1. No category

Science as (Historical) Narrative
Author(s): M. Norton Wise
Source: Erkenntnis (1975-), Vol. 75, No. 3, WHAT (GOOD) IS HISTORICAL EPISTEMOLOGY? (
November 2011), pp. 349-376
Published by: Springer
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Erkenn
(2011)75:349-376
DOI 10.1007/S10670-01
1-9339-2
Science
as (Historical)
Narrative
M. NortonWise
27September
21October
Received:
27September
2011/Accepted:
2011/Published
online:
2011
MediaB.V.2011
Science+Business
© Springer
mode of explanationin physicsvia deductionfrom
Abstract The traditional
I
herewithexplanationvia simulations.
partialdifferential
equationsis contrasted
different
arguethatthedifferent
technologies
employedconstitute
languages,which
The narratives
thataccompanysimulations
and
different
sortsofnarratives.
support
theirmeaningare typicallyhistoricalor naturalhistoricalin kind.They
articulate
themto
explaincomplexphenomenaby growingthemratherthanby referring
come
generallaws. Examplesof such growthsimulationsand growthnarratives
in quantumchaos,snowflake
and
fromtheevolutionof wave functions
formation,
Etruscangenetics.The examplessuggesta few concludingremarkson historical
explanation.
1 Introduction
The followingreflections
derivefromtwoquitegeneralfeaturesof contemporary
role of technologiesin science.The
science.The firstconcernsthe all-important
in
I willbe seekinga
modes
of
scientific
secondis a remarkable
explanation.
change
the
role
of
narrative.
relationbetweenthesetwofeatures
through
in
have come to regardtechnologies
Concerning
technologies,
manyhistorians
We
scienceas providingtools to thinkwith,as well as to workwithmaterially.
andaction,oras technologies
regularly
analyzetheirroleas activeagentsofthought
Butin thisthehistory
anothermajordevelopment.
ofknowledge.
ofsciencemirrors
The sciences themselveshave become much more intimatelytied up with
as theHistory
ofScience
20November
Delivered
2009,
Lecture,
Society
Distinguished
originally
Arizona.
Phoenix,
M.N.Wise(И)
ofHistory
forSociety
ofCalifornia,
LosAngeles
andCenter
andGenetics,
Department
University
LosAngeles,
CA90095-1473,
USA
(UCLA),
e-mail:
[email protected]
Springer
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350
M.N.Wise
thaneverbeforeand scientists
arechangingtheirviewof theirrole.A
technologies
comes fromShirleyTilghman,molecularbiologistand
quite specificstatement
presidentof PrincetonUniversity,
assertingthat"while progressin science and
can be catalyzedby entirely
new theoretical
it is moreoften
engineering
insights,
thecase thatrevolutionary
advancesspringfromthearrivalon thescene of new
to exploreunresolvedquestionswithnew
technologiesthatallow investigators
tools, or to ask previouslyunapproachable
questions"(Tilghman2009). More
broadly,considertheNobel Prizesin physicsawardedin 2007 fortheharddisk
and again in October2009 forfiberopticsand digital
(giantmagnetoresistance)
cameras(chargecoupleddevices).Not everyonewelcomesthechange.Exemplary
is a recentarticle by Paul Forman decryingthe primacyof technologyin
(Forman2007).
postmodernity
Turningto modes of explanation,a numberof historiansof science have
in surprising
observedthatexplanationsare becominghistoricized
ways. Sylvan
Schweberpioneeredsuch reflections
and othershave developedsimilarviews
(Schweber1993; Dalmédico 2004, pp. 83-85; Wise 2004; Creageret al. 2007).
Withrespectto physicsin particular,
theideal ofdeductionfromtimelessuniversal
laws has been losing its grip in favorof formsof explanationthathave an
historical
character.
increasingly
- suggestthatwe need
- on technology
Thesetwoobservations
andon historicity
a way to talkaboutexplanations
thatincorporates
therelationship
betweenthem.
One possibility,and the one I will propose here, is to treattechnologiesof
formsof explanatory
I
narratives.1
knowledgeas languagesthatsupportparticular
will develop this viewpointwith respectto mathematical
physics,comparing
explanationvia deductionfrompartialdifferential
equationswithexplanationvia
withextensionto an historical
In conclusion,I willsuggest
simulation.
simulations,
thattraditional
ofhistory
tocomparenarrative
philosophy
requiresa majorupdating
history,not with deductionfromgeneral laws (a comparisonthat has been
inthefieldfor50 years)butwiththemorenarrative
formofsimulations.
ubiquitous
2 WrittenLanguage as Material Technology
A starting
in literary
criticism
thatexplicitlytreat
pointcan be had fromwritings
written
A recentexampleis RussellBerman's FictionSets
languageas technology.
Culture.Bermantreatswritten
, Liberty
, and Western
youFree: Literature
language
as a materialization
ofspeech.Whilespeechdependson face-to-face
contactandon
oral tradition,
of
writingmaterializesspeechby providinga visualrepresentation
1 In
ontherelation
oftechnologies
tonarratives
I aminspired
works
of
reflecting
directly
bytherecent
onthewaynarrative
functions
intheuseofmodels
2001,2007).
Mary
Morgan
byeconomists
(Morgan
More
I havelongfollowed
theworks
ofHans-Jörg
forexample,
histhoughts
on
generally,
Rheinberger,
andReflection
ch.11):"Experimental
contain
remnants
ofolder
Narration,
(1997,
Historiality,
systems
as wellas shreds
narratives
andtraces
ofnarratives
havenotyetbeenrelated"
that
(p. 186).Theyare
ofepistemic
relevant
onnarrative
structure
inevolution,
sources,
"generators
novelty"
(p.229).Other
andmathematics,
are(Beer1983;Haraway
are
1989;Alexander
2002),although
primatology,
they
concerned
with
howstructures
ofscientific
broader
cultural
narratives.
express
primarily
understanding
Springer
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Narrative
as (Historical)
Science
351
to some degreeobjectifieslanguage(in the
oral expression.This materialization
to
senseof makingit intoan object)and thereby
providesa measureof autonomy
the writtentext. "The materializedrealizationof language in writingis the
of literature"
conditionthatallows fortheautonomization
(Berman2007, p. 64).2
is notone of technological
determinism
butof technological
Berman's argument
within
a
social
context
of
political,economic,and
possibility,figuredalways
In
and
written
action.
societies
cultures,
languagecompeteswith
complex
religious
modes of writing
othermodes of symbolicexpression(e.g., art) and different
but
the process of
with
each
other
(literature,
history,philosophy),
compete
its
This
has
reached
is general.
process
pinnaclein alphabetic
symbolicabstraction
which
the
canonical
example
suggeststhe place of
languages Greek being
"
I
will
in
Berman'
s
title.
add
mathematical
"WesternCulture
languagesto this
assessment.
of written
The keycontribution
language,on Berman's account,is autonomy:
ofthewriter
andofthereader,inbothspace
ofthetextandwithitautonomy
autonomy
and time.In otherwords,writingmay be said to provideour most pervasive
of distance"in space and time(Porter1995,pp. ix, 14, 92, 200-208;
"technology
1999). Thus writtenlanguagelooks somewhatlike BrunoLatour's "immutable
mobiles" (Latour 1986, 1990, 1999). But like them,Berman's languages as
norparticularly
mobileunlessmediations
areactuallyneither
immutable
technologies
of manykindsfacilitatetheirmovement,
typicallyby continualtransformation.
Nevertheless,
knowledgethrough
objectification.
theydo support
traveling
The autonomy
ofwritten
languageis also crucialto itsroleas a vehicleofcritical
andin scienceas itis in
Thisis as trueinhistory
andcreativeimagination.
reflection
and acting,
thecapacityto createnew waysof thinking
literature.
Writing
supports
as shown,forexample,byKlein(2003). Such a claimwouldnotbe at all surprising
ifwe werethinking
X-rayimaging,
onlyof theusualsortof materialtechnologies:
electronmicroscopy,PCR (polymerasechain reaction),GWAS (genome wide
associationstudies),orfMRI(functional
magneticresonanceimaging).We tendnot
to thinkof writtenlanguagesin the same way, but we should.Their creative
ofparticular
in part,I willargue,thecapacityto supportnarratives
function
reflects
takeon different
formsindifferent
kindsabouttheobjectsofscience.The narratives
formin mathematical
areasandtheychangeovertime.It is thischangein narrative
based on deductions
from
bycontrasting
explanations
physicsthatI willexemplify
equations(PDE's) withexplanationsobtainedfromcomputer
partialdifferential
simulations.
3 Partial Differential
Equations in the Historyof Physics
a
in thehistoryof physics,and certainly
One of themostpervasivetechnologies
of
the
of
creative
has
been
continually
evolvinglandscape
imagination,
technology
2
historicist
as a defense
Berman
wants
toemploy
hisviews
onlanguage
against
postmodern
Although
A keysource,
onthat
andfoil,for
much
ofhisdiscussion
doesnotdepend
relativism,
perspective.
Berman
is (Ong1982).
â Springer
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352
M.N.Wise
PDEs and methodsof solvingthem.Theyconstituted
fornearly200 yearsboththe
meansand thegoal of explanation.
