Spreading Chaos Popularization

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DOI: 10.1177/0741088303261035

2004; 21; 32Written CommunicationDanette Paul

Spreading Chaos: The Role of Popularizations in the Diffusion of Scientific Ideas

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WRITTEN COMMUNICATION / JANUARY 2004

Spreading ChaosThe Role of Popularizations

in the Diffusion of Scientific Ideas

DANETTE PAULBrigham Young University

Scientific popularizations are generally considered translations (often dubious ones) ofscientific research for a lay audience. This study explores the role popularizations playwithin scientific discourse, specifically in the development of chaos theory. The methodsincludeda reviewof thepopular andthe semipopular books on chaos theoryfrom1975to1995, interviews with key figures, and an analysis of the citations in scientific research

journals to Gleicks well-known popularization, Chaos: Making a New Science. Theresults indicate thatpopularizations take different formsas a scientific revolution devel-opsinto normalscience. At variouspoints, popularizations areused by scientists to finda broad,interdisciplinary, scientificaudience,to showinterestin thefield, to disseminatelines of inquiry, and to help establish the authors priority claim.

Keywords: rhetoric; popular science; scientific rhetoric; Gleick; citation;popularization

According to the dominant (Hilgartner, 1990) or the canonical

view (Grundmann & Cavaill, 2000; Myers, 2003), scientific popular-izations aregenerally considered translations (often dubious ones) ofscientific research for a lay audience. As several scholars have noted,this canonical view of popularization relies on several assumptions.First, popularizations aretouted as a necessarybridgefor theincreas-inggapbetween thespecializedknowledge of scientists andthecom-mon knowledge of the general public. Second, the general public, theaudience for popularization, is homogeneously uninformed on top-icsof science (i.e.,a blank slate) (Myers, 2003).Third,popularizations,particularly in the20th century, are a one-way exchange of ideas from

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Authors Note: I acknowledge withthanks Cory Brown, Noella Jeo, andJane Birchfor their help with gathering, coding, and rating the data in this study.

WRITTEN COMMUNICATION, Vol. 21 No. 1, January 2004 32-68DOI: 10.1177/0741088303261035 2004 Sage Publications

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scientists to the public. Fourth, the purpose of scientificpopularizations is to promote science by creating interest in the gen-eral public (Bensaude-Vincent, 2001). Fifth, scientists involvementwith popularizationsis relatively recent andis primarilyto gain morepublic support in times of shrinking budgets (Grundmann &Cavaill, 2000). Finally, popularizations generally lose something inthe translation (see discussions in Charney, 2003, and Fahnestock,1993).

However, several scholars, including Hilgartner (1990), Grund-mann and Cavaill (2000), Bensaude-Vincent (2001), Gulich (2003),and most recently Myers (2003), have challenged the assumptionsunderlying the canonical view. Hilgartner has argued that popular-

ization isa matterof degree (p. 528) ratherthanof a genre clearly dis-tinct from science. Grundmann and Cavaill have questioned theassumption that popularizations are communicating only with thegeneral public. Bensaude-Vincent has disputed the inevitability of agap between the knowledge of scientists and that of the public. AndGulichhas shown that the exchange between experts and nonexpertscanbe dynamic ratherthan unilateral. Although these studies presentimportant challenges to the assumptions about popularization, theygenerally focus on what is considered the primary purpose ofpopularizationsto educate, persuade, or communicate withthe gen-eral public.AlthoughBensaude-Vincent, Grundmann and Cavaill,andMyers all recognize scientists as potential readers of popularizations,they do notconsiderthepossibleconsequences these readers have for

science; in other words, they do not consider what, if any, rolepopularizations play within the scientific community.

To determine what role popularizations play within a scientificcommunity, I examine the relatively recent development of nonlineardynamical systems, commonly called chaos theory (beginning in ap-proximately 1975).1 In this study, I argue that popularizations playedan important role in diffusing concepts of chaos theory within andacross disciplinary boundaries in science itself. I begin by brieflylooking at the development of the canonical view of popularizations,then challenge that view with an analysis of the role of popular-izations in the development of the chaos theory, including interviewswith James Yorke, the mathematician who, with coauthor Li, firstnamed the phenomenon chaos, and with science writer James

Gleick, author of the best-selling 1987 popularization, Chaos:MakingaNew Science, andfinally, by examiningthecitations of Gleicks Chaos. Iargue that although the text ofChaos and the interview with Gleick

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indicate that Gleick holds a canonical view of popularization (a trans-lation of science for a lay audience), scientists and mathematiciansused this popularization both as a teaching tool and as a crediblesource for research.

THE DEVELOPMENT OF THE CANONICAL VIEW OFPOPULARIZATIONS

To claim that popularizations play a role in scientific research,beyond simply creating interest in the general public, seems almostnonsensical. After all,scientific popularizations aredefinedas science

addressedto a general, lay, or nonexpertaudience. Or as Myers (2003)puts it, popularizations are defined in terms of what they are notand what they are not is science (p. 265). However, studies of sci-ence demonstrate that, historically, both popular science and pop-ularizations have playedan importantrole in scientific development.In this brief review, I will demonstrate that the conflation of the issuesof accessibility, quality, and insider social status2 overtime eventuallyled to the so-called traditional perspective of popularizations aseither watered-down or inaccurate science with little effect on scien-tific discourse.

Bensaude-Vincent (2001) argues that the roles and the audiencesfor popular science have changed over time (also see Gibbons et al.,1994, and Grundmann & Cavaill, 2000). According to Bensaude-

Vincent, in the 18th century, there were no clear-cut demarcationsbetween amateurs and scientists (p. 102). Consequently, all discus-sions of science were accessible to all educated and interested per-sons. In other word, theaudience forscience wasan enlightened pub-lic. Bensaude-Vincents (2001) discussion of French science andBazermans (1989) and Atkinsons (1999) historical studies of theRoyal Society in England demonstrate not only that amateurs playeda vital role in the development of science but also that amateurs andpublic discussions of scientific topics helped create a critical mass forcreating a scientific community and for disseminating information.3

Therefore, access and quality were not limited to a group of scientificinsiders.

Thedemarcationof gentlemenamateursandof menof science into

two distinct social groups began the development of two somewhatcontradictory trends at the end of the 18th century and during the

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19th century.4 On one hand, the professionalization of science slowlybegan creating a distinction between insiders and outsiders. Forexample, beginning in the 1820s, the Royal Society began to limit theinfluence of amateurs (Gregory & Miller, 1998). Over thecourse of the19th century, standardized training and methods and the use of spe-cialized language limited thepublics ability to access scientific infor-mation. On the other hand, the rising middle class, along withincreasing literacy and the promotion of science as an extension ofcommon sense, created a trend during this same period to put sci-ence within everyones reach (Bensaude-Vincent, 2001, p. 103).These two movements led to popular science and academic sciencegradually [forming] two distinct but parallel networks (p. 105) and

created the need for popularizations to bridge the gap between scien-tists and thepublic. Thus, the audience forscience wasboth scientistsand the consuming masses.

Although issues of accessibility and of insider social status aroseduring the 19th century, these issues were not necessarily linked toquality. For example, William Whewell, scientist and philosopher ofscience who was active in the British Association for the Advance-ment of Science, and Mary Somerville, who translated LaPlaces

Mcanique Cleste, both made what were generallyconsidered qualitycontributions to science, although their work was primarily address-ed to a popular audience.5 In addition, many of the most importantscientific arguments of the day, such as Darwins Origins of the Species(1958), were published for a general educated readership (see Camp-

bell, 1987). Thus, in the 19th century it was possible to make a contri-bution to science via popularscience and even in popularizations. Butby the end of the century, the motive for doing so was becomingincreasingly suspect among scientists.

