growth of order or information at the same time entropy is increasing. He pointed out that if the equilibration rate of the matter was slower than the rate of expansion, then the "negative entropy" (defined as the difference between the maximum possible entropy and the actual entropy) would increase. Claude Shannon identified this negative entropy with information, though visible structural information in the universe may be less than this "potential" information. If everything that happens was certain to happen, as determinist philosophers claim, no new information would ever enter the universe. Information would be a universal constant. There would be "nothing new under the sun." Every past and future event can in principle be known (as Pierre-Simon Laplace suggested) by a super-intelligence with access to such a fixed totality of information. It is of the deepest philosophical significance that information is based on the mathematics of probability. If all outcomes were certain, there would be no “surprises” in the universe. Information would be conserved and a universal constant, as some mathematicians mistakenly believe. Information philosophy requires the ontological uncertainty and probabilistic outcomes of modern quantum physics to produce new information. From Newton’s time to the start of the 19th century, the Laplacian view coincided with the notion of the divine foreknowledge of an omniscient God. On this view, complete, perfect and constant information exists at all times that describes the designed evolution of the universe and of the creatures inhabiting the world. In this God’s-eye view, information is a constant of nature. Some mathematicians argue that information must be a conserved quantity, like matter and energy. They are wrong. In Laplace's view, information would be a constant straight line over all time, as shown in the figure. If information were a universal constant, there would be “nothing new under the sun.” Every past and future event can in principle be known by Laplace's super-intelligent demon , with its access to such a fixed totality of information. Since William Thomson (Lord Kelvin), James Clerk Maxwell, and Ludwig Boltzmann, most physicists and astronomers have believed that the universe began with a high degree of organization or order (or information) and that it has been running down ever since. Hermann Helmholtz described this as the “heat death” of the universe. Mathematicians who are convinced that information is always conserved argue that macroscopic order is disappearing into microscopic order, but the information could in principle be recovered, if time could only be reversed. This raises the possibility of some connection between the increasing entropy and what Arthur Stanley Eddington called “Time’s Arrow.” Kelvin’s claim that information must be destroyed when entropy increases would be correct if the universe were a closed system. But in our open and expanding universe, Layzer showed that the maximum possible entropy is increasing faster than the actual entropy. The difference between maximum possible entropy and the current entropy is called negative entropy, opening the possibility for complex and stable information structures to develop. We can see from the figure that it is not only entropy that increases in the direction of the arrow of time, but also the information content of the universe. We can describe the new information as "emerging." Layzer showed that this standard view was wrong for our expanding universe.David Layzer is a Harvard cosmologist who in the 1960's made it clear that in an expanding universe entropy would increase, as required by the second law of thermodynamics, but that the maximum possible entropy of the universe might increase faster than the actual entropy increase, making room for the
Roger PenroseIn his 1989 book The Emperor's New Mind, Penrose speculated on the connection between information, entropy, and the arrow of time.
Recall that the primordial fireball was a thermal state — a hot gas in expanding thermal equilibrium. Recall, also, that the term 'thermal equilibrium' refers to a state of maximum entropy. (This was how we referred to the maximum entropy state of a gas in a box.) However, the second law demands that in its initial state, the entropy of our universe was at some sort of minimum, not a maximum! What has gone wrong? One 'standard' answer would run roughly as follows:Clearly, Penrose's "standard" answer is the work of David Layzer. Penrose met Layzer at a 1973 conference at Cornell University on the "Arrow of Time."True, the fireball was effectively in thermal equilibrium at the beginning, but the universe at that time was very tiny. The fireball represented the state of maximum entropy that could be permitted for a universe of that tiny size, but the entropy so permitted would have been minute by comparison with that which is allowed for a universe of the size that we find it to be today. As the universe expanded, the permitted maximum entropy increased with the universe's size, but the actual entropy in the universe lagged well behind this permitted maximum. The second law arises because the actual entropy is always striving to catch up with this permitted maximum.