Canonicalexamples,roughlyin chronological
order,include:Lagrange'sequations,Laplace's equation,thediffusion
equation,the
wave equation,the Navier-Stokesequation, Hamilton'sequation,Maxwell's
equations,theSchroedinger
equation,and manyothers.The ubiquityof PDE's in
is
reflected
in
the
toolboxesof mathematical
standardized
physics
techniquesthat
of
to
to
the
twentieth
learned
deal
with
thearrayof
everyphysicist
century
employ
and
circumstances
in
which
could
be
These
texts-as-toolboxes
systems
they
applied.
cametobe knownsimplybytheirauthors'names,forexample:CourantandHilbert
(1953) or Morse and Feshbach(1953). Courantstressedin his Prefaceto their
of the
Englisheditionthattheysoughtthe unityof sciencethrough
preservation
relationbetweenphysicalintuitionand mathematics:"MathematicalMethods
in problemsof physicsare developedand theattempt
is madeto shape
originating
resultsintounifiedmathematical
theories"(Courantand Hilbert1953, pp. v-vi;
however,Courantand Hilbert
p. 265). Despitetheirappeal to physicalintuition,
the
bare
tools
of
mathematical
methods.
The physicist
mustcome to
provideonly
the toolbox familiaralreadywith a wide range of physicalproblemsand an
whichthemathematical
methodsshouldhelpto
accompanying
physicalintuition,
and
to
refine.
This
intuition
is
essential
to
creative
use of thetoolbox.
develop
any
it
relates
the
to
a
PDE
a
Typically,
physicalproblem
through storyabouta pieceof
theworld.It is thisrelationof storyto mathematical
structure
thatinterests
me here
(Morgan2001, 2007).
We can easily generatean instructive
wherewe
exampleforheatconduction,
seek to explain how an initialconcentration
of heat spreads out througha
conductingmaterial.Modernphysicistscome to the problemknowing(at least
thatJosephFourieranalyzeditat lengthin hisAnalyticalTheoryofHeat
implicitly)
- heat
of 1822andthathe treateditin termsof measureablemacroscopic
quantities
- and macroscopicparameters
and temperature
of thematerial conductivity
and
- independent
heatcapacity
of whatheatmightbe.3Subsequently,
we do nothave
tostartout,as Fourierdid,byreflecting
on thenatureofheatandbyarguingagainst
the then-reigning
Laplacian view that physicalexplanationsshould reduce to
betweenatoms,althoughwe do need to have a similar
microscopicinteractions
background
storyat hand.
Followingthe spiritof Fourier'sanalysis,we can begin our storyof heat
witha picture,
conduction
metalbarheatedbriefly
at thecenter
Fig. 1, ofa uniform
to producean initialtemperature
distribution
and
the
T¡
by imagining bar to be
and
on
all
that
itconductsheatonlyalong
insulated
so
sides,
infinitely
long
perfectly
itslength.To appreciatetherendering
of thestoryas a materialization,
it is helpful
to see it as actuallybeingwritten
outwithpen and paper,associatingthesketched
mathematics,
diagramwitha simplified
usingA to symbolizea verysmallchange.
Withinthe idealized sketchwe remarkfurther
thatno heat should be lost in
or
that
the
heat
element
Ax of thebar AF/Axshouldbe
conduction,
leavingany
3 Foranaccount
ofthehistorical
ofthis
move
from
tomacroscopic
for
analysis
significance
microscopic
British
see(Smith
andWise1989,
Itwascritically
for
such
diverse
areas
physics,
important
pp.149-168).
as electrostatics
thewavetheory
of light(MacCullagh),
elasticsolids(Stokes),
and
(Green),
(Maxwell).
electromagnetic
theory
£) Springer
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as (Historical)
Narrative
Science
353
*T
n
/
4r
-+
л*
/ y-
y
Ыо
"¿7 - ~ л Zi
•=.
F
с
( 6tfy'Juí.f«'í?>i)
'
Лх ч
- л их:
^-f&L)
(.ДХУ
ЛХ■УГ
?х*
¿>Г
_ ik¿r
*"
с п
in an infinitely
distribution
bar,withan initial
T¡
Fig.1 Heatconduction
longmetal
temperature
intime
to7}
spreading
withtimeAT/Atmultiplied
bytheheat
equal to itsrateof decreaseof temperature
capacitya ,
AF/Ax = -aAT/At.
theempirically
rulethatthefluxofheatat anypoint
Thenwe incorporate
supported
to thetemperature
shouldbe proportional
gradientthere,
F = -cAT/Ax,
of thebar.Substituting
thesecondequationin thefirst
whereс is theconductivity
we obtain,
A(AT/Ax)/Ax = (a/c)AT/At.
To putit intotheformal
Thisequation,however,is notmathematically
rigorous.
in
of
differential
we
need
to
call
ourbackground
language partial
equations,
story
aboutatomsto justifytreating
a finitephysicalelementof thebar,containing
the
atoms
to
the
and
as
that
contribute
a
c, an
many
together
macroscopicparameters
at all. If the
infinitesimal
mathematical
elementhavingno microscopicstructure
to
arguments
storyis plausible,thenwe can carryoutsomestandardmathematical
convertA in theprevioussequenceintoa partialdifferential
9 bytakingthelimitas
theelementshrinks
to zero.4The processwillyieldthepartialdifferential
equation,
=
a2T/0x2 (a/c)0T/0t.
in space
ThisPDE, calledthediffusion
equation,shouldgovernthedevelopment
andtimeof anyinitialtemperature
distribution
T¡ intoa laterone 7}, as indicatedin
Fig. 1. There is nothingparticularly
strikingabout our narrativeexcept thatit
4 Fourier's
ownrationale
forthis
standard.
Poisson
anentire
wasbynomeans
(1835)devoted
procedure
booktochallenging
itsvalidity.
Springer
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354
M.N.Wise
a perfectly
standard
exemplifies
procedureforderivingPDEs in physicsand thatit
outusinga specializedlanguagethatphysicists
is written
havelonglearnedto speak
and to writeas the naturallanguageof theirsubject.The result,as the written
and objectified
of ourthinking
about
equation,givesa materialized
representation
theproblemof heatconduction.
In orderto interpret
theconsequencesof our reasoning,we have now to find
solutionsto theequation.Luckily,physicists
haveonlyto openCourantandHilbert
to finda conciseversionofFourier'sfamoussolution,theFourierseries,alongwith
a proofthat the series will convergefor any physicallyrealistic(piecewise
continuous)function.5
Theyprovidea deductiveproofof thegeneralformof the
- and thisis now thebasic
solutions.But deductions,
to be physicallymeaningful
where
point requirespecificsettings,
interpretation
playsa crucialrole.
Considerthe analysisthatWilliamThomson(laterLord Kelvin) presentedin
1846. For his inaugurallectureas Professorof NaturalPhilosophyat Glasgow
he enteredthe debate over the source of the earth'sheat and the
University,
of theincreaseof temperature
withdepthobservedin deep mines.Did
significance
thedistribution
resultfroma primitive
centralheat,graduallycoolingovertime,as
Fourierhad argued,or fromothereffects,
suchas thesolarsystemhavingmoved
intoa regionofcoolertemperature,
as Poissonsuggested?
Thomsonapproachedthe
problembyaskinga question:couldthediffusion
equationalwaysbe runbackwards
froma present
stateto a preceding
state.He distinguished
threecases,depending
on
whether
theFourierseriesfora temperature
distribution
wouldconvergeordiverge.
he believed,impliedthatitcouldnotbe the
Divergenceforanypresentdistribution,
foronlya finite
productof anypreviousstate,or could have no age; convergence
wouldimplya finite
for
pasttime,precededbydivergence,
age; whileconvergence
all past timewould implyan unlimitedage. Only adequatedata on the present
distribution
of temperature
wouldsufficeforchoosingbetweenthealternatives,
but
Thomson'sown beliefscertainly
inclinedhimtowarda finiteage.6
His analysisdependedon a subtlestoryaboutthedistinction
betweenphysical
and mathematical
withrespectto sharptemperature
impossibility
impossibility
He wouldsoon
changes(cusps,corners,
jumps,etc.),whichhe thought
divergent.
realizethatthisintuition
was untenable.Nevertheless,
it is apparentthatalthough
Thomsonwroteout his argument
in theformof a deductiveproof,thediffusion
creationnarrative
abouttheoriginand
equationcarriedwithit a deeplymeaningful
would enterdirectlyintohis enunciationof the
age of theearth.This narrative
SecondLaw of Thermodynamics
in 1850/51.
I stressthenarrative
because
we do notnormally
thinkof mathematical
aspect
deductionsas narratives.
and
Hilbert
Courant
do
their
best to striptheir
Indeed,
mathematical
methodsof all narrative
elements.And yet,the toolboxcannotbe
thenarrative
back in. This is
constructively
employedin theworldwithout
putting
with
to
economic
models.
MaryMorgan'sargument respect
5 Courant
andHilbert
refer
thereader
to"elementary
(1953,
pp.69-73).Forphysical
they
applications,
texts"
forpiecewise
continuous
functions
wasgiven
in
(p.4,n.l).Theconvergence
proof
byDirichlet
1829(1889)and(1837).
6 Discussion
andreferences
in(Smith
andWise1989,
Thomson
maynotyethavebeen
pp.192-194).
with
s work
familiar
Dirichlet'
onconvergence.