When science became standardized in the 20th century with rigor-ous training, regulated scientific practices, and peer-reviewedforums, the publics ability to participate in science or to have accessto scientific texts was severely limited by the highly specialized lan-guage, expensive equipment, and counterintuitive theories, such asthe newphysics. These features, which excluded thepublic from par-ticipation, also led to a conflation of accessibility, quality, and insidersocial status. In this conflation, accessible texts (such as popular-izations) necessarily lack quality, whereas insider status in science

ensures quality, creating a seemingly unbridgeable gap between sci-entists and the lay audience. Bensaude-Vincent (2001) notes that

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the term popular science no longer refers to any specific practices ordiscourse of science. . . . The notion of popular science as distinct fromprofessional science is no longer acceptable. Any non-professionalpractice for science . . . is labeled pseudo-science. (pp. 105-106)

Therefore, the audience for contemporary science is experts, and theaudience for popularizations is, in Bensaude-Vincents word, theignorant masses. This perception of audiences does not allow for thepossibility that popular science or popularizations could affect thedevelopment of scientific knowledge. Instead, the role of populari-zations seems to be limited to translating the science to allow the gen-eral public to recognize the wonder of science and, thereby, increasethe publics willingness to fund science. In other words, contempo-

rary science seems to foster the canonical view of popularization.This analysis shows that thecanonicalview limitsourunderstand-

ing of the audience and therefore the potential purposes of scientificpopularization. Thus, Bensaude-Vincent (2001) rightly argues thatthe assessment of the increasingly unbridgeable gap between scien-tists and the publicholds only if one accepts a deceptive image ofthepublic as the uniformly ignorant masses. It also limits our under-standing of experts. Myers (2003) also claims that assumptions aboutexperts and nonexperts can also be deceptive, stating that

despite being apparently so self-evident, the distinctions betweenexpertandlay audiencesbreaks downalmost assoon aswetry toapplyit more widely. . . . Experts become less expert as soon as they step out-side of their limited area of expertise. (pp. 267-68)

The audience for popularizations, then, is more accurately seen asincluding not only the ignorant masses and the experts but also theknowledgeable amateur and the slightly less expert scientist; there-fore, the increased specialization of science in the 20th century, whichlimits the ability of scientists to participate in science outside of theirareas of specialization, mayactually increase rather than decrease thenumber of scientists who are part of the nonexpert readership ofpopularization.

The recognition of scientists as part of the nonexpert readership ofpopularization and this historical analysis reveal the possibility for

popularization to have an effect on the development of science. First,historically, popular science and popularizations have played a rolein the development of science. Second, scientists have consistently




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used popularizations to achieve scientific goals such as introducingnew ideas, providing a forum for discussion, advancing lines ofresearch,or working across disciplinary boundaries. Third, examplesfrom the Royal Society and the debate over evolution show thatpopularizations and popular science are particularly important innascent and revolutionary science.6 This claimisfurther supported byThomas Kuhns (1970) work on scientific revolutions. According toKuhn, one sign of a revolution in science is the appearance of textsthat are accessible to the general public. In cases of scientific revolu-tion, whether as a result of incommensurability(Kuhn,1970) or of theMax Planck effect, in which scientists divide along generational linesin their support of a new idea (Harris, 1994, p. 47), or of just the ordi-

nary difficulties of introducing new ideas into science (Paul &Charney, 1995), popularizations seem a plausible way to spread anewparadigm. Although other scholars have recognized thevalue ofpopular science or of popularizations in historical studies, none haveexplored the possibility that popularizations could have an effect oncontemporary science. In the next section, I examine how popular-izations are used to diffuse revolutionary ideas in contemporaryscience by looking specifically at the development of chaos theory.

A HISTORY OF POPULARIZATIONS IN CHAOS THEORY

Chaos theory, or nonlinear dynamics, makes a particularly inter-

esting case study for the effects of popularizations on the dissemina-tion of research. First, scientists working in the field claim that chaostheoryis a revolution in science, affecting many disciplines and mak-ing it plausible that popularizations would be used to spread theword.7 Second, although many of the mathematical concepts onwhich chaos theoryis founded were well established by themid-20thcentury (some had been around since the end of the 19th century), thetheorys value was not well recognized. Before computers, nonlinearequations were hard to calculate, especially beyond a few iterations.Once the advent of computers allowed for multiple iterations, chaostheory challenged the foundation of science: predictability. As itsvaluebecame clear, pioneersin the field, includingRobert May, JamesYorke, Benoit Mandelbrot, Ilya Prigogine, and Mitchell Feigenbaum,

rushed to get the message out. According to Yorke, the recent winnerof the Japan Award,8 chaos as a concept was established by 1973. . . .

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Mathematicians knew about it, but nothing was written down. And,our goal was to figure out a way to tell the people who should knowabout these things (personal communication, June 22, 1995).

A review of their early important articles demonstrates that, intheir quest to get the message out, some scientists and some mathe-maticians published in unconventional forums to reach a broaderaudience. Starting in 1977, a steady streamof popularizations in Eng-lish was published on chaos or on chaos-related phenomena. Al-though other scholars have recognized the value of popularizationsin terms of public relations, this analysis shows that popularizationsplayed a role in the development of chaos theory. In my analysis,these publications seem to come in four stages:

1. a revolutionary stage, which includes the publication of unusual textsin traditional forums;

2. a semipopular stage, which includes popularizations of research byearly pioneers in chaos;

3. a popularizationstage, which includespopularizationsabout thefieldthat seemed to reflect the canonical view; and

4. a transitional stage,in whichtextdesignedto introduce or to trainnewscientists, suchas introductions andtextbooks,began to replacepopu-larizations, indicating the normalization of the revolution (for a list ofthe popularizations discussed here, see Table 1).

These stages reflect the development of a scientific revolution. In theearliest days of a revolution, scientists working in normal science

begin to notice some anomalies, which they publish in normal outletsand in normal formats; an example of this type of article would beEdward Lorenzs articles on the butterfly effect on weather patterns,considered by many the first articles addressing the as yet unnamedphenomenon in the 1960s.

Revolutionary Stage

The revolutionary stage began in chaos in the 1970s as some scien-tists started to recognize that these anomalies were more than just afew exceptions. However, trying to make a revolutionary claim istricky. AsKeith andZagacki (1992)have arguedin theirassessment ofthis period, tryingto introduce revolutionary ideas puts scientists inaparadoxical situation in which they must reject and at the same timeseek the approval of established science. In addition to the paradoxproblem, scientists trying to publish revolutionary ideas also face




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Table1

ASelectedListofWell-KnownPopularizationsofChaosTheorybyScientists

andbyMathematicians

Year

Author

Title

Semipopu

larsciencestage

1977

Mandelbrot

(Englishtranslation

Fractals:Fo

rm,C

hanceandDimension

ofthe197

5Frenchversion)

(Lesobje

tsfractal:forme,hasard,e

tdimension)

1980

Feigenbaum

UniversalBehaviorinNonlinearSystems

inLosAlamosResearch

1980

Prigogine(E

nglishtranslationof

FromBeing

toBecoming(Lanouvellealliance)

the1979

Frenchversion)

1983

Mandelbrot

TheFractalNatureofGeometry

1984

PrigogineandStengers

OrderOutofChaos

Popularizationsstage

1986

Crutchfield,

Farmer,Packard,andShaw

Chaosin

ScientificAmerican

1987

Gleick

Chaos:MakingaNewScience

1989

Stewart

DoesGodPlayDice?TheNewMathematicsofChaos

1993

Lorenz

TheEssenceofChaos

1994

Cohenand

Stewart

TheCollapseofChaos



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other challenges, including incommensurability, or the inability todraw on a shared vocabulary and understanding that leads to theinability to communicate (Kuhn, 1970, pp. 200-201), and the MaxPlanck effect,thephenomenon wherebytwoopposingcampsdivideover paradigmatic issues along generational lines (Harris, 1994, p.47). As Harris (1994) puts it, The young Turks propose conceptualreorganization, and theelders in thefield repress thatreorganization(p. 47). In other words, to publish, revolutionaries must overcomeparadox, incommensurability, and repression.

