PHYSICS IS NOT “JUST PHYSICS” 1 Running head: Physics Is Not “Just Physics”

When physics is not “just physics”: Complexity science invites new measurement frames for exploring the physics of cognitive and biological development. Damian G. Kelty-Stephen Wyss Institute for Biologically Inspired Engineering Harvard University [email protected] James A. Dixon Center for the Ecological Study of Perception and Action Department of Psychology University of Connecticut [email protected] Post-print of paper published by Critical ReviewsTM in Biomedical Engineering, vol. 40, pp. 471-483. Copyright 2012 Begell House.

Corresponding author: Damian G. Kelty-Stephen Wyss Institute for Biologically Inspired Engineering Harvard University 3 Blackfan Circle Boston, MA 02115 Phone: (703) 300-3375 Email: [email protected]

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PHYSICS IS NOT “JUST PHYSICS” 2

Abstract The neurobiological sciences have struggled to resolve the physical foundations for biological and cognitive phenomena with a suspicion that biological and cognitive systems, capable of exhibiting and contributing to structure within themselves and through their contexts, are fundamentally distinct or autonomous from purely physical systems. Complexity science offers new physics-based approaches to explaining biological and cognitive phenomena. In response to controversy over whether complexity science might seek to “explain away” biology and cognition as “just physics,” we propose that complexity science serves as an application of recent advances in physics to phenomena in biology and cognition without reducing or undermining the integrity of the phenomena to be explained. We highlight that physics is, like the neurobiological sciences, an evolving field and that the threat of reduction is overstated, and we propose that distinctions between biological and cognitive systems from physical systems are pretheoretical and so optional. We review our own work applying insights from postclassical physics regarding turbulence and fractal fluctuations to the problems of developing cognitive structure. Far from hoping to reduce biology and cognition to “nothing but” physics, we present our view that complexity science offers new explanatory frameworks for considering physical foundations of biological and cognitive phenomena. Keywords: physics, biology, cognition, reduction, turbulence, fractals, complexity

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PHYSICS IS NOT “JUST PHYSICS” 3

The goal-directed behavior of biological systems bears strong resemblance to the phenomena of broadly distributed, nonlinear complex physical systems. This observation has inspired generations of scientists to pursue explanations of biological phenomena in terms of their underlying physics. Like many other researchers, we have adopted methods and concepts from physics in pursuit of a theory of perception and action, phenomena that are clearly within the realm of biology (e.g., most recently, 1, 2). Invoking explanatory concepts from physics repeatedly draws some variant of the question: “Do you mean that biology can be explained by physics?” We sense that this question stems from the conviction that explaining biology with concepts from physics smacks of reductionism, and that reductionism is bad. More explicit statements of this position can be found in the literature. As theoretical biologist Stuart Kauffman 3 put it: “Biology is really not just physics” (p. 43). The neurobiological sciences have appeared to some as simply being different, too complex, too broad, for it to be “just physics” (e.g., 4, 5 ). Because the science of complexity has its foundations in modern physics, this is an important issue for complexity-based accounts of biological phenomena. What sorts of commitments are entailed by adopting a physics-based framework for biological systems? In our view, answering this question requires the careful consideration of a number of issues. In what follows, we outline these issues and discuss our current take on them. I. RELATIONS NOT REDUCTIONS Importing concepts from physics to explain phenomena in biology immediately raises the specter of a particular form of scientific orthodoxy in which the only allowable explanations are those that invoke causal properties from smaller scales to larger scales. Typically, the smaller-scale, explanatory properties are from physics or chemistry, and the larger-scale, to-be-explained properties are from biology or the behavioral sciences. This orthodoxy has both a methodological edge, suggesting that science should always be driving towards smaller scale, physical measurements, and an ontological edge, suggesting that biological phenomena are nothing more than the physical processes that produce them. Practicing scientists may recognize that this version of “reductionism” is something of a caricature, but at the same time they also tend to feel that it is a discredited approach to science. Interestingly, among philosophers of science 6, 7, reductionism is a much broader concept than that described in the above caricature. Inquiry into reductionism ranges over a number of dimensions (e.g., ontological, theoretical) and a host of distinctions. Further, the status of “reductionism” is very much open to debate. Among the many points one can glean from this literature are that: 1) instances of the caricature above are a rarity in actual scientific practice, and 2) we might be better served to replace the term “reduction” with “relation”, both because “relation” comes with less baggage and because it so clearly invites further specification 8. Placing biological phenomena in some relation to methods and concepts developed in physics seems noncontroversial. For example, energy, mass, and temperature, concepts from Newtonian physics are essential to modern biology. A host of biological phenomena stand in relation to these concepts, and theories in many biological domains include them as foundational elements 9. Our central points here are that careful consideration of “reductionism” shows it to be a nuanced concept