â Springer
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as (Historical)
Science
Narrative
355
a modelrequiresa narrative
This activityof manipulating
device,such as a
sets
off
a
told
with
the
model.
which
The
structure
or system
question,
story
in
and shapesthestoriesthatcan be told,but
portrayed themodelconstrains
withoutstoriesshowinghow thestructure
works,we cannottell whatmight
elements,we cannotapply
happenin specificcases. Withoutthesenarrative
model-structures
directlyonto the facts of the economic world, nor
in themodel
worldrepresented
demonstrate
outcomesaboutthehypothetical
(Morgan2001, p. 361).7
To put this in the termsif my own example,the mathematical
technologyas
of
differential
and
their
solutions
equations
providesa (nonlanguage partial
to which physicistsattachinterpretive
narratives
narrative)deductivestructure
of the courseof
abouta wide varietyof phenomena.That deductivestructuring
an explanation
in physics.The explanatory
eventshas longdefinedwhatconstituted
has
been
on
the
to
the
exclusionof the attached
deduction,
however,
emphasis,
in explanation.
and withthat,theexclusionof anything
like historicity
narratives,
4 QuantumChaos
PDE's
Turnnowto morerecentworkin physicsthatbeginsto introduce
historicity.
has
of analysisin manyareasbuttheirrelationto explanation
are stillthemainstay
the
Their
weakness
had
been
that
since
1970s.
always
they
changedfundamentally
weresolubleonlyforrelatively
simplesystems(e.g.,theSchroedinger
equationfor
the hydrogenatom withone electron)and became unmanageablefor the vast
which
ofreal-world
majority
problems(e.g.,an atomwithmorethantenelectrons),
In
involve
mathematics.8
these
areas
of
intractable
complexity,
computer
typically
whetherbeginningfroma PDE or not,have becomethe meansand
simulations,
perhapseven the goal of explanation.The temporaldevelopmentof a robust
simulation,typicallyfollowedvisuallyon screen,now explainsthe dynamical
of knowledgehas changeddramatically.
behaviorof thesystem.The technology
the
One cannotlearnit fromCourantand Hilbert.It requiresinsteadmastering
and
non-linear
associated
of
dynamics,
languages computationalmathematics,
visualizationsoftware.These new modes of speakingand writinghave changed
bothwhatcan be knownand how it can be known.And theybringwiththem
thatare morehistoricalin form.
narratives
explanatory
An examplecomesfromthearea of quantumchaos,itselfa kindof oxymoron,
sincethequantumuncertainty
principleoughtto blurthesensitivedependenceon
classicalchaos and shouldsmoothoutquantum
initialconditions
thatcharacterizes
7 In "Prisoner's
2x2
howtheapparently
Dilemma,"
(2007)illuminates
poverty-stricken
Morgan
thestories
with
which
forthefamous
a rich
andvaried
setofmeanings
matrix
dilemma
through
acquires
surround
it.
economists
andinterpret
8
ofdeductive
andreductive
andPines
andgivea polemical
(2000)citethissituation
critique
Laughlin
that
a fundamentally
different
mechanics
intheir
manifesto
forthetwenty-first
arguing
quantum
century,
is required
thecomplex
ofeveryday
lifeandtheir
todealwith
emergent
properties.
approach
systems
collaborators
newphysics
of"complex
matter"
andtheir
callthis
thestudy
They
adaptive
(p.30).They
in(Laughlin
etal.2000).
extend
tomesoscopic
bio-molecular
theanalysis
including
systems,
systems,
â Springer
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M.N.Wise
356
thebehavior
Fig.2 Simulating
ina stadium
ofelectrons
billiard
andTomsovic
1993,
(Heller
p.43)
wave functions.
A quite accessiblediscussionof representative
phenomenawas
givensome timeago by Eric Hellerand StevenTomsovic.9Considera geometry
of either
calleda stadiumbilliard(Fig. 2), forwhichtheboundary
maybe thought
as a ringof iron
as a wall thatreflects
electronsor experimentally
theoretically
It shouldlie in the
atomsimplantedon a sheetof copper.Its size is important.
mesoscopicborderregionbetweenthemicroscopicworldof quantummechanics
and the macroscopicworldof classical mechanics(roughly,betweenten and a
forelectronsmoving
thousandatoms).The problemis to findthewave function
aboutin thisbilliard.The Schroedinger
equationshouldgovernthequantumwave
butit is notsolubleexceptby numericalmeans,defying
function,
physicalinsight,
whiletheclassicalmotionis chaotic,so thatthereare no stableclassicalorbits.
thatEricHellerpioneeredin 1984,he and Steven
Nevertheless,
usingtechniques
Tomsovicwere able to findsolutionsby usinga conceptuallysimplecomputer
simulation(Heller 1984). It beginsfroma semi-classicaldepictionof bundlesof
"electrons"are strange
particlesbouncingaroundtheenclosure.These substitute
billiard
balls
but
have a phase and
hybridobjects. They move like classical
and
interfere
associated
with
them.
Therefore,they
constructively
amplitude
and
like
of
lower
amplitude,to
destructively waves, buildingup regions higher
simulatequantumwave functions.
"The pictureis one of a swarmof trajectories
carryingamplitudeand phase aroundwiththem" (Heller and Tomsovic 1993,
9 Heller
ofcomplexity
see
within
trends
inthephysics
andTomsovic
(1993).Ontheplaceofthiswork
WiseandBrock
(1998).
Springer
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as (Historical)
Narrative
357
andyet,
p. 42). Thatis,theyarefictional
objectswhichserveas toolsforcalculation,
as the authorsemphasize,theyyield intuitiveunderstanding
and explanationof
quantumphenomena.They do so, I will argue,as the subjectsof a narrative
an evolutionary
theirhistory,
describing
history
generated
by thesimulation.
The simulationproceeds by generatingmany thousandsof such swarms,
fromthesamepointbutwithslightly
different
directions
and velocities.
beginning
Afterbouncingaroundthestadiuma fewtimestheirsummedamplitudesyielda
wave function
distributed
theentirespace. Figure3 showscharacteristic
through
wave functions(eigenstates)corresponding
to what would be threedifferent
in the two lower
periodicorbitsfor classical particles,which are represented
theirsymmetric
twins).Along these
picturesby heavyblack lines (but omitting
wheretheparticleswouldbe reflected
back and
periodicbutunstabletrajectories,
thesimulation
revealsthatthewave functions
forth,
acquirehighamplitude.
This remarkableresult, which Heller named "scarring" in his original
publication,is unexpectedquantummechanically.Yet the simulationmakes it
in terms of the physical intuitionsof classical mechanics.
understandable
"Unavoidablywe thinkclassically about systemsof more than a couple of
is a matter
of
particles."For HellerandTomsovictheneedfora classicalnarrative
our everydayexperienceratherthanof any ontologicalpriority.
Theirclaims for
classicalunderstanding
are pragmatic:"We will sidestepthephilosophicaldebate
and focuson theissuesof usefulapproximations
and physicalinsight"(Hellerand
Tomsovic 1993, p. 38). And yet,emphasizingthe factthatnew phenomenaare
revealedby theclassicalmotion,theyadoptcausal language:"Periodicorbitsthat
are not too unstablecause scarring"(Heller and Tomsovic 1993, p. 42). This
ofcause to theclassicaltrajectories
attribution
of as simplya way
mightbe thought
of talking,
a semi-classicalnarrative
whosefunction
is
indeed,as a wayof forming
to show how thesimulationsassistintuition.
But theirrole extendswell beyond
intuition.
thatexistwithinthe fullquantum
They also revealphysicalproperties
solutionbutlie outsideof itsframeof reference
as "hiddendynamicalsymmetries"
role
(Hellerand Tomsovic1993,p. 40). Thatis, theyplayan essentialexplanatory
notavailableotherwise.
This is notto suggestthatquantumtheoryis false,or even
butthatin themesoscopicdomainbothquantumand classicalaspects
incomplete,
are presentsimultaneously.
Both theoretically
and experimentally
theyforma
realistichybridwhichrequiresbothquantumwaves and classical trajectories
for
explanation.
It is this strongexplanatoryrole of the hybridobjects thatI want firstto
emphasize.But the way in whichtheirnarrativeconnectsto the mathematical
simulation
fromtheheatconduction
maynotyetlook so verydifferent
example.I
wantalso to stress,therefore,
thattheexplanationof a scarredwave function
is
obtainedonlythrough
theprocessofdevelopment
in time,or "evolution,"as Heller
and Tomsovicexpressit.10The simulationgeneratesan evolutionary
explanatory
narrative
to replacethedeductivenarratives
associatedwithPDE's like
traditionally
10
willinsist
theprocess
isnotproperly
that
evolution
butonly
Nodoubt
called
Biologists
development.
arecorrect,
butI willmaintain
theauthors'
broader
andbelow
as anindication
oftheir
they
usagehere
orientation.
biological
â Springer
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358
M.N.Wise
Fig.3 Semi-classical
simulations
reveal
"scarred"
characterized
bya
eigenstates,
ofamplitude
buildup
along
orbits
(black
classically
periodic
lines
andTomsovic
) (Heller
1993,
p.40)
thediffusion
equationandSchroedinger's
equation,andthisnarrative
aspectis now
moreexplicitlypresentin theexplanation.To evoke thisaspectmoredirectly,
it
be
to
and
in
a
Heller
Tomsovic's
"swarm"
the
form
of
may helpful put
evolving
with
to
4.
reference
simplestory,
Fig.
Once upona timetherewas a localizedswarmof semi-classical
electrons
that
setouton a seriesofjourneystoexplorea stadiumbilliard.It traveledinitially
towardtherighthandend,whilegraduallydiverging.
Bouncingoffthatend,
the spreadingswarmpropagatedtowardthe leftwhile beingreflected
also
fromthe side walls, with interference
betweenits manifoldtrajectories
becomingincreasingly
complex.By thetimeits entiresystemof interfering
had
been
severaltimes,it filledthewhole
reflected
backand forth
trajectories
stadiumin a complexpattern
of amplitudes,
lookingforall theworldlike a
fullquantumwave function.
Upon repeatingthisexploratory
processmany
£) Springer
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as (Historical)
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359
ofa wavefunction
simulated
A localized
(topleft),
Fig.4 Evolution
semi-classically.
packet
traveling
itsinterfering
totheright,
isreflected
backandforth
until
fill
thestadium
and
(Heller
initially
components
Tomsovic
1993,
p.44)
times,the packet discoveredthat it could generatea varietyof special
"scarred"patterns
ofclassical
(Fig. 3), in whichthescarsrevealedtheeffects
thatlay hiddenwithinits dynamicalstructure.
periodictrajectories
They
persistedfarlongerthanexpectedin thelifeof thewave function.
