> ?bjbjcTcT 3t>>Idd
8t_dU( TYBF%0U!*!! U!d m:
Naturalizing Libertarian Free Will
David Layzer
Department of Astronomy, Harvard University
Libertarian free will is incompatible with the thesis that physical laws and antecedent conditions determine events other than the outcomes of quantum measurements. This thesis is not a consequence of physical laws alone. It also depends on an assumption about the conditions that define macroscopic systems (or, in some theories, the universe): the assumption that these systems (or the universe) are in definite microstates. This paper describes a theory of macroscopic initial conditions that is incompatible with this assumption. Standard accounts of classical and quantum statistical mechanics characterize the initial conditions that define macroscopic systems by probability distributions of microstates, which they customarily interpret as representing incomplete descriptions. In the theory described below, the initial conditions that define a macroscopic system are shaped by the systems history and represent objective indeterminacy. This interpretation is a consequence of a simple but far-reaching cosmological assumption supported by astronomical evidence and by methodological and theoretical arguments. It entails a picture of the physical universe in which chance prevails in the macroscopic domain (and hence in the world of experience). Because chance plays a key role in the production of genetic variation and in natural selection itself, evolutionary biologists have long advocated such a picture. Chance also plays a key role in other biological processes, including the immune response and visual perception. I argue that reflective choice and deliberation, like these processes and evolution itself, is a creative process mediated by indeterminate macroscopic processes, and that through our choices we help to shape the future.
I. The presumption of determinism
The proposition that physical laws and antecedent conditions determine the outcomes of all physical processes (other than quantum measurements) is widely regarded as the cornerstone of a naturalistic worldview. Defenders of libertarian free will who accept this proposition must therefore choose between two options:
(1) They can argue (against prevailing opinion among neurobiologists) that some brain processes involved in choice and decision-making are, in effect, quantum measurements that is, that they involve interactions between a microscopic system initially in a definite quantum state and a macroscopic system that registers some definite value of a particular physical quantity.
(2) They can argue that our current physical laws specifically, the laws of quantum mechanics need to be revised. For example, the physicist Eugene Wigner has argued that Schrdingers equation must be modified to account for certain conscious processes (perceiving the outcome of a quantum measurement).
This paper explores a third possibility: that the presumption of determinism is false.
The laws that govern macroscopic processes and the initial conditions that define the systems to which these laws apply have a statistical character. They involve probability distributions of microstates governed by the laws of quantum mechanics (or classical mechanics when it applies). Physicists have usually assumed that macroscopic systems can be idealized as closed systems in definite microstates. They have justified the use of probability distributions to describe macroscopic states by arguing that it is nearly always impossible to prepare a macroscopic system in a definite microscopic state or to discover through measurements which microscopic state a macroscopic system is actually in. I will argue that the probability distributions that figure in statistical mechanics represent not incomplete knowledge but an objective absence of certain kinds of microscopic information. The argument rests on a pair of cosmological assumptions: An exhaustive description of the state of the cosmic medium shortly after the start of the cosmic expansion (a) does not privilege any position or direction in space and (b) contains little or no (statistical) information.
Within physics proper, these assumptions draw support from two main arguments. They contribute to an understanding of quantum measurement; and they serve to ground the statistical assumptions that underlie derivations of the statistical laws that govern irreversible macroscopic processes. The picture of the physical world that emerges from these cosmological assumptions is more hospitable than the usual picture to the worldview of biology. For example, it is consistent with the view that chance events, such as the meteor impact that caused the dinosaurs to die out, have played a prominent role in the history of life, and the view that key processes in evolution, the immune response, and perception have objectively indeterminate outcomes. I will argue that some of the brain processes that mediate deliberation and choice likewise have indeterminate outcomes.
II. Making room for indeterminism
How can a picture of the physical world that incorporates existing physical laws fail to predict that the outcome of every physical process (quantum measurements excepted) is predictable in principle? Before addressing this question, I need to review the standard case for determinism.
A. A closer look at determinism
By determinism I mean the thesis that physical laws connect a fully described initial state of a closed system to each of the systems subsequent states. Our current physical laws are domain-specific: different physical laws govern the microscopic, macroscopic, and astronomical/cosmological domains. In addition, the conditions under which we can regard a system as effectively closed are not the same in the three domains. So we need to consider the domains separately.
1. The microscopic domain
This is the domain of quantum mechanics. Quantum laws are deterministic: the present state of a closed quantum system determines its future state. This assertion may seem to contradict the fact that quantum measurements have unpredictable outcomes, but it does not. In a quantum measurement, a quantum system (for example, an atom) interacts with a (necessarily) macroscopic measuring device. So quantum measurement has one foot in the quantum domain and one in the macroscopic domain. The quantum measurement problem consists in formulating an account of quantum measurement that bridges the two domains.
2. The macroscopic domain
This is the domain populated by middle-sized objects, the objects of ordinary experience.
Macroscopic theories include classical mechanics, the physics of fluids, electromagnetic theory, the theory of heat and its transformations, and theories governing irreversible transport processes such as heat flow and diffusion.
It is a familiar fact that knowable macroscopic initial conditions do not always determine a macroscopic systems future states. For example, the science of dynamical meteorology does not allow one to make reliable long-range weather forecasts. To take a simpler example, cited by Poincar in a famous essay on chance I will return to later, we cannot predict the direction in which a cone initially balanced on its tip will topple. The cones initial state is one of unstable equilibrium. How such states evolve depends sensitively on the initial conditions. Poincar discovered a class of dynamical processes in celestial mechanics that likewise depend sensitively on initial conditions. This class includes chaotic (as opposed to regular) orbits in systems of mutually gravitating particles. Two regular orbits in closely similar initial states diverge slowly; two chaotic orbits in closely similar initial states diverge at an exponential rate.
Poincar assumed that the cone and the particle in its chaotic orbit were initially in definite (classical) microstate, governed by deterministic laws, even if we do not or cannot know what these states are. Since the microscopic laws of motion (for Poincar, Newtons laws) are deterministic, he concluded that determinism prevails in the macroscopic, as well as the microscopic, domain. Thus in Poincars picture of the world, chance was an intersubjective rather than a truly objective phenomenon. The replacement of classical descriptions and laws by quantum descriptions and laws left this conclusion unchanged.
3. The astronomical/cosmological domain.
This is the domain of Einsteins theory of gravitation, general relativity, of which Newtons theory is a limiting case. General relativity is a deterministic theory. Its field equation link classically described states of the universe and of effectively closed systems (stars and galaxies, for example) at different times. But it presupposes theories that describe the physical state of the cosmic medium and physical conditions in stars and galaxies; thus it presupposes the theories that prevail in the macroscopic domain. These theories in turn presuppose theories of the microscopic processes that underlie macroscopic processes. For example, the Maxwell-Boltzmann theory of gases assumes that a gas is composed of particles whose motions and interactions are governed by Newtons laws of motion.
Physicists customarily assume that macroscopic laws not only depend on the deterministic laws governing microscopic processes but also that they are reducible to these. That, in a nutshell, is the scientific case for determinism. In each domain physical laws and appropriate initial conditions uniquely determine the future states of closed systems. It depends crucially on the assumption that the statistical laws of macrophysics are reducible to the deterministic laws that govern closed systems in definite microstates.
B. Breaking the grip of determinism
1. The strong cosmological principle
I will argue that indeterminacy enters physics not through the measurement postulate of quantum mechanics but via a cosmological initial condition I call the strong cosmological principle. It has two parts:
a) There exists a system of spacetime coordinates relative to which an exact statistical description of the universe does not privilege any position or direction in space.
b) This description is exhaustive.
The assumption that the average properties of the universe do not determine a preferred position or direction in space is usually called the cosmological principle. It is conventionally viewed as an approximate simplifying assumption that defines one of many possible models of the universe. Part a) asserts that, contrary to this interpretation, the cosmological priniciple is an exact property of the universe.
Part b) needs a word of explanation. Theoretical physicists take it for granted that our current physical laws are incomplete. Quantum mechanics, broadly interpreted to include particle physics and quantum field theory, is manifestly in need of unification; and theorists have been engaged for decades in efforts to unify quantum mechanics and general relativity. In addition, there are phenomena whose explanations will not (theorists believe) require new or modified laws but for which adequate theories do not yet exist. A standard example is the phenomenon of turbulence in classical fluid dynamics. Another example is quantum measurement. In these respects our current description of the universe is incomplete.
But that description involves more than laws. It also involves auxiliary conditions initial and boundary conditions that physicists need to specify in order to apply physical laws to specific phenomena. Auxiliary conditions serve to define physical systems, from atoms and subatomic particles to the astronomical universe. The specification of initial and boundary conditions is the part of the description to which the adjective exhaustive in part b) applies. I intend it to imply that when you have specified all possible spatial averages of relevant physical quantities (or enough of them to allow you to calculate the rest), you are done; nothing remains to be specified.
A statistical description that satisfies part a) cannot be exhaustive if the universe is finite. For example, a finite universe would have a largest galaxy, whose mass would be part of an exhaustive description and whose center of mass would be a privileged position.