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PHYSICS IS NOT “JUST PHYSICS” 4 rather than a monolithic form of orthodoxy, and that recasting “reduction” as “relation” invites us to ask how things work, rather than worry about demarcations between fields. II. THERE IS NO SUCH THING AS “JUST PHYSICS” A. First Premises. All scientific explanation starts from first premises, the points which are assumed and the points that will so be excused from needing explanation in the first place. To illustrate, and to be perfectly candid about our position, we will start here by stating our own first premise, or at least the premise that seems to us to be the bedrock of explanations: All measured fluctuations reflect the flow of energy. On the face of it, this premise might sound starkly reductionist, and it certainly does seem to rule out intentional agency as a primitive. Put differently, we reject, as a starting premise, the idea that measured fluctuations might generate themselves independent of any prodding by another factor. This is a choice on our part, for good or for ill: we would like to see how well fluctuations in biology might be considered no different, for instance, from a flag flapping in the wind. After all, fluctuations in a flapping flag may be somehow understood as the interaction of the wind’s kinetic energy, and the flag’s kinetic and potential energy. If our premise is false, then the necessary alternative in this example is for the flag to contribute all of some fluctuation irrespective of or in the absence of physical factors. In the context of the flag example, clearly sounds spooky. But we think researchers should find it equally spooky when applied to organic matter. However, every premise, ours included, carries its own philosophical baggage— deeper premises that lurk below what seemed so primitive. Hence, readers may well find our premise no less troublesome than its alternatives. The word “fluctuations” suggests that we assume there is some material “stuff” that might change, vary, or wiggle somehow. We assume these changes can be “measured,” that is, encoded by numbers under conditions that are valid and consistent enough to support an explanation. The word “reflect” suggests our expectation that valid measurements carry evidence about real effects of other stuff called “flow of energy.” “Energy” is a concept that physicists invented to make sense of how things might move. Close on its heels were the other inventions “mass” and “space” to close the logical loop on what energy might move and what it might move it through. Space is just bare extent, of some sort, with no dimensionality specified a priori, and mass is stuff that has extent, i.e., that takes up space. Einstein suggested that mass is tightly-packed energy, which either helps us by reducing the number of complete inventions running rampant in a physical description or confuses us by giving up on the now widespread suggestion that energy is not a specific material substance. Space has been found to have little absolute existence outside of any given explanatory framework, no intrinsic geometry, and a completely flexible definition depending on the problem under study and the measurement framework assumed by the scientist 10, 11. Physics is not reality but a description of what we are trying to know about reality 12 . Physics has no final answers about anything, despite recent success and acclaim. The efficacy of concepts from physics (e.g., energy) is no guarantee of their internal consistency, finality, or universality. Physicists have often found that one kind of physics will hold in one case while another case may need another. The physics of building bridges is the Newtonian mechanics describing interactions of solids in a Euclidean three-

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PHYSICS IS NOT “JUST PHYSICS” 5 dimensional space. The physics of global positioning system (GPS) satellites depends on Einstein’s theory of relativity that was housed in a double-elliptical Riemannian space. Theories from physics, and their concomitant methods, have a range of utility, even in physics. III. PHYSICS DOES NOT ENTAIL INEVITABLY GREATER DISORDER AND DECAY Our concern here is that physicalist explanations of biology and mind resort to well-trodden pre-theoretical distinctions that may be restricting new conceptual advancement. One major obstacle is a common pre-theoretical decision that, life and cognition are clearly exceptional cases with regards to the normal proceedings of the physical world. The neurobiological sciences often make two distinctions, first, a dichotomy between life and physics and, second, the dichotomy between cognitive life and non-cognitive life. Physics, the story runs, allows only that all aggregates of molecules and atoms run towards progressively greater disorder and decay; thus, physics disallows novelty. Life and cognition are set up as unassailable, graded departures from the general rule of physics that holds for non-living stuff and, to a great degree, nonintelligent life forms, respectively (e.g., 4, 5). We find these distinctions ill-posed for two major reasons. First, the notion that physics entails greater and greater disorder simply does not hold. Clearly structure is the major feature of our physical world. That is, the world observed and remarked upon by scientists widely contains a variety of patterns that are uncontroversially identified as “structure.” There are plenty of examples of growing disorder and decay close to home and easily observed: light bulbs go out, screen doors eventually fall off their hinges, kitchens become messier, and milk can be spilled. Similarly, individual organisms become more disorganized, more prone to unhealthy mutation, and less flexible in response to external changes in the environment. All of that said, the focus on the disorder and decay overlooks a wide swath of examples of growth, accretion, and complexification. Multicellular bodies can grow from single cells, fluids take on turbulent patterns, tectonic plates shift producing new geological formations, and new ideas and inventions are generated by fertile minds. We can attribute all exceptions to disorder and decay to life or to cognition, but it is not so obvious that this attribution resolves the question, and we expect that this attribution actually makes the problem of understanding life and cognition more difficult than it has to be. Second, the scientist and the law most often cited for formalizing and generalizing the insight that physical systems universally run to disorder and decay, namely, Boltzmann and the second law of thermodynamics, did not actually accomplish what posterity has credited them with 13. The second law was an observation that adiabatically isolated systems in equilibrium might lose heat applied to it (i.e., entropy might decrease). It was a derived from observations and models of heat transfer that began with the assumption that heat was not appreciably different between neighboring molecules. The second law does not address open systems, systems that exchange energy and matter with their surround, or any system far from equilibrium. Living systems are necessarily open systems, and so fall outside the direct purview of the second law. IV. THE NEUROBIOLOGICAL SCIENCES MAY ISOLATE THEMSELVES BY KEEPING PHYSICS AT BAY