Consequently, scientists advocating revolutionary science oftenturn to new strategies in their publishing and in their writing to reacha broader audience (Paul & Charney, 1995). Most scientists believe

that science is a communal enterprise. Therefore, publishing success-fully and reaching a broad audience are important to increase thechances of finding like-minded scientists who areinterested in work-ing on similar projects. Most scientists believe that science requires acritical mass of scientists working together to make real progress inthe field. For these reasons, scientists are willing to risk trying newstrategies to find a broader and a more receptive audience. Often,these newstrategies result in unusual texts in traditional forumsor intraditional texts in unusual forums. Some texts that seem to reflectnew strategies include the now famous article that named the phe-nomenon chaos by Tien-Yien Li and James A.Yorke (1975), the firstreviewarticle on chaos in Natureby Robert May (1976), the article thatintroduced a universal constant for chaos by Mitchell Feigenbaum

(1978), and a newsletter sent by Joseph Ford, beginning in the late1970s, which would eventually become the first journal of chaos the-ory, Physica D.

In their 1975 publication,Li and Yorke placeda slightly unconven-tional article in a somewhat unusual forum. They published PeriodThree Implies Chaos in a university journal rather than in a research

journal. According to Yorke,

the reason we published Period Three Implies Chaos in The Mathe-matics Monthly is that we felt that, while a lot of people would be inter-ested in it and that this journal was not going to cover all of those peo-ple, this was the best we could do in terms of hitting a broad audience.(personal communication, June 22, 1995)

This strategy workedforLi andYorke better than they anticipated, asYorke explains, saying,




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I think Liand I feltthatthis would be a topic thatwould beof consider-able interest to people. We did not think that people would suddenly

become interestedin this topic as if a tidal wave had hit. (personalcom-munication, June 22, 1995)

Robert May and Joseph Ford also tried unusual formats. May(1976) published a review article in Naturebefore there was anythingto review. Aquick lookat the51 references inthereviewisvery reveal-ing. Twenty references (39%) are preprints, in press, or published in1975 or in 1976in other words, a year or less old. An additional 12references (24%) are published in the 1970s, making them 6 years oldor less, together accounting for 32 references, or almost two thirds ofthereferences (63%).In hisreview, Mayaddresses a general audience,

stating that he is discussing a phenomenon that occurs in many dis-ciplines including biological, economic and social sciences (p.459). He opens his review with a brief discussion and a definition ofthephenomenonbutspends most of thereviewdiscussing hisaims inwriting the review article: to set up a new research area. He ends hisintroduction with an evangelical plea for educators to teach theseequations to students so they can see the wild things a non-linearequation can do (p. 459). Ford, also trying to get the word out butfinding no formal outlets, began to send a newsletter to anyone hethought wouldbe orshouldbe interestedinchaos.It consistedmostlyof preprints and of citationsto what he considered importantarticles,including those of Lorenz, Yorke, May, and later, Feigenbaum.

Feigenbaum (1978), after many rejections, was able to publish hisarticle introducing a universal constant for chaos in a traditional out-let, The Journal of Statistical Physics, but he published it with anunusual introduction and this disclaimer: At present our treatmentis heuristic. In a sequel, an exact theory is formulated and specificproblems of rigor isolated (p. 25). It is interesting to note that evenafter the sequel came out a year later, the heuristic remained themost widely cited article in the field. (For more extensive discussionsof Yorkes and of Feigenbaums early articles, see Paul & Charney,1995.) These strategies were successful not only in getting work pub-lished but also in establishing a critical mass of scientists working onchaos.By 1980, scientists interestedinchaoshadtheirfirstconference.

Although these new strategies eventually allowed scientists inter-

ested in chaos theory to publish in traditional forums, the audiencefor those publications was primarily limited to scientists in their ownfields. According to Keith and Zagacki (1992), the quest for glory in

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modern science is, in a significant sense, the quest for revolution. Tobe one of the giants of science, it is sufficient to have been on the lead-ing edge of a successful revolution (p. 165). To lead a revolution, sci-entists work must move beyond their own specific research area.Publishing semipopulararticles maybe an attempt to do thatto dif-fuse their ideas and to extend their reach.

According to Kaufer and Carley (1993), diffusion is the process ofspreading an idea into new areas. Reach (measured in subsequentcitations) is the outcome of diffusion, reflecting the influence of thoseideas. Diffusion is related to the idea or to the text, whereas reach isrelated to the author and to the authors influence (p. 125). AlthoughFords newsletter and the conference helped diffuse ideas across dis-

ciplinary boundaries, researchers needed a new strategy to extendtheir reach.

Semipopular Stage

In the semipopular stage in the early 1980s, researchers started topublish their specific findings in popular andin semipopular forums.Despite the accessible language, these popularizations seem to beaddressed to scientists rather than to a general audience. In addition,they seem to be an attempt to diffuse the scientists ideas across disci-plinary boundaries. As chaos theory develops, researchers use thiskind of publication to secure the status of claims from their past workas the research moves into new areas. The publications to be consid-

ered in the semipopular stage are by Feigenbaum, Mandelbrot, andPrigogine.

Feigenbaum (1980) published Universal Behavior in NonlinearSystems, an article that he described as semipopular, in Los AlamosResearchshortly afterpublishing hisheuristicand itssequel. Hismoti-vationfor writing this semipopular article is unclear. Itmaysimply bethat the institutethat supported his researchasked himto feature it intheir journal, or he may have wanted to discuss his work in a less for-mal setting. In either case, the audience for the Los Alamos article wasmore interdisciplinary than for Statistical Physics. Universal wasreprinted in the collection Universality in Chaos, edited by PredragCvitanovic in 1984.9 These two general outlets helped to diffuseFeigenbaums ideas and to extend his reach without diminishing the

quality of his work.The motives of Mandelbrot and of Prigogine for publishing semi-

popular texts is much clearer. As Robert T. Kelley (1993) argues in his




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article on semipopular texts in chaos theory, both Mandelbrot andPrigogine [sought] to make the important general implications oftheir work accessible to a broader audience (p. 133). And they wroteseveral versions. They both started with a French version; in 1975,Mandelbrot wrote Les objets fractal: forme, hasard, et dimension; in 1979,Prigogine and Stengers wrote La nouvelle alliance. Shortly thereafter,

both came out with English versions: Mandelbrots Fractals: Form,Chance and Dimension in 1977, and Prigogines From Being to Becomingin 1980. Then, several years later, both came out with another Englishversion: Mandelbrots The Fractal Nature of Geometry in 1983, andPrigogine and Stengers Order out of Chaos in 1984.

With their first books, Mandelbrot and Prigogine were merely

attempting to diffuse their ideas across disciplinary boundaries. Intheearly text, Fractals:Form,Chanceand Dimension, Mandelbrot (1977)is very concerned about using the semipopular genre (see Kelley,1993). In a section title, he announces that This Essay Mixes Styles: IsSemi-Popular and Scholarly. He asks for tolerance regarding thenumerous compromises that are unavoidable whenever one mixesstylesbutinsists that it is awork of erudition (Mandelbrot,1977,p.22) . Inhis early text, From Being to Becoming:Timeand Complexity in thePhysical Sciences, Prigogine, a Nobel Prize winner, seems comfortablewith hispopularbook with a title that alludes to Heideggers Time andBeing and its clearly philosophical stance. But both, in these early

books, are trying to find othersparticularly scientistswho willrecognize the value of their ideas.

The timing of the second set of texts is particularly interesting. Inthe earlier articles, the authors are clearly trying to find a broaderaudience across disciplinary lines; that is, to diffuse their ideas.Although chaos was interdisciplinary with established mathematicalconstructs, those mathematical constructs needed to be connected tophysical systems if they were to cross disciplinary boundaries and tohave a lasting impactonother fields. When Feigenbaums1978 articleprovideda mathematical constant, it alsoprovideda physical connec-tion to mathematicalmodels anda methodof demonstrating theexis-tenceof thechaosphenomenonin various physical systems. That arti-cle created an explosion of interest that reached its height in 1984. Itwas at approximately this time that both Mandelbrot and Prigoginepublished their second popularizations. (It was also the time of the

reprinting of Feigenbaums popularization.)The second set of books, coming at the height of interest in chaos,

seems to be intended to stake claims, extendingtheir authors reaches

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by reminding scientists of their prior work and of its relationship tothe new excitement about chaos theory. According to Kaufer andCarley (1993), one way authors extend their ultimate reach is by sec-ondary communications about their reach, which includes otherrelated communications. In this case, the ultimate reach is extended

by the additional popularizations.For example, Mandelbrot (1983) compares the two versions of his

popularworks, stating, myprevious Essays[sic]stressesrelentlesslythat the fractal approach was both effective and natural. . . . In thepresent Essay [sic], to the contrary, I am precise in claiming credit(p. 3).Thenhe quotes another scientist, F. J.Dyson, stating, fractal isaword invented by Mandelbrot (p. 3). James Gleick (1987), Robert

Kelley (1993), and Susan Prince (1984), who interviewed Mandelbrotshortly after the second book came out, all noted that Mandelbrotseemed very concerned about his place in history. In an interviewwith Prince, Mandelbrot states that I had to convince my publisherthat if the book was beautifully illustrated and not too technicallywritten, it would attract a much wider audiencesthan if I just directedit to scientists (p. 52). Furthermore, he notes, no one disputes mefull credit for this discovery. After all, I was in the wilderness a long,longtimewhile peoplelaughed atmyideas. That the theoryismineisnever argued (p. 52).