This narrative
of an evolvingswarmsharesmorewiththenarratives
of natural
than
with
the
deductive
solutions
of
differential
history
partial
equations.At first
it
seem
that
the
difference
is
not
so
since
PDEs
can be said to
glance might
great,
controltheevolutionof a function
in space and time,as we saw forthediffusion
of
heat.But as partof thedeductivecharacter
of PDEs, proofsof theexistenceand
uniquenessof solutionsplay a criticalrole.No suchproofsexistforthesimulated
solutions.Theirexistenceis discoveredby the simulations,
and the solutionsare
not
the
simulations
typically unique.Instead,repeatedmanytimes,
mapouta space
of possiblesolutions.Theypresenta generative
that
does
notderivefrom
process
law
a
but
is
more
like
the
of
seed
into
a
any general
growth
plant.And it is the
the
that
the
of
morphological
properties
"plant"
developduring periodofgrowth
- that occupy the centerof
here the symmetric
orbitsand theirperiodicities
attention.
and on
bothin the mathematics
They are objectifiedand materialized,
thelanguagesin whichtheirevolutionis written.
In thissense,the
screen,through
Springer
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distributions
that emerge (the explananda) are essentiallyhistoricalobjects;
furthermore,
theycan be understood
only throughtheirhistories(explanans).I
will return
to thisagreement
of objectand explanationin conclusion.
5 Physicsas Natural History
Naturalhistorians
in morphologies,
havealwaysbeeninterested
theirdiversity,
and
theirpatternsof growth,but only relativelyrecentlyhave physicistsbegun to
mode forexploringthe architectures
of nature.An
employthe natural-historical
will
is
the
most
of
us
think
of thetypical
of
snowflakes.
study
example
Perhaps
snowflakeas exhibitingan intricatelybeautifulgeometricalpattern,highly
withsix identicalarms.This is theimagewhoseexplanationthewitty
symmetric,
Descartestoo(Fig. 5a)
Snowflake.
Keplerreducedto "nothing"in hisSix-Cornered
thehexagonalsymmetry,
highlights
notingthatit is "impossibleformento make
anythingso exact." And Robert Hooke (Fig. 5b) ascribes this perfectionof
snowflakes
to the "Geometrical
Mechanismeof Nature"(Kepler 1966; Descartes
1965,pp. 313f;Hooke 1961,p. 91).
This familiar
of ideal mathematical
formas thefoundation
fororder
assumption
and beautyin naturecontinuedto governstudiesof snowflakesfromthe 17th
thatfull
throughmuchof the twentieth
century;despitewidespreadrecognition
was veryrare.In a movethatis stilltypical,Hooke ascribed
hexagonalsymmetry
theirregularity
thathe regularly
observedunderthemicroscope
to "thethawing
and
of theflakebythefall,and notat all to thedefectof theplastickvirtueof
breaking
Nature."And stillin 1931 (Fig. 6) in a classic collectionof photomicrographs
by
W. A. Bentley,knownfortheirexquisitebeauty,onlytwo of nearly200 plates
containnonsymmetric
images,withtheremarkfromhis physicist(meteorologist)
thatthey"maybe attributed
collaborator
to fortuitous
disturbances
of one kindor
another
in thecourseof theirgrowth"(Hooke 1961,p. 91; Bentleyand Humphreys
1931,p. 14).
Thereis at leastone majorexceptionto thisrule,containedin a big volumeby
UkichiroNakaya,publishedin Englishin 1954,summarizing
his extensivework
ofsnowflakes
(1961,facing
88)
(1965,312)andb Hooke
Fig.5 Sketches
bya Descartes
Springer
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as (Historical)
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361
fromthe 1930s and early40 s (Nakaya 1954).11Trainedas a nuclearphysicist,
in thenorthofJapan,
Nakayafoundhimselfwitha positionat HokkaidoUniversity
withno facilities
fornuclearresearchbutwithplentyofsnow.So he turnedwithhis
of snowflakes,both the
studentsand collaboratorsto takingphotomicrographs
naturalsortand thosetheycouldproduceartificially
whilespendinglonghoursin a
under
verycold laboratory
(Fig. 7a). It containeda chamberforgrowingsnowflakes
variableconditions
of temperature
and humidity.
artificial
Figure7b showshis first
flake.Findingthat"a perfectly
snowflakeis veryrarelyobserved,"
symmetric
whetheron the slopes of Mt. Tokachior in the laboratory,
Nakaya studiednonand irregularity,
whichimmediately
focusedattention
on the
hexagonalsymmetry
normalprocessesof growth,ratherthanonly on supposedstatesof perfection.
itseems,is noteasilysubsumedunderideal geometrical
forms.Figure8a,
Growth,
a fewof hisphotomicrographs.
b, с reproduce
Figure8c, showingstagesofgrowth,
meritscomparisonwithtraditional
sequencesfromnaturalhistory,such as the
seventeenth
of a frogfromegg to
century
imagesin Fig. 9, showingthelifehistory
tadpole to maturityand the developmentof a seed into a floweringplant
1682,plateXII).
(Swammerdamm
Such a zoo of irregularity,
and growth,
eventhoughproducedunder
asymmetry,
was notthesortof thingthatinterested
controlled
conditionsin a laboratory,
most
in the 1950s,particularly
notelementary
forwhom
physicists
particlephysicists,
elementary
particleswereahistoricalmathematical
objects,eternaland universal.
models.Nakaya's snowThey soughtexplanationswithinelegantmathematical
flakesgainedlittlerecognition.
The climateforworklikeNakaya's changeddramatically
duringthe70, 80, and
90 s as problemsofcomplexity
becameevermoreimportant
in mainstream
physics
research.12
It is onlyveryrecently,
at CaliforniaInstitute
however,thata physicist
in
of Technologyhas takenup snowflakes
as partof his workon pattern
formation
nonlinear,nonequilibrium
systems.KennethLibbrechthas extendedNakaya's
naturaland artificial
crystalswithmuchhigherresolution
equipment(Fig. 10). In
2006 he publishedwhathe calls a Field Guide to Snowflakes.
Libbrecht'sField
Guideand hisextensivewebsitecontainphotomicrographs
of an amazingdiversity
ofnaturalforms(Libbrecht
2006,201la). I taketheterm"fieldguide"tobe explicit
thatnaturalhistory
and thestudyof nonlinear
recognition
dynamicalsystemshave
muchincommon,especiallycomplexity.
writesaboutsnowflakes
Indeed,Libbrecht
intermsoftheir"lifehistory,"
a "story"muchliketheone I suggested
constructing
above forquantumchaos. The storyyieldsa diagramand a lesson: "Complex
history
[yields]Complexcrystalshape" (Libbrecht2011b).
Thatlessonis apparent
also in theworkof twoofLibbrecht's
who
collaborators,
do simulations.
Evena decadeago itwas notpracticable
to simulatetheevolutionof
a snowflake
at highresolution.
Butthemathematicians
JankoGravnerat University
of CaliforniaDavis and David Griffeath
at University
of WisconsinMadisonhave
11Lorraine
Daston
hasrecently
ofanearlier
etal. 1893).See
mademeaware
(Hellmann
exception
etal.(2007,pp.148-155).
Daston
EventheBigBangtheory
andevolution
ofthecosmos
nottohaveturned
elementary
particles
appear
intohistorical
because
arenotknown
means.
objects,
presumably
they
byevolutionary
Ô Springer
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362
M.N.Wise
ofsnowflakes
andHumphreys
1931,
Fig.6 Photomicrographs
(Bentley
p. 147)
model thatreplicates
produceda three-dimensional,
mesoscopic,computational
- dendrites,
needles,prisms,
manyof the basic formsor "habits"of snowflakes
- sidebranches,sandwichplates,
etc.- along with theirmore intricate"traits"
hollowcolumns,anda variety
ofsurfaceeffects,
orhieroglyphs:
ribs,
ridges,flumes,
circularmarkings,
and othermorechaoticpatterns(Gravnerand Griffeath
2009,
traits,
p. 1; habits,p. 17). Figure11 showsseveralexamples.
Gravner
andGriffeath
model,which
employa conceptually
simplecomputational
froma smallseed of ice surrounded
growsa virtualsnowflake
by watervaporand
of watervaporfromthe crystal;
governedby only threemechanisms:diffusion
ratesat the
freezingand meltingin a narrowboundarylayer;and attachment
boundarythat favorconcavities.Despite this conceptualsimplicity,however,
of themodelin a continually
implementation
requires
updatingcellularautomaton
and therefore
manyparameters
large amountsof computingtime.For example,
Springer
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Science
363
forgrowing
with
chamber
snowflakes
andb first
artificial
snowflake
1954,
Fig.7 a Laboratory
(Nakaya
pp.144,152)
becausetheunitscomposingthevirtualcrystalare takento be hexagonalprisms,
attachment
ratesfornewunitshavetobe specified
forthosethatattachinall possible
combinations
of endsand sides (Fig. 12). A similarmultiplicity
appliesto melting
rates.Densityanddrift
andfreezing
the
velocityadd twomoreparameters.
