We aren’t saying that our model is more probable than another model; we’re saying it exposes what is possible.” 
I have no trouble believing in mathematical modeling as a powerful form of metaphor, representation of the possible, or prosthesis for the imagination. But the reigning, reductive neo-Darwinist paradigm — in other words, the modern synthesis — remains well entrenched, and its defenders staunch in its support. Hamilton and John Maynard Smith, along with the population geneticist George R. Evolutionary theory must encompass cultural processes just as human history must encompass biological ones. He concludes that natural selection favors those who copy others efficiently, strategically, and accurately; that nonhuman species lack cumulative cultures because of their “low-fidelity copying mechanisms”; that teaching evolves where the benefits outweigh the costs; and that language first evolved to teach close kin. Analyzing the winning strategy, Laland concludes that observing and copying are tremendously valuable, much more so than innovating on one’s own except “in extreme environments that change at extraordinarily high rates,” which must be rare in nature. Taking part in their conversations has in turn informed my own work in the history of evolutionary theory. Organisms survive if they happen to achieve an optimal state of genetic affairs, one that maximizes some function for greater reproductive success. Appleton, 1896), 1:533–58, on p. D.  Marcus W. The game also included three different “moves” — “innovate,” “observe,” and “exploit” — representing different phases of asocial or social learning. 19, on p. 551. Neither observed behaviors nor any other macrolevel phenomenon could play a causal role in evolution according to this school of thought. But mathematical modeling does have a distinctive feature that sets it apart from other interpretive modes: notwithstanding Gell-Mann and Feldman, it tends to disguise itself as proof rather than representation. We called these novel inventions ‘cultural seed traits.’ Then, one of four possible events could occur”: a new seed trait could be acquired by novel invention; two traits could be combined to produce a new one; one trait could be modified; or a trait could be lost. The conclusion is persuasive, but the tournament seems to me more a way of expressing than of proving this point: the virtual agents and their behaviors and strategies of course constitute an interpretive representation of natural processes. Reading his important and heartfelt book, the to-date summary of a groundbreaking career, I had similar feelings as I did at the conference. By which I mean, what function do biologists intend their mathematical models to serve? ¤
 Joseph Fracchia and R. 58. This seems to me more credible, but it still assumes that we can meaningfully represent cultural forms as quantifiable bits, and that this will add more to our understanding of the role of cultural forms in evolutionary processes than simply trying to describe this role in qualitative terms. In that way I think they can be valuable.”  Feldman, who pointed me to Gell-Mann’s characterization of models as “prostheses of the imagination,” added that “insofar as the model assists in the interpretation, then it has value.”  On another occasion, Feldman told an interviewer, “[p]eople who make models for a living like I do don’t actually believe they’re describing reality. The other principal tenets — such as “cultural drive” and “gene-culture co-evolution” — are not quite first principles, but they seem to me ways of understanding how the feedback-loop of evolution encompasses cultural forms. These include “a tendency to adopt the majority behavior,” “copying the behavior of others when uncertain,” and “disproportionately attending to the behavior of groups.” Such social tendencies, once established, must surely enter into any legitimate evolutionary picture of fish.  Thomas Henry Huxley, “On the Reception of The Origin of Species” (1887), in The Life and Letters of Charles Darwin, edited by Francis Darwin (New York: D. Huxley, upon reading the On the Origin of Species, to figuratively smack his forehead, exclaiming: “How extremely stupid of me not to have thought of that!”  Such grand, organizing ideas, which create conceptual sea-changes that render them retrospectively (but only retrospectively) obvious, can emerge only from richly informed interpretative analysis. ¤
Jessica Riskin is a history professor at Stanford University, where she teaches courses in European intellectual and cultural history and the history of science. She is the author, most recently, of The Restless Clock: A History of the Centuries-Long Argument Over What Makes Living Things Tick (2016). The game involved virtual “organisms” or “agents” engaging in a hundred “behavior patterns,” with varying rates of success resulting in greater or lesser “fitness” (i.e., survival and reproduction). In this gene-centric view, all higher-order entities — individual organisms, their behaviors and interactions — are epiphenomenal, controlled by and reducible to genes, so that any apparent agency or intention on the part of an organism is illusory. Hamilton, Price, and Maynard Smith developed a game-theoretic approach to modeling the behaviors of organisms in the struggle for survival. (Oxford: Oxford University Press, 2006), 229. Their persuasiveness overwhelms my failure to believe in a proof-value for the mathematical models. OCTOBER 31, 2018