Part b) would also be false if a deterministic classical theory, rather than quantum physics, prevailed in the microscopic domain, even in an infinite universe. For suppose the particles were randomly distributed. An exhaustive description would specify the distance between the centers of mass of each particle and its nearest neighbor. With probability 1, no two of these distances would be equal, because the number of particle pairs is countably infinite while the set of positive real numbers is uncountably infinite. So a description that merely specified statistical properties of the distribution could not be exhaustive. By contrast, a statistical quantum description of an infinite medium that conforms to the strong cosmological principle could be exhaustive.
If the strong cosmological principle holds at a single instant, it holds at all times, because our present fundamental laws are invariant under spatial translation and rotation; that is, they treat all positions in space and all directions at a point in space impartially. The strong cosmological principle extends this kind of invariance to the auxiliary conditions that define the universe. This extension, though unorthodox, is consistent with the abundant observational evidence that bears on it measurements of the brightness of the cosmic microwave background and of the spatial distribution and line-of-sight velocities of galaxies.
It is also supported by a methodological argument: The initial conditions that define the universe dont have the same function as those that define models of stars and galaxies. We need a theory of stellar structure to apply to a wide range of stellar models because stars have a wide range of masses, chemical compositions, angular momenta, initial magnetic fields, and ages. But there is only one universe.
Finally, the strong cosmological principle contributes to the solution of a purely scientific puzzle that goes back to Newton. Experiment shows that local inertial coordinate systems (coordinate systems relative to which free particles are unaccelerated) are themselves unaccelerated relative to the coordinate system defined by observations of the cosmic microwave background and the spatial distribution and line-of-sight velocities of galaxies. Newton conjectured that the fixed stars are uniformly distributed throughout infinite Euclidean space and that they, along with a particular inertial reference frame, are at rest relative to absolute space. But Newtons own theory of gravitation does not throw light on this coincidence. Einsteins theory of gravitation does. It predicts that local inertial reference frames are unaccelerated relative to the (essentially unique) coordinate system defined by the cosmological principle.
2. Cosmology and probability
An exhaustive description of an infinite universe that satisfies the strong cosmological principle has a statistical character. It cannot specify, say, the value of the mass density at a particular point at some moment, because such a specification would privilege that point; even in an infinite universe the probability of finding another point at which the mass density had exactly the same value would be zero. Instead, an exhaustive description specifies (among other things) the probability that at any given point the value of the mass density lies in a given range.
This probability has an exact physical interpretation: It is the spatial average of a quantity that takes the value 1 at points where the mass density lies in the given range and takes the value 0 elsewhere. That is, it is the fractional volume (or, more generally, normed measure) of the set of points where the mass density lies in the given range.
With this interpretation of probability, Kolmogorovs axioms of probability theory become true statements about physical space, and probability itself acquires a physical interpretation: The indeterminacy inherent in probabilistic statements reflects the indeterminacy of position in a description of the universe that satisfies the strong cosmological principle.
3. Randomness and order
Two related properties of probability distribution statistical entropy and information play important roles in the following discussion. The statistical entropy of a discrete probability distribution EMBED Equation.DSMT4 is the negative mean of the logarithm of the probability ( EMBED Equation.DSMT4 ). As Boltzmann and Gibbs showed, it is the statistical counterpart of thermodynamic entropy. Shannon emphasized that it is a measure of the randomness of discrete probability distributions in other scientific contexts and made it the centerpiece of his mathematical theory of information.
Information is a measure of order. Different authors define it differently. I define it here as the amount by which a probability distributions randomness falls short of the largest value that is consistent with appropriate constraints. If this largest admissible value is fixed, an increase in the statistical entropy of the probability distribution that characterizes a physical state is accompanied by an equal decrease in its information. But we will encounter situations in which the largest admissible value of the statistical entropy is not fixed and in which statistical entropy and information both increase.
Statistical mechanics characterizes (macroscopic) states of thermodynamic equilibrium by maximally random, or information-free, probability distributions. The probability distributions that characterize non-equilibrium states contain information. This can take a number of qualitatively different forms. For example, in a closed gas sample, the relative concentrations of chemically reactive constituents may deviate from their equilibrium values; the temperature may not have the same value at every point in the sample; the fluid velocity may not vanish everywhere; vortices may be present; and so on.
As discussed below, I take randomness to be the primordial condition of the cosmic medium. The cosmic expansion and, later, other physical processes create information. But in general the probability distributions of microstates that characterize macrostates of macroscopic systems contain only a tiny fraction of the information needed to specify a definite microstate of the system; they assign comparable probabilities to an enormous number of microstates. Thus macroscopic systems cannot in general be assigned definite microstates. Because microstates evolve deterministically, this condition is necessary for macroscopic indeterminacy.
III. Growth and decay of order
Current theories of the early universe posit that shortly after the beginning of the cosmic expansion, the cosmic medium consisted of uniformly distributed elementary particles whose relative concentrations corresponded at each moment to thermodynamic equilibrium at the temperature and density prevailing at that moment. The average properties of the cosmic medium during this early period depended on the values of physical constants that figure in theories of elementary particles and on the parameters needed to define a general-relativistic model of a uniform, unbounded medium. Density fluctuations, with a spectrum that depends on a small number of additional parameters, may also have been present. But there is no evidence (to my knowledge) to suggest that additional non-statistical information was needed to fully describe the state of the cosmic medium during this period.
But if the early universe was information-free, how did the information-rich structures that form the subject matter of astronomy, geology, biology, and human history come into being?
A. Cosmic evolution and the Second Law
Some physicists have held that a scenario in which information comes into being is impossible because it would contravene the second law of thermodynamics. Rudolf Clausius, who introduced the concept of entropy and formulated its law, expressed the law in these terms: The entropy of the universe goes toward (strebt nach) a maximum. This has often been interpreted to mean that universe must have begun in a highly complex and orderly state and is becoming increasingly uniform and undifferentiated. I think this interpretation is mistaken, for two reasons.
First, in an expanding universe, entropy production is not necessarily accompanied by a loss of information. An important example, discussed below, is the genesis of chemical information information associated with the far-from-equilibrium relative abundances of the chemical elements.
Second, I think it is questionable whether the notion of entropy applies beyond the macroscopic domain in which it was originally defined and in which it has been exhaustively tested and confirmed. In particular, the following argument suggests to me that it doesnt apply to self-gravitating systems.
In classical thermodynamics, entropy is an additive property of extended systems in thermodynamic equilibrium. The definition of entropy extends naturally to systems in local, but not global, thermodynamic equilibrium and to composite systems whose components are individually in global or local thermodynamic equilibrium. It also applies to systems in fixed external gravitational, electric, or magnetic fields. The law of entropy growth predicts, and experiments confirm, that as a closed system that meets these criteria evolves, its entropy increases. Experiments also confirm that eventually a closed system settles into an unchanging state, called thermodynamic equilibrium, in which its entropy is as large as possible. This state is uniquely determined by the values of two of the systems macroscopic properties, such as temperature and volume, and by the values of quantities that are conserved by particle reactions at the given temperature and volume. Can the notions of entropy and its law, so defined, be extended to a self-gravitating gas cloud?
We can regard a sufficiently small region of such a cloud as a gas sample in an external gravitational field. We can therefore calculate its entropy, and conclude from the Second Law that physical processes occurring within the region generate entropy. If the clouds large-scale structure is not changing too rapidly, we can then conclude that local thermodynamic equilibrium prevails. We can even define the entropy of the cloud as the sum of the entropies of its parts.
But because gravity is a long-range force, the cloud as a whole does not behave like a closed gas sample in the laboratory. Although heat flow, mediated by collisions between gas molecules, tends to reduce temperature differences between adjacent regions, the cloud does not relax into a state of uniform temperature. Instead, it relaxes through fluid motions driven by interplay between gravitational forces and pressure gradients toward a state of dynamical equilibrium (or quasi-equilibrium). If the cloud has zero angular momentum, the quasi-equilibrium state has spherical symmetry. The mass density and temperature are constant on concentric spheres and increase toward the center of the cloud. But unlike any macroscopic system to which the Second Law applies, a self-gravitating gas cloud has negative heat capacity: adding heat to the cloud causes its mean temperature to decrease; withdrawing heat causes its mean temperature to increase. So if the cloud can radiate, it grows hotter as it cools.
In such a gas cloud, microscopic processes convert kinetic energy associated with particle motions into radiation, which makes its way toward the surface of the cloud and eventually escapes into space. The loss of energy causes the cloud to contract. As a result, its mean temperature increases and the temperature gradient between the center and the surface becomes steeper. Eventually the core of the cloud becomes hot enough to ignite nuclear reactions that burn hydrogen into helium. These energy-releasing (and entropy-producing) reactions drive the core toward chemical equilibrium, simultaneously creating new deviations from thermodynamic equilibrium in the form of a composition gradient between the core and its envelope. When the core temperature becomes so high that the rate at which hydrogen-burning nuclear reactions in the core release energy balances the rate at which energy is being lost at the surface, the contraction stops and a slowly changing, far-from-equilibrium state ensues. The Sun is now in such a state.
Local entropy-generating processes play an essential role in the process just sketched. Heat flow and radiation tends to level temperature gradients, molecular diffusion tends to level concentration gradients, internal friction (viscosity) tends to level fluid-velocity gradients. All these processes generate entropy. But the mutual gravitational attraction of its parts continually steepens temperature and concentration gradients within the cloud. While Newtons theory of gravitation allows one to extend the notion of gravitational potential energy, initially defined for an object in the Earths gravitational field, to a self-gravitating cloud, no such extension has, to my knowledge, been shown to be possible for the notion of entropy.