Although
in
totalnumbercouldbe reducedby makingrealisticassumptions,
freeparameters
arms
the model remainnumerous,even whenconsideringonly fullysymmetric
and top-bottom
The evolutionof a single
(twelveidenticalhalf-arms)
symmetry.
takesabout24 h on a moderndesktopcomputer.
suchsnowflake
Gravnerand Griffeath
forthrightly
acknowledgethatitis notveryclearjusthow
withphysicalprocessesandthattheir
theirintuitively
correlate
plausibleparameters
do nottreatimportant
issues of non-symmetry,
simulations
randomness,
singularthatis, thefullpanoplyof contingencies
thataffectgrowth.
ities,and instabilities,
believethattheevolutionary
simulations
Theynevertheless
provide"explanations"
of naturalsnowflakes,
of manyof thecharacteristics
bothin generalmorphology
andin thedetailsof theirtraits.Runmanytimesover,withvarying
the
parameters,
simulations
the
of
snowflakes
and
their
mechanisms
explore space possible
probable
offormation,
somewhatas we haveseenforquantumchaos.Theseexplorations
too
discovernew properties,
suchas a "sandwichinstability"
(whichaccountsforthe
factthatmostsnowflakes
sandwiches)andtheysuggest
actuallyconsistoftwo-plate
new phenomenathatwill requirenew kindsof laboratory
observations
on real
suchas ridgesgrowingin theinterior
betweentwoplatesrather
thanon
snowflakes,
theoutsidesurfaces.
and discoveries
Even morethanin thecase of quantumchaos,theexplanations
obtainedin the photomicrographs
and simulationsof snowflakesare natural
inkind.Keytermsaretrait
historical
, habit,morphology
,
, seed, lifehistory
, evolution
notonlydeal literallywithobjectsof naturalhistory,
fieldguide.The simulations
a kindof botanicalgardenof snowflakes,
butthetraitsof thedifferent
generating
genera and species in the garden are explained by the conditionsof their
read as evolution.The principlesgoverningtheevolutionmay not
development,
Ф Springer
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364
M.N.Wise
andfour-fold
Fig.8 a Three
b irregularities,
and
symmetry,
с growth
1954,
(Nakaya
pp.383,
389,257)
Springer
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Science
as (Historical)
Narrative
365
ofgrowth
ofa frog
anda plant
1682,
(Swammerdamm
Fig.9 Stages
plateXII)
be the Darwinianprinciplesof variationand selectionbut theyare nevertheless
howtheentirephylogeny
derives
simplegenerative
principles
capableofexplaining
fromsomething
like a commonancestordevelopingundervaryingenvironmental
conditions.13
Thatis,thesimulations
an evolutionary
narrative
thatexplains
generate
13Abetter
bethegrowth
ofmany
kinds
different
oftissues
from
a single
kind
ofstem
cell.
analogy
might
etal.(2000)alsoinvoke
"evolution"
with
Laughlin
(p.35)- along
growth
(p.32),aging
(pp.32,34),and
orbehavior,
theanalogy
ofphysical
to
matter,
(as incomplex
adaptation
adaptive
p. 36)- tocapture
Indeed
offer
thehint
thephenomenon
that
ofprotection
ofa
biological
processes.
they
(independence
from
small
inmicroscopic
structure
orlaws)mayinbiology
"arise
mesoscopic
physical
system
changes
from
thenecessity
oftolerating
diversity."
Springer
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366
M.N.Wise
ofsnowflakes
201la)
(Libbrecht
Fig.10 Photomicrographs
thenatural
orderofsnowflakes
as an essentially
historical
order.Everyindividual
is a
of
its
full
A
of
and
accidents.
snowflake
is
an
uniqueproduct
history,
contingencies
historical
and
its
virtual
is
its
This
is
a
from
the
object
history explanation.
longway
traditional
narratives
ofphysics,whichtreatphysicalobjectsas timeless
explanatory
mathematicalthingsexplained by deductivesolutionsof partial differential
equations.And of coursethe languageof growthreplacesthatof deductionand
reduction.14
Finally,theroleof visualization
requirescomment.Visual imageshave always
beencrucialin physicsto guideintuition
and reasoningand to illustrate
problems
andsolutions.
Buttheroleof visualization,
andof languagesof visualization,
in the
narratives
simulations
is
forit
different,
explanatory
generatedby
qualitatively
serves
as
the
direct
and
the
effective
means
for
typically
representation,
only
the
and
its
intricate
results.
The
to
simulation, be
understanding, growthprocess
must
a
for
understandable,
incorporate technology convertingthe calculations
the
cellular
automaton
intoan objectaccessibleto thesenses.Thus
performed
by
14
ofthis
kind
arenotsosurprising
forsimulations
infield
sciences
likegeology,
butthe
Explanations
isthesame:
andtheir
simulations
often
natural
histories
narratives
(Oreskes
point
explain
bysupporting
2007).
Ф Springer
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as (Historical)
Science
Narrative
367
snowflakes
andGriffeath
2009,p. 13)
(Gravner
Fig.11 Simulated
ofa snowflake
ofhexagonal
theevolution
0-3sides
Fig.12 Basisforsimulating
byattachment
prisms:
and0 or1ends(Gravner
andGriffeath
2009,p.3)
Gravnerand Griffeath
employMATLAB and POV-RAY softwareto make their
cellularautomaton
suitablefordirectcomparison
visuallylegible,witha resolution
with photomicrographs.
Slide shows and movies accompany these new
technologies.
â Springer
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M.N.Wise
368
6 Etruscan-TuscanSimulation:Evolutionof the Populationof Tuscany
in thesense of naturalhistory,
has
So farI have wantedto showhow historicity,
of simulation
new technologies/languages
in physicsthrough
enteredexplanations
do not yet seem
But lest thesenarratives
narratives.
thatgenerateevolutionary
simulation
and use it to
I
more
historical
take
a
historical,
obviously
up
properly
reflect
backon history
itself.
Tuscansto
debateover therelationof present-day
Considerthe long-standing
believe
theirsupposedancestors,
theEtruscans.ManyTuscan familiessteadfastly
and linguistscontend
thattheyderivefromthe Etruscans,while archaeologists
culturaland linguistic
thattheEtruscansdisappearedas a distinct
populationafter
to
In
an attempt
in
the
second
B.C.
were
Roman
century
citizenship
they
granted
a
of
of
the
Etruscan-Tuscan
relation, group
generatean evidentiaryaccount
of Ferrara
or "genetichistorians,"at the University
geneticists,
anthropological
simulation
and StanfordUniversityhave used genealogical
techniquesto
investigatea wide varietyof "historicalscenarios" (Belle et al. 2006). They
DNA fromthe bones in Etruscantombs,
began with ancientmitochondrial
and
by 22 haplotypes,
obtainingviablesamplesfrom27 individualscharacterized
theycomparedtheseEtruscansequenceswithmodernmtDNA frompeople in
Etruscanarea of Etruria,with49 individuals
Tuscantownslocatedin theformer
characterized
by 40 haplotypes.A softwareprogramcalled SERIAL SIMCOAL
(for serial coalescent simulationproceedingbackwards in time) produced
candidategenealogiesconnecting
thetwo samples,representing
potentialmodels
ran
of evolutionary
betweenEtruscansand Tuscans.The simulations
relationships
over 100 generations(2,500 years) using differentmodels- I would add
- of demographiceventsand social structure,
with 1,000 simulations
narratives
conductedfor each model. Judgments
of goodness-of-fit
of each model in
comparisonwiththeempiricaldata werethenbased on medianvalues fromeach
set of 1,000 replicatesfor several measuresof diversitywithinand between
populations.
The models (and narratives)for varioushistoricalscenarios(Fig. 13) were
basicallyof two types:singlepopulationmodelsand twopopulationmodels.The
directdescentfromEtruscansto
single populationmodels (top), representing
Tuscans, includedseveral variants:populationof constantsize, exponentially
expandingpopulation,expandingpopulationwithprecedingfoundereffectsand
alternativemutationrates, and an originalexpansion followed by a severe
bottleneck(Model 5), representingpoor Etruscan living conditionsafter
assimilation
intotheRomanstate(i.e., negativeselection).None of thesemodels
for
of genealogicalcontinuity
matchedverywell theobserveddata on haplotypes
Etruscansand Tuscans.The modelsfortwoseparatepopulationsof Etruscansand
Tuscans (bottom)began with an initialdivergence240-500 generationsago,
precedingexpansionin eitherpopulation.Then variousscenariosof expansion
and migrationwere added, with eithermutualmigrationsfrom240 to 100
of Etruscansto Tuscans.Finally,the
generations
ago or morerecentmigrations
elite
dominance
was
considered
of
by a small subsetof migrating
possibility
EtruscansfromabroadwhoseDNA just happensto be whatwas preservedin the
Springer
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as (Historical)
Narrative
369
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I
Recent
^^
>r22^
-migration
I r=-0.025
r=0
I r=-0.025
r=0
y
y
I N,«300,000
'
/ N,«300,000
'
0¿r
"b T
-!¿T
ok-JN.=1000 0¿r
0ÖN,«1000
Generation Models
Generation Models
6-7-8
9-10
100
"A
'
/fl
N,=25.000
models
Etruscans
(E) toTuscans
(T) (Belleetal.2006,p.8016)
Fig.13 Evolutionary
relating
burial sites. They mighthave formeda social elite who dominatedthe local
Tuscan populationand perhapsmixed with them. Of these alternatives,
the
ancientmigration
modelgave thebestfitto theobserveddata,indicating
thatthe
two populations(Etruscansand Tuscans) became independent
over 100 generationsago, so thatany genealogicalrelationship
since thenis veryweak,or so it
seemedinitially.
But the historicalscenariosdid not quite end there.In more recentwork
thesegenetichistorians
haveconsideredmodernTuscansfromthree
(unpublished)
- Casentino, Murlo, Volterra
- and have used the
differentareas separately
simulationprocedureto comparethemindividually
withtheEtruscans.The data
fromMurlo and Volterraonce again fita two populationmodel,in whichthe
Etruscansmaycontinueintothemedievalperiodbutthendisappearentirely.