LAST SPRING, I attended a conference in New Mexico featuring evolutionary biologists working on a new research program they have been calling the “extended evolutionary synthesis” (EES). Mathematical models are interpretative from the get-go. Lewontin himself, together with the historian Joseph Fracchia, argued in a 1999 paper against the idea of cultural evolution. Would it be possible for it to come right out of the positivist closet? An example is his game-theoretic tournament to study social learning. Cultural “traits” that are independent of one another occur no more often in nature than young ladies with perfectly geometrical features distributed all on one side of their two-dimensional heads. Wouldn’t a scientific method that unapologetically declared itself as interpretive and representational be in keeping with Laland’s revolutionary program to write cultural forms into evolutionary theory? A biologist wrote an equation on the whiteboard in which one of the variables was a “w.” He then circled the w, explaining that it represented “culture,” and pointed out that under certain conditions, the value of “w” would tend toward zero, while under other conditions it would tend toward 100. Cultural practices must be causes as well as results of evolution because any result of the evolutionary process becomes a feature of the world of causes shaping the continuation of that process.  Feldman, quoted in Elizabeth Svoboda, “Finding the Actions that Alter Evolution,” in Quanta Magazine, Jaunary 5, 2017, https://www.quantamagazine.org/culture-meets-evolution-the-marcus-feldman-qa-20170105/. More generally, the principle that many animals are social, and that their sociality necessarily plays a role in the evolutionary process, has the retrospective obviousness of all grand, organizing ideas once stated, a most notable example being the idea of natural selection itself, whose retrospective obviousness led T. H. 4, Theme Issue 38: The Return of Science: Evolutionary Ideas and History (Dec., 1999), pp. For example, it brings a tendency I’ll call “either/or-ism”: a tendency to represent as separate and discrete, the better to count them, things that are in fact mixed and blended. This is not a criticism: interpretation is essential to (and ineradicable from) any attempt to understand the world. For example, Laland describes several series of experiments designed to show that fish can learn from one another, and to investigate how and under what conditions they do so. Could we say that “the arts” has a y-percent effect on birth rate or life expectancy? I can’t help wondering if that’s a sound assumption. For example, Richard Dawkins has adapted it to his own theory of gene functioning, emphasizing that the “strategies” in question are behaviorally defined and do not require the ascription of consciousness, let alone agency, to the strategic agent. These include the precept that cultural practices — in particular teaching, imitating, and copying — are causes as well as results of evolution; that in mammals and especially humans, such cultural practices have accelerated evolutionary development by constantly creating “new selection regimes” in a process that Laland, citing evolutionary biologist Allan Wilson, calls “cultural drive”; and that, accordingly, in humans especially, there has been a “gene-culture coevolutionary dynamic.” The first of these — that cultural practices are causes as well as results of evolution — seems to me incontrovertible, but more like a first principle than like an empirical result. Representations should, though, declare themselves as such. Perhaps these individual culture variables might in principle add up to a single, overarching W, but for the moment, no one claims to be able to make that summation. Lewontin, “Does Culture Evolve,” in History and Theory Vol. But insofar as a mathematical model is taken to prove rather than to argue or represent, that’s where I think it can mislead. As is often the case in longstanding debates, we actually agree on the essentials: that nature and culture are at bottom made of the same stuff — in fact, of one another — which no humanistic or scientific inquiry can legitimately disregard. While I understand and admire these biologists’ conclusions, I keep wondering: Why these methods? In one variation, the experimenters trained the demonstrator fish to swim directly up narrow vertical tubes to reach their meal; this was a highly esoteric skill that no fish figured out on its own, without training, but the guppies did readily learn it from one another. In my experience, teaching is often a win-win process, a non-zero-sum game, in which the teacher learns at least as much as the pupil, rather than a donation by the teacher to the pupil. Uppermost among these is heated agreement: Laland’s essential tenets seem to me profoundly right, some indeed incontrovertible. Darwin promised that this approach would be its own reward: “[W]hen we thus view each organic being, how far more interesting, I speak from experience, will the study of natural history become!”  Laland’s evolutionary science, as portrayed in Darwin’s Unfinished Symphony, might as well come right out and declare itself as such: it is precisely that “far more interesting” study. 