B. Chemical order
The history of life begins with the first self-replicating molecules or molecular assemblies, but its prehistory begins with the formation of hydrogen in the early universe. The burning of hydrogen into helium in the core of the Sun releases energy at the same rate as energy is lost in the form of sunlight (and neutrinos). Solar photons drive metabolic, biosynthetic, and reproductive processes in plants and algae, which store energy in information-rich molecular forms that animals use to fuel the chemical processes that mediate their basic biological functions. Life as we know it exists because hydrogen is so plentiful. It is plentiful because only about a quarter of it was consumed early on in reactions like those that keep the Sun and other stars of similar mass shining.
In the very early universe, reactions between elementary particles were so fast that they were able to maintain near-equilibrium relative particle abundances corresponding to the instantaneous values of the rapidly decreasing temperature and mass density. As the universe continued to expand, its rate of expansion decreased, and so did the rates of the equilibrium-maintaining particle reactions; but the latter decreased faster than the former. Eventually, the reaction rates became too slow to maintain the relative concentrations of particle kinds near their equilibrium values. Relative concentrations of particle kinds close to those that prevailed during that era were frozen in. Meanwhile, the universe continued to expand, its temperature and mass density continued to fall, and the gap between the actual statistical entropy per unit mass of the cosmic medium and the value appropriate to thermodynamic equilibrium widened. This gap represents chemical information.
Like the gradients of temperature and mass density in stars, chemical information was created in the early universe by a competition between processes on vastly different scales, governed by different physical laws. Entropy-generating particle reactions, governed by the laws of quantum mechanics, drove the chemical composition toward equilibrium; the cosmic expansion, governed by the laws of Einsteins theory of gravitation, drove the chemical composition of the cosmic medium away from equilibrium.
Some of the chemical information created in the early universe is now being converted into biological information. Because the Sun and other stars of similar mass formed from hydrogen-rich material, they are long-lived sources of light in the visible, infrared, and ultraviolet regions of the electromagnetic spectrum. The energies of photons emitted by the Sun reflect the temperature of the light-emitting layers roughly 6,000 degrees on the Kelvin scale. The energies of individual photons that reach the Earth are therefore much greater than those of the ambient photons, whose energies correspond to temperatures around 300 degrees Kelvin. This disparity makes it possible for solar photons to drive the chemical reactions that maintain the cells of photosynthetic organisms in far-from-equilibrium states.
Every link in the chain of processes that connects the early universe to the creation of information in human brains (including several I havent mentioned) is now understood in some depth and detail. The only novel feature of the preceding account is the claim that information is an objective component of the world that physical theories describe.
IV. Macroscopic systems and history
Molecules, atoms, and subatomic particles do not have individual histories. Two hydrogen atoms may be in different quantum states, but otherwise they are indistinguishable. By contrast, objects of ordinary experience are individuals, each with its own history. I will argue that the statistical laws that govern macroscopic processes likewise have a historical character. Unlike the ahistorical laws of quantum mechanics and general relativity, they depend on the initial and boundary conditions that define the systems they apply to; and these conditions are expressed by probability distributions descended from the probability distributions that characterize the early cosmic medium.
Boltzmanns transport equation illustrates these claims. Boltzmann represented the state of a closed sample of an ideal gas by a probability distribution of the (classical) microstates of a single molecule in the sample, a microstate being defined by a molecules position and velocity. His transport equation relates the rate at which this probability distribution changes with time to the rates at which molecular collisions throughout the sample populate and depopulate single-molecule states.
From the transport equation Boltzmann inferred that a quantity he called H the negative of the single-molecule probability distributions statistical entropy decreases with time until it reaches its smallest admissible value. Thereafter it doesnt change. The probability distribution that characterizes this state of statistical equilibrium has a unique form (derived earlier by Maxwell) that depends on two parameters: the number of molecules per unit volume and the statistical counterpart of absolute temperature.
Maxwell and Boltzmann identified statistical equilibrium with thermodynamic equilibrium. Boltzmann showed that the quantity H is the statistical counterpart of thermodynamic entropy. Thus the H theorem is the statistical counterpart, for an ideal gas, of the Second Law.
Boltzmanns transport equation is the starting point for derivations of laws governing specific irreversible processes in gases, such as heat flow and molecular diffusion. These derivations yield formulas that relate the coefficients that appear in these laws (thermal conductivity and diffusivity) to properties of the gas molecules and the laws that govern their interaction. This enables physicists to to deduce the values of parameters that characterize the structure and interaction of gas molecules from macroscopic measurements. The internal consistency of such efforts leaves little room for doubt that Boltzmanns theory is substantially correct.
Boltzmanns theory has also served as a model for theories of irreversible processes in other macroscopic systems, such as dense gases, liquids, solids, and plasmas; and these theories, too, enjoy strong experimental support.
Yet for all their practical success, Boltzmanns theory and other statistical theories of irreversible processes raise foundational issues that are still debated today.
A. Objectivity versus intersubjectivity
The second law of thermodynamics and the laws that govern irreversible processes are widely held to be observer-independent features of the external world. Statistical theories link these macroscopic laws to microphysics. Yet these theories characterize macrostates by probability distributions that are standardly interpreted as reflecting an observers incomplete knowledge of the objective physical situation (in which every closed macroscopic system is in a definite microstate).
By contrast, an account of cosmic evolution that incorporates the strong cosmological principle makes information and statistical entropy objective properties of the physical world, created and destroyed by historical processes linked to conditions that prevailed in the early universe. History determines what kinds of information are (objectively) present in the probability distributions that characterize initial macrostates and what kinds are objectively absent. By situating statistical theories of irreversible processes within a historical account of initial and boundary conditions, we eliminate the taint of subjectivity. The problem of justifying assumptions about initial and boundary conditions for particular macroscopic systems and classes of macroscopic systems remains, of course, but it is now a soluble scientific problem.
B. Entropy, Boltzmann entropy, and Gibbs entropy
Boltzmanns theory applies to ideal gases; Gibbss statistical mechanic applies not only to samples of an ideal gas but to any closed system of N particles governed by the laws of classical mechanics. Its quantum counterpart, quantum statistical mechanics, preserves the overall structure of Gibbss theory and its main theorems.
Like Maxwell and Boltzmann, Gibbs identified thermodynamic equilibrium with statistical equilibrium. Boltzmanns theory reproduces the classical thermodynamic theory of an ideal gas, with the statistical entropy of the probability distribution of a single molecules microstates in the role of thermodynamic entropy and a parameter that characterizes the maximum-statistical-entropy probability distribution in the role of absolute temperature. Gibbss theory reproduces the whole of classical thermodynamics, with the statistical entropy of the probability distribution of a closed macroscopic systems microstates in the role of thermodynamic entropy and a parameter that characterizes the maximum-statistical-entropy probability distribution in the role of absolute temperature. So Boltzmanns theory may appear at first sight to be a limiting case of Gibbss. But Boltzmann proved that the statistical entropy of the single-molecule probability distribution increases with time (unless it has already reached its largest admissible value), while Gibbs proved that the statistical entropy of the probability distribution of the microstates of the sample as a whole is constant in time.
The resolution of this apparent contradiction is unproblematic. It hinges on a mathematical property of statistical entropy. The statistical entropy of an N-particle probability distribution can be expressed as the sum of two contributions. The first contribution is N times the statistical entropy of the single-particle distribution. The second contribution is associated with statistical correlations between molecules of the gas sample. The constancy of the N-particle statistical entropy is consistent with the growth of the single-particle contribution. Taken together, Boltzmanns H theorem and Gibbss proof that the statistical entropy of the N-particle probability distribution is constant in time imply that the second contribution the contribution associated with intermolecular correlations decreases at a rate that exactly compensates the growth of the first contribution. In terms of information: the decline of single-particle information in a closed gas sample is matched by the growth of correlation information.
Although Boltzmann correctly identified the thermodynamic entropy of a closed gas sample with the single-particle statistical entropy, his derivation of the H theorem the statistical counterpart of the Second Law as applied to an ideal-gas sample had a technical flaw. The derivation rests on an assumption (known as the Stosszahlansatz) that cannot in fact hold for a closed gas sample. A stronger form of this assumption states that correlation information the amount by which the information of the single-molecule probability distribution, multiplied by N, falls short of the information of the N-molecule probability distribution is permanently absent. As weve just seen, this assumption cannot be true, because the decay of single-molecule information creates correlation information at the same rate. So even if correlation information is initially absent, it cannot be permanently absent.
The persistence of correlation information in a closed system poses a threat to the very notion of thermodynamic equilibrium. Poincar proved that a closed, initially non-uniform dynamical system cannot relax into a permanent state of macroscopic uniformity; after an initial period of relaxation, it must eventually returns to a non-uniform state resembling its initial state. For example, if the left half of a gas sample is initially at a higher temperature than the right half, heat flow equalizes the temperature throughout the sample; but eventually an uneven temperature distribution resembling the initial distribution reasserts itself. The recurrence time the precise meaning of eventually depends on how closely the revenant distribution resembles the original. The closer the resemblance, the longer the recurrence time. In any case, though, it greatly exceeds the age of the universe.
