

Maxwell’sequations,which,ashenotes ina footnote, incorporate theprincipleof the

constancyof thespeedof light,and theprincipleof relativityandapplies themto the

situationinwhichwehaveanextendedbodyemittingapairoflightpulsesinopposite

directions,effectivelyoutlininganotherthoughtexperiment.26

Einsteinthenconsidersthechangeintranslationalkineticenergyofthebodyasaresult

ofemitting the lightpulses.Theproblemis, theexpression for thekineticenergyofa

particle isnotstraightforwardlyextendable to thatofanextendedbody inrelativistic

physics.So,Einsteindefinedthekineticenergyofsuchabodymovingwithspeedvina

giveninertialreferenceframeasthedifferencebetweentheenergyofthebodyinthat

referenceframeanditsenergyinaninertialreferenceframeinwhichitisatrest(see

Ohanian2009, p. 168).With this at hand, he could then obtain an expression for the

changeinkineticenergyofthebodywhenitemitsthepulsesoflightinitsrestframe,as

observed from amoving frame. Finally, he took the low-speed approximation of the

energy,byneglectingmagnitudesoffourthandhigherorders,andsubstitutingthatinhis

expressionheobtained,inmodernform,E=mc2.Interestingly,givenwhatwastocome,

he concluded with the speculation that ‘It is not impossible that with bodies whose

energy-content isvariabletoahighdegree(e.g.withradiumsalts) thetheorymaybe

successfully put to the test’ (1905 p. 3). On theWittgensteinian approach,wewould

26Thus,wemightviewthiscaseasakindofhybridofthesortofthoughtexperimentsexaminedaboveanda‘pure’theoreticalderivation.

expectshort,simplederivationstobeunsurprising.Thus,giventhebrevityandapparent

simplicity of the derivation, this approach cannot account for the surprise felt over

Einstein’sresult.27

Why,then,wouldEinstein,oranyoneelse,havebeensurprised,asPoppersuggests?

Thequestionbecomesevenmoreacuteonceitisacknowledgedthatsomerelationship

betweenmassandenergywaswell-knownatthetimeinthecontextofelectromagnetic

radiation.ThelikesofHeaviside,AbrahamandLorentz,amongothers,all investigated

howthemassofachargedobjectchangesinanelectromagneticfield,yieldingthenotion

of‘electromagneticmass’,withHasenöhrlderivingtheexpressionE=(4/3)mc2.Poincaré

(who together with Lorentz is famously associated with the ‘discovery’ of Special

Relativity)didexpressanattitudeofsurpriseinthiscontext,butassociateditwiththe

conclusionthatifmass,asan‘essentialpropertyofmatter’isreducibletoenergyinthis

manner,thenmatteritselfcannotbesaidtoexist (Poincaré1906).

PerhapstheanswertoourquestionliesintheobservationthatEinstein’sresultreplaced

the above line of research with the relationship between E=mc2 and more general

principleshavingtodowiththenatureofspaceandtime(somethingdrivenhomeby

Minkowski’s ‘reformulation’ofthetheory).Inthatcasethesurpriseisassociatedwith

theestablishmentofsucharelationshipbetweenanalreadyknownresult(broadlyand

grantedthedifferenceinnumericalfactor)andthesegeneralprinciplesthateventually

cametobeappreciatedasunderpinningaverydifferentviewoftheworld.28Theanswer,

then,toPopper’squestionisthatEinsteinwasthefirsttoobtainthatrelationship.