Butto
data
from
the
Casentino
known
for
its
isolation
everyone'ssurprise,
valley,long
withinItaly,does seem to fita singlepopulationmodel(analogousto Model 5 of
Fig. 13) beginningfromthe Etruscansand continuingto expand throughthe
medievalperiod.The populationundergoesa sharpcontraction
with
corresponding
theBlack Death of themid-fourteenth
and
then
to
century,
expandsagain up the
This
remarkable
of
present.
finding genealogicalcontinuity
dependsentirelyon
modern
Tuscans
into
local
more
isolatedthanmost
subdividing
very
populations,
historians
wouldhave thought
theCasentinianclaimto
credible,whilesupporting
of theEtruscans.Theycan now tella moreelaborateand
beingdirectdescendents
crediblehistorical
narrative
to explaintheirorigins.
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M.N.Wise
370
7 Conclusion:We Know What We can Grow
In theprecedingexamplesI have movedfroman ahistorical
deductiveaccountof
threeincreasingly
heatconduction
historicized
narratives
aboutelectrons,
through
andEtruscans,
to drawouthowtheirhistoricity
is produced
snowflakes,
attempting
usedto realizethem,thatis, to growthem,andthereby
bythetechnology/language
to knowthem.Butifmathematical
havebegunto acta bitlikehistorians,
physicists
whatis it theyhave learned,and whatcan we learnfromtheirefforts?
Each simulation
started
beginswitha so-called"scenario"thatgetsthehistory
and proceedsthrough
an evolutionary
to a possiblelaterstate.The
development
plausibilityof the associatedstorydependson the continuity
providedby the
evolving series of states and on the degree to which this evolutioncan
the fullrangeof empiricalinformation
available. So farthislooks
incorporate
prettymuchlike a formof whathistoriansnormallydo in exploringhistorical
narratives.
Historiansare constitutionally
empiricist.They generallyattemptto
writea storywitha beginning,middle,and end which incorporates
as much
factualinformation
as possibleintoa coherentaccount,wherecoherencedepends
above all on continuity
of peopleand processes.The historymaybe written
from
a cultural,social, political,economic,or otherperspective;the factsmay derive
froma wide varietyof sources;and interpretation
and judgmentare always in
play, but in general,convictioncomes withnarrativecoherenceand empirical
to most historians.But the
adequacy. This much will seem unproblematic
means
analoguein simulatedhistoriesmayhelp to remindus of whathistoricity
at a deeperlevel.
There existsa large philosophicaland historicalliterature
on explanationin
narrative
narratives
can "explain"
history,
revolvingarounda debateoverwhether
at all and if so how.The canonicalreference
from
pointforthisdebate,extending
the1960sto thepresent,
is CarlHempel'sarticlesof 1942 and 1963on explanation
in history(Hempel 1965a, 2001). Hempel's view that explanationrequires
undergenerallaws,orcoveringlaws,reflected
hisimplicitassumption
subsumption
thatphysicssuppliesthe model forall naturalscience and thatexplanationsin
physicsreston the sortof deductionsfromPDE's withwhichI began (or on
statistical
laws,whichI omithere).15
Whentheanalyticphilosopher
of historyArthur
Danto tookup thedefenseof
narrative
explanationin the 1960s, he arguedthatone could inscribehistorical
("atomic sentences")into the Hempelianmold of generallaws
micro-changes
causal connections
betweenevents,whilenevertheless
thatfor
governing
insisting
the macro-changes
("molecularsentences")of narrativesdescribinglong-term
"no generallaw need be foundto covertheentirechange" (Danto
developments
can explainif
1985,p. 255). His virtuosologicno doubtestablishesthatnarratives
15
s brief
discussions
of"historic-genetic"
orsimply
1965b,
Hempel'
"genetic"
explanation
(Hempel
its
hereferred
toanaccount
ofanevent
2001,pp.287-289),
pp.447-453;
Hempel
bywhich
bytracing
orgenesis,
seem
for
andsimulations,
butHempel
reduced
narratives
origins,
any
might
promising
quickly
validgenetic
to a sequence
ofstages
connected
bynomological
perhaps
explanation
explanation,
combined
with
description.
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Science
as (Historical)
Narrative
371
deductions
fromgenerallaws can,butitdoes littleto illuminate
hownarratives
are
in naturalsciencethatdo notdependon generallaws.
relatedto explanations
More literarily
inclinedphilosophers
of history,
like HaydenWhite(1973) and
Paul Ricoeur(1984), have arguedthatnarrative
historyis morelike fictionthan
naturalscience. Simplifying
theirdeep and subtleexplorations,
the implication
seemsto be thatnarrative
eithercannotbe judgedin termsof whether
explanation
itestablishesobjectivetruths
abouteventsin therealworld(White)or at leastthat
theemphasisneeds to be placed on narrative's
creativerole in transforming
such
eventsintosomething
(Ricoeur).Yet a thirdstrand,represented
quitedifferent
by
David Carr (1986), rejectingboththe relevanceof the generallaw approachto
narrative
and thedisconnectbetweensuchnarratives
historical
and thereal world,
are deeplygroundedin our everydayhumanexperienceof
arguesthatnarratives
the world in time and thattheyexplain by providingstoriesthatmatchthat
temporalexperience.
featureof thisongoingdebateis thatit so consistently
Perhapsthemoststriking
over the yearshas takenthe Hempelianmodel of scientificexplanationas its
reference
forcomparing
narrative
withscience.16Thatassumption
runsthroughout
a 2008 forumin thejournalHistoryand Theoryon HistoricalExplanation.David
Carr,in the lead article,surveysthedebateand his own positionin it, regularly
associatingthe "scientific"withHempel'scoveringlaw modeland theclaim that
"any genuineexplanationmustbe in keepingwitha causal-scientific
approach
borrowed
fromphysicalscience.Today,ofcourse,itis biologicalrealitythatserves
in thisrole.As we've seen,thereduction
of all realityto physicalrealitygoes hand
in handwitha reduction
ofall scienceto physicalscienceas thepreferred
modelof
scientific
explanation."(Carr 2008, p. 28). The succeedingthreearticlesin the
whilepursuingotherinterests,
eitherreinforce
thisimageof scienceor do
forum,
nothingto contestit.
The problemwiththislongtradition
in philosophy
ofhistory,
ofcourse,is thatit
is so completely
outoftouchwithdevelopments
in naturalsciencesincethe1970 s.
heat conductionwith
Hempelianexplanation,as I have indicatedby contrasting
has littlepurchasein thesciencesof complexity,
quantumchaos and snowflakes,
and thereare no coveringlaws in biology,at leastnonefromwhichanything
very
as currently
specificcould be deduced. The philosophyof history,therefore,
practiced,offerslittlegroundforexploringthe conceptof narrative
explanation
withinthenaturalsciences,whereithas beensupposednotto exist.17Nevertheless,
16This
Danto's
belief
that
herepresented
thehistoricizing
"revolution"
initiated
despite
explicit
by
Thomas
Kuhn
andNorman
Hanson
theHempelian
viewofscience
(Danto1985,p. xi).The
against
didnotstress
science
asnarrative,
nordiditattack
deduction
asexplanation.
Itdid
revolution,
however,
insist
that
observation
is always
andsubject
tointerpretation,
canbeseenas
which
theory-dominated
a narrative
inhistory
ofscience.
thrust,
introducing
especially
s brief
Ricoeur'
reference
toexplanations
in"cosmology,
andbiology"
and
See,however,
geology,
certain
ofhistory
asexplanations
inwhich
isatwork
toestablish
retrodiction
conditions
parts
necessary
forsomething
tohavehappened
butprediction
basedonsufficient
conditions
is notpossible
(Ricoeur
1984,135).
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372
M.N.Wise
theefforts
ofphilosophers
to articulate
theproperties
ofnarrative
andhowit
history
here.
explainsraiseseveralpointsof interest
7.1 Objectand Explanation
Carr's basic pointis that"narrativeis at the rootof humanreality"and "It is
becauseof [the]closenessof structure
betweenhumanactionand narrative
thatwe
can genuinelybe said to explainan actionby tellinga storyaboutit" (Carr2008,
of conscioushumanagents.If such
p. 29). His focus is on the intentionality
werenecessaryforhistorical
it wouldhave no analoguein
narrative,
intentionality
naturalscience.Muchhistorical
without
reference
to
narrative,
however,is written
butalso histories
ofprehistoric
intentions,
especiallysocialandeconomichistory,18
humans,non-human
animals,and everysortof livingor non-living
thing.In any
seemsmuchbroaderthanintentionality:
"thepointof
case,Carr'sgeneralargument
emphasizingthe samenessof formbetweennarrativeexplanationand what it
explainsis to show thatthe narrativeexplanationdoes not inhabita different
conceptualuniversefromtheexplained"(Carr 2008, p. 29). He may be saying
somethinglike this: the validityof an explanationdependson the explanation
whatwe taketheproperties
of theobjectof explanationto be. On this
mirroring
reading,the successfuldeductionof simple quantumwave functionsfromthe
Schroedinger
equationexplainsthembecausewe believethemto be objectswhose
is governedby thatequation,a beliefjustifiedby agreementwith
development
observations.
But whenthedeductionsfail,as theydo forthemesoscopicdomain,
anotherformof explanationis required,whichHeller and Tomsovicobtainby
in a simulation,
a semi-classicalnarrative
growingthedistribution
incorporating
takento represent
thecomplexentanglement
of quantumand classicalproperties.