If these scientists were trying to make a claim, Mandelbrot wasmore successful than was Prigogine. For although no one does dis-pute Mandelbrots claim,some do notseePrigogines work as related

to the chaos of Feigenbaum and of Yorke. Yet Prigogine is also clearlytrying to extend his reach in chaos theory. First, he renames his book,From Being to Becoming, to Order out of Chaos, thenhe adds a new fore-word by Alvin Toffler. In the foreword, Toffler (1984) touts Prigo-gines work by prominently mentioning Prigogines Nobel Prize, bychastisingAmericansfornotreadingthebook,10 andby comparing, inanalogy, Newtonianism to Prigoginianism (p. xxvi). However, inGleicks well-known popular history of chaos theory, as Porush(1993) notes, Prigogine is only mentioned in a footnote. Gleick saysthatPrigoginewasnotpartofthestoryhewastelling;noneofthepeo-ple he interviewed were talking about him (Porush, 1993, p.160).Prigogine, in an interviewwith Porush, claims that this slight reflectsGleicks American interestshe is telling the American story to an

American audience (p. 159).However, Gleick is not the only one who dissociates Prigogines

award-winning work from chaos theory. In his popularization, in




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1992, Edward Lorenz, the author of the butterfly effect, complimentsPrigogines work while noting that it is not part of what he means bychaos. After interviewing Prigogine and other scientists involved inthe development of chaos, John Horgan (1996), a science writer, notesthat other scientists are generally dismissive of Prigogines work.Horgan also implies that it may be the fact that he waxes philosophi-cal in his popularizations that causes some scientists to dismiss hiswork. Although meeting their goal with varying degrees of success,Mandelbrot and Prigogine areclearly addressing scientists with theirpopularizations. The goalsof the popularizations in thissemipopularstagefinding an audience, creating interest in an area of research,and staking a claimseem more closely aligned with the goals of

research articles than with thegoals articulated forpopularizations inthe canonical view.

Popularization Stage

In the popularization stage that began in the late 1980s, the popu-larizations present a broader11 view of the development of chaos inthe larger context of science. By the time these popularizationsappear, chaos theory is well established. Research areas have beenestablished, National Science Foundation grants have been awardedfor researchcenters, Fordsnewsletter has become the journal PhysicaD, and other journals have also been established that focus on thechaos phenomenon. There seems to be less of a need for popu-

larizations within the scientific community. The popularizations thatappear in this stage, in many ways, seem to be more traditionalpopularizations in the canonical senseaddressed to a general audi-ence, in a popular forum, primarily for entertainment or enlighten-ment. Many appeared in traditional popularization outlets, such asthe series of articles on chaos theory published in New Scientist.

Although some of the authors are scientists who were working inthe field, such as Crutchfield, Farmer, Packard, and Shaw (a group ofgraduate students from the University of California at Santa Cruzwhopublishedan article in ScientificAmerican), the two most success-ful authors were not leading chaos scientists. The most successful is

James Gleick, a science journalist, and the other is Ian Stewart, a math-ematicianwhohas writtenseveral otherpopularizations. Theirbooks

clearly seem to beaddressing a popular audiencerather than address-ing scientists in a roundabout way. Whereas Mandelbrot and Prigo-gine, in their popularizations, seem to be trying to advance their own

Danette Paul 45



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research and to shape the field, Stewart and Gleick seem most inter-ested in telling a good story. Giventhe canonical perspectiveof booksin this period, they would seem to be theleast likelyto affectscientificresearch.

Both Gleicks and Stewarts books have had popular and criticalsuccess, were widely reviewed in research journals, and were recom-mended rather than condemned by most scientists. However,Gleicks Chaos has been far and away the most successful, spendingapproximately 8 months on The New York Times Bestsellers List.Indeed, Chaos has been one of the most successful popularizations inrecentmemory. According to Buchman (1991), Only 5 Science bookshave made the best sellers list from [1975-1988], and two were about

the history of Science (p. 6). Gleicks very successful book was fol-lowed by a number of other popularizations, including Stewartsbook Does God Play Dice?, an edited collection of the popular articlesby leading scientists in chaos theory originally published in New Sci-entist, two more books by James Gleick,12 and the publication of a lec-ture seriesby EdwardLorenz. This periodends with another book byStewart, which announces The Collapse of Chaos.13

Transitional Stage

In the 1990s, the transitional stage began in which popularizationswere replaced with introductions and textbooks. The first in thisgroup is Baker and Gollubs (1990) Chaotic Dynamics. On their back

cover, they claim that this is thefirst text to provide a short,quantita-tive introduction to chaos. In their preface, they note that since theintroduction of chaos theory, there have been works directed at spe-cialists and a few popular books and articles that give the flavor ofchaos but do not allow the reader a significant measure of participa-tion (p. vii). In this stage, leading experts, such as Edward Ott and

James Yorke, begin to write textbooks to train the next generation ofscientists.This final stage indicatesa transitionbacktonormalscience.

GLEICKS INTENTIONAL FALLACY

From the preceding analysis, it is clear that in at least three of

the four stagesrevolutionary, semipopular, and transitionaltheauthors are primarily concerned with the scientific community. Theyare getting the word out, crossing disciplinary boundaries, staking




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their claim, and educating the next generation of scientists. Only inthe popularization stage, the stage that most clearly reflects thecanonical or thedominantview of popularizations, is thetext primar-ily directed to a popular audience. Yet, as I will demonstrate with acitation analysis, these popularizations not only attracted scientistsattention but also had a substantial impact on the development andon the research in chaos theory.

Thefirst step I took to investigate therole of popularizations in sci-ence was to interview a number of scientists, including James Yorke,and a science journalist, James Gleick, the author of the most success-ful popularization on chaos theory. Gleicks declared motivation forwriting Chaos reflects thecanonical view of popularizations. By that, I

do not mean that Gleick has a naive or a simplistic view of popu-larizations. In fact, when I used the word popularization during theinterview in May 1997, Gleick critiqued such a view, saying, I neverliked the word popularizations. I think it connotes heres this bodyof knowledge, now were going to explain it in simple terms to a layaudience (J. Gleick, personal communication, May 1, 1997). He wasaware of having a more complex audience than just ordinary people.He assumed that a lot of scientists have read it as a matter of inter-est, and he knew that the book is used a lot in courses. But as hesaid, the primary purpose of my book . . . is the point of view of a

journalistthat is, whats news? This book, I think, it was, to someextent, history, so as Ive said, I wastelling a story(J.Gleick, personalcommunication, May 1, 1997).

Gleicks perspective is canonical; that is to say, he is writing pri-marily to a general audience about the topic primarily because it isinteresting. He is interested, but not invested, in chaos theory. Hedescribed his writing about chaos theory as sort of accidental,growing out of biographies he wrote on Mandelbrot and on Feigen-

baum, saying,

Im fascinated by a lot of things in physics, but a lot of them fromthe point of view of ordinary people have gotten fairly esoteric, andspecialized, and scholastic, and chaos seemed to be looking at thingsin a fresh way and looking at things I could describe to people like me.(J. Gleick, personal communication, May 1, 1997)

Finally, he sees hisbook as completely separate from science: Im notaware of having any particular influence among scientists in spread-ing the news.