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PHYSICS IS NOT “JUST PHYSICS” 6 Wherever scientists in neurobiological fields have drawn a deep line in the sand between biology and cognition on one side and physics on the other, they often do so at the price of guaranteeing that either biological and cognitive sciences or physical sciences are to be special and, to some degree, untouchable by other fields. Making this distinction often involves recourse to concepts such as “life,” “organisms” (or “selves”) and behavior that is “intentional.” According to this distinction, physics is a field devoted exclusively to molecules, quarks, and heat transfer, the biological and cognitive sciences claim ownership of phenomena beyond the scope of physics. Strong versions of this approach grant unique causal powers to organisms. For example, according to Kauffman 3, “organisms are parts of the furniture of the universe, with causal powers of their own, that change the actual physical evolution of the universe” (p. 43). Introducing entities with new causal powers is an profound step for any theory; one is essentially defining the rules of the game by committing to a particular metaphysics. Knowing whether a set of metaphysical commitments will create confusion or clarity can be difficult, a priori. However, it seems self-evident that adequate definition of the fundamental elements would be pre-requisite for a theory based on those elements. Unfortunately, despite valiant efforts to define what is and what is not an “organism” 14, there remains little consensus as to what distinguishes organisms from non-organisms 15 or what constitutes greater or lesser organismic complexity 16. Of course, as noted above, physics is full of hard to define entities. However, positing the fundamental difference of a science becomes more challenging when the new ill-defined entities are completely beyond the scope of another science. A similar preponderant view in cognitive sciences requires that explanation of cognition make reference to latent cognitive processes, functions located inside the neural hardware and exerting distinctly cognitive causal powers. According to this view, any attempt to account for cognitive performance that does not make appropriate reference to these special causal powers “is unfortunate because latent cognitive processes are exactly what cognitive scientists are interested in” (17, p. 91). Carving scientific knowledge up into different disciplines each with its own preferred causal variables comes with severe challenges. For instance, a popular theme in the neurobiological sciences is the use of information: specialized components and processes generate specific informative signals, and these signals travel along communicative pathways in the biological or cognitive system. Attempts to define the concepts of “organism” and “life” have notably invoked the capacities of determining what information refers to and generating information-appropriate actions as defining features of biological systems 18. In short, according to this view, biological systems can make use of information, and non-organic physical systems cannot. This view involves making a loan of intelligence, that is, assuming that the participating entities are acting with specialized expertise that has not otherwise been explained 19. For instance, we can explain visual perception by describing how eyes contain photoreceptors, that is, neurons particularly expert in decoding the information carried by light to the eye, but this explanation requires first loaning to photoreceptors the intelligence necessary to respond specifically and reliably to optical stimuli. We hope that these loans will be paid back, but often, one loan of intelligence leads to another, as one specialized function is explained in terms of another. In this example, we might explain the photoreceptors’ expertise in responding to optical stimuli as a property coded for by genes. However,

