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Creativity theorists widely agree that no matter the creative process under scrutiny, a thorough understanding of it necessarily entails a prior identification and examination of the product it generates. The creative product can be an idea or an object, the only condition being its novelty and appropriateness. By novel, it is understood that practitioners of the specific domain to which the product is supposed to make a contribution, recognize in it some property or properties that were absent in other works. On occasions, as with mass-consumption goods, the opinion of the large public helps to determine what is actually novel. Certainly, as everybody knows from daily experience, the novelty of a product alone is generally insufficient to declare that it is truly creative. Thus, to better discriminate between authentic creative attributes and ephemeral newness, scholars have required the new product to be also appropriate. Appropriateness, in this context, is the capacity of the product to solve an existing problem; in other words, its social value. This last prerequisite implies that the novel creation – even though original – is in agreement with the established tradition of the domain. Creativity researchers have found that only products satisfying these two requirements generally catch the attention of the field and, if accepted, are systematically transmitted from one generation to the next.
That the evaluation of a creative product relies on the judgement of those actively taking part in the field has crucial consequences with respect to the more suitable approach to creativity. This implies, among other things, that a full comprehension of the creative process must inevitably consider the social and cultural context where the creative product has been conceptualized and materialized. It is currently believed that this model, integrating sociocultural issues and results from the individualist approach, should give a better understanding of creativity. This broad contextualist perspective on creativity is the one I will follow in this section; the AdS/CFT correspondence of string theory is going to be my example.
The reasons why it is proper to consider that the AdS/CFT conjecture was novel and appropriate when it first came out is something that needs little explanation. The way gauge theories and gravitational physics were connected in Maldacena’s original paper was without precedent; never before had someone suggested an equivalence with such a precision and scope. In this sense, it was definitely novel. Its appropriateness is also easy to observe. It is well know that the problem of finding a model relating pure gravitational phenomena, such as black holes, and particle physics has been for many years a demanding challenge – defeating some of the most brilliant theoretical physicists of the last decades. Maldacena’s conjecture represented a serious step in the resolution of this longstanding problem. That the novel proposal was creative was in its time recognized by the entire community of theoretical physicists (consider, for example, the innumerable times the original paper was cited right after its publication). That Maldacena himself was a creative person was readily appreciated by his peers when, but to cite one of the many rewards he received, he was called to join the prestigious Institute for Advanced Study in Princeton.
In the first essay I reported partially on the main ideas of the AdS/CFT correspondence. There, I also referred to some of the people that were involved in the elaboration and widespread acceptance of the proposal. Black holes, branes, AdS spaces, holography, and plane wave limit were main concepts; Juan Maldacena, Edward Witten, Igor Klebanov, and Alexander Polyakov were some of the participants in this vast enterprise. In the first part of this section I will elaborate upon the discussion of essay 1, this time stressing the collaborative nature of the process that finally led to the AdS/CFT correspondence. My goal in the second part will be to accentuate the role played by other less visible, but in my opinion no less essential, contributors.
Maldacena submitted his paper to arXiv on Wednesday 26 November 1997; the next day it was online[source]. In the Acknowledgments, the by then associate professor of physics at Harvard University recognized his debt of gratitude to some of his closest colleagues: Gary Horowitz and Andrew Strominger – both also from Harvard. Other string theorists with which he had interesting but less influential discussions were also thanked: Rajesh Gopakumar, a young string theorist who had recently obtained his PhD from Princeton University (the same year Maldacena also graduated from Princeton); Renata Kallosh, a theoretical physicist from Stanford University with strong interests in gravitational phenomena such as black holes and cosmology; Cumrun Vafa, a string theorist from Harvard who was studying the physics of black holes from the string theory perspective; and Edward Witten, the indisputable leader of the theory. By the time Maldacena’s article was published, these physicists had already made significant contributions to string theory; in particular to the understanding of black holes. For example, Strominger and Vafa were well known for having counted the number of quantum states of charged black holes and deduced the Bekenstein-Hawking entropy formula using string theory arguments[source]. What these authors had done in January 1996 for extremal black holes (charged black holes where the charge equals the quantity of mass) was extended one month later by Horowitz and Strominger to near extremal black holes[source] – by the same days a similar result was obtained by Callan and Maldacena[source].