Although the assumption that correlation information is permanently absent cannot be true, some authors have argued that the Stosszahlansatz may nevertheless hold to a good approximation for periods that are long by human standards but short compared with the Poincar recurrence time.
Another approach to the problem of initial conditions starts from the remark that no gas sample is an island unto itself. Can the fact that actual gas samples interact with their surroundings justify the assumption that correlation information is permanently absent in a nominally closed gas sample? And if so, is it legitimate to appeal to environmental intervention?
J. M. Blatt has argued that the answer to both questions is yes. The walls that contain a gas sample are neither perfectly reflecting nor perfectly stationary. When a gas molecule collides with a wall, its direction and its velocity acquire tiny random contributions. These leave the single-particle probability distribution virtually unaltered, but they alter the histories of individual molecules, thereby disrupting multi-particle correlations. Blatt distinguished between true equilibrium (in the present terminology, sample states characterized by an information-free probability distribution) and quasi-equilibrium, in which single-particle information is absent but correlation information is present. He argued, with the help of a simple thought-experiment, that collisions between molecules of a rarefied gas sample and the walls of its container cause an initial quasi-equilibrium state to relax into true equilibrium long before the gas has come into thermal equilibrium with the walls. Walls impede the flow of energy much more effectively than they impede the outward flow of correlation information.
Bergmann and Lebowitz have constructed and investigated detailed mathematical models of the relaxation from quasi-equilibrium to true equilibrium through external intervention. More recently, Ridderbos and Redhead have expanded Blatts case for the interventionist approach. They construct a simple model of E.L. Hahns spin-echo experiment, in which a macroscopically disordered state evolves into a macroscopically ordered state. They argue that in this experiment, and more generally, interaction between a nominally isolated macroscopic system and its environment mediates the loss of correlation information by the system.
Blatt noted that the interventionist approach has not found general acceptance.
There is a common feeling that it should not be necessary to introduce the wall of the system in so explicit a fashion. ... Furthermore, it is considered unacceptable philosophically, and somewhat unsporting, to introduce an explicit source of randomness and stochastic behavior directly into the basic equations. Statistical mechanics is felt to be a part of mechanics, and as such one should be able to start from purely causal behavior.
The historical account I have been sketching supplies a hospitable context for the interventionist approach. Macroscopic systems are defined by their histories, which determine the kinds and quantities of information in the probability distributions that (objectively) characterize their initial states. A historical account also justifies the necessary assumption that the environments of macroscopic systems are usually characterized by maximally random, or information-free, probability distributions of microstates.
C. The origin of irreversibility
The laws of statistical macrophysics discriminate between the direction of the past and the direction of the future; the laws that govern the microscopic processes that underlie macroscopic processes do not. What is the origin of irreversibility, and how can it be reconciled with the reversibility of microscopic processes?
The conflict between microscopic reversibility and macroscopic reversibility is rooted in the idealization of perfect isolation. This idealization works for atoms, molecules, and subatomic particles, but it fails for macroscopic systems, for two related reasons. It implies that macroscopic systems are in definite microstates, and it detaches the histories of individual physical systems from the history of the universe.
In the account I have been sketching, historical processes supply the initial conditions that define physical systems and their environments. These initial conditions are expressed by probability distributions, which a historical narrative links to the probability distributions that objectively characterize the early universe. This narrative supplies the directionality (the arrow of time) that characterizes the laws of statistical macrophysics but not their underlying microscopic laws. The probability distributions that characterize the initial states of physical systems and their environments also help to shape the macroscopic laws that govern these systems (the derivation of Boltzmanns transport equation depends on statistical assumptions about the gas samples to which the equation applies). For this reason, statistical macroscopic laws lack the universality of microscopic laws. They apply to particular classes of macroscopic systems under broad but limited ranges of physical conditions.
V. Indeterminism
The case for macroscopic determinism rests on the widely held view that macroscopic descriptions are just microscopic descriptions seen through a veil of ignorance. On this view, macroscopic systems are actually in definite microstates, but we lack the resources to describe them at that level of detail. I have argued that the strong cosmological principle entails a different view of the relation between macrophysics and microphysics. Historical processes link the probability distributions that characterize macroscopic systems in statistical theories like those of Boltzmann and Gibbs to a statistical description of the early universe. The probability distributions that figure in that description represent an objective absence of information about the microstructure of the early cosmic medium. We cannot assign macroscopic systems definite microstates (except at temperatures close to absolute zero) not because we lack the resources to determine them but because an exhaustive description of the universe that comports with the strong cosmological principle does not contain that kind of microscopic information.
Once we give up the idea that a macroscopic description of the world is just a blurred version of an underlying microscopic description, we can no longer infer macroscopic determinism from microscopic determinism. Instead we must consider specific macroscopic processes whose outcomes might be unpredictable in principle. The most promising candidates are processes whose outcomes scientists conventionally attribute to chance (while maintaining that objectively, chance doesnt exist).
B. Poincars account of chance
In the essay cited in section I, Poincar divided chance events into three groups: those whose causal histories are extremely sensitive to small changes in the initial conditions; those whose causes are small and numerous; and events that lie at the intersection of unrelated causal histories (coincidences).
The first group is exemplified by a perfectly symmetric cone balanced on its tip. The slightest disturbance would cause it to topple over. If we had a complete description of the cones environment, we could predict the direction in which it would fall. Since we dont have such a description, we represent the initial disturbance by a probability distribution. The classical laws of motion map this probability distribution onto a probability distribution of the possible orientations of the fallen cones axis. In the context of Poincars deterministic picture of the physical world (We have become absolute determinists, and even those who want to reserve the rights of human free will let determinism reign undividedly in the inorganic world at least.), both the initial and final probability distributions represent incomplete states of knowledge.
An account of the same experiment that incorporates the view of initial conditions described in the last section leads to a different conclusion. Each of the cones classical microstates is defined by the angular coordinates of its axis and their rates of change. We can represent such a state by a point in an abstract four-dimensional state space. Now, no experimental technique can produce a state represented by a single point in a continuum, even in principle. To represent the state of a cone initially balanced on its tip we need to use a probability distribution of classical microstates whose representative points are smoothly distributed within some neighborhood containing the point that represents the unstable equilibrium state. No matter how small that neighborhood may be, the classical laws of motion map the probability distribution of initial states onto a probability distribution of final states that assigns a finite probability to every finite range of final orientations. Because the initial probability distribution represents objective, historically determined indeterminacy (rather than incomplete knowledge), the cones final orientation is unpredictable in principle. The probability distribution that characterizes the cones initial macrostate evolves deterministically into a probability distribution that objectively characterizes a continuous range of distinct macrostates. Which of these macrostates actually occurs is a matter of pure, objective chance.
The cones evolution is extremely sensitive to small changes in the initial conditions. Extreme sensitivity to initial conditions is the defining feature of what is now called deterministic chaos. Two decades before his essay on chance appeared, Poincar had discovered that the orbits of particles in a system of mutually gravitating particles, such as the solar system, are of two kinds: regular orbits, for which a small change in the initial conditions produces a new orbit that deviates slowly from the original one; and chaotic orbits, for which a small change in the initial conditions produces a new orbit that deviates from the original orbit at an initially exponential rate. The mathematical literature now contains many other examples of dynamical systems that evolve deterministically but, from a practical standpoint, unpredictably.
Weather systems are a particularly striking example of such systems. In 1961 Edward Lorenz explained why it is impossible to predict tornados. He found that numerical solutions to a mathematical model of a weather system were extremely sensitivity to round-off errors in the initial conditions. As Lorenz put it later, The flap of a butterflys wing can change the weather forever.
Accidental measurement errors exemplify Poincars second group of chance phenomena. Scientists assume that errors thatcannot be assigned to known causes result from myriad small, unrelated causes of random sign and magnitude. Analogously, the position and velocity of a molecule in a gas sample or of a microscopic particle suspended in a liquid are resultants of innumerable random collisions with ambient molecules. In these and similar examples, the randomness that scientists posit may be genuine, objective randomness. For example, if a gas samples history determines only its macroscopic properties (chemical composition, temperature, mass), as is generally the case, a complete description of the sample does not assign each molecule a definite position and a definite velocity.
Poincars third group of chance phenomena includes life-altering coincidences, like Pips encounter with the escaped convict in the opening chapter of Dickens Great Expectations. In a deterministic universe every event is a consequence of antecedent conditions. When an event results from the intersection of seemingly unrelated histories, we attribute it to chance because our weakness forbids our considering the entire universe and makes us cut it up into slices. In a description of the universe that comports with the strong cosmological principle, true coincidences abound though, of course, not all events we customarily attribute to chance are objectively unpredictable. A separate historical argument is needed in each instance.
B. Chance in biology
Unlike other animals, we can imagine, evaluate, and decide between possible courses of action. Other species have evolved traits that help them to survive in particular environments, but we alone have been able to invent ways of making a living virtually anywhere on Earth. And we alone respond not only flexibly but also creatively to challenges posed by a seemingly unpredictable environment. This creative capacity has been shaped by evolution. I will argue that the biological processes on which it rests embody the same strategy as evolution itself.