The Arrow of TimeLayzer identified what he called the "historical arrow of time" (the direction of increasing information) with the "thermodynamic arrow of time." The phrase "time's arrow" was coined by Arthur Stanley Eddington. In a 1975 article for Scientific American called The Arrow of Time, Layzer wrote:
the complexity of the astronomical universe seems puzzling.Layzer specifically identified this process as generating novelty and contradicting a Isolated systems inevitably evolve toward the featureless state of thermodynamic equilibrium. Since the universe is in some sense an isolated system, why has it not settled into equilibrium? One answer, favored by many cosmologists, is that the cosmological trend is in fact toward equilibrium but that too little time has elapsed for the process to have reached completion. Fred Hoyle and J. V. Narlikar have written: "In the 'big bang' cosmology the universe must start with a marked degree of thermodynamic disequilibrium and must eventually run down." I shall argue that this view is fundamentally incorrect. The universe is not running down, and it need not have started with a marked degree of disequilibrium; the initial state may indeed have been wholly lacking in macroscopic as well as microscopic information. Suppose that at some early moment local thermodynamic equilibrium prevailed in the universe. The entropy of any region would then be as large as possible for the prevailing values of the mean temperature and density. As the universe expanded from that hypothetical state the local values of the mean density and temperature would change, and so would the entropy of the region. For the entropy to remain at its maximum value (and thus for equilibrium to be maintained) the distribution of energies allotted to matter and to radiation must change, and so must the concentrations of the various kinds of particles. The physical processes that mediate these changes proceed at finite rates; if these "equilibration" rates are all much greater than the rate of cosmic expansion, approximate local thermodynamic equilibrium will be maintained; if they are not, the expansion will give rise to significant local departures from equilibrium. These departures represent macroscopic information; the quantity of macroscopic information generated by the expansion is the difference between the actual value of the entropy and the theoretical maximum entropy at the mean temperature and density. deterministic view of the world, with significant implications for human freedom:
Novelty and Determinism We have now traced the thermodynamic arrow and the historical arrow to their common source: the initial state of the universe. In that state microscopic information is absent and macroscopic information is either absent or minimal. The expansion from that state has generated entropy as well as macroscopic structure. Microscopic information, on the other hand, is absent from newly formed astronomical systems, and that is why they and their subsystems exhibit the thermodynamic arrow. This view of the world evolving in time differs radically from the one that has dominated physics and astronomy since the time of Newton, a view that finds its classic expression in the words of Pierre Simon de Laplace: "An intelligence that, at a given instant, was acquainted with all the forces by which nature is animated and with the state of the bodies of which it is composed, would - if it were vast enough to submit these data to analysis - embrace in the same formula the movements of the largest bodies in the Universe and those of the lightest atoms: nothing would be uncertain for such an intelligence, and the future like the past would be present to its eyes." In Laplace's world there is nothing that corresponds to the passage of time. For Laplace's "intelligence," as for the God of Plato, Galileo and Einstein, the past and the future coexist on equal terms, like the two rays into which an arbitrarily chosen point divides a straight line. If the theories I have presented here are correct, however, not even the ultimate computer - the universe itself - ever contains enough information to completely specify its own future states. The present moment always contains an element of genuine novelty and the future is never wholly predictable. Because biological processes also generate information and because consciousness enables us to experience those processes directly, the intuitive perception of the world as unfolding in time captures one of the most deep-seated properties of the universe.
Note that the deterministic Laplacian universe contains exactly the same information at all times - nothing new under the sun. In 1990, Layzer extended these ideas in his book Cosmogenesis: The Growth of Order in the Universe. He added a discussion of quantum mechanics and its implications for free will. First he noted a number of paradoxes, between microscopic quantum systems and the macroscopic universe, between standard thermodynamic macrophysics and cosmology, between irreducible randomness and human ignorance, and between the objective timeless being of the Laplacian view and the subjective human experience of becoming and change.