In the second version of Maldacena’s paper[source], appearing on 8 December 1997, he added two names to his list for “discussions at various stages of this project”: Alexander Polyakov and Paul Townsend. Polyakov, from Princeton University, is an eminent Russian-American theoretical physicist author of momentous breakthroughs in quantum field theory. Among Polyakov’s many radical ideas, he is known for having introduced in the early eighties a gravity/particle physics relationship making use of physical strings in four dimensions[source]. His five-dimensional string model, where the fifth dimension is interpreted as the minute thickness of the string, is widely regarded as a precursor of the AdS/CFT correspondence. On the other hand, Paul Townsend is a British theoretician whose domain of expertise is supergravity. Thanks to his deep knowledge of supergravity he made some crucial contributions to string theory; most notably, the elucidation of the role of the multidimensional objects called branes. (Remember that Maldacena used branes for generating the background of the string theory side of the correspondence. See essay 1.) From Maldacena’s article alone it is very hard to make out why he actually included these two physicists. We will tentatively speculate that he realized too late his omission, deciding to remedy it in his second version.
A third version of the paper[source] was online on 22 January 1998, three months after the original one. In this new version, there were still the six string theorists acknowledged in the first version, however, one of the physicists included in the second version was missing: Paul Townsend. If it was difficult to determine the true reasons why Maldacena decided to add Polyakov and Townsend, it seems still harder to reasonably explain why he dropped Townsend from the last version of the paper. Fortunately, we do not need to find an explanation to this (see below). What I wanted to prove with this example was that Maldacena was far from being the only physicist trying to formulate a link between gravity and particle physics. Indeed, he was part of a well established field of research, with its defined problems and committed participants; a web of cooperation that, moreover, Maldacena was prompt to explicitly recognize.
Extra evidence that the process leading to the AdS/CFT conjecture was collaborative can be extracted from Maldacena’s original article. We will look this time at the reference list. The first version contains 50 entries: 58 published papers, one unpublished work by Strominger, private communications with four string theorists (Ofer Aharony, Shamit Kachru, Nathan Seiberg, and Andrew Strominger), and the advanced book on general relativity written by Stephen Hawking and George Ellis. In the second version there are 62 entries: 86 published papers (twenty-eight more than the previous version) and the three other items already mentioned. This version also contains in its first page several lines that are absent in the original submission:
This enhancement of supersymmetry near the horizon of extremal black holes was observed in [5,6] precisely by showing that the near throat geometry reduces to AdS×(spheres). AdS spaces (and branes in them) were extensively considered in the literature [7,8,9,10,11], includding [sic] the connection with the superconformal group. An aspect studied in detail was the supersingleton representations of AdS spaces . For cases with 32 supersymmetries it was shown in [6,11] that the singleton representations describe the Goldstone multiplet, which describes the center of mass motion of the branes. In the limit we are taking this is a free multiplet. Of course, the multiplets related to relative motion are not free.
The piece that Maldacena attached starts from “precisely by showing ... .” References from  to , containing 18 papers, were new.
In the third, and last, version there are 8 more papers cited and another book. The book is a collection of articles on supergravity edited by Abdus Salam and Ergin Sezgin. Most of the additional papers contain results from the mid-eighties concerning supergravity and AdS spaces. One of the new references is to a group of colleagues that pointed out to Maldacena a “sign error.” The extract quoted above was shortened until “... connection with the superconformal group”; the rest was removed from this version.
Two reasons can be put forward in order to explain the growth of the reference list. The first is sociological: the extra references were added due to the persuasive notifications the author received from colleagues indicating to him that he was missing some of their works. (These “warnings” are common practice among users of the online theoretical physics database.) The second is theoretical: the author realized that his original formulation of the correspondence could be improved. (One of the problems Maldacena faced when formulating the AdS/CFT correspondence was the boundary conditions of the AdS space and the definition of a gravity theory within it. Most of the works he added were specifically on this subject; including the references from  to  in the preceding quotation and the book of Salam and Sezgin.)