Certainly, many years later, Meitner recalled her own surprise over Einstein’s result

whenhepresenteditinatalkinSalzburgin1909,writing:

‘AtthattimeIdidnotrealisethefullimplicationsofthetheoryofrelativityandthe

wayitwouldcontributetoarevolutionarytransformationofourconceptsoftimeand

space.Inthecourseofthislecturehedid,however,takethetheoryofrelativityand

27 Havingsaidthat,thederivationisflawed(foranoverview,seeOhanian2009). 28WearegratefultoAaronMeskinforacoffeehouseconversationonthisissue.

fromitderivetheequation:energy=masstimesthesquareofthevelocityoflightand

showedthattoeveryradiationmustbeattributedaninertmass.Thesetwofactswere

sooverwhelminglynewandsurprisingthat,tothisday,Irememberthelecturevery

well’(Meitner1964,p.4;seealsoRife2019andSime1997,p.39)29

Meitner,ofcourse,togetherwithOttoFrisch,subsequentlyusedtheformulatoexplain

nuclearfission,makinggoodonEinstein’sobservationinthepenultimatelineofhis1905

paperasindicatedabove.

Granted, then, the surprise associated with Einstein’s result, what is its epistemic

significance, if any?Again,wehave to take carewhen it comes to the requirementof

inexplicabilityinthecontextofagiventheory.IfthatistakentobeSpecialRelativityitself,

thenclearlytheresult,beingderivedfromthattheory,isnotinexplicableintermsofit!

However, the above historical considerations suggest that we should take the ‘given

theory’ to be the classical ‘electromagnetic worldview’ of the time, with any

confoundment,inMorgan’ssense,associatedwiththeestablishment,inthatcontext,of

thederivationof the relationshipbetweenenergyandmass– somesuch relationship

havingalreadybeenposited–fromafundamentalreconceptualizationofspaceandtime.

Furthermore,asinthecaseofthoughtexperiments,reflectingonthesurpriseassociated

withsuchtheoreticalderivationssuggeststhatitshouldbecharacterizedas‘productive’.

Inthenextsectionweshallconsiderhowthisformofsurprisemightbesituatedwithin

anappropriateepistemicframework.

5. SurpriseandTheoreticalFertility

ConsideragaintheexampleofBecquerel’sdiscovery:notonlywasitdisruptive,inaway

thatmightbepartially,atleast,capturedbythenotionof‘confoundment’butitwasalso

fruitful.Itwasdisruptiveinthatitoverturnedexistingaccountsofradiativephenomena

and,ultimatelyofcourse,itcontributedtotheoverturningofclassicalphysics;anditwas

29 It has been suggested that what surprised Meitner were the technological implications of the result. However, granted that she is recalling her past surprise, this does not seem plausible given that such implications were not apparent in 1909.

also,clearlyandrelatedly,immenselyfruitful,withBecquerelhimselfpublishingseven

papersonthephenomenonimmediatelyafterwards,initiatinganintenseprogrammeof

researchinvolvingtheCuriesandmanyothers,ofcourse.Jumpingaheadover120years,

followinghersurveyofscientistsworkingattheLargeHadronCollider,Ritsonconcluded

that‘Thekindsofnoveltyframedasmostvaluablearethosethatviolateexpectationsand

aredifficulttoincorporateintotheexistingstructuresofknowledge.Insuchinstances,

disruptiontotheexistingontologyorwaysofknowingwerevalued’(2020,p.2).30

In this case, involving the discovery of novel properties of particles, she argues that

scientistscashoutthevalueofsuchnovelresultsintermsofindicatingadirectionfor

future research: ‘This appraisal that potentially theoretically unexpected results can

provide future fertility helps us to begin to understand how results that contradict

expectationscanbevalued.’ (ibid.,p.7).Thus,Ritsonargues, thepositiveappraisalof

disruption is based on forward looking assessments of future fertility, or forms of

heuristicappraisal.Shenotes,inparticular,thecommentsofscientistswhoareeffusive

in their assessment of the fertility of a disruptive result because it would point

researchersinthedirectionoffutureresultsthatmightaccommodatethedisruption.

Here,contradictingexpectationsmightbeunderstoodasgoingbeyondbeinginexplicable

in terms of a given theory and in this sense, being disruptive is broader than

confoundment.Theinterchangeabilityofmassandenergyisappropriatelycharacterised

as disruptive in this sense and, as expressed by Einstein, was also fertile in that it

indicatedthedirectionoffutureresearch.Thissenseof‘futurefertility’wascapturedby

Peirce with the phrase ‘esperable uberty’, applied to the ‘hoped for’ ‘fruitfulness’ or

‘fertility’ of scientific theories (see French 1995). Peirce himself characterised this in

termsofbeing‘gravidwithyoungtruth’(1913).