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It is interesting to note that most of the scientists I interviewed inthe 1990s do not share this perspective. In the early 1990s, DavidCharney and I interviewed 12 scientists as part of a study of scientificreading. We asked them a series of questions that included, amongothers, How did you become involved in chaos theory? Who are theleading expects in the field? Have you read James Gleicks Chaos?What did you think about it? Not surprisingly, all the scientists weinterviewed hadread thebook, andtheir opinions generallyreflectedthe comments of reviews ofChaos in professional journals. That is,their responses were positive overall, with a few complaints consis-tent with those found in reviews;Gleick hadexcluded toomuch mathor had focused too much on one group or had not focused enough on

another. What was surprising was the frequency with which theymentioned Gleick in responses to some of the other questions. Forexample, one scientist who had worked in chaos theory for 30 yearssaid that the leading expert in the field was a fellow named JamesGleick. Another scientist, when asked how he became involved inchaosstudies, responded that hehadbeenhavinga conversationwithanother scientist in a bar, and the other scientist told him he ought toread a book called Chaos. Two other scientists, when asked abouttraining graduate students, said they had started training graduatestudents by having them read Chaos.

Later, for another project, I interviewed James Yorke and several ofhiscolleagues andstudents.Again, all of thescientists,postdocorates,and students had read Gleicks book and had positive things to say

about it. Yorke advocated the value of popularizations in general.First, he stated that Ian Stewart, I think, does a really outstanding

job. . . . When people like Ian Stewart write articles, I think, this has atremendous impact (J. Yorke, personal communication, July 18,1995). He then discussed the value of popularizations in introducingpeople to the field, saying,

Theres a lot of emphasis given to role models. . . . Jim Gleick is able towrite about people. . . . So hestalkingabouta reasonablynarrowgroupof people and these thenformrole models. . . . Itsparks peoples imagi-nation. Ive always felt that popular articlesare usefulfor getting into afield.The more technical articles are less useful. . . . It looks like Gleickswill be of considerable interest to high schoolstudentsand perhaps get

them to move into mathematics. (J. Yorke, personal communication,July 18, 1995)




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As these interviews show, all the scientists had read and valuedGleicks account of the field. In addition, all felt that it had had animpact on the field and that that impact ranged from good publicityforthe fieldtotheirstudentsor theirown introductionstothefield.

WhenImentionedsomeoftheseexperiencestoGleick,hewasalit-tlesurprised anda little suspicious. When I asked himwhat impacthethought he might have on the field, he said, as noted above, that hedid not know of any impact on the field. Then, considering the ques-tion, he said,

I suspect thatif mybook was usefulto scientists, itwas probably tosci-entists on thefringes of this field or whowere working in fairly distantareas and wanted a quick introduction or something like that. I cer-tainlydont believe that my book has enoughtechnical content to be inany way authoritative for somebody who wants technical understand-ing of these issues. (J. Gleick, personal communication, July 18, 1995)

I reportedon thescientists comment that statedthat he wasa leadingexpert in the field. He responded,

I think that comment reflects ignorance. Nobody in the field wouldconsider me an experton chaos theory. I might have been an expertin ahistory of science point of view, so I would be pleased and flattered if ahistorian of science said I wasan expertin thefield, but fora scientist tosay Im an authority in sciencethats not correct. (J. Gleick, personalcommunication, July 18, 1995)

I clarified that the scientist had meant that Gleick has a broad view ofthe field, then I told him that he had been granted some authority

because his book had been cited in research articles. He responded,

Woulditbe cited?I wouldbe careful about that.Iveseen mybook citedoccasionally, and I think it tends to be cited in an appropriate context;thatis, in the context ofa lot of people orsomebody said . . . [Chaos the-oryhas]gottenpopular....Mybookdoesntgetcitedinthewayascien-tificarticlegets citedastheplace that isauthoritativeon a particular sci-entific point. (J. Gleick, personal communication, July 18, 1995)

Clearly, James Gleick, a science writer, didnotanticipate that hispop-

ularization, Chaos: Making a New Science, would be used by scientistsin any significant way. It is equally clear that it was. All the scientists

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that I interviewed had read the popularization; the majority recom-mended it to their students as an introduction to the development ofchaos theory, some recommended the book to colleagues, and onewas introduced to chaos theory through reading it. Furthermore,although Gleicks interviewreveals his canonical perspective of pop-ularizations, for the scientists, popularizations seem a potential strat-egy in the rhetoric of revolutiona method of getting the word out.

THE CITATION STUDY

Although the previous section provides strategies and opinions of

individual scientists on the potential use of popularizations, specifi-cally of Gleicks popularization, Chaos, it does not show whetherpopularizations have been widely used by scientists in chaos theory.Nor does it show the consensus of opinion about the value of suchpopularizations. Although it seems unlikely that scientists wouldreach a consensus on the value of a particular popularization, thestandard methods of reportingandof evaluating researchdo providesuch a mechanism. As Dorothy Winsor (1993) has argued, consensusin science is particularly important in that a field that devalues per-sonal insights . . . necessarily looks for consensus as a sign of validity(p. 128). However, scientists do not actually reach consensus byrepeating other scientists experiments. Instead, scientists form

judgments of knowledge claims based on how consistent published

results arewith their ownwork. . . . What countsas knowledgegrowsoutof an achievedconsensus (p.128).According to Winsor, any sci-entific article is like a freeze frame froma film. It is a momentin a dis-ciplinary discussion (p. 128). In addition, Caroline Miller andMichael Halloran (1993) have demonstrated that the relationship

between a particular scientific work and its intellectual forbears [sic][or citations] is central to the ethos of the work, in that it is an articula-tion of the relevant intellectual community (p. 108). Thus, what anypublishedscientific article representsis a momentin thescientific dis-course, andwhat anycitationin such an article reveals is thevaluetheciting author places on the cited work. Therefore, an examination ofthecitation pattern of a particular work over time reveals a consensusabout its place in and its value to scientific discourse. If a populariza-

tion is cited in a research journal, then a consensus on its value to thescientific discourse can be examined.




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To explore if and how popularizations affected scientific dis-coursemore broadly, I examined thecitationsto James GleicksChaos:

Making a New Science, as listed in Science Citation Index (SCI), fromthe publication ofChaos in 1987 to 2000. The first citation appeared in1988. Duringthis 12-year period, 409citationswere made to Chaos, onaverage, 34 times a year (the most citations occurred in 1990 [54]; thefewest citations occurred in 2000 [9]). The number of the citationsalone indicates that Chaos has had a significant impact on the field ofchaos theory. This number of citations is unusually high for any arti-cleor book citedinresearch articles.Only 0.5% of scientific articles arecitedmore that 100times;only0.2% of scientific articlesarecited more

than 500 times. The average numberof citations for a scientific articleis 5. By comparison, Tien-Yien Li andJames Yorkes (1975) classic arti-cle Period Three Implies Chaos was cited 450 times in the first 20years of publication (Paul, 2000). As can be seen in Figure 1, thecitations also follow thenormal pattern of citation, with a peak inthe3rd year followed by a decline over time (McCain & Turner, 1989).This pattern is similar to the citation pattern of the classic article byMitchell Feigenbaum (1978), Quantitative Universality (Paul,2000). Therefore, the citations to Gleicks Chaos do not seem to differfromthecitations ofsuccessful scientific researcharticlesin chaosthe-ory, either in quantity or in frequency pattern. These findings showthat, at the very least, Chaos has been and continues to be part of thescientific discourse.

However, merely knowing how many times a source is cited doesnot reveal how and why it was. To answer these questions, I drew aconvenience sample from the articles identified in SCI as those that

Danette Paul 51

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Figure 1. The pattern of all citations for James Gleicks Chaos: Making a New

Sciencefrom 1988 to 2000.