The argument of the previous paragraph allows me to hypothesize about Townsend’s fate in Maldacena’s paper: appearing and then disappearing from the Acknowledgments. First of all, notice that at the same time that Maldacena resolved to acknowledge Townsend “for discussions” he also added four articles authored by him – all of them dealing with supergravity in AdS backgrounds. My guess, thus, is that immediately after Maldacena’s paper was published online, he was notified about Townsend’s works on supergravity in AdS spaces (maybe by Townsend himself). Since he was aware that his proposal needed assistance in this particular point, he contacted Townsend. After several discussions he decided to thank him. Later on, Maldacena realized that the discussions, or communication, they had held together were not worth a citation in his paper.
At this point, I will like to add a couple of remarks concerning the web of collaboration spun around the AdS/CFT paper. The previous counting confirms that the social network has a tied structure: members recognize contributions from others but at the same time want to be appreciated as having something to do with the new idea. In our case, other string theorists and theoretical physicists, such as supergravity theorists and particle physicists, wanted to see their contributions acknowledged. This is evidence of the dialectical relationship already pointed out existing between novelty and adherence to tradition present in every creative product. On the other hand, this shows that the web of interconnections between participants is very vibrant. In fact, membership is so involving that Maldacena had to excuse himself for his omissions: “My apologies to everybody I did not cite in the previous version of this paper.”
Previous to the publication of his groundbreaking article, Maldacena had already written several papers with prime contributors to string theory. In addition to the physicists already named, he also collaborated, among others, with Sergio Ferrara, Steven Gubser, Igor Klebanov and Leonard Susskind. Undoubtedly this network of collaborations was indispensable for his ideas to come to fruition. For sure, some of these people had a greater impact in Maldacena’s learning process and creativity, however, all of them influenced him. Maldacena’s PhD dissertation[source] is illuminating in this respect. In the Acknowledgements he wrote:
I am very grateful to my advisor, Curtis Callan, for teaching me many things, sharing his ideas with me and encouraging me. I am also grateful to Igor Klebanov and Andreas Ludwig for the ideas they shared with me and the research we did together.
I am also very grateful to David Lowe, Gary Horowitz, Andy Strominger and Lenny Susskind for very interesting discussions and collaborations in which some of this work was done.
I am thankful to Amanda Peet for getting me interested in black holes and fruitful collaboration. I also had nice and stimulating discussions with … .[source]
A list of sixteen people follows, including the Argentinean physicists that introduced him to the subject. Finally, his “friends outside physics” are thanked.
In the Encyclopedia of Creativity already referred to, there is an instructive article on “Group Creativity.” Here is how the concept is defined: “The development of novel ideas requires some basic knowledge in a variety of areas. This knowledge is often attained in group contexts through the role of teachers, mentors, and colleagues. These individuals may directly provide information or direct or motivate the knowledge acquisition process. Individuals may also learn to model the work and creative styles of key individuals in their group or social context. Colleagues and peers are used to obtain feedback on novel ideas or discoveries.”[source] The similarity of the pieces of this definition and the elements of the acknowledgments in Maldacena’s PhD dissertation is very striking. Let us trace a parallelism between the two. In order to write his PhD thesis, and consequently to formulate the AdS/CFT conjecture, Maldacena was required to know about multiple things, including supergravity, black holes, conformal field theory, string theory, and a lot of mathematics. These themes were learnt with the assistance of his colleagues and teachers, for instance, Strominger, Vafa, Susskind, and Callan. This valuable information was whether directly provided by these people, as evidenced when Maldacena writes “teaching me many things” and “sharing his ideas with me,” or they motivated him to look at them more carefully, “encouraging me” says Maldacena. He also recognizes that many of his previous works were carried out in close cooperation with them, “very interesting discussions and collaboration in which some of this work was done.” From this personal testimony we can declare without doubt that the AdS/CFT conjecture was the creative product of a group of string theorists working in close and “fruitful collaboration.” That Maldacena’s creative work was the product of a collaborative action was something that once again he was ready to acknowledge.