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PHYSICS IS NOT “JUST PHYSICS” 7 with this new loan of intelligence to the genome, we burden ourselves with the added responsibility of how the genome might have anticipated optical stimuli 5, 20. Scientists in the neurobiological fields sometimes take a curious position with regard to these issues. Everyone agrees on the need to keep on digging deeper and to arrive at better explanations of ideas, terms, and distinctions that may simply be placeholders for the parts that we don’t understand currently. However, an important question is whether digging deeper and arriving at better explanations ever leads to the integration of insights within each neurobiological field with insights from outside neurobiological fields. Setting up novel causal powers and making loans of intelligence serve to make the neurobiological fields special sciences, and it’s not clear whether these theoretical moves reflect real differences or whether they are meant as territory markers beyond which other sciences are deemed not welcome. As we noted above, some members of cognitive science define their field not simply in terms of the focus on phenomena termed “cognitive” and having to do with thoughts, judgments, decisions, etc. but also in terms of the kinds of mechanisms invoked to explain these phenomena 17. Strictly observing a finite set of predetermined mechanisms and causal powers may give rise to fascinating, instructive research, but it is not so much a resistance to reduction by physics as it is a new reduction to a different set of primitive building blocks. It successfully seals a field off, preventing contamination but also insight from other fields and dramatically limiting the set of possible discoveries and explanations to the novel causal powers assumed at the outset. Are organisms entirely the property of neurobiological sciences? Certainly, organisms are not simply derived from the notions of classical physics, and the concept of an organism has reflected theoretical refusals to accept classical physics as an exhaustive framework for understanding biology and cognition 14, 21, 22. But what about more recent developments in physics? Physics is rife with problems that, physicists have found, are intractable to classical physics, but the shortcomings of classical physics have been the stimulus for new insights and new solutions to long-standing challenges. Physics is not so monolithic or inflexible that a failure of classical physics is a failure of physics in general. Where physics has so far failed, it is important to remember the option of “new physics” rather than the more exclusionary option of “not physics” 23, 24. All of physics could turn out to be sorely inadequate to explain neurobiological phenomena. The novel causal powers posited may serve the purpose. The question of intelligence loans will remain, for physics as well as every other field: how do any proposed causal powers arise in the first place? Our concern is not so much that neurobiological fields give up their proposed causal powers, but disallowing attempts to explain the same phenomena with alternate mechanisms and causal powers that had not been envisioned from the start seems dangerous. Whether or not any given mechanism gives rise to any given phenomenon should be an empirical question 2, 25. Perhaps organisms and minds cannot be understood through physical principles, but we do not think that this possibility has been exhaustively explored, especially given the fact that physics is a work in progress. V. PROGRESS IN PHYSICS OFFERS NEW EXPLANATORY OPTIONS Some of the most exciting developments in post-classical physics have come from the recognition that the notion of inevitable disorder and decay of systems is not a necessary conclusion. Physicists have discovered that systems in disordered, uniform

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PHYSICS IS NOT “JUST PHYSICS” 8 states can, in fact, develop towards non-uniform, ordered states. Perhaps the inevitability of disorder and decay is just an independent axiom, a pretheoretical choice that scientists in the neurobiological fields can make or can avoid. If so, we are left in a similar position as mathematics found itself in the nineteenth century when it was discovered that Euclid’s fifth axiom was independent from the other axioms 10, 11. Relaxing this single axiom may give the neurobiological sciences more flexibility to open up its doors a wider set of candidate casual powers and to allow more innovative, perhaps more general explanations for its phenomena. Although Euclid’s fifth axiom itself has little to do the neurobiological sciences, the revolution in geometry and mathematics that followed its relaxation did yield new insights that may be crucially relevant to the neurobiological sciences. According to Euclid’s fifth axiom, for any line and a point not on the line, there is one and only one other line intersecting both at a right angle to the first line. When it became known that this axiom was independent and potentially optional, what followed in the field of mathematics was an exciting, intellectually tumultuous period in which geometry became empirical and even experimental. Relaxing the one, independent axiom allowed scientists to imagine new formalisms for space, dimensionality, and so for ways of relating physical quantities. Among these new geometries was the Riemannian doubleelliptical space that, as mentioned above, allowed the development of GPS. Geometries are important for scientific insights in that they provide frameworks for describing how systems are extended, how systems vary and evolve. And the novel flexibility in the field of geometry allowed a novel flexibility in the kinds of available scientific explanations and solutions. While the above is simply a cautionary analogy about what can arise from relaxing certain assumptions, we can give this analogy a good deal more substance. The emergence of new geometries, new ways of considering space and extent dovetailed elegantly with the discovery of new physical phenomena that have turned the supposed inevitability of decay and disorder on its head. Here, we will point to a particularly compelling pairing of geometry with physical phenomenon that begins to suggest how phenomena of growth and complexification (as in biology and cognition) need not be at odds with or especially different from physical phenomena. Specifically, we will point to the physical phenomenon of turbulence and the mathematical formalism of fractal geometry. On one hand, turbulence is the quintessential example of detailed order and patterning appearing just when classical physics might intuit greater disorder and uniformity, of nonlinearity and novelty just when classical physics would have dissolution and simplification. On the other hand, fractal geometry has been the computational means of describing the convolutions of turbulence. A. Turbulence Physicist Richard Feynman famously called turbulence “the most important unsolved problem of classical physics” 26. This possibly brash statement has stood the test of time 27, 28. Turbulence has to do with the way fluid flows at high speeds and under constraints. Feynman pointed out that classical physics was fairly confident about the nature of fluid flow only under two conditions: 1) if the fluid were pushed only very slowly or 2) if the fluid were very viscous like honey. Under conditions of slow flow, fluids can move uniformly in relatively parallel columns or sheets; this kind of flow is called “laminar,” from the Latin for “thin sheet.” Flow changes with increases in a