The growth
narrative
to
playsa criticalrole.It is forthisreasonthatI havereferred
thequantumdistributions
and to snowflakes
as historical
objects.The bestway to
explaintheirproperties
(perhapsthe only way) is to writetheirhistories,using
newtechnologies
ofwriting.
The sameis trueoftheCasentinians,
who
sophisticated
morecloselyfitCarr'scriterion
ofhumanagency,eventhoughwe knownothing
of
theirintentionality.
Presented
in thisway,an explanation
via a simulation
withan associatedgrowth
narrative
ofas a generalformofexplanation
ofthingsthatdevelop
mightbe thought
in time,of whicha deductionfroma PDE is a subset.In a limiteddomain,or in
the deductionmay supplythe need forexplanation,
relativelysimplesituations,
namely,whereitprovidesa directsolutionthatdevelopsin space andtime,as from
Ti to Tfin theheatconductionexample.A simulationcould be done to findthe
solutionevenin thatsituation,
In short,
althoughdeductionmaybe moreefficient.
we need notthinkof simulations
as an inferior
stand-infora preferred
and ideal
formof explanationby deduction;theymightbe said insteadto reachfora more
formof explanation,
via historical
narrative.
satisfying
18I leaveoutofaccount
thebelief
oftheAnnales
school
that
socialhistory,
because
and
quantitative
mathematical
isscientific
rather
than
which
isprecisely
thedichotomy
I am
models,
narrative,
employing
rejecting.
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as (Historical)
Science
Narrative
373
7.2 Chronicleand Narrative
A secondissue,andone thatgoes backtoArthur
narrative
Danto,is thata historical
is muchmorethana chronicleof eventsand in factcould not be written
by a
in
the
events
ch.
The
historian
must
be
able
to
(Danto 1985, 8).
participant
pickout
whatwill be relevantin relationto futureevents,whichcan only be knownin
This reflection
leads to Danto's conceptof "narrative
sentences,"which
retrospect.
andwhichcouldnotbe written
movea storyfromearlierto latermoments
bya mere
chronicler.One mightask whethersimulatedhistoriesare anythingmore than
andthusnotnarratives
at all. ButI believethat,inthisrespect,
simulators
chronicles,
in
as
are muchthe same position historians.
They mustrunpossible simulated
historiesin orderto arriveat knownor knowableoutcomes,muchlike historians
in orderto arriveat themostplausibleones.
narratives
exploringvarioushistorical
7.3 Causalityand Contingency
A somewhatdifferent
question related to the chronicleproblemis whether
simulationsgeneratea mere sequence of states,withno identification
of what
connectsthem,such as a law, perhapscausal. I thinkthisis notthecase. In the
forexample,thepossicontinuously
updatingcellularautomatonforsnowflakes,
on theprecedingstate,on
bilitiesforeach successivestatedependverysensitively
andon instabilities.
Withrespecttothegrowth
of
thevicissitudes
oftheenvironment,
thesuccessionof statesis similarto thatforall complex
snowflake,
anyparticular
are so greatthatlawlikehistoriesof
humanprocesses,in whichthecontingencies
kindsofeventshappenarenotlikelyto be credible.Moreforcefully,
whyparticular
ifphysicists
cannotgivea lawlikeaccountofa snowflake,
whywouldanyoneseekto
orofwhyDarwintookup eugenics.
givea lawlikeaccountoftheFrenchRevolution
in retrospect
Whathistorians
can do well in theirnarratives,
however,is determine
andmotivations
todo whatthey
theconditions
underwhichpeoplehadtheresources
of possibility
ratherthanas
in factdid do. These are betterdescribedas conditions
conditionsor causes thatgeneratean outcome.Similarly,to runa
determining
as in theEtruscancase, is to findtheconditions
of possibility
simulation
backward,
of Etruscans,
(or not)forTuscandescendents
perhapstheCasentinians.
Historians
arequiteconsciousofhowcontingencies
constantly
disruptlawlikeor
itselfis a vexedissue.
causalstories.On theotherhand,themeaningofcontingency
like JohnBeattyhave written
penetrating
paperson the subjectfor
Philosophers
to
evolutionary
biology,and it wouldbe good to extendtheirnuancedreflections
in history(Beatty1995, 2002, 2006). I notehereonlythatformost
contingency
of outcomes,
historians
such contingency
shouldat least includethecontingency
underslightly
different
meaningthateventscould have turnedout verydifferently
conditions.
7.4 Local and Global
Because contingencies
This is another
matter,so does localityand specificity.
common theme of historicalnarrativesthat reappears in simulations.The
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M.N.Wise
374
in the particularpaths of snowflakesfallingfor an hour through
differences
conditions
oftemperature
andhumidity
formations.
produceverydifferent
changing
and
Volterra
rather
different
Casentino
Tuscans,just as midSimilarly,
grow
nineteenth
Berlin
and
Paris
different
On the
century
grewrecognizably
physicists.
otherhand,nothingis fullylocal. Local meaningsand dynamicsdependon more
In thisthesimulations
of electronsin a stadiumand evenof
globaldevelopments.
in
are
to be properly
snowflakes the atmosphere perhapstoo self-contained
cannot
to
conditions
outside
their
self-reflexive
historical.
They
respond changing
algorithms
(althoughnothingin principlewouldprohibitmoreextendedenvironare morehistorically
mentalconsiderations).
The Etruscansimulations
realisticin
this respectbecause theirscenarioscan accommodatea considerablerangeof
historicaldevelopments.
Casentinianhistory,for example,dependson Roman
too are quitelimitedin theircapacity
conquestand theBlack Death.But historians
thedetailedexplanatory
withmoreglobal
to interrelate
powerof local narratives
concerns.Satisfaction
no doubtlies in movingback and forthbetweendifferent
levelsof explanation.
These various aspects of the analogue betweensimulationsand historical
narratives
all pointtoa verygenerallesson:explanations
ofthebehaviorofcomplex
narratives.
Naturalscientists
seemto
systems
mayalwaysrequirea turnto historical
be takingon thatview(see Libbrechťslesson,above),albeitless inassociationwith
itselfthanwithnaturalhistory
andbiology.In recognition
of theneworder,
history
historians
andphilosophers
ofscienceneeda newepistemological
slogantoreplace
some of thebaggageleftover fromstudiesof the ScientificRevolutionand the
whichmade abstractions
fromworkingmachines,in the formof
Enlightenment,
Newton'sLaws and Lagrange'sEquations,thecradleforall scientific
explanation.
To put it differently,
we have lived too long withthe adage of the mechanical
"We knowwhatwe can make,"or in theversionofthehistorian
Vico,
philosophy:
"thenormof thetruth
is to havemadeit" (Costelloe2003). An appropriate
update
fortheera of simulations
wouldbe: "We knowwhatwe can grow."Or concretely
in termsoftheEtruscansimulation:
EtruscanDNA liveson in Casentino,
probably.
Forextensive
I thank
discussions
Lorraine
andmylongDaston,
Acknowledgments
Mary
Morgan,
timecollaborator
andmuseElaineWise,alsoGuidoBarbujani,
Krishna
Veeramah,
Kitcher,
Philip
Manfred
andanespecially
Anearlier
from
referee.
version
benefited
Laubichler,
probing
anonymous
comments
ofparticipants
intheconference
onHistorical
attheMaxPlanck
Institute
for
Epistemology
ofScience,
24-26July
2008.
History
References
A.R.(2002).Geometrical
TheVoyages
andthetransformation
Alexander,
of
landscapes:
ofdiscovery
mathematical
Press.
CA:Stanford
Stanford,
practice.
University
J.(1995).
Theevolutionary
thesis.
In:G.Wolters
andJ.G.Lennox,
incollaboration
Beatty,
contingency
withP. McLaughlin
inthebiological
andrationality
sciences
theories,
(Eds.),Concepts,
(pp.
Press.
Konstanz;
45-81).Konstanz:
Universitätsverlag
Pittsburgh:
University
Pittsburgh
Thehistoricity
InR.E. Auxier
J.(2002).
ofnature?
that
ismight
havebeendifferent?
Beatty,
Everything
& L. E. Hahn(Eds.),Thephilosophy
Greene
ofMarjorie
(pp.397-416).
Chicago:
OpenCourt.
J.(2006).Replaying
life'stape.TheJournal
103, 336-362.
Beatty,
ofPhilosophy,
^ Springer
This content downloaded from 128.97.27.21 on Thu, 23 Apr 2015 17:13:07 UTC
All use subject to JSTOR Terms and Conditions
Science
as (Historical)
Narrative
375
inDarwin,
narratives
Beer,G. (1983).Darwin's
Eliot,andNineteenth
plots:Evolutionary
George
London:
Fiction.
Century
Routledge.
E.M.S.,Ramakrishnan,
J.L.,& Barbujani,
G.(2006).Serial
coalescent
simulations
U.,Mountain,
Belle,
a weak
between
Etruscans
andmodern
Tuscans
[Electronic
Version].
relationship
suggest
genealogical
103, 8012-8017.
Academy
ofSciences,
Proceedings
oftheNational
doi:10.1073/pnas.0509718103.
W.J.(1931).Snow
W.A.,& Humphreys,
NewYork:
McGraw-Hill.
Bentley,
crystals.
R.(2007).Fiction
setsyoufree:Literature,
andwestern
IowaCity:
culture.
Berman,
liberty,
University
ofIowaPress.
D. (1986).Time,
andhistory.
Indiana
Press.
Carr,
narrative,
Bloomington:
University
anditsmalcontents.
47, 19-30.
D. (2008).Narrative
andTheory,
Carr,
explanation
History
T (2003,winter).