The biologist with the “w” variable and I were thus reenacting an intellectual confrontation that has been going on for decades. 3, on p. Mathematical modeling, like any mode of interpretive analysis, also has its limitations and pitfalls. Still, I experienced a moment of comical culture shock at the recent meeting I attended. ¤
To elaborate further, consider an experiment Laland describes, performed with his postdoctoral student Hannah Lewis. 324.
 Marcus Feldman, in conversation, August 2018.  Murray Gell-Mann, “Plectics,” in John Brockman, ed., Third Culture: Beyond the Scientific Revolution (New York: Touchstone, 1995), Ch. But while he has been constructing this revisionist scientific theory, he has often supported it by traditional methods. Unlike in Maynard Smith’s applications of game theory to evolution, Laland and his collaborators were not looking for an optimum in the form of a single function or property to be maximized. Alongside the mathematical models are descriptions drawn from experiments and observations, some extending over decades. Game-theoretic modeling has been a hallmark of neo-Darwinist reductionism and, specifically, of the denial of any kind of evolutionary agency to the evolving organism. Why mathematical modeling? 52–78, on pp. While the modern synthesis proposes that epigenetic, developmental, ecological, and cultural processes are all products of evolution, the EES claims they are causes as well as products. When I expressed a certain dubiousness about representing “culture” with a single variable, an EES biologist explained to me that the variables standing for “culture” in biologists’ mathematical models are not meant to denote the entire Gestalt, but rather quantifiable bits of culture: a single behavior, for example, that might be taught, learned, transmitted, or counted, and whose effects on survival and reproduction can be measured and modeled. The program aims to go beyond the so-called “modern synthesis” of the mid-20th century, which joined Darwinism to Mendelian genetics, whose mathematical formulations could be simply and straightforwardly expressed. To put my point another way, culture plays as crucial a role in evolutionary theory as it does in evolution. Are they meant to prove claims about evolution?  Richard Dawkins, The Selfish Gene (1976), 30th anniversary ed. But I have learned from teaching college freshman and sophomores that naïve questions from untrained newcomers can be the hardest and most useful, which emboldens me to ask mine. Only in the last 25 years or so has the more expansive vision of the EES slowly begun — against much resistance — to establish itself in mainstream biology. “Nothing,” he maintained, “is implied about intention.” A strategy was merely “a behavioural phenotype,” in other words, “a specification of what an individual will do [in a given situation].”  These “strategies,” therefore, involved no ascription of internal agency, but merely outward observations of behavior.  Neither behaviors, nor agency, nor consciousness, nor culture operates causally at any level of Dawkins’s picture; all reduces to just gene functioning. C. But I wonder if that’s necessarily true in all cases of nonhuman teachers.)