If the conceptualization of the conjecture engaged the cooperation of a huge amount of people, the further articulation of it required the participation of many other string theorists and theoretical physicists. In the review article published by Maldacena and collaborators in 1999[source], only one year after his innovative article, there were already more than seven hundred entries in the reference list. The extent of this bibliography attests to the large number of people that were in one way or another involved in the ideation and elaboration of the AdS/CFT correspondence. Hundreds of people were cited, including string theory experts, postdoctoral researchers and graduate students appertained to dozens of institutions around the globe. Moreover, some of them were string theorists, others were not. In conclusion, the construction and acceptance of the AdS/CFT correspondence involved a large number of contributors, each of them with their own unique knowledge, skills, personal motivations and social authority.
Like in any other joint project, in string theory the merit of the final product depends on the level of coordination attained by the participants. In order to achieve a high standard, the collaborative activity requires the participants’ acquaintance with a set of rules and conventions. Without this communal basis no collaborative product can see the light. In string theory these conventions are usually learnt during the formation period. By following the teachers’ instructions or simply imitating the behaviour of professors and more advanced peers, the student learns how to read research articles, perform complicated computations, define and solve problems of diverse degrees of difficulty, give a talk, participate in formal and informal discussions, submit a paper, learn how to work with local and distant colleagues, and so forth. It is worth mentioning that these rules and conventions are embodied not only during formal teaching but also in informal situations, such as lunch breaks, chats in the corridors, casual meetings in the cafeteria, and quick visits to the teachers’ offices. Professional string theorists will hardly call into question the collaborative nature of the scientific research they carry out – as the AdS/CFT case shows. However, I think there are some important details that could be added to the discussion. In the rest of this chapter I will continue talking about collaboration, cooperation, and collective work, but this time in a broader sense. We will still see string theory as a collective activity, but this time collective will be written with capital “C.”
Let us begin by remembering what a creative product was: something original and appropriate. This definition implied that the creative product was never creative per se; it was creative only according to a set of conventions established by a group of people entrusted with the task of setting the novelty and social value of new products. In the words of the psychologist of creativity Mihaly Csikszentmihalyi:
Thus, whether an idea or product is creative or not does not depend on its own qualities, but on the effect it is able to produce in others who are exposed to it. Therefore it follows that what we call creativity is a phenomenon that is constructed through an interaction between producer and audience. Creativity is not the product of single individuals, but of social systems making judgements about individuals’ products.[source] (Italics in the original.)
In the first essay I talked about the “in” and the “out,” treating them as if they were two distinct social spaces. Now, I will argue that this distinction is artificial and inaccurate. Actually, to understand what string theory is and how it has evolved, we do not need such division. In the following discussion what really matters is not whether the person has a degree in string theory or not, or the number and impact of his or her publications, but rather the task he or she carries out and without which the scientific work would not exist. Take, for instance, some of the most famous authors of popular science books who are not members of the string theory community. Should we consider Steven Weinberg and Stephen Hawking two outsiders just because they have never published a single paper on string theory? And, what about their contribution to the early education of a whole new generation of string theorists that grew up reading their books? Because, the truth is that many contemporary string theorists have picked up most of the conventions of the domain from these first readings. So, I am not interested in the in and the out as two distinct spaces where membership to one or the other is defined by the level of expertise in string theory, but as sociological entities whose members are recognized by the contribution they have made to the production and progress of the theory. In a refinement of what was done in essay 1, we can say that all these people constitute the superstring world; or, in other words, the in. The goal of the second part of this section is hence to deepen the theoretical analysis of essay 1, showing how the network of cooperation leading to string theory has indeed involved much more actors than generally imagined.