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PHYSICS IS NOT “JUST PHYSICS” 9 parameter called the Reynolds number, which is directly related to velocity and to distance traveled and inversely related to viscosity. If fluid travels faster, longer, or with less viscous resistance, laminar flow breaks down and gives rise to a bustling network of swirling eddies at many different scales. Lewis Fry Richardson 29 suggested the metaphor of a cascade to describe turbulence. Though each eddy alone might suggest a coherent vortex, the turbulent flow manifests as a broadly distributed hierarchical structure in which eddies collide with each other, dissolve into bigger eddies, and spawn smaller eddies. Turbulence is a subtle mix of intricate, interwoven coherent detail and, at the same time, maddening unpredictability. Attempts at numerical simulation often involved Navier-Stokes equations, but the prediction window for such modeling was always very short. Later attempts to model turbulence invoked chaotic maps that enlisted relatively few dimensions (sometimes specific parametrizations of Navier-Stokes equations) and, stunningly, produced unpredictable behavior from low-dimensional determinism (Lorenz, 1963). Another focus of modeling turbulence involved the power-law relationships. Kolmogorov 30 studied the fluctuations in fluid-flow over progressively larger distances. What he found was that, over a limited range of distances, the variance of flow velocities increased as a power law of distance, with variance growing at a fractional exponent of distance. As Reynolds number increased, this power-law extended over progressively more distances; that is, the same fractional exponent appeared to hold over a progressively wider range of distances as flow became more turbulent. Hoping to have tamed the unpredictability of turbulence with a scale-invariant power-law relationship, Kolmogorov posited that this power-law form should hold universally for turbulent flow regardless of the details of flow. Kolmogorov also went so far as to assume that the scaleinvariance of this power-law entailed a sort of uniformity in turbulence. Perhaps Boltzmann was still correct, and perhaps even turbulent flow tended, in some sense, towards a disordered uniformity. As it turned out, turbulence still managed to buck even this illusion of uniformity. Later work found that the power-law scaling relationships exhibited by turbulent flow could vary widely across space or across time. However, even though Kolmogorov’s 30 notion of uniformity failed to hold, the efficacy of power-law relationships for describing turbulent behavior persisted. Even if a single power-law relationship does not hold, the variety of power-law relationships within a given case of turbulent flow may be crucial for modeling, understanding, and predicting turbulence. This approach remains competitive today and has evolved within the framework of fractal (and more generally, multifractal) geometry 31. This observation brings us to the companion in the pair we indicated above. Before moving on, we might only remark that turbulence is a wonderful example of how there need be nothing simple about the mechanics at play in purely physical phenomena. B. Fractal geometry Another of the geometries that arose from the relaxation of the fifth axiom was fractal geometry. Fractal geometry was a particularly radical departure from Euclidean geometry. Euclidean geometry describes smooth, continuous objects in terms of their extent along orthogonal or linearly independent components. Euclidean geometry assumes that dimensions are integer in number and that they reflect a strict coordination in which no dimension conflicts or overlaps with another. Fractal geometry describes a