Yet Laland’s conclusions are extremely persuasive. Laland has devoted his career to pioneering work against reductive, simplistic, and dogmatic accounts of evolution, building brick by brick a sound case for the richer and more complex vision of the EES. They did not pre-judge what had to happen in order for an organism to win the competition. These processes travel in the real world as aspects of a single organic entity and not as separate blocks. In another series of experiments, the experimenters offered certain stickleback fish rich feeding patches and others poor ones, while observer fish watched from a distance; the humans then observed the observer fish to see whether and what they learned. Feldman, “Dissent with Modification: Cultural Evolution and Social Niche Construction,” in Melissa J. They wondered whether conceptualizing entities like “the idea of monotheism” as “cultural units” begged crucial questions — for example, how can we count up these units in a population, and what are their laws of inheritance and variation? “There is no one transhistorical law or generality,” they contended, “that can explain the dynamics of all historical change.”  Marcus Feldman disagreed, albeit not specifically with regard to the existence of general laws explaining the dynamics of all historical change; rather, he defended the notion of “observable units of culture,” which he did not associate with grand organizing ideas such as monotheism. Laland explains that to model the effects of high-fidelity transmission of information on the longevity of cultural forms or “traits” in a population, he and Lewis “assumed that there are a fixed number of traits that could appear within a group through novel inventions and that are independent of any other traits within a culture. It seems a category mistake to think that we can represent such a welter by a single variable, or that the whole jumble could act as a discrete thing having a single quantifiable effect on some other discrete thing. 38, No. For now, we can simply use the little w’s to build discrete cultural bits or forms into an evolutionary model. The geological record, he said, was a collection of fragments of the most recent volume of “a history of the world imperfectly kept, and written in a changing dialect.” He urged people to join him in considering natural history in these terms: to “regard every production of nature as one which has had a history” to be pieced together by interpretation of scant evidence. I think this is because Laland’s conclusions are based on the kind of profound knowledge that comes only from a wealth of direct experience and — yes — keen, richly informed interpretation. The winning strategy was an unpredictable, complex mix of behaviors, although it did represent an overall optimum solution composed of behavioral bits. Rather, they set the competitors loose and waited to see who would triumph. The roots of this movement extend back to the early 1970s, to the work of Richard Lewontin at Harvard, and Luigi Luca Cavalli-Sforza and Marcus Feldman at Stanford, among others. Indeed, some scientists describe their use of mathematical models in these very terms. Fracchia and Lewontin maintained that there could be no such general laws because cultural phenomena, unlike atoms and molecules, differ from one another in their properties and dynamics of transmission and change. In particular, they have been addressing the modern synthesis’s paucity of information about developmental biology. They die out when they fail to do so. They are not drawn in pastels or composed in prose, but the fact that they are programmed on a computer makes them no less a representation. But, despite our deep accord, this biologist and I are thinking incommensurately about methods, about how to put our two fields into communication. I can believe in these conclusions, not as proven by the tournament-experiment, or the cultural-trait-transmission model, or the other mathematical models, but as interpretively, argumentatively presented by these models. If the latter, why choose this particular means of expression, representation, advocacy? Darwin’s Unfinished Symphony lists as discrete alternatives, for example, animals learning innovations socially from one another versus inventing them independently; the cultural drive hypothesis operating through natural selection on social learning proficiency versus social learning incidence; humans being more accomplished than other primates due to “chance factors” or because of a “trait or combination of traits that were uniquely possessed by our ancestors”; that high-fidelity transmission of information might have been achieved by our ancestors through language or alternatively through teaching; learning a skill such as stone-knapping to make a cutting tool by reverse-engineering from a finished sharpened flake, or else by imitation, or else by various forms of non-verbal teaching; or else by verbal teaching; and young individuals acquiring skills either asocially by trial and error, or else socially by copying, or else socially by being taught by a tutor “at some cost to the tutor.” In each of these cases, “both, and” seems more plausible to me than “either, or.” (Additionally, in the last case, must teaching involve a cost to the tutor? More than a hundred people of various ages and backgrounds took part in the game. Perhaps the sort of teaching that humans do is qualitatively different from the sorts that other animals do: a teacher macaque might not derive the same intellectual benefits from teaching to compensate for the loss of time that could be spent eating or reproducing. This is because a mathematical model, like a verbal description, contains many layers of interpretation. An example of an observable cultural unit for Feldman is a behavior or custom that follows statistical rules of transmission, and that can therefore be a legitimate object of mathematical study. His method is mathematical modeling, and mine is thick description. 