30Asoneoftherefereeshasremindedus,weshouldbecarefulnottogeneralisetoofarfromthiscasestudyastheremaybeexamplesofresultsthataresurprisingbutarenotdisruptive.OnesuchthathasbeensuggestedistherecentcaseoftheGoogleDeepMind‘AlphaFold’proteinfoldingalgorithmthatcanapparentlyaccuratelypredictmanyproteinstructuresfromtheiramino-acidsequence.However,manycommentatorshaveemphasisedthatthisdoesnotsolvethe‘protein-foldingproblem’insofarasnoexplanationisgivenforthestructuresobtainedandinthatrespectthisisnotacaseoftheoreticalderivation,whichiswhatwe’reinterestedin(see,forexample,Ball2020).

Thequestionthennaturallyarises,onwhatbasismightwetakesuchfertilityinatheory

tobe‘hopedfor’?Andfurther,howmightweevaluatewhetheragiventheoryismoreor

lessfruitfulthanothers?Wesuggestthatthesurpriseevincedbycertainconsequences

ofthetheoryisonewayofdeterminingits‘esperableuberty’.

ThisseemsevidentinthecaseofE=mc2,particularlygiventhattherelationshipbetween

mass and energy had already been noted in the special case of the electromagnetic

context.That itcouldbegeneralisedthroughbeingderivedfromthetheoryofSpecial

Relativityisindicativeofthewaythattheorycanberegardedas‘gravidwithyoungtruth’.

AndthehopethatitwouldbefruitfulwasthenconfirmedbyMeitnerandFrisch’sresult.

Recent discussions of the value of such theoretical fertility have been shaped by

McMullin’s (1976) distinction between fertility in terms of the actual success that a

theoryhasinopeningupnewavenues,dealingwithproblemsandanomalies,etc.,which

hecalls‘proven’orP-fertility;andfertilityinthesenseofdesignatingthepotentialofa

theory for future development,which he calls ‘untested’ orU-fertility. The former, of

course,isretrospective,andisassociatedwiththeepistemicappraisalofatheory,being

indicativeofsomedegreeof‘fit’,again,betweenthetheoryandtherelevantsystem(ibid.,

p.264),whereasthelatterisassociatedwithitsheuristicappraisal.

InthecaseofE=mc2,weseemtohaveanobviouscaseofamovefrom‘U-fertility’in1905,

or1909inMeitner’scase,to‘P-fertility’in1939,thetheory’sfertilitybeing‘proven’by

thediscoveryofnuclearfission.Note,however,thatitisnotacaseofovercomingsome

anomaly,asMcMullinhasit,butratherthatoffertilitymanifestedintermsofa‘newand

powerful’extensionofthetheoryofrelativity.However,ifU-fertilityistakentohaveonly

heuristicvaluethenitandthesurpriseassociatedwiththetheoreticalentailmentprior

toitsconfirmationandshifttoP-fertilitymightappeartohavenoepistemicvalueatall

(seeNolan1999).However,thisignoresthe‘esperable’orhopedforaspect.Werecall,

again, that although the extension of Einstein’s theorywas ‘new’ andhencemight be

regardedastheoccasionforsurprise,therelevantphenomenon,generallycharacterized,

wasnotentirelynovel.Aswehavesaid,thissuppliedgroundsforhopethatthetheory

was indeed fertile. And this in turn suggests that, as with ‘mere’ surprise and

confoundmentweneedtomovebeyondMcMullin’sclassification,atleasttosomedegree.