1. Evolution
Ernst Mayr has emphasized the role of chance in evolution:
Evolutionary change in every generation is a two-step process: the production of genetically unique new individuals and the selection of the progenitors of the next generation. The important role of chance at the first step, the production of variability, is universally acknowledged (Mayr 1962), but the second step, natural selection, is on the whole viewed rather deterministically: Selection is a non-chance process. What is usually forgotten is the important role chance plays even during the process of selection. In a group of sibs it is by no means necessarily only those with the most superior genotypes that will reproduce. Predators mostly take weak or sick prey individuals but not exclusively, nor do localized natural catastrophes (storms, avalanches, floods) kill only inferior individuals. Every founder population is largely a chance aggregate of individuals, and the outcome of genetic revolutions, initiating new evolutionary departures, may depend on chance constellations of genetic factors. There is a large element of chance in every successful colonization. When multiple pathways toward the acquisition of a new adaptive trait are possible, it is often a matter of a momentary constellation of chance factors as to which one will be taken (Bock 1959).
Mayrs view on the role of chance draws support from a body of observational evidence ranging from molecular biology to ecology. Within this vast domain, chance events are ubiquitous. They not only supply candidates for natural selection. They also determine its direction at crucial junctures.
2. The immune system
One of evolutions responses to the challenges posed by an unpredictable environment is the immune system. Plants and animals are susceptible to attack by a virtually unlimited variety of microorganisms. In vertebrates the immune system responds by deploying white-blood cells (lymphocytes) each of which makes and displays a single specific kind of antibody a protein capable of binding to a specific molecular configuration on the surface of another cell. The immune system must be able to deploy a vast array of distinct antibodies far more than can be encoded in an animals genome; and all of these antibodies must fail to recognize the animals own cells. To meet these requirements, the immune system uses a modified form of evolutions cyclic two-step strategy:
Step 1a: the generation of diversity by a random process. During a lymphocytes development from a stem cell, the gene that encodes the antibody it will eventually display is randomly and imprecisely assembled from several widely separated segments of DNA. Thus different stem cells evolve into lymphocytes that display different antibodies. Each stem cell is the progenitor of a clone of lymphocytes that make and display identical antibodies.
Step 2a: selection for failure to recognize an animals own cells. Immature lymphocytes that bind to an animals own cells die, leaving behind a population of lymphocytes that is still diverse enough to cope with invasions by foreign cells.
Step 2b: selection by a foreign cell. The binding of a circulating lymphocyte to a foreign cell causes it to proliferate, producing a clone of lymphocytes all of which make, display, and discharge into the blood the same antibody. This step concludes the primary immune response.
Step 1b: renewed generation of diversity. A few members of the clone selected by a particular foreign cell remain in the blood. When the same foreign cell reappears, these memory cells mutate very rapidly, producing new, more highly specialized candidates for selection.
Step 2c: renewed selection. Some of these candidates fit the invading cell even better than their precursors. Repeated many times, this cycle constitutes the secondary immune response, which is both quicker and more massive than the primary response.
3. Visual perception
The visual system represents evolutions solution to a different problem posed by the unpredictability of the environment. We need to be able to distinguish between the faces of family members and strangers. More generally, we need to be able to distinguish between faces and other visual configurations. More generally still, we need to be able to pick out objects from a visual field that is not intrinsically differentiated. In short, we need to be able to convert a pair of retinal images into a three-dimensional scene populated by objects endowed with meaningful attributes. How does the visual system make sense of visual stimuli that lack intrinsic meaning?
The art historian E. H. Gombrich arrived at an answer to this question by an indirect route. He began by asking himself: Why does representational art have a history? Why do visual artists represent the visible world differently in different periods? Gombrich argued that painters do not indeed cannot simply record what they see. They must master a complex technique for producing visual illusions. And perception, he argued, must work the same way. The history of representational art, he wrote, is a secular experiment in the theory of perception an account of how artists discovered some of [the] secrets of vision by making and matching.
The secret of vision is that what we see is the result of a mental construction. Initially, and at every subsequent stage of this construction, a candidate percept, or schema, is put forward, tested, and altered in the light of the tests outcome. The conscious image is the final, stable schema:
[T]he very process of perception is based on the same rhythm that we found governing the process of representation: the rhythm of schema and correction. It is a rhythm which presupposes constant activity on our part in making guesses and modifying them in the light of our experience. Whenever this test meets with an obstacle, we abandon the guess and try again ...
The psychologist Ulrich Neisser has given a clear and comprehensive account of the cyclic theory of perception and cognition. More recently, the neuropsychologist Chris Frith contrasts old-fashioned linear accounts of perception with accounts that model perception as a loop, as Gombrich did:
In a linear version of perception, energy in the form of light or sound waves would strike the senses and these clues about the outside world would somehow be translated and classified by the brain into objects in certain positions in space. ... A brain that uses prediction works in almost the opposite way. When we perceive something, we actually start on the inside: a prior belief [i.e., schema], which is a model of the world in which there are objects in certain positions in space. Using this model, my brain can predict what signals my eyes and ears should be receiving. These predictions are compared with the actual signals and, of course, there will be errors. ... These errors teach my brain to perceive. [They] tell the brain that its model of the world is not good enough. The nature of the errors tells the brain how to make a better model of the world. And so we go round the loop again and again until the errors are too small to worry about. Usually only a few cycles of the loop are sufficient, which might take the brain only 100 milliseconds. ... So, what we actually perceive are our brains models of the world. ...You could say that our perceptions are fantasies that coincide with reality.
Pre-existing schemata constrain the construction of visual percepts. Some of these are present at birth; we can only see what the architecture of the brain allows us to see. Visual illusions and ambiguous figures illustrate different aspects of our inability to overcome such genetic constraints. Other schemata, like those that enable a skilled painter or caricaturist, to create a convincing representation, are constructed during the artists lifetime.
The processes that enable us to make sense of aural stimuli (spoken language, music), presumably involve cycles of making and matching, as well as hierarchical schemata analogous to those that underlie the perception of visual stimuli.
4. Perception and neurobiology
The neural underpinnings of perception are not yet fully understood. Gerald Edelman and his colleagues and Jean-Pierre Changeux and his colleagues have offered models that are similar in many respects but differ in others. Changeux summarizes his view of perception as follows:
The key postulate of the theory is that the brain spontaneously generates crude, transient representations ... These particular mental objects, or pre-representations [Gombrichs and Neissers schemata, Friths beliefs], exist before the interaction with the outside world. They arise from the recombination of existing sets of neurons or neuronal assemblies, and their diversity is thus great. On the other hand, they are labile and transient. Only a few of them are stored. This storage results from a selection! ... Selection follows from a test of reality [which] consists of the comparison of a percept [perceptual activity aroused by sensory stimulation.] with a pre-representation. (Italics in original)
Citing Edelmans work as well as an earlier book of his own, Changeux emphasizes that the generation of diversity (as well as selection) plays an essential role in learning:
Knowledge acquisition is indirect and results from the selection of pre-representations. Spontaneous activity plays a central role in all this, acting as a Darwinian-style generator of neuronal diversity. (emphasis added)
5. The capacity for reflective choice
All animals learn from experience. They tend to repeat behaviors for which they have been rewarded in the past and to avoid behaviors for which they have been punished. Some animals, though, learn from experience in ways that allow for risk-taking, exploratory behavior, and delayed rewards. Economists, students of animal behavior, and cognitive neuroscientists have developed algorithms that seek to mimic such flexible learning strategies, and have constructed hypothetical neural networks that instantiate algorithms of this kind. For example, learning algorithms usually use a reward prediction error signal (the difference between the actual reward and a suitably weighted average of previous rewards) to evaluate candidates for choice. Some investigators have found evidence that the activity of midbrain dopamine neurons functions as a reward prediction error signal.
It may well be that much of human learning and decision-making is mediated by neural architecture that instantiates complex and sophisticated algorithms of this kind. In light of what ethologists have learned about the behavior of monkeys and apes, it would be surprising if this were not the case. But humans seem to have an extra, qualitatively different capacity for learning and decision-making: a capacity for reflective choice. We are able construct mental representations of scenes and scenarios that are not directly coupled to external stimuli (as in perception) or to movement (as in reflexes). We call on this capacity when we imagine possible courses of action, and then go on to imagine the possible consequences of each of these invented candidates for choice. Our ancestors used it when they painted pictures on the walls of their caves and created the first human languages. We use it when we compose an original sentence or a tune or when we try to solve an abstract problem. It allows us to reconstruct the distant past from fragmentary evidence and to envision the distant future. It makes possible the life of the mind.
The brain of every animal contains a model of the world a hierarchical set of schemata, some of which can be modified by the animals experience. Our models of the world are different from those of other animals not just because they are more susceptible to modification through learning. They also contain a theoretical component that is missing from the world models of other animals: a set of invented beliefs about animals, gods, weather, the Sun, the stars, other people, and ourselves. The theoretical component reflects the distinctively human capacity for imagination and invention. What are the biological underpinnings of this capacity? How does the brain generate the patterns of neural structure and activity on which imagined scenes and scenarios supervene?
Presumably, imagination and invention rely on the same strategy as perception and learning: making and matching the construction, testing, and stabilization of progressively more adequate schemata. This cyclic process is constrained at many levels. At the deepest level lie evolutionarily ancient value systems diffusely projecting centers in the brainstem that release a variety of neuromodulators and neurotransmitters. These systems evolved to reward actions that promote survival and reproduction and discourage actions that threaten survival and reproduction. At a higher level in the hierarchy are the ethical schemata we acquire in childhood through indoctrination and education. Near the top are the schemata that define the skills and values we acquire and hone during our lifetimes. These resident schemata constrain and regulate the candidates for selection the brain generates when it constructs a new schema.