Vico.In:E. N. Zalta(Ed.),TheStanford
Giambattista
of
Costelloe,
encyclopedia
Retrieved
2011from
I
3 April
http://plato.stanford.edu/archives/win2003/entrie
philosophy.
s analysis
citeCostelloe'
ofGiambattista
Italorum
ex linguae
Vico,De antiquíssima
sapientia
eruenda
librir
tres(1710),
52.
originibus
D. (1953).Methods
of mathematical
vol 2. Original
R., & Hilbert,
Courant,
physics,
published
1924-1928.
Berlin:
London:
Interscience.
edition,
revised,
Springer.
English
laws:Modelsystems,
A. N.H.,Lunbeck,
without
E.,& Wise,M.N.(Eds.).(2007).Science
Creager,
narratives.
N.C.:DukeUniversity
Press.
cases,exemplary
Durham,
A. (1985).Narration
andknowledge,
theintegral
text
Danto,
including
ofAnalytical
of
Philosophy
Columbia
Press.
History
(1964).NewYork:
University
andmixing:
A new'Fin-de-Siècle'
A. D. (2004).Chaos,
. InM. N. Wise(Ed.),
Dalmédico,
disorder,
Historical
on recent
science
Duke
Growing
explanations:
perspectives
(pp.67-94).Durham:
Press.
University
P. (2007).Objectivity.
NewYork:
ZoneBooks.
L.,& Galison,
Daston,
onmethod,
andmeteorology
R.(1965).Discourse
Descartes,
[1637],
(P.J.Olscamp,
geometry,
optics,
Bobbs-Merrill.
Trans.).
Indianapolis:
Funktionen
durch
G. L. (1837).Ueberdie Darstellung
Sinus-und
Dirichlet,
ganzwillkührlicher
derPhysik,
Cosinusreihen.
/,152-174.
Repertorium
une
G. L. (1889).Surla convergence
desséries
a représenter
Dirichlet,
trigonométriques
quiservent
4
deslimites
données.
Journal
fürdiereine
undangewandte
fonction
arbitraire
entre
Mathematik,
inL. Kronecker,
& L. Fuchs
Dirichlets
2
Werke,
(Eds.),G. Lejeune
(1829),157-169.
Reprinted
vols.(vol.I: 118-132).
Berlin:
Reimer.
ofscience
inmodernity,
oftechnology
inpostmodernity,
andofideology
P.(2007).
Theprimacy
Forman,
andTechnology,
23, 1-152.
inthehistory
oftechnology.
History
D. (2009).Modeling
A three-dimensional
J.,& Griffeath,
Gravner,
mesoscopic
snow-crystal
growth:
1601.
Review
E, 79, 1-18.doi:10.1
[Electronic
Version].
approach
Physical
103/PhysRevE.79.01
visions.
NewYork:
Нага
D. (1989).Primate
Routledge.
way,
Hamiltonian
E. J.(1984).Bound
state
ofclassically
chaotic
Scarsof
Heller,
systems:
eigenfunctions
53, 1515-1518.
doi:10.1103/
orbits
Review
Letters,
Version].
[Electronic
Physical
periodic
PhysRevLett.53.1515.
mechanics
E. J.,& Tomsovic,
S. (1993).Postmodern
Heller,
[Electronic
Version].
Physics
quantum
46(1),38-46.doi:10.1063/1.881358.
Today,
R. (1893).Schneeskry
stalle:Beobachtungen
undStudien.
Berlin:
Hellmann,
G., & Neuhaus,
Mueckenberger.
InC.G.Hempel
Thefunction
ofgeneral
lawsinhistory
C.G.(1965a).
[1942].
(Ed.),Aspects
of
Hempel,
andother
London:
essaysin thephilosophy
ofscience
(pp.232-243).
scientific
explanation,
Macmillan.
ofscientific
InC. G. Hempel
C. G. (1965b).
(Ed.),Aspects
ofscientific
Hempel,
Aspects
explanation.
inthephilosophy
London:
Macmillan.
Andother
essays
ofscience
explanation:
(pp.331-496).
inscience
andhistory
In:ThePhilosophy
ofCarlG.Hempel:
C.G.(2001).Explanation
[1963].
Hempel,
inscience,
andrationality
NewYork:
Oxford
Studies
Oxford,
(pp.276-296).
University
explanation,
Press.
R.(1961).Micrographia
Dover
Publications.
Hooke,
[1665].NewYork:
Press.
J.(1966).Thesix-cornered
Clarendon
[1611].Oxford:
snowflakel
Kepler,
inthenineteenth
U. (2003).Experiments,
Klein,
models,
chemistry
papertools:Cultures
oforganic
Press.
CA:Stanford
Stanford,
century.
University
with
В. (1986).Visualization
andcognition:
andSociety:
Latour,
Knowledge
Thinking
eyesandhands.
intheSociology
Studies
PastandPresent,
6, 1-40.
ofCulture
Ô Springer
This content downloaded from 128.97.27.21 on Thu, 23 Apr 2015 17:13:07 UTC
All use subject to JSTOR Terms and Conditions
M.N.Wise
376
in
In M. Lynch
& S. Woolgar
В. (1990).Drawing
Latour,
(Eds.),Representation
things
together.
MA:MITPress.
scientific
Cambridge,
practice
(pp.19-68).
InB. P.Latour
thesoilintheAmazon
forest.
В. (1999).Circulating
reference:
Latour,
(Ed.),
Sampling
MA:Harvard
Pandora's
: Essays
onthereality
studies
ofscience
(pp.24-79).Cambridge,
Hope
Press.
University
ofeverything
R.В.,& Pines,
D. (2000).Thetheory
Versioni.
[Electronic
ofthe
Proceedings
Laughlin,
97, 28-31.
National
Academy
ofSciences,
R. В.,Pines,
D., etal. (2000).Themiddle
Version].
Proceedings
ofthe
way[Electronic
Laughlin,
97, 32-37.
National
Academy
ofSciences,
tosnowflakes.
Press.
K.G.(2006).Fieldguide
St.Paul:Voyageur
Libbrecht,
2011from
K. G. (2011a).Snowcrystals.com.
Retrieved
3 April
Libbrecht,
http://www.its.caltech.edu/
atomic/snowcrystals/photos/photos.htm;
http://www.its.caltech.edu/atomic/snowcrystals/ph
htm;
http://www.its.caltech.edu/atomic/snowcrystals/photos3/photos3.htm.
K. G. (2011b).Snowcrystals.com.
Retrieved
3 April2011from
Libbrecht,
http://www.its.caltech.
edu/atomic/snowcrystals/faqs/faqs.htm.
andtheeconomic
world.
Journal
M.S. (2001).Models,
8y
stories,
ofEconomic
Methodology,
Morgan,
361-384.
s dilemma:
Modelsituation?
M. S. (2007).Thecunouscaseof theprisoner
Exemplary
Morgan,
narrative?
InCreager
etal.2007,pp.157-185.
vol2. NewYork:
P.M.,& Feshbach,
H.(1953).Methods
McGraw-Hill.
Morse,
oftheoretical
physics,
Harvard
Natural
andartificial.
Press.
U.(1954).Snow
crystals:
Cambridge:
University
Nakaya,
Thetechnologizing
NewYork:
andliteracy:
oftheword.
Ong,W.J.(1982).Orality
Routledge.
andambitions
ofmodels
ingeology.
N.(2007).
From
tosimulation:
Oreskes,
meanings
scaling
Changing
In:Creager
etal.2007,pp.93-124.
Bachelier.
S. D. (1835).Théorie
dela chaleur.
Paris:
Poisson,
analytique
inscience
T. M.(1995).Trust
andpublic
innumbers:
Thepursuit
Porter,
ofobjectivity
life.Princeton:
Princeton
Press.
University
T.M.(1999).
andtheaccounting
idealinscience.
InM.Biagioli
Porter,
(Ed.),Thescience
Quantification
studies
NewYork:
reader
(pp.394-406).
Routledge.
inthetesttube.
H.-J.
a history
(1997).Toward
ofepistemic
things:
Synthesizing
proteins
Rheinberger,
Press.
Stanford:
Stanford
University
P. (1984).Timeandnarrative
& D. Pellauer,
Ricoeur,
, Vol.1. (K. McLaughlin
Trans.).
Chicago:
ofChicago
Press.
University
inphysical
46, 34-40.
S. S. (1993).Physics,
andthecrisis
Schweber,
Physics
theory.
Today,
community,
M.N.(1989).Energy
Abiographical
andempire:
Smith,
С.,& Wise,
study
ofLordKelvin.
Cambridge:
Press.
Cambridge
University
deWalcheren.
J.(1682).Histoire
desinsectes.
Utrecht:
Guillaume
Swammerdamm,
generale
toadvance
fortransformative
S. (2009,October
fund
science
13).Schmidt
Tilghman,
through
support
a $25M endowment
from
andhiswife
fund
CEOEricSchmidt
technology
[announcing
Google
NewsatPrinceton.
Retrieved
3 April
2011 from
http://www.princeton.edu/main/new
Wendyl.
archi
ve/S25/54/00M94/.
H. (1973).Metahistory:
Thehistorical
innineteenth-century
Baltimore:
White,
imagination
Europe.
Johns
Press.
Hopkins
University
on
M.N.(2004).Afterward.
InM.N.Wise(Ed.),Growing
Historical
Wise,
explanations:
perspectives
Press.
science
Durham:
DukeUniversity
recent
(pp.327-332).
inHistory
andPhilosophy
M.N.,& Brock,
D. (1998).Theculture
ofquantum
chaos.
Studies
Wise,
of
Modern
29, 369-389.
Physics,
Ö Springer
This content downloaded from 128.97.27.21 on Thu, 23 Apr 2015 17:13:07 UTC
All use subject to JSTOR Terms and Conditions