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PHYSICS IS NOT “JUST PHYSICS” 10 more unruly framework in which an object can have fractional dimensionality instead of integer dimensionality. These fractional (hence “fractal”) dimensions are estimated from the sort of fractional exponents that characterized Kolmogorov’s 30 power-law. More heterogeneous systems manifest a family of multiple fractional exponents, yielding what is known as multifractality. On first glance, this description may seem like so much contrarian obfuscation of what could just be a more elegant Euclidean worldview. However, fractal geometry was developed with the facts in mind that 1) all of our measurements of non-quantum objects we encounter empirically are patchy and not smooth and 2) to make matters more complicated, this patchiness can vary over time and space. Fractal geometry emphasizes the rugged, curdled aspect that contaminates any sort of Euclidean view we might take of our measurements. Whereas Euclidean geometry tidily directs the dimensional traffic so to prevent any collision or confusion among orthogonal dimensions, fractal geometry represents an attempt to formalize the collisions, even as they lead to rippling and fracturing across very many scales. Fractal geometry emphasizes space in terms of how deeply fluctuations are embedded within each other. Fractal geometry was developed in large part to understand turbulence, or at least to rein some of this madness behind a family of power-law relationships that may expand or contract, disappear or change depending on the conditions for turbulent flow. The variety in power-law relationships examined in fractal and multifractal analysis provides a way to express the nested structure across multiple scales of a turbulent field 31-33. And while it has been ably applied to the fluid-dynamics problems it was originally designed to solve, its applicability has gone much further. Fractal geometry has become a framework in which to consider phenomena that had previously seemed too fitful, too unruly, and too resistant to classical-physical decomposition, namely biology 34, 35. The fractal and multifractal relationships found in biological and cognitive fluctuations suggest turbulent flows exactly where the neurobiological fields have sometimes discounted a role for physics. Fractal geometry has begun to suggest that the biological and cognitive phenomena—such frustrating embodiments of healthy, thoughtful, complexifying exceptions to disorder and decay—may have deeply to do with turbulence 1, 36 . Our own work deals with the emergence of novel structure in cognitive systems. A hallmark of cognitive systems is context-sensitive behavior, that is, actions addressing environmental structure with a blend of both stability and flexibility and with a capacity for supporting a wide range of complex coordinations with environmental structure. Cognitive systems appear to act in task-oriented ways according to intentions, and intentionality provides a powerful framework in which to understand the behavior of cognitive systems. Intentions have to do with the powerful faculty of reference, in which cognitive systems appear to draw meaning from signs and stimuli not directly imbued with meaning. To explain this task-oriented, reference-driven behavior, the prevailing view in cognitive science refers to a class of computational mechanisms designed to construct, deploy, and interpret mental representations that translate the world of environmental structure to the mental, neural world within 17. This prevalent approach thus involves a firm break with physicalism, a certainty that the principles of physics are not enough to support the rich complexity of cognition. Intentions, representation,

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PHYSICS IS NOT “JUST PHYSICS” 11 reference, and computation are treated as novel factors that distinguish the cognitive or biological from the strictly physical 4, 5. Explanation in terms of representations and intention reflects the pretheoretical choice of a measurement frame in which distinctly cognitive factors perch delicately atop a foundation of neural activity. Neural activity often provides the substrate for cognitive dynamics in this view. However, given that neurons are treated in their electrochemical and mechanical properties, neurons may not sum together to produce intentions or other cognitive factors. Nevertheless, cognitive scientists may grant a loan of intelligence to neural systems to do the job they require, namely, to make cognitive systems out of physical ones or at least to provide cognitive systems a physical support. What dedicated roles neurons may play for specific cognitive functions may be folded back onto inferential engines within the cognitive architecture (e.g., 37), genetic predispositions (e.g., 38), or evolutionary explanations for how a history of natural selection steered cognitive architectures to address specific current cognitive demands (e.g., 4). The challenge of all three of these attempts to seal up the explanatory divide is that they all require recourse to a yet further loan of intelligence to account for how we, as physical systems, project the appropriate hypotheses from an unbounded set of possible hypotheses, translate the chemistry of genes into not simply biological structures but also into cognitive ones, and experience generations of natural selection driven by a purpose not to be actualized until the present day. All these challenges remain unanswered 5, 39-41. We are curious to explore the physical underpinnings of cognition and to determine how well the intentions, representations, references, and computations might fall out of the physics underlying the development of the cognitive system. We do not think that intentions, representations, and the like are fictions. Far from it, we think that these phenomena are some of the crowning achievements of cognitive systems, well worth our attention and deserving of explanation. Intentions, representations and the like may have causal power to move cognitive systems, we would agree. However, we do not think they deserve to be instated as primary causal factors, beyond which there might be nothing else and that are themselves different things altogether from physical stuff. We do not understand where they come from, but we are suspicious of the notion that they require such a hard break from the physics of phenomena swirling around cognitive systems, from the physics of things less often credited with intentionality and reference. Little as we want to explain away cognition and biology as “nothing but” physics, we also have trouble with the intuition that there is physical stuff on one side of the scientific balance and stuff for biology and cognition cleanly on the other. The biological and cognitive stuff certainly appears very gracefully ordered and ornate, very stable and robust, but we do not see any less order or stability in the physical stuff. We suspect that cognitive and biological stuff is not exceptional for its order and its development, and that it comes to be in large part through similar mechanisms that promote new order and development of structure in physical stuff. The cognitive system is a vast distributed system with various modalities and ways of using its own on-board (i.e., internal) energy potentials probing the energy distributions surrounding it in the environment (e.g., 21, 22). The embedding of the cognitive system in its environment is so deep and thoroughgoing that it is indeed difficult to separate one from the other, system from environment. All we have proposed so far, from our first premise above, is that the measurable fluctuations in this system-