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used Chaos as a source, selecting all the citations in journals found inmy university library. The sample included 231 citations accountingfor 56% of all citations to Chaos from 1988 to 2000. To examine the useof citations, I analyzed seven factors for each citation:

Genre: The genre of the text in which the citation occurredresearcharticle, review article, technical note, or commentary;

Audience: Theaudience addressedby thetextlay, member, or expert; Location: The location of the citation in the textintroduction, body,

conclusion, other, or only in the references; Function: The rhetorical function the citation performed in the text

interest, definition, support, reference, popular interest, or popularresource;

Popularizations: The use of other popularizations as a source; Discipline: The disciplinary focus of the journals; and Nationality:The nation in which thehome institutionsof theauthors is

located.

(For definitions of factors and of coding, see the appendix). The cod-ingwasverified byanother reader(30citations, accounting for 13%ofmy sample). The comparison of our coded samples showed a highcorrelation:genre,K= 0.78;audience,K= 0.96; location,K= 0.93; func-tion, K= 0.84. Thecorrelation ofpopularizationisnotas high, K=0.70;however, it was still in an acceptable range. This correlation may belower because accurately distinguishing popularizations from aca-demic sources requires a greater acquaintance with the field than my

raters had. Independent raters were not used to check the coding ofthe disciplines of the journals and the authors nationalities.

The results of this analysis can be most clearly presented underfour headings: alignment with orthodoxy, rhetorical centrality, diffu-sion, and context of other popularizations.

Alignment with Orthodoxy

Are thearticles that cite Gleicks book part of the traditional genresand journals central to science? Although all the articles in this studyare in research journals, the citations could be in editorials, bookreviews, or letters to the editor rather than in actual research articles.StephenHilgartner (1990) hasargued that,on a continuum, popular-

ization is a matter of degree (p. 528). At the center of the continuumare research articles. On the upstream of the continuum are the tradi-tionalmethods used formaking andforreportingscientific claims; on




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thedownsideare more popular forums, such astextbooksand reportsin the media. In reviewing Hilgartners continuum, Myers (2003)asks, Are news articles at the beginning ofNature . . . specialist orpopularizing texts? (pp. 270-271). For our purposes, we can recastthis question as, Are the articles that cite Gleicks book specialist orpopularizing texts?

In an attempt to tease out answers to this question, I classified thegenres of the texts in which the citations occur. I classified texts asresearch articles if they make a new claim or further develop a new

approach or area that expands a new claim; as review articles if theyattempt to place a body of established research in a context; as techni-cal notes if they clarify or expand a small detail of establishedresearch; or as the commentary if they are not subject to the peer-review process or are identified as editorials or as opinions.

As can be seen in Figure 2, the majority of the citations (63%) toGleicks Chaos are in research articles. Of the remaining citations,approximatelyhalf are inothergenres of peer-reviewed texts,16% arein review articles, and 3% arein technical notes. Therefore, 82%of thecitations are in peer-reviewed texts. Only 18% of the citations are incommentary. Figure 2 also tracks the percentage of citations in vari-ous genres over time. I hypothesized that citations to textbooks or tomore academic introductions to the field might replace those to Chaos

as they became more readily available over time. So I looked at thegenres of the citations in three 4-year periods: early (1988-1991), mid-dle (1992-1995), and late (1996-2000). In fact, the percentage of the

Danette Paul 53

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Figure 2. A comparison of the percentage of sample citations in each genre in

the early, middle, and late periods to the total percentage.NOTE: N= 231.



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citations in research articles increased significantly from .58 in theearly period to .72 in the late period, although the overall number ofcitations in this period went down.

Figure3 shows those audiencesthat areaddressed in thearticles in

which Chaos is cited. Because genre often determines audience, audi-ence and genre are closely tied. It is not surprising, therefore, that asimilarly high percentage, 89%, of the articles are addressed to anexpert audience. Because the citations are in journals, very few areaddressed to a layaudience (1%); the remaining citations(10%) are inarticles that assume that audience members share membership in anorganization or a discipline but do not assume or require expertknowledge from that audience. These include prefaces to special top-icsissues, presidential addresses, andencomiums, such as a piece cel-ebrating mathematics on the 300th birthday of Sir Isaac Newton.

Clearly, the vast majority of the citations are in research articlesaddressedto expertaudiences. AsJohn Swales (1990)notes,In manyscholarlyandresearch drivendiscourses, researcharticles arethe key

genre both qualitatively and quantitatively. . . . The [researcharticles]still remain at the center of the spider web (p. 177). What is strikingabout the citations for this popularization is their alignment with


Lay1% Member

10%

Expert89%

Figure 3. The percentage of sample citations addresses to each audience.NOTE: N= 231.



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science orthodoxyandwith hierarchy, notonly in theaudience andingenre but also in the authors and the journals. Several of the authorsare presidents of their organizations (several commentary texts arepresidential addresses), some are leaders in nonlinear dynamic sys-tems. Less surprisingly, a few authors are the stars of Gleicks book,such as Robert May and James Crutchfield. With some exceptions,most of the journals are well-known, prestigious journals, such asNature, Lancet,theJournal of Fluid Mechanics, IEEE,and Physics Letters.Taken together, these figures show that the citations to Chaos are inresearch articles that are addressed to experts and that are in presti-gious journals.In otherwords,the majorityof thecitations arealignedwith the traditional genres and with journals central to science.

Centrality

Although the articles in which the citations are found are alignedwith the research orthodoxies of the field, the citations themselvesmay be, as Gleick assumed, primarily references to the popular inter-est in chaos theory or to some historical or biographical notes aboutthefieldand thescientists in thefieldand therefore maynotbe impor-tant to the authors main arguments or central to the scientific dis-course of the areas discussed. As I have previously argued (Paul,2000), the location of the citations and their rhetorical functions indi-cate how important they are to the argument.

For this study, the possible location of the citations in the texts

included theintroduction, thebody of thetext, theconclusion,orsim-ply in the references section. As Swales (1990), Paul and Charney(1995), and I (Paul, 2000) have argued, placing citations in the intro-duction most strongly signals that the work is central (i.e., very valu-able) to a largerscientific discourse. Ontheotherhand, if a text is citedonly in the reference section, then it has minimal centrality. The cen-trality of citationsplacedin the body andin theconclusion sections ofan article can only be judged in context. To determine how the cita-tions were used in context, I consider six functions: (a) to show inter-estinthefieldorresearcharea,(b)todefinechaos,(c)tosupportaspe-cific claim, (d) to provide a reference for additional reading, (e) tosignal popular interest, or (f) to provide a resource for additionalreading that specifically identifies the reference as a popular text.

Figure 4 compares the location of all the sample citations regard-less of article genre (N= 231) to the citations in only the research arti-cles (N= 147).

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As can be seen in Figure 4, nearly half, 49%, of the citations are inthe body, which may or may not indicate centrality. However, morethan a third of the citations, 37%, are in the introduction. To put thisresult in context, in my 2000 study on citations of research articles, anaverage of 62%of citationsto Feigenbaumsarticles were foundin theintroduction; the percentage of his articles cited in the introductionnever dropped below 50%. On average, 52%of thecitationsto articles

by Yorke were found in the introduction; yet, for one article, just 37%of the citations were in the introduction and for another, only 12%.Although the percentage of citations to Gleicks Chaos is lower, it still

seems an impressively high rate for a popularization written by anonscientist, indicating that the work is valued by the community orat least that the citingauthorbelievesthat the workis valuedby his orher community.

Figure 5 compares the function of all citations in the sample (N=231) to the function of the citations in the research articles (N=147).Theprimary functionsof thecitations inboth casesarealmost equallysplit between showing interest (30%), based on Swales (1990) Move1, andproviding support fora particular claim (34%). The majority ofthe citations are used with no reference to the popular origins of thetext (82%).

Only 18%of thecitations indicate that thereference is to a popular-ization. The citations that function as either popular or resource

include general comments of popular interest, such as article 12-1989,Chaosis theaspect of self-organizingthat hasreceivedthe most pop-ular attention (Soltzberg, 1989, p. 187) or article 16-1990, The public


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Figure 4. A comparison of the location of all citations in the sample (N= 231)with the location of the citations in the research articles (N= 147).