Consider:the‘potential’thatatheoryhasforfurtherdevelopmentmaybefarranging,

covering all sorts of possibilities, from the trivial to the implausible. How shouldwe

determinewhichareindicativeofthetheorybeing‘gravidwithyoungtruth?Disruptive

surprisemayactasa‘flag’insuchcases.Einstein’stheoryofSpecialRelativitywas‘U-

fertile’inallsortsofways,ofcourse;anditsP-fertilitywas(eventually)demonstrable.

ButwhatMcMullin’sdistinctionfailstocaptureisthe ‘esperable’orhopedforfertility

markedbythekindsofexpressionsofsurprisewehavenotedhere.Thus,thisexample

nicelyillustratesthatthedivisionbetweenheuristicandepistemicappraisalmaynotbe

ascleanassomemighthope(seealsodaCostaandFrench2003,Ch.6).31

6. Conclusion:TheDisruptiveNatureofSurprise

We began by considering Morgan’s distinction between ‘mere’ surprise and

confoundment,wherethelatterisdistinguishedfromtheformerbyvirtueoftherelevant

result being inexplicable in terms of a given theory and thereby laying beyond our

control.Wehavearguedthat,firstofall,considerationsofthevalueofsurpriseinscience

shouldbe extended to thought experiments and theoreticalderivations and secondly,

thatitisusefultoseetheseasalsomorethan‘merely’surprisingandasdisruptive,ina

productivesensethatisbroaderthanconfoundment.32

Inallofthecasesconsideredherewecantiethesurpriseinvolvedtoacertain

disruptivefeature.InthecaseofbothGalileo’sthoughtexperimentandEinstein’stheory

of Special Relativity, the disruption was to pre-existing theoretical frameworks. It is

perhapsalmosttrivialtodescribetheE=mc2resultasdisruptive,giventhesubsequent

31Arefereehassuggestedthattakingsurpriseasamarkoffruitfulnessmightberelatedtocertainaccountsofcreativity(see,forexample,Livingston2009andThagardandStewart2011).TheremayalsobeaconnectiontowhatSheredosandBechtel(2020)call‘imaginativesuccess’,wherebyapossiblemechanismisimaginedthatcohereswiththeavailableevidenceandistakentobehypotheticallycapableofproducingarelevantexplanandumrelatingtosomephenomenon(itisthenanothersteptodeterminewhetherthatmechanismisactuallyresponsibleforthatphenomenon).Thereismoretosayhere,particularlywithregardtotheroleoftheimagination,butweshallleavethatforanotheroccasion. 32Notethatourargumentsheredonotrequireonetoadoptarealiststancetowardseithertheoriesorthoughtexperiments.Onemightbeananti-realistofwhateverkindandstillmaintainthatsurpriseingeneralisvaluableinscience,notleastasindicativeofacertainfruitfulness,aswehaveindicatedhere,wherethatisdisengagedfromanynotionofthetheoriesthataredevelopedasaresult‘latchingonto’theworld,inwhateverrealistsense.

history.Nevertheless,itisworthnotingthatitcanbeseenasmultiplyso,beginningwith

remarksastoits‘cosmicalimportance’(Aston1922),andcontinuingwiththegrowing

realisationoftheimplicationsofFrischandMeitner’suseofit.Justasscientistsvaluethe

disruptiveexperimentalresultsinvestigatedbyRitson,sotheyvaluethisaspectofboth

thoughtexperiments,suchasGalileo’sandtheoreticalderivations,suchasEinstein’s.

Ofcourse,thisisnottheonlyrespectinwhichsurprisemayhavevaluealthough

itmaybe themost pertinent in the theoretical context. And although it is difficult to

conceiveofphenomenainandof themselvesas ‘fertile’ inthisrespect,onecansurely

extend the notion beyond themost theoretical levels to those typically described as

‘phenomenological’.33

Our core claim, then, is that focussing on this disruptive aspect allows us to

articulate an account of ‘productive surprise’ that accommodates surprising thought

experimentsandtheoreticalderivations.Wesuggestthatthisoffersabroaderand,aswe

havesaid,moreusefulperspectivefromwhichtoviewsurpriseinscience.34

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