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PHYSICS IS NOT “JUST PHYSICS” 12 embedded-in-environment reflect the displacement of energy. Where they energy comes from, we do not presume to know, but the way the fluctuations spread should tell us, we hope, how and perhaps where energy is flowing. Neurobiological wisdom on the function and mechanics of the neurons supporting cognition surely does not refute the point that cognitive systems run on a transaction between on-board energy potentials internal to physiology and stimulus energy from the surrounding environment. We simply take this notion at face value and follow the explanatory thread of clues to be found in fluctuations. Fluctuations could proceed or spread linearly, or they might behave otherwise. Whatever geometry they embody, we have sought to follow the fluctuations and hope to discern what sorts of physical principles might be in play under the hood of the cognitive system. The fluctuations turn out very often to be fractal, and this fact has turned our attention to the possibility that turbulence may be a key attribute of the physics driving the development of cognitive structure. Although by no means universal and by no means homogenous under all measurement conditions, there is a growing precedent for finding fractally structured fluctuations in the cognitive system 35, 42, 43. The fractal—and more broadly, multifractal—structure of fluctuations distributed across the body reflect the nonlinear interactions across scales of space and time, and this evidence of turbulent flows underlies the stability of biological function (e.g., 36, 44). This evidence of turbulent flows may also have crucially to do with cognitive and perceptual structure 1. We have proposed that cognitive structure reflects the confluence of flows unfolding through the cognitive system with the changing constraints in the context for action 45. In line with our expectation that fluctuations bespeak energy flows, we have found that the changes in these fractal fluctuations predict changes in the way that cognitive systems approach, use, respond to, and generally relate to the available sensory information in the world. Changes in embodied fractal fluctuations have so far predicted the discovery of novel mathematical relations for solving visuospatial reasoning problems 46, 47, the mastery of both induced and explicitly instructed rules in card-sort tasks 47, and the use of mechanical information for haptic perceptual judgments 48. The backdrop for our work has been a pretheoretical choice to consider cognitive systems in a measurement frame made up of physical systems that may or may not exhibit the turbulent flows found in cascades. We do not blind ourselves to the need to explain intentions and representations, nor do we blind ourselves to the role that such factors inevitably play in explanations of cognition. However, we do, from time to time, assume a lens clouded over to cognitive views of the organisms under study: we assume now and then that we know nothing about the thoughts and goals of the systems we study, and that we have only the traces of a physical system. If we consider the time series of fluctuations that we can measure from a system situated in a task environment, what might we learn from those fluctuations about the underlying physics? If these fluctuations could be due to nothing but energy flows—how ever broadly construed— what sorts of structure might they reflect? And what sort of behaviors might they support within the constraints set up by the task? Wiping the lens again and bringing cognitive phenomena back into view, do these fluctuations have anything to do with the impressive feats of cognitive systems? Do these fluctuations provide new insights into the coordination of cognitive system with task environment? Our work has answered these last two questions solidly in the affirmative, and though there is much work yet to do, we