The composition of a work of art illustrates the complementary roles of randomness and constraint. The constraints are partly of the artists own making but also owe much to the tradition within which he or she is working. We recognize J. S. Bachs compositions as belonging to the Baroque tradition but also as being inimitably his. A work of art owes its style to the constraints. It owes its freshness and originality (without which it wouldnt be a work of art) to the richness and variety of the images that made their way into the artists mind during the creation of the work. And because the process that generated these images has, as I suggest, a random component, its outcomes are unpredictable in principle.
What brain structures and patterns of brain activity might supply the neural substrate for the schemata weve been discussing? Changeux has suggested that the initial schemata, or pre-representations, are dynamic, spontaneous, and transient states of activity arising from the recombination of preexisting populations of neurons. He has also suggested that variability may arise from the random behavior of neuronal oscillators, but it may also be caused by transmission failures across synapses. And he has speculated about how evolving schemata might be evaluated and stabilized.
6. Consciousness
Up until now I have not mentioned consciousness. Understanding the biological basis of freedom and understanding the biological basis of consciousness present related but distinct problems. Neuropsychologists agree that choices and decisions result from largely unconscious physical processes. These neural processes have two distinct outcomes. One is the willed action; the other is the awareness of willing the action. Is the awareness of willing an action also its cause?
From a thorough examination of the evidence bearing on this question the psychologist Daniel Wegner has concluded that the answer is no:
It usually seems that we consciously will our voluntary actions, but this is an illusion. ... Conscious will arises from processes that are psychologically and anatomically distinct from the processes whereby mind creates action. (emphasis added)
A famous experiment by Benjamin Libet and his co-workers supports Wegners thesis. Volunteers whose brain activity was being continuously monitored were instructed to lift a finger when they felt the urge to do so, and to report the time (indicated by a spot moving around a clock face) when they felt that urge. A sharp increase in brain activity heralded the lifting of a finger. But this spike occurred a third of a second, on average, before the volunteers became aware of the urge. Since a cause must precede its effect, the urge could not have been the cause of the action.
Although Libets experiment provides a useful quantitative datum bearing on hypotheses about how brain states are related to consciousness, it does not bear directly on the present account of free will. Libet himself endorsed this opinion:
My conclusion about free will, one genuinely free in the nondetermined sense, is then that its existence is at least as good, if not a better, scientific option than is its denial by deterministic theory.
The present account supports this view. It has been concerned not with idealized (and often trivial) choices between two given alternatives but with what Ive called reflective choice, in which the alternatives may not be given beforehand, or not completely given, and in which one works out and evaluates the possible consequences of each imagined alternative. Much of the work involved in such processes undoubtedly does not rise to the level of consciousness. But consciousness accompanies the parts of the process that seem to us most crucial.
In this respect, consciousness seems to play the same role as it clearly does when we learn to execute complex tasks. A violinist masters a difficult passage by a more or less protracted conscious process. When she comes to play the passage in a performance with fellow-members of her string quartet, she is no longer conscious of the intricacies of the passage or of the technical difficulties she has mastered. Her mind is on shaping the passage to meet the complex and not completely predictable musical demands of the particular moment. She screens out everything else. This often-noted feature of consciousness irresistibly suggests that it has a (biological) function. T. H. Huxleys steam locomotive runs perfectly well without its whistle, but the whistle nevertheless has an essential warning function.
VI. Libertarian free will
I have argued that the traditional view of free will, which holds that we are the authors of actions that help shape the future, fits comfortably into the conceptual framework of biology, which in turn fits comfortably into an unconventional but conservative picture of the physical world. In conclusion, let me review the key points of the argument.
The picture of the physical world I advocate is conservative in that it assumes that all of our current well-established physical theories are valid in their respective domains. It is unconventional in the way it links these domains to one another and in the role it assigns to chance. These features of the new picture are consequences of the assumption that an exhaustive description of the state of the universe at very early times (a) does not privilege any position or direction in space (the strong cosmological principle) and (b) depends only on physical constants and (perhaps) a few additional parameters. The strong cosmological principle entails that an exhaustive description of the physical universe has a statistical character and that the probabilities that figure in it have a concrete physical interpretation: the probability that a certain condition obtains at a particular instant of cosmic time is the fractional volume of the set of points at which the condition obtains at that instant.
Like Gibbss statistical mechanics and its quantum counterpart, an account of cosmic evolution that comports with these cosmological assumptions characterizes macroscopic systems and their environments by probability distributions of microstates. These probability distributions are conventionally viewed as incomplete descriptions of systems in definite though unknown, or even unknowable, microstates. The present account interprets them as complete descriptions. Because microstates evolve deterministically, the conventional interpretation implies that macroscopic systems evolve deterministically. In the present account, by contrast, a macroscopic systems initial state need not uniquely determine its subsequent states.
Macroscopic indeterminism is an essential feature of biologys conceptual framework. Theodosius Dobzhansky famously wrote that nothing in biology makes sense except in the light of evolution, and Ernst Mayr emphasized that chance plays a key role in both genetic variation and natural selection. Yet, as Mayr often stressed, this role clashes with the very limited and specific role that physicists conventionally assign to chance. An account of cosmic evolution that incorporates the cosmological assumptions mentioned above is hospitable to the biological worldview of Dobzhansky and Mayr.
Living organisms and populations are constantly challenged by unpredictable events in their environment. At the same time, macroscopic unpredictability opens up evolutionary opportunities, as when a seed borne aloft by unpredictable air currents colonizes a new habitat. The cyclic two-step strategy described by Mayr, which uses chance to defeat chance, is embodied not only in evolution itself but also in some of its products, including the immune response and visual perception. I have argued that libertarian free will is such an adaptation.
NOTES
60 Garden Street, Cambridge, MA 02138, email: layzer@fas.harvard.edu
PAGE 34
For a modern defense of libertarian free will and a critical discussion of the issues that separate libertarian free will from compatibilist accounts, see Robert Kane, The Significance of Free Will, Oxford University Press, New York, 1996
E. P. Wigner, Two Kinds of Reality in Symmetries and Reflections, MIT Press, Cambridge, 1967
A closed system is one that in no way interacts with the outside world. All physical systems (except the universe) interact to some extent with the outside world, but many can be idealized as closed for specific purposes. For example, celestial mechanics treats the solar system as closed: it ignores gravitational forces exerted by stars other than the Sun.
Henri Poincar, Le Hasard in Science et Mthode, Flammarion, Paris,1908. Reprint: Paris: ditions Kim. English translation: James R. Newman, ed., The World of Mathematics, Simon and Schuster, New York, 1956. Page references are to the English translation.
S. Weinberg, Gravitation and Cosmology, John Wiley and Sons, New York, 1972, Chapter 15
The value of an additive property of an extended system is the sum of its values for the weakly interacting parts into which we can imagine the system to be divided. Internal energy and entropy are additive in this sense; temperature is not.
For a cloud of finite mass, an equilibrium state of uniform temperature does not exist.
For example, the provenance of elements such as zinc that play an essential metabolic role. Heavy elements form in the cores of stars much more massive than the Sun. These short-lived stars explode, thereby enriching the interstellar medium within which the Sun evolved from a proto-star.
Particles of the same kind are indistinguishable in a stronger sense that defies visualization: the quantum state of a collection of particles of the same kind electrons, say, or photons must be described in mathematical language that does not allow one to distinguish between members of the collection. For example, we may say that one of a pair of electrons is in state a and the other is in state b but we may not say that electron 1 is in state a and electron 2 in state b. A wave function that assigns electron 1 to state a and electron 2 to state b does not represent a possible two-electron state.
Classical thermodynamics rests on the empirical rule that a nominally isolated macroscopic system or a system in thermal contact with a heat reservoir at a fixed temperature eventually settles into a state in which all measurable properties of the system have unchanging values. This state is called thermodynamic equilibrium. Because the definition of entropy relies on the notion of thermodynamic equilibrium, the second law of thermodynamics cannot be used to explain the empirical rule.
The single-particle probability distribution is, in Gibbss phrase, a coarse-grained version of the N-particle probability distribution. But the spin-echo experiment, discussed below, shows that in some experimental situations the coarse-grained entropy of a nominally closed system decreases with time.
The Stosszahlansatz, introduced by Maxwell, says the incoming velocities of molecules that are about to collide are statistically uncorrelated; their joint probability distribution is the product of the individual (marginal) probability distributions.
J. M. Blatt, Prog. Theor. Phys. 22, 1959, p. 745
Thus in applying Poincars theorem, we must include the walls and their surroundings in the closed dynamical system to which the theorem refers; and this step nullifies the theorems conclusion: eventually becomes never.
P. J. Bergmann and J. L. Lebowitz, Phys. Rev. 99, 1955, p. 578; J. L. Lebowitz and P. J. Bergmann, Annals of Physics 1, 1959, p. 1
T. M. Ridderbos and M. L. G. Redhead, Found. Phys. 28, 1988, p. 1237
E. L. Hahn, Phys. Rev. 80, 1950, p. 580
ibid. p. 747
ibid. p. 1380
ibid. p. 1386
Ernst Mayr, How to carry out the adaptationist program? in Toward a New Philosophy of Biology, Cambridge: Harvard University Press, 1988, p. 159
Ernst Mayr, Accident or design, the paradox of evolution in G.W. Leeper, ed., The Evolution of Living Organisms, Melbourne: Melbourne University Press, 1962
W.J. Bock, Evolution 13, 1959, 194-211
This is a very incomplete account of the vertebrate immune system. For a more complete account, see any recent graduate-level textbook on molecular and cell biology.