Conflicts and Paradoxes The relation between quantum physics, which describes the invisible world of elementary particles and their interactions, and macroscopic physics, which describes the world of ordinary experience, has perplexed physicists since the birth of quantum physics in 1925. Viewed as a system of mathematical laws, quantum physics includes macroscopic physics as a limiting case. By that I mean that quantum physics and macroscopic physics make the same predictions in the domain where macroscopic physics has been strongly corroborated (the macroscopic domain), but quantum physics also successfully describes the behavior and structure of molecules; atoms, and subatomic particles (the microscopic domain). Yet from another point of view, macroscopic physics seems more fundamental than quantum physics. As we will see later, the laws of quantum physics refer explicitly to the results of measurement. But every measurement necessarily has at least one foot in the world of ordinary experience: it has to be recorded in somebody's lab notebook or on magnetic tape. So quantum physics seems to presuppose its own limiting case — macroscopic physics. This is the mildest of several paradoxes that have sprung up in the region where quantum physics and macrophysics meet and overlap. The relation between macrophysics and cosmology is also problematic. The central law of macroscopic physics — the second law of thermodynamics — was understood by its inventors, and is still understood by most scientists, to imply that the Universe is running down — that order is degenerating into chaos. How can we reconcile such a tendency with the fact that the world is full of order — that it is a kosmos in both senses of the word. Some scientists say, "The contradiction is only apparent, The Second Law assures us that the Universe is running down, so it must have begun with a vast supply of order that is gradually being dissipated. But this way of trying to resolve the difficulty takes us from the frying pan into the fire, because, as we will see, modern cosmology strongly suggests that the early Universe contained far less order than the present-day Universe. Astronomical evolution and biological evolution are both stories of emerging order. Nevertheless, the views of time and change implicit in modern physics and modern biology are radically different. The physical sciences teach us that all natural phenomena are governed by mathematical laws that connect every physical event with earlier and later events. Imagine that every past and future event was recorded on an immense roll of film. If we knew all the physical laws, we could reconstruct the whole film from a single frame. And in principle there is nothing to prevent us from acquiring complete knowledge of a single frame. This worldview is epitomized in a much-quoted passage by one of Newton's most illustrious successors, the mathematician and theoretical astronomer Pierre Simon de Laplace (1749-1827):We ought then to regard the present state of the Universe as the effect of its previous state and the cause of the one that follows. An intelligence that at a given instant was acquainted with all the forces by which nature is animated and with the state of the bodies of which it is composed would — if it were vast enough to submit these data to analysis — embrace in the same formula the movements of the largest bodies in the Universe and those of the lightest atoms: Nothing would be uncertain for such an intelligence, and the future like the past would be present to its eyes. The human mind offers, in the perfection it has been able to give to astronomy, a feeble idea of this intelligence.Much the same view of the world was held by Albert Einstein:The scientist is possessed by the sense of universal causation. The future, to him, is every whit as necessary and determined as the past.Most contemporary physical scientists would probably agree with Laplace and Einstein. The world they study is a block universe, a four-dimensional net of causally connected events with time as the fourth dimension. In this world, no moment in time is singled out as "now." For Laplace's Intelligence, the future and the past don't exist in an absolute sense, as they do for us. How does life, regarded as a scientific phenomenon, fit into this worldview? A modern Laplacian might reply: Living organisms are collections of molecules that move and interact with one another and with their environment according to the same laws that govern molecules in nonliving matter. A supercomputer, supplied with a complete microscopic description of the biosphere and its environment, would be able to predict the future of life on Earth and to deduce its initial state. Implicit in the present state of the biosphere and its environment are the precise conditions that prevailed in the lifeless broth of organic molecules in which the first self-replicating molecules formed, And implicit in the conditions that prevailed in that broth and its environment is every detail of the living world of today. If you believe that living matter is subject to the same laws as nonliving matter and few, if any, contemporary biologists would dispute this assertion - this argument may seem compelling. Yet it clashes with two key aspects of the evolutionary process as described by contemporary evolutionary biologists: randomness and creativity. Randomness is an essential feature of the reproductive process. In nearly every biological population, new genes and new combinations of genes appear in every generation. Reproduction, whether sexual or