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PHYSICS IS NOT “JUST PHYSICS” 13 see some explanatory value in anchoring those impressive feats of cognitive performance in the turbulent physics often ignored in more traditional cognitive formulations. The measurement frame we have chosen leaves open the possibility that cognition develops as a cascade 2. We do not presume to be alone (e.g., 35, 49), but here is what we have in mind: Through the embedding of cognitive system in its task environment, onboard energy potentials in the body and stimulus energy together conspire across very many scales to stir up a cascade colored by turbulent flows across the body. Cascades lead to complex, richly context-sensitive structures fluctuating according to fractal scaling, and perhaps more importantly, cascades give rise to stable, robust structures that can far outlive the immediate energy flows that made them. One of the celebrated reasons for invoking representations is that, when stimulus energy disappears, the cognitive system must have some way of retaining a trace of it. However, we see in this reason a dismissal of the physical possibilities here. Cascades can exhibit their turbulent forms long after the creative energy flows have ceased 50, 51, from the order of seconds to millions of years 52. There is even evidence that these persisting turbulent forms in the environment serve as perceptual cues to stimuli no longer present, as shown by the aquatic creatures who hunt by following the lasting hydrodynamic trails left in the wake of fleeing prey 53. There may be no clear distinction between stimulus and the turbulent structures they occasion. We expect that such promise of stability might one day lead cascade-based theories of cognition to be competitive with the traditional approaches. V. CONCLUSION We have presented evidence and arguments for our own views of multifractality and neurobiological phenomena elsewhere. Our present considerations are less concerned with that specific content than they are with the general strategy of pursuing physical concepts to help support explanations of biological and cognitive phenomena. It is possible, we think, to pursue physical foundations for biological and cognitive phenomena without “explaining away” biology and cognition. We worry that, in all of the resistance to “just physics” in the neurobiological sciences, this point may sometimes be lost. Nothing need take away or diminish the stunning wonders that life and mind present. Biological and cognitive systems really do seem nothing short of miraculous. That said, to be fair, physics is fairly miraculous too. Weak and strong forces, gravity, turbulence, quantum electrodynamics—all of these phenomena are quite stupendous. It has proven remarkably difficult to write down a set of equations that show these phenomena to be “nothing but” anything. All of these miracles can stay miracles if we only want to consider them in a vacuum. We can decide that neurobiology is something other than physics, but that strikes us as a premise, one with particularly troubling implications: If neurobiology is really nothing but the traffic of specifically neurobiological factors, then we are faced with telling a just-so story for how these neurobiological factors came about—or how they always existed, ever different from physics. Such a story will be heavily mortgaged; loans of intelligence will be required to build it. Alternatively, we can relax the premise of incommensurability between biology and physics, and try to tackle the problem of how some physical stuff acts differently from other physical stuff. This path need not require everything to be molecules and quarks, and nor does it leave us with yawning chasms between causal powers. We suggest that the explanatory role of physics in biology is an open issue: we do not think that physics has progressed enough either to explain

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PHYSICS IS NOT “JUST PHYSICS” 14 neurobiology or, on the other hand, to merit disqualification from the set of candidate concepts for understanding neurobiology. We think that science becomes diminished when lines are drawn in the sand and when causal powers are invoked as purely special to a given phenomena. As a field, physics has managed to withstand fairly jarring divides and has stared down some rather terrifying philosophical quandaries about its subject matter. Physicists have found themselves forcibly reminded that they do not study reality so much as they do measurements 45. The laws of thermodynamics appear to hold for appreciably large systems, but these large systems are made up of tiny quantum objects that are much more fickle 54, with attributes depending upon the measurement frame that scientists apply. For instance, consider the fact that a single molecule can have three independent temperatures at once (i.e., translational, rotational, and vibrational; 55) and then consider that this observation complicates thermodynamical accounting. Still, physicists allow this fickle plurality of phenomena to coexist. Phenomena and the laws explaining them depend on their boundary conditions, the measurement frame in which phenomena are observed and in which the laws are said to hold. Instead of invoking a fundamental divide between physics and biology, it may be more constructive to seek more clarity about which laws and physical regularities are applicable to which measurement frame 56. Our own attempts to bring physics to bear on neurobiological questions have been exactly in pursuit of consulting new measurement frames. Physics does not have to be a reduction; it may simply provide a fresh look at the problem, especially as physics itself progresses to afford new perspectives. We are wary of reductions to physics that undersell the full-blown complexity of biology and cognition. However, we are equally wary of reducing any biological or cognitive phenomenon to nothing but smaller, simpler biological and cognitive factors 57. This latter policy guarantees the miracle but seals it up into a mystery. Physics strikes us as providing rich options for neurobiological explanation. Acknowledgments The authors acknowledge the Wyss Institute for partial support of this manuscript; thank M. T. Turvey, Ramesh Balasubramaniam, and an anonymous reviewer for their insights; and dedicate this work to the memory of Guy Van Orden. References 1. Dixon JA, Holden JG, Mirman D, and Stephen DG. Multifractal dynamics in the emergence of cognitive structure. Topics in cognitive science. 2012;4:51-62. 2. Stephen DG, Anastas JR, and Dixon JA. Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics. Frontiers in Physiology. 2012;3:102. 3. Kauffman SA. Reinventing the sacred: A new view of science, reason, and religion. New York: Basic Books; 2008. 4. Pinker S. How the mind works. 1997. NY: Norton. 1997; 5. Deacon TW. Incomplete nature: how mind emerged from matter. WW Norton; 2011. 6. Silberstein M. Emergence and reduction in context: Philosophy of science and/or analytic metaphysics. Metascience. 2012;21:1-16. 7. Wimsatt WC. Reductionism and its heuristics: Making methodological reductionism honest. Synthese. 2006;151(3):445-475. 8. Van Gulick R. Reduction, emergence and other recent options on the mind/body problem. A philosophic overview. Journal of Consciousness Studies. 2001;9(10):1-34. 9. Rosenberg A, and McShea DW. Philosophy of biology : a contemporary introduction. New York, NY: Routledge; 2008.

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