E.H. Gombrich, Art and Illusion, Princeton: Princeton University Press, eleventh printing of the second, revised, edition, 1961, with a new preface, 2000
Ibid. p. 29
Ibid. pp. 271-2
See Ulric Neisser, Principles and Implications of Cognitive Psychology, San Francisco: W.H. Freeman, 1976
Chris Frith, Making Up the Mind, Oxford: Blackwell, 2007, pp. 126-7
Ibid. pp. 134-5
Gerald M. Edelman and Vernon B. Mountcastle, The Mindful Brain, Cambridge: MIT Press, 1978; Gerald M. Edelman, Neural Darwinism, New York: Basic Books, 1987; Gerald M. Edelman and Giulio Tononi, A Universe of Consciousness: How Matter Becomes Imagination, New York: Basic Books, 2000; Edelman, Second Nature, New Haven, Yale University Press, 2006, and other references cited there.
Jean-Pierre Changeux, The Physiology of Truth: Neuroscience and Human Knowledge
translated from the French by M.B. DeBevoise, Cambridge: Belknap Press/Harvard, 2004, and references cited there.
Ibid. p. 6.
Jean-Pierre Changeux, Neuronal Man, Princeton: Princeton University Press, 1985, p. 139
Jean-Pierre Changeux, The Physiology of Truth: Neuroscience and Human Knowledge
translated from the French by M.B. DeBevoise, Cambridge: Belknap Press/Harvard, 2004, p. 58
For recent reviews, see Nature Neuroscience, Volume 111, Number 4, April 2008, pp. 387-416.
Hannah M. Bayer and Paul W. Glimcher, Neuron 47,Issue 1,2005, 129 141 and references cited there
Gerald Edelman, Second Nature, New Haven, Yale University Press, 2006, and earlier references cited there.
Changeux, The Physiology of Truth, p. 59
Loc. cit.
Op. cit., pp. 61-2
Daniel M. Wegner, The Illusion of Conscious Will, Cambridge: MIT Press, 2002, p. 1
Ibid. p. 1
Ibid. p. 29
Benjamin Libet, C.A. Gleason, E.W. Wright, and D. K. Pearl, Time of conscious intention to act in relation to onset of cerebral activity (readiness potential): The unconscious initiation of a freely voluntary act, Brain 106, 623-42
For a plausible and detailed hypothesis about the neural correlate of consciousness, see Gerald Edelman and Giulio Tononi, A Universe of Consciousness, New York: Basic Books, 2000. For more on Libets experiment, see Kane, op. cit. Note 12, p. 232.
Benjamin Libet, Do We Have Free Will in Robert Kane, ed., The Oxford Handbook of Free Will, Oxford: Oxford University Press, 2002
(bcde{LnoabEFH
*+.Füʬʬʬ{tgtjh&Jh-D0JUh&Jh-Dh*vh-D56h*vh-D5 h-D6hih-D6h
>h-D6jh-D0JUh!~h-DCJhh-Dhh-Dh&h-Dh!~h-D5CJjhih-D0JUhih-Dh&Jh-D5CJhih-D5CJh-D(&5deLop)aW-.,gd-D$a$gd-D$gd-Dgd-D,!!!!##$$L%V%&%&c&j&&&')))+)P)S)--.......~////0y0002266;;;;O=P==H>??~BBCC輴hh-Dhrph-Dh
>h-Dhrph-D6h*vh-D5h&Jh-D6h
>h-D6h:uh-Djhh-D0JUh*vh-D6h&Jh-Dh*vh-Dh-D h-D69,-!!!!!""&#)$)%)R)S){,|,.......//b00gd-Dgd-D$gd-D00(2478;K>?CCCCCFdGHHHHHQKM%PRRRR$gd-D$gd-Dgd-DCCh-D0JUjh&Jh-D0JUh&Jh-D0Jh&Jh-D6h&Jh-Dh!~h-D5 h-D6jh-D0JUh
>h-D6hbywh-Dh-D8DYZѨҨثOPҬ[{|b#&'*35opᘃjhh-D0JUh!~h-D6hh-D h-D6jh-D0JU h-D5h!~h-D5CJhph-Dh!~h-D5jhbywh-D0JUhbywh-D6h-Djh&Jh-D0JUhbywh-Dh&Jh-D3ӨԨުߪOlXY|}I$gd-Dgd-Dgd-D"#$45qrxygd-Dgd-D$gd-DvwM37}r ,- bܼܯ뤚hh-D6jh-D0JUh-Dh!~h-DjhSth-D0JUh%ngh-D6hh-D6hoh-D6hh-D6hSth-Dh!~h-D6hh-Djhh-D0JU9q
9;q^_`st$%12$gd-Dgd-Dgd-D2E=>Z[rs
2LMNL]^ltu+.
ehfgźhh-D0Jh&h-D6hSth-D0Jhh-Dh-Dh!~h-D6hh-Dhh-D6htwgh-Dhh-D6hh-Djhh-D0JU<2&5
zgd-D$gd-Dgd-D
y
z
'(xcd+###$$%$'$($*$+$-$.$0$ҽҭٽҞҞjh-DUjh-D0JUh!~h-D6h!~h-D5CJ h-D6hh-D6hh-D6hh-D6jhh-D0JUhh-DhSth-DhSth-D0JhSth-D6h-Djh-D0JU1zrQ!#####$$$&$'$)$*$,$-$/$0$3$4$A$B$C$6%%'(d$gd-Dgd-D0$3$5$6$<$=$?$@$C$D$$%6%7%a%{%%%%'''%'7'b'c'j'k'o'''((
((5(f(g(h(\)])))**\,],x,z,,,,,,,--F-G-o-}-/h0h-Dhuh-Dhuh-DCJh&Jh-Dh!~h-Dh!~h-D6 h-D6jh-D0JUh-D0JmHnHu
h-D0Jjh-D0JUh-Dh
>h-DCJ=(g(\))*F-6/o0n112
3U33333G4455Y6g6y66,7>78
d,1$7$8$H$gd-D/!/5/6/7///W0`0n0o0p0v00m1n1o1~1111111122222222233
3363B3C3E3T3U3V3d3o3s33333333334F4G4H444444455555hh-D5hh-Dh%ngh-Dh!~h-D5h&Jh-D h-D5h!~h-Djh-D0JUhph-Dh-D h-D6G555555Y6Z6[6`6g6h6i6n6x6y6z66666667,7-7.737=7>7?7@7m7~7778>8f8s8888889999999999999999:?::::::::::$;hh-D^J_H aJ$h(h-D6h(h-Dhh-Dhtwgh-Dhh-D h-D6h-Djh-D0JUH89999?:::c;;;
< <w<<<=>???$gd-D
1$7$8$H$gd-D
d,1$7$8$H$$;*;+;b;c;d;m;v;;;;;;;;;;<< <
<<
<<<< <!<5<S<v<w<x<<<<<<<<<p=u=v=y====>Ƽ| h-D5hh-DhSth-Dhoh-Dhh-Dhtwgh-D h-D6h(h-D6h(h-Dh-Djh-D0JUhh-DB*ph!hh-DB*^J_H aJ ph!hh-DB*^J_H aJ phfffhh-D^J_H aJ 0>>~>>>>>??h!~h-D5CJjh-D0JUhSth-Dh-D h-D61
0:p-D/ =!"#$%9Dd
|B
SA?2) 438ymUdD+`!w9W?,qM `P0xcdd``> $X aJ`R`0Be%,&FF(@q9. b 0A $37!L
>Ymevp5cҊ!)A4͇WJ\12Ldj AMa!2ZQΫP0buADC) 438ymUdvP0%xTn@uW
B 'FCpq։- 8!z\nHW0qS#Ub7;.q.@VNpJbh^?EsWkODz Z/N=1iq5PNr/|ǋU!W
yGr|y0
vLCwp
Ɨ
zٮ.L=\$Q_iŪlK7aijdv9_۸cñbZ]ukP֓ZFJC1M/!4LΡA
a7D7(&v7IzRt19
u1M
Ԣ.ΰz1e::)Gl\3\bWuxMU#LZF6鍶!%}ڂ܈ ];}j)uҍeDZzTG+%Sdcu,s/c>o`r$TnB*麉u-xH5H6`u͑jΧ;<[v=JN[}tj"Neh0]n2QiFhR!b?IwT]g2R]vbZA6iD̊ BvRrnWVz8W+=sggK0(
vֈ]nyP[JZ(-VkJӌb
P1FIA)Qu@ESq@}o%/;Dd
0B
SA?2<b|3o/#K}+`!Է2hYi
Pg`m:xcdd```d``baV fx8@b,PY=F (@q9. b 0dHo@penR~Cn.+jdxnėHH*aITTYtK0Z`v@Hfnj1CRy1.Lcdl7*A]<Tb*#ܭ
Lh;[-HqkЭ!,y@^
+zXc5)6BsKR
?v?2-0B8@S
).j$ňAIXPe`=kCb|3o/#K@Pg`mpxTAoT礡z,jyTB.'zo
h!RfO
l?vBjj@pgWU΄ynVEXyy3|3=; ;eބtp
GxC,PkHdz|] vBNxoH͌9D3PI $ p`XV vpMpTrBqXx`I
VzbEEb A?".^ R wF8(|)bpheuy%TUbkʨmе:`@؎n0Sz.L"lf3DZ`$x#F|11')1vkn`xfL!?M8Y>2sq
rxAu,h<Ѐ9h0z0|WضJ升b;Ҳ
~g.~uÏ(7D5JѤw!b%噇3.YEt
?