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has been made more aware . . . of chaos theory by the best-sellingbook (Desouza-Machado, Rollins, Jacobs, & Hartman, 1990, p. 321).There are also some rather jubilant encomiums, including the Ameri-can Institute of Physics Annual report, which opens with, A NewYork Times article . . . was headlined Top Books of 1988: Spies andPhysics. Didhe say physics? Yes. Best-seller list in 1988 included Ste-phenHawkingsABrief Historyof Timeand JamesGleicksChaos: Mak-ing a New Science (American Institute of Physics, 1988, p. 47). AsGleick predicted, some of the citations to Chaos do make reference topersonalities and to significant events. For example, article 10-1988,

which is in the introduction to a Physica D special issue titled Prog-ress in Chaotic Dynamics: Essays in Honor of Joseph Fords 60thBirthday, cites Gleickforan anecdote about Fordsassessment of thefirst conference, inwhichhe introducedchaostheoryin a paperwith aDuffing equation: My daddy played with Duffing equations, mygranddaddy played with Duffing equations, and nobodys seen any-thing like what you were talking about (Hellman, 1988, p. 121).However, these citations account for only a very small portion of thecitations.

Thevast majority of thecitations reflect standardcitingpracticesinscience, such as the standard methodof showing interest in the intro-duction, as seen in article 1-1988, Applications range from airfoilsdesignto plasmaphysics, from oilrecovery to studies of combustion

(Steen, 1988, p. 418). Others provide support for specific claims. It isinterestingto note that Chaos is often used when the original scientificsource is both obvious and available, such as references to Shaws

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Figure 5. A comparison of the function of all citations in the sample (N= 231)with the function of the citations in the research articles (N= 147).



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dripping faucet or to Lorenz equations or to what are called Lyapu-nov exponents. At times, these citations include both the reference tothe original source and to Gleicks Chaos.

When referring readers to Chaos for additional reading, whetherthey mention itspopularorigins ornot, many authors praiseit openly.As article 27-1990 states, There has been an excellent popular book-length account (Middleton, 1990, p. 3). None of the 231 citations arenegative. Three are questionable, such as article 6-1988, Chaos isnow the most notorious and well-studied source of complex behav-ior arising in nonlinear deterministic processes, (Crutchfield, 1988,p. 770) but then continue without negative comment; so notoriousmay be used here to simply mean well known. This is not surprising,

for as Dorothy Winsor (1993) reports, scientists are more likely toignore articles that they do not like than they are to cite them with anegative comment and thus increase the citations of those articles.Most interesting is article 2-1991. The citation is in the acknowledg-ment and reads, J. Gleick for the inspiration to bring this chaos tolight (Altenberg, 1991, p. 67). Clearly, the author wants to acknowl-edge the role that Chaos played in shaping his ideas, but it is equallyclear that he thinks a citation to a popularization is not appropriate inthe body of the text. All in all, citations to Chaos seems to function likestandard citations, in contrast to Gleicks assertion that my bookdoesnt get cited in the way a scientific paper gets cited as the placethat is authoritative on a particular scientific point (J. Gleick,personal communication, July 18, 1995).

Diffusion

One of the claims that I have made is that scientists usedpopularizations to reach a broader audience. One method of explor-ing this claim is to examine diffusion both geographically anddisciplinarily. It was for this reason that I tracked the location of theauthors home institutions and the disciplines represented by the

journals in which the citations are found. Figure 6 shows that themajority of authors areaffiliatedwith institutions in theUnitedStates(55%); however, over time, there is an increase in diversity, with a sig-nificant decrease in the number of Americans, from 65% in the earlyperiod to 46% in the late period.

The disciplines of the journals in which Chaos are cited are rela-tively diverse. The greatest concentration of citations were in biology

journals (48%), and only 10% were in physics journals (see Figure 7).




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By comparison, citations to articles by leading chaos scientists aremore likely to appear in physics journals, the discipline of Feigen-

baum and Yorkes coauthors (65%), with only 3% appearing in biol-ogy journals (Paul, 2000). These findings indicate that the citations tothepopularization have more interdisciplinary depth. In terms of dif-fusion, the citationsto the popularization reach a more diverse groupof authors over time and have greater disciplinary diversity than dothe citations to the research articles of Feigenbaum and Yorke.

In the Context of Other

Popularizations

In this final area, I tried to determine how often other popular-izations were citedinresearchjournals. I measuredthis in twoways:acitation count using the SCI for three other popularizations for thesame time period and the percentage of times that articles that citedGleicks Chaos cited other popularizations by scientists. During thesame time period, 1988 to 2000, Prigogines Order Out of Chaos wascited405 times; Mandelbrots The Fractal Natureof Geometry was cited202 times;andthe Santa Cruz graduate students Chaos, publishedin Scientific American (Crutchfield et al., 1986), was cited 84 times. Inthe citation analysis, I looked at the reference section to determine ifChaos was the only popularization cited or if other popularizationswere cited as well. Chaos was cited 55% of the time with otherpopularizations. The findings from these two measures indicate thatthe citing of popularizations is not limited to Gleicks Chaos.

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Figure 6. A comparisonof the nationalities ofalltheauthors inthesample inthe

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This study of the citations to Gleicks Chaos clearly demonstratesthat this popularization hashadandlikelycontinuesto have an effectontheresearch inthefield. Itsuseis closely aligned with orthodoxsci-ence. Thefunctionresults indicate that Chaos wasmostoftenusedasagood reviewwouldbe usedto show interest, to provide definitions,

and to support specific claims, and this functional usage remainedconsistent across genres and over time. In addition, Chaos seems tohave been instrumental in diffusing ideas across disciplines andacross nations. Also, this study gives some indication that otherpopularizationsare used inthesame wayin this field.It seemstoindi-cate that in chaos, scientists who wrote semipopular books to diffusetheir ideas chose a winning strategy.

CONCLUSION

Scientists within the field of chaos theory wrote the populariza-tions to evaluate, to rethink, and to locate their own work in a larger

context, particularly in the early development of the field. Scientistsin other fields used Gleicks Chaos, often along with other popular-izations, to explore concepts not yet available in their traditional


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Figure 7. A comparison of the journal disciplines for citations of research arti-

cles ofFeigenbaumand Yorke (N= 612) as reported inPaul (2000)with thejournal

disciplines of citations of popularizations reported in this study (N= 409).NOTE: Geo = geology, Bio = biology, E&T = engineering and technology.



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sources, thereby diffusing the early concepts of chaos theory frommathematics and from physics into the life and social sciences. Thus,even popularizations written to a popular audience primarily toentertain and to delight can have a substantial impact on the field.Although this study can only report on how specific popularizationsfunctioned in chaos theory, the results are compelling enough toargue for expandingour conception oftheroleof popularization fromdescribing a science tohelpingto defineit. Theequation forwhy somewrite and others read scientific popularization is not such a simpleequation as scientists produce, writers translate, publishers sell, andan ignorant but awed public buys. Scientists produce science, butthey also produce, read, and participate in scientific popularizations

for a variety of reasons. In turn, their participation in scientific popu-larization, whether as contributors, producers, or readers, has conse-quences for science.

APPENDIXFactor Definitions and Coding

All specific analyses of the citation are to the first citation in the text.

Audience

Audience indicates to whom the text is addressed.

1. Lay: addressed to a nonexpert, general audience with no expectationof specialized knowledge of a particular area.2. Member: addressedtomembers ofa professional group ofexperts,but

does not call on the members expertise.3. Expert: addressed toexperts ina fieldthat requiredtheaudience touse

their expertise.

Genre

Genre indicates thetypeof text,such as research articles,notes, letters,andso forth.

1. Research articles: journal articles that have primary data,present newmathematical models, or present a new theoretical model.

2. Review articles: journal articles that review previous research. Gener-ally, this genre is signaled in the abstract or in the introduction andrefers to surveying or review or to exploring past research as the pri-mary basis for the conclusions.

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3. Note: A technical note is an explanation of a small aspect of previousresearch. It is often labeled as a note.

4. Commentary: Commentariesare opinionpieces or letters to theeditor.They are often in news and notes sections or are labeled as opinion oras commentary. They express the authors perspective and do notattempt to account for all other previous research. This may includeencomium.

Location

Location indicates the part of the text in which the citation is placed.