60, 72. He described natural history as a form of deeply interpretive historical scholarship. Biologists involved in the EES have been calling for a broader and less reductive view of evolution, unrestricted to Mendelian genes. Likewise for the separate and distinct occurrence of novel invention, combination, modification, or loss of cultural forms. Of course I’m by no means the first to raise the question, nor indeed have such objections been confined to humanists. Such experiments, Laland reports, have established certain social tendencies in fish. Could we say, for example, that in a given society, “culture” influences “politics” by some quantifiable amount x? Darwin’s own method was explicitly so. Brown, ed., Explaining Culture Scientifically (Seattle: University of Washington Press, 2008), Ch. These are diametrically opposite in trajectory, one abstractive and reductive, the other concretizing and expansive. Maynard Smith’s approach has inspired the most reductive of neo-Darwinists. Darwin’s Unfinished Symphony is a record of his resounding success. “Perhaps,” I thought, “we don’t mean quite the same thing by ‘culture.’” To a humanist, or anyway to this one, “culture” is an abstract noun encompassing many things of many kinds: processes, objects, habits, beliefs both explicit and implicit. Of course, I’m not opposed to representing cultural forms in these Cubist terms any more than I’m opposed to Picasso’s portraits of Dora Maar. In one set of experiments, Laland and his students and collaborators trained guppies to take certain routes to find rich food supplies, then observed other untrained guppies, in various conditions, learn from their trained fellows. Dawkins indeed refers to “unconscious strategists,” the deliberate oxymoron encouraging the reader to accept these apparent ascriptions of agency to genes as radical denials of any such agency. These EES revisionists are interested in feedbacks: in how developmental processes, along with ecological and even cultural ones, feed back into one another, into genetic and other forms of inheritance, and therefore into evolution. ¤
Kevin Laland, author of Darwin’s Unfinished Symphony, was an organizer of the conference I attended and is a leader of the Extended Evolutionary Synthesis research program. Maynard Smith accordingly emphasized that his technical definition of “strategy” was strictly behaviorist. Culture plays as crucial a role in science as it does in nature. This model, in its relation to real cultural forms, seems to me the equivalent of a Cubist painting. After offering several examples of social learning in animals — such as Japanese macaques who learn from one innovative macaque to wash their sweet potatoes before eating them, and fish who learn from one another where the rich feeding patches are located — Laland asks what might be the best “social learning strategy.” He explains that the “traditional means to address such questions is to build mathematical models using, for instance, the methods of evolutionary game theory.”
Game theory became a standard model in evolutionary biology in the early 1970s with the work, notably, of the British theoretical evolutionary biologists W. To express these ways of understanding in the language of mathematical modeling seems fine, if one likes to do that, but no more definitive than expressing them in words. These will surely seem naïve questions to any biologist reading this. Price. But in Darwin’s Unfinished Symphony, Laland describes how he and his collaborators used game theory in an innovative way, to design a virtual world in which they hosted a tournament. Their work was foundational to the neo-Darwinist, gene-centric program that Laland has devoted his career to challenging. The theoretical physicist Murray Gell-Mann warned that we must be careful, regarding models, “not to take them too seriously but rather to use them as prostheses for the imagination, as sources of inspiration, as acknowledged metaphors.  Charles Darwin, On the Origin of Species by means of natural selection, or the preservation of favoured races in the struggle for life (London: John Murray, 1859 [1st ed.]), 310–311, 485–486. As it turned out, I had somewhat misunderstood the situation. Or rather to express, represent, or advocate certain interpretive views of evolutionary processes? Again, let me be clear that I think that’s fine — indeed, inevitable — because interpretation is ineradicable from any attempt to understand the world.  John Maynard Smith, Evolution and the Theory of Games (Cambridge: Cambridge University Press, 1982), 5, 10. As part of this development, EES biologists have been increasingly interested in culture, among other forms of transformation and transmission, and so have welcomed the input of humanists, including philosophers and historians of science like me, whose job it is to study and understand culture.
We aren’t saying that our model is more probable than another model; we’re saying it exposes what is possible.”