!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~'Root Entry F@tBData
WordDocument3tObjectPoolB@tB_1185086777 FBBOle
CompObjUObjInfo
FMathType 5.0 EquationDNQEEquation.DSMT4DSMT5MacRomanTimesSymbolCourierMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A
pi
{}Equation Native _1185003822FBBOle
CompObj
UFMathType 5.0 EquationDNQEEquation.DSMT4DSMT5MacRomanTimesSymbolCourierMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A
"-Ppi
logpObjInfo
Equation Native "1Table!SummaryInformation(\ii
"՜.+,D՜.+,@hp
Hewlett-Packard CompanyJTitleH 6>
MTMacEqns
!"#$%&Oh+'0,
(08@David LayzerNormalBob Doyle2Microsoft Office Word@@Vd#@A@A]*~GVT$m bE&" WMFCD ?_lVT$m EMF_$I*U"
%%Rp@Times,0, ,,PZ ,,,x ,OZ ,, yu], , u]
T,X)3*Ax Times] #,X ,,6\,,y\$,dv%%%TTY/@@LP -!"Rp@Times,P,,4,PZ,,,,OZ,, yu],, ,u]
T,X)3*Ax Times,rX]
;Yw,6\,,y\D,,dv%%%%%%TT/@@pLP TT/@@pLP !%%%T" /@@p
LhNaturalizing
/@@ULgenetic variation and in natural selection itself, evolutionary biologists have long 1,3,,2,!,22,2222,2!,',-,22',!,22222,"02231''2,2,221!"T{/@@lLadvocated such a picture. Chan,222,,,2'3,2,2,2",C2,2T\|-/@@|l-Lce also plays a key role in other biological ,,,'22.0',3.1!2,222,!2221,,!"T //@@NLprocesses, including the immune response and visual perception. I argue that 2!2,,'','2,22312,NN22,!,'222',,222(2,2,!-,222 ,"13,2,!"Tk/@@
L`reflective!,!-,2,TTk/@@LP Tk/@@ILchoice and deliberation, like these processes and evolution itself, is a ,22,,,222,2,!,222,2,',2!3,-'',',22,22222',!',!"Tt/@@q1Lcreative process mediated by indeterminate macros,!,,2,3!2-,''N,2,-23022,-!N2,,N,-"2'T}/@@qLcopic processes, and that ,22,2!2-,'',',223,!"Tt!5/@@1Lthrough our choices we help to shape the future. 2!221222!,22,,'H,3,22'2,2,2,!22",TT"N5/@@"LP -!"Rp@Times,,#, ,PZ#, ,t!,",OZ#, , yu] ,#, Lu]
T,X)3*Ax Times\`@a
p ,P`@a
8 ,6\t ,t ,y\ ,Ldv%%%%%%!T<Q/@@(L T|Q/@@L\ "'%Ld!??%(%%%TTQ/@@LP -!"%%%%%%!%%%TT/@@LP1""%%%TT(6/@@LP T )= 6/@@)#L60 Garden Street, Cambridge, MA 02122H,!2,28!-,C,N2!21,ZH222T> 6/@@> "L38, email: layzer@fas.harvard.edu22,N,-0-,!]!,'2-!2,!2,23TT6/@@LP -!"%%666666666666666666666666666666666666 6 66 6
6
66
6
66666666
6
66
6
66666666666666666666d."System??????????????????--@Times---
2
SZc ,c'@Times------
2
jZc
2
jlc ]---2
j
cNaturalizing
2
jcLibertarian 2
jb cFree Willa
2
jc ,c'------
2
Zc
2
lc ---2
cDavid Layzer
2
Rc ,c'@Times---------
2
Zc
2
lc SL2
+cDepartment of Astronomy, Harvard University
---,c--- 2
1'---
2
c ,c'---
2
Zc ,c'---2
lMcLibertarian free will is incompatible with the thesis that physical laws and ,c'z2
lJcantecedent conditions determine events other than the outcomes of quantum ,c'2
lcmeas 2
Mcurements. This thesis is not a consequence of physical laws alone. It also ,c'2
lNcdepends on an assumption about the conditions that define macroscopic systems ,c'2
lPc(or, in some theories, the universe): the assumption that these systems (or the
,c'+2
)lcuniverse) are in defiY2
)4cnite microstates. This paper describes a theory of ,c'|2
>lKcmacroscopic initial conditions that is incompatible with this assumption. ,c'2
RlRcStandard accounts of classical and quantum statistical mechanics characterize the
,c'R2
gl/cinitial conditions that define macroscopic syst A2
gH$cems by probability distributions of ,c'y2
|lIcmicrostates, which they customarily interpret as representing incomplete
,c'2
lScdescriptions. In the theory described below, the initial conditions that define a ,c' @Times-@Times- @Times-@Times- @Times--k2
l@cmacroscopic system are shaped by the systems history and repres
2
cent objective ,c'w2
lHcindeterminacy. This interpretation is a consequence of a simple but far
2
c-2
creaching ,c'n2
lBccosmological assumption supported by astronomical evidence and by
,c'2
lPcmethodological and theoretical arguments. It entails a picture of the physical
,c' 2
lcuniverse in whk2
@cich chance prevails in the macroscopic domain (and hence in the ,c'}2
lLcworld of experience). Because chance plays a key role in the production of ,c'2
!lUcgenetic variation and in natural selection itself, evolutionary biologists have long ,c':2
6lcadvocated such a picture. ChanO2
6-cce also plays a key role in other biological ,c'2
KlNcprocesses, including the immune response and visual perception. I argue that
,c'2
_l
creflective
2
_c y2
_Icchoice and deliberation, like these processes and evolution itself, is a t,c'U2
tl1ccreative process mediated by indeterminate macros
22
taccopic processes, and that ,c'U2
l1cthrough our choices we help to shape the future.
2
Uc ,c'@Times------,cC2
Z( 2
'-@ !Z----
2
c ,c'------,c--- 2
Z1'---
2
^c @2
a#c60 Garden Street, Cambridge, MA 021
>2
"c38, email: layzer@fas.harvard.edu
2
c ,c'--ccccccccccbbbbbbbbbbbbbbbbaaaaaaaaaaaaDocumentSummaryInformation8CompObjy^666666666vvvvvvvvv666666>6666666666666666666666666666666666666666666666666hH6666666666666666666666666666666666666666666666666666666666666666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH Z`Z25Normal
hdh CJOJQJ_HaJmH sH tH DA`DDefault Paragraph FontRiRTable Normal4
l4a(k (No ListDT@DA
Block Texthhx]h^h4+@4*vEndnote Text>*@>*vEndnote ReferenceH*6@"6*v
Footnote Text@&@1@*vFootnote ReferenceH*2@B2
>Header
h!2 @R2
>Footer
h!.)@a.
>Page NumberPK![Content_Types].xmlj0Eжr(Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu*Dנz/0ǰ$X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6_rels/.relsj0}Q%v/C/}(h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xmlM
@}w7c(EbˮCAǠҟ7՛K
Y,
e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$!)O^rC$y@/yH*)UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f
W+Ն7`gȘJj|h(KD-
dXiJ؇(x$(:;˹!I_TS1?E??ZBΪmU/?~xY'y5g&/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ
x}rxwr:\TZaG*y8IjbRc|XŻǿI
u3KGnD1NIBs
RuK>V.EL+M2#'fi~Vvl{u8zH
*:(W☕
~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4=3ڗP
1Pm\\9Mؓ2aD];Yt\[x]}Wr|]g-
eW
)6-rCSj
id DЇAΜIqbJ#x꺃6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8քAV^f
Hn-"d>znǊ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QDDcpU'&LE/pm%]8firS4d7y\`JnίIR3U~7+#mqBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCMm<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK!
ѐ'theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6+_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-!
ѐ' theme/theme/_rels/themeManager.xml.relsPK]
b7HKa
LS[q0syxYѠov,=ZLtyc 7
U$t
,+
_
C=L]nz$6|AOX 4CR?<7
t !C/Wy0$/5$;>?,0Rz2z(8?AAAB(B*B7::!!8@0(
B
S ?)*jPpPqPuP{{~~QY-4ǞDNyV_do #$$&&'')*,-/05@BC 079Cbjkow)|)~))))****++++,,....7 7myJ0O07 73333LPp
.-'!+!S!&&&7 7-DV;@7P@UnknownG*Ax Times New Roman5Symbol3.*Cx ArialC MArialMTArialKMTimes-RomanTimes3*Ax TimesA BCambria Math h++↕,f]*~]*~4dJJ2QPY2!xxDavid Layzer Bob Doyle
F'Microsoft Office Word 97-2003 Document
MSWordDocWord.Document.89q