A good starting point is the exploration of the social function of some celebrated physicists that have written influential popular science books. Usually, these authors are well known physicists with a high status within the field. This position could have been reached by several of the following reasons: the physicist (1) has made crucial contributions to the specific domain he is talking about, (2) is the recipient of a prestigious award, (3) has founded or is a member of a distinguished institution, (4) has written a standard textbook, and (5) is the author of previous minor popular science materials. This past experience and recognition, in addition to, of course, literary competence and an attractive and sellable character, is a precondition for being regarded as a potential credible science populariser. The distribution system, in particular science editors and publishers, knows very well who these physicists are. Contrary to less known science writers who have to struggle to see their texts published, these known physicists can practically publish everything they write; in fact, most of the time they are commissioned to do so. Weinberg’s Preface to The First Three Minutes, published in 1977, recounts how he came to write it: “This book grew out of a talk I gave at the dedication of the Undergraduate Science Center at Harvard in November 1973. Erwin Glikes, president and publisher of Basic Books, heard of this talk from a mutual friend, Daniel Bell, and urged me to turn it into a book.”[source] The weight of the author is extolled on the front page of a later edition: “STEVEN WEINBERG. Winner of the 1979 Nobel Prize for Physics.” Something similar occurred with Hawking’s book. Hawking was known to many theoretical physicists long before his A Brief History of Time came out. However, concerning the greater public, it was only in the early eighties that he started gaining some prominence within the press. Hawking’s growing reputation converged with the perspective of a profitable business, launching the project: “For almost as long as he had known him, Mitton [science director of Cambridge University Press at the time and editor of Hawking’s previous technical texts] had been intimating to Hawking that he should attempt a cosmology book aimed at the popular market.”[source] As a note aside, it is interesting to notice that without the participation of these visionary intermediaries who knew the market of popular physics and its potentialities, these two influential books would not have been published nor written, ever; with all the negative consequences that this would have meant to the progress of string theory.
As soon as these noted physicists reach public recognition as popular science writers, they acquire an extra authority within the field and beyond: from now on they are entitled to discern and tell others what the essence of the domain is and in which direction should it develop. They become a sort of religious leaders that tell people what they should and what they should not think about. In the case of Weinberg and Hawking, and independently of their wishes in this concern, the popularity that followed their publications converted them into “gurus” of theoretical physics. As a rule, everything they say is regarded with the highest admiration and is assimilated in order to behave in accordance with it. This rationale has different effects depending on the social involvement of the recipient. For the sake of clarity, I will classify the latter in four groups: professional physicists, younger researchers, newcomers, and lay public. For professional physicists, that is, those that have spent much of their lives doing physics within the field, the message is unequivocal: keep doing the right things. For young researchers, such as advanced PhD students and postdocs, the idea transmitted is that the domain has still unsolved fundamental problems and that they should focus on them. For newcomers it conveys the following suggestion: this is what we physicists do and if you want to become one of us you have to learn this, and this, and this (see below). Finally, for the lay public the rationale is intended to promote the idea that research in, for example, experimental high energy physics or string theory, deserves the utmost public attention and support.
These physicists are also in charge of creating plausible connections between present-day research and the greatest achievements of the past. That is why it is not uncommon to read famous histories of physics that naively conform to the current situation of the domain, depicting a steady line of development beginning in the prehistory and concluding in the present time. Clear example of this is when Weinberg and Hawking write about the human quest for a final theory of physics and affirm that such a pursuit has lasted for the entire history of physics (see essay 3). In the present situation, where science is increasingly complex and many of the precepts of the career are learnt in popular science books, the implications of this strategy cannot be underestimated.
In addition to constructing the rationale aimed at persuading a large audience of the value of the specific scientific research, physicists in the public eye typically also act as gatekeepers. We have seen how popular science writers behave as “domain gatekeepers,” that is, how the new position gives them consent to decide what is worth being incorporated to the domain and what has to be rejected. Now, I want to briefly comment on how they perform as “field gatekeepers.” This last function is very important since in general this is what a fresh student of physics will assimilate when reading a popular science book. This is done most authoritatively by a notable scientist, however, it must be stressed that they do not need to be specialists in the discussion they are taking part in. Indeed, many times the most vehement supporters of a scientific program are persons not trained professionally within the domain. This is the case of Weinberg and Hawking, who are not string theorists but openly support its attempt to unify the laws of physics – they rely, like many others do, on the authority of experts. Scientists with a recognized reputation, such as Weinberg and Hawking, are by and large those authorized to be gatekeepers. However, sometimes science writers also take part in the debate. For this reason, even if strictly speaking these physicists and science writers are not string theorist experts, it is right to consider them as part of the superstring world.