1. Introduction

2. Body3. Conclusion4. Other: graphic and table notes, notes, acknowledgments, and

abstracts0. Only in the references or work cited

Function

Function indicates therole that thecitation plays in theargument; specifi-cally, this analysis is aimed at determining whether the reference to GleicksChaos is similar to traditional citations in research journals or if it signals thereference as popular or nonspecialist.

1. Interest: used toshowinterestby academicsor otherwaysofestablish-

ing the territory of study(Swales, 1990), including claimingcentrality,making topic generalizations, and giving accounts of the field. Sig-naled by lists of fields orby areas of study and/or the use of the wordinterest. Forexample,Recent interest in theconcept of chaos andtheprogress inunderstanding itsrolein deterministic systems has ledto aconsiderable revival of interest by physicists in nonlinear dynamics(Saperstein & Mayer-Kress, 1989, p. 217). However, areas that nameseveral areas to prove a specific aspect of chaos theory should be con-sidered support.

2. Definition: used to providea definition of chaos or of relatedphenom-ena. It may also be a definition itself. Often signaled by words likedefined, called, or term. For example, The term chaos is now com-monly used when referring to the revolutionary science which worksto analyze and unify the behavior of complex systems (Farkas,

Yamashita, & Perkins, 1990, p. 1889).3. Support: used to support an assertion about some aspect of chaos

theory. Generally, differs from Interest because it focuses on one




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particular aspect rather than discussing chaos theory as a whole.Forexample, Infact, themotion along this manifold is quite similarto Shaws dripping faucet dynamics (Samardzija & Greller, 1989,p. 479).

4. Reference: used to indicate further reading without reference to levelof expertise. Forexample, Gleicksbookby thesametitlegivesa mostreadable overview of the development and nature of the field (Bas-singthwaighte & van Beek, 1989, p. 699). Even if the author uses un-usual adjectives for scientific articles such as notorious or fascinating,the segment is considered a reference if no direct mention of expertiselevel is made. If a reference tononspecialists is made ina second cite ofChaos within a paragraph or two of the original, then the citationsshould be considered either Popular or Reference.

5. Popular: used to make reference to Chaos as a popular source. Forexample, Chaos is the aspect of self-organizing that has received themost popular attention (Soltzberg, 1989, p. 187).

6. Resource: used to indicate further reading for nonspecialists. Forexample,Thereadermayreferto...thebookofGleickforaverypop-ular non-mathematical treatment of the notions of chance, randomoccurrence, erratic behavior, catastrophe, and chaos (Arle & Simon,1990, p. 297).

Popularizations

Popularizationindicates whetherthe citationto JamesGleicks Chaos istheonly popularization cited in the article. Items in established journalseventhose that might be news or letters to theeditorarenotconsidered popular-

izations. Popularizations includeall articleswrittenin journalsfor a layaudi-ence, such as American Scientist or Scientific American, and they include thepopularizations discussed in this article, listed in the chart below. It does notincludetextbooks or books specifically designedforscientists. It includesthepopularizations discussed in this study:

B. Mandelbrot: Fractals: Form, Chance and Dimension M. Feigenbaum: Universal behavior in nonlinear systems in Los

Alamos Research I. Prigogine: From Being to Becoming Mandelbrot: The Fractal Nature of Geometry I. Prigogine and I. Stengers: Order out of Chaos Crutchfield, Farmer, Packard, & Shaw: Chaos in Scientific American I. Stewart: Does God Play Dice?

0 = Only citation to popularization is Chaos1 = More citations to popularization

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Nationality

Nationality indicates the location of the authors home institutions,relying on the permanent address as the final determiner of the authorsinstitution.

1. American2. British3. European4. Eastern European, including Russia and all former Soviet Bloc

countries5. Asian6. South Pacific, including Australia, New Zealand, Philippines, and

Pacific Island

7. Canadian8. African

This coding of nationality does not indicate the authors nationalities butrather where their institutional homes are. For example, it is possible thatY. H. Ku, Xiaoguang Sun, or Nikola Samardzi are not U.S. citizens, but theymay be. On the other hand, Robert May is not a U.S. citizen; he is British. Inany case, home institutions indicate the authors opportunities forinteraction.

NOTES

1.Theterm chaostheory is somewhatproblematic. JamesYorke namedthe phenom-enon chaos, andthe termhad been widelyused both in scientificcircles,mostlyas deter-ministic chaos, and in popular texts. However, some scientists never use the term for avariety of reasons.Some, likeMitchell Feigenbaum,prefer themoreacademic nonlineardynamics; some aretrying to avoid theassociation with thepopular term; others do notuse thisname, preferring a term of their own;and some use it but only for a limitedsetof phenomena. Inaddition, thenameshave changed over time; thephenomenaare cur-rentlycalled nonlinear dynamicalsystems.Myuseofchaos is influencedby my interviewswithJamesYorke andby the wide recognition of that name because of the influence of

James Gleicks best-selling Chaos.2. The focus on these three issues resulted from suggestions by an anonymous

reviewer for Written Communication.3. In France, for example, so-called enlightenedamateurspromotedscience asthe

only legitimate basis for enlightened societies (Bensaude-Vincent, 2001, p. 102). Dur-

ing this time, public conversations of science were more than just an area of interest;rather, they were public participation in the scientific endeavor (Bensaude-Vincent,2001, p. 102). In England, all membersof the Royal Societyconsidered themselves partof the scientific enterprise. This sense that all members of theRoyal Society were equal



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partners of thescientific enterprisechangedover time asthe sense that professionalsci-entists, rather than royals, clergy, andaristocrats, should runthe Society. The attemptsto have members recognize this distinction began seriously withNewtonspresidency(see Atkinson, 1999).

4. Although the movement in the Royal Society to distinguish between workingscientists and amateurs began as early as Newtons presidency in 1703 (see Atkinson,1999), actually limiting in or excluding gentlemen amateurs from the society did not

begin until the 1820s (Gregory & Miller, 1998).5. A host of other examples for the impact of popularizations exists. Auguste

Comte criticized both the scientists who used esoteric language to exclude the publicandthose whoattempted to make money from popular sciencethevulgarisatuerswho transform an educational project into a commercial enterprise (Bensaude-Vincent,2001, p. 104). Yet Comtealsogavepopular lectures in astronomy, carefully dis-tinguishing between vulgarizations (the French equivalent of popularizations) andpopular science. Jane Marcet, who inherited wealth and married well, clearly did not

write for money but to educate women (Myers, 1997). Margaret Huggins, the wife ofastronomer William Huggins, believed that the progress of science andthe growthofits literature required a newkind of popularizer that preparedmaterialsfor experts(Lightman, 1997, p. 61). Her friend, Agnes Clerke, did just that, writing a history ofastronomy. Others popularizers, such as Mary Somerville, were valued by both scien-tists andthe public.Although Somerville nominally addressed her text to women, shesaw herself as making a contribution to science (Myers, 1997,p. 46; see also Lightman,1997, p. 63).

6. Bensaude-Vincent (2001) also discusses the use of popularizations to promoteEinsteins theory of relativity.

7. Whether chaos theory is a scientific revolution in the Kuhnian sense is up forgrabs. Although nonlinear dynamical systems have certainly changed the face of sev-eral disciplines,somescientists maintainthatit wasa natural part ofnormal science, cit-ing its 19th-century antecedents.However, the actual statusis unimportantbecause,asKeith and Zagacki (1992), Kelley (1993), Paul and Charney (1995), and Porush (1993)

have demonstrated, those working in the field clearly considered chaos a revolution.8. The Japan Award is generally considered the third most prestigious prize inmath.The first is theNobel Prize,followed by theFieldsMedal. Yorke washonored forhis work in chaos.

9. Cvitanovics collection,Universality, is oneof theearliesttextsthat fits thetransi-tional stage of popularization, predating almost all of the texts in the popularizationstage.It is variouslydescribedas a collection, anintroduction, anda technical popular-ization.I classifiedit asan introductionbecause it explicitlystatesthatit is forscientistsandfor students of science. Inaddition,most of thearticlesin thecoll

Documents

Spreading Chaos Popularization