In the preceding paragraphs we saw that popular science authors have been carrying out functions that many sociologists and historians of science have neglected. At least three are the crucial tasks these authors have fulfilled: they have provided the domain with a rationale intended to specify the worth of the present research and indicate the direction it should take in the future; they have created a solid connection with the past, reinforcing the motivation for current investigations; finally, their books have generated a mechanism that standardizes the action of the participants, reducing the undesirable attitudes with regard to the domain and the field. Previously, since they are well known to every physicist, we have only considered examples from Weinberg and Hawking; however, understandably this can as well be extended to some string theorists. David Gross is one of them: ‘‘The fact that it [superstring theory] has begun to address some questions that have been around for 70 or 80 years and reconciles relativity and quantum mechanics convinces me that it is on the right track. Unless you have some faith, you’re not going to stay in this kind of speculative field.’’[source] In one sentence Gross has brilliantly summarized the three roles above mentioned of the popular science writer. However, the basic point of the present argument is that this task is not reserved to experts in string theory, but instead it can be performed by any person with the adequate background. This is a job that inevitably somebody has to do, and this is exactly what Weinberg, Hawking and many other non-string theorists have been doing. In modern science communication is not optional, since if it is not done or it is performed insufficiently the progress of the research would be compromised.
Professional physicists, younger researchers, newcomers, and the lay public, all of them share a set of conventions with the science writer. Fundamental concepts and main motivations are the basic assumptions for the comprehension of the text. But, if the readers can understand and faithfully reproduce what it is written in the book it is only because they have gone through a systematic process of learning. Other books, articles, and lectures have provided them with the necessary background to follow the discussion. Popular science writers and publishers know this interdependence very well and take it into account at each step of the publishing process. In so doing, moreover, they predict how every single detail of the discourse will affect the reader and how he or she will respond to it. So, since every popular science product contemplates the intellectual or emotional reaction of the public – whether a popular science book, a museum, a TV program or a public talk – it inevitably shows the sign of the audience’s participation. This is evident in methodical presentations, such as Weinberg’s and Greene’s books, but the same principle applies to works of less influential people, such as professional science writers and internet users.
But, professional science writers are not the only ones trying to participate in the dissemination of the theory’s ideas and significance. Many readers, fascinated by popular books on string theory have decided to collaborate in this effort. After reading Michio Kaku’s book Hyperspace, a reviewer in amazon.com wrote: “I have always been a fan of theoretical physics and this book brought together all the reasons why I am such a fan. The work that these physicists are doing is so amazing everyone in the world should be told about.”[source] Another reader went still further and found a way to help string theorists: “This book has played a key part in my gaining an interest in theoretical physics. I have even made a site about parallel universes. This book explains many different theories in an extremely lucid manner. It’s a must for one who’s interested in theoretical physics. It’s also a must if you’re interested in the show ‘Sliders.’ Check it out!”[source]
One of the problems I face in teaching at a small liberal arts college is providing for our english, theatre, and music majors, a substantive introduction to modern physics. We have to get beyond the basics of heat, light and sound, and we have to talk about quarks, and black holes, relativity, the quantum theory, and the whole wonderful universe. Finally, a book has arrived that does all of this, and wonderfully unifies all of physics under its main mast of symmetry. These things captive our students. ... I have been using materials from their website, for years, but finally it all comes together in a book that I can assign to my students. This book is great ... [Ellipsis in the original.] I repeat, it is great. ... This book will hook my students, and will sit prominently on their bookshelves, in their homes, when they become lawyers, doctors, statesmen, and composers, a ready reference to all that is the mystery of nature, for the rest of their lives.[source]
I would not like to conclude without quoting Howard Becker, whose sociology has been an inspiration for my approach to the history of string theory (just exchange art for science or string theory): “Works of art, from this point of view, are not products of individual makers, ‘artists’ who possess a rare and special gift. They are, rather, joint products of all the people who cooperate via an art world’s characteristic conventions to bring works like that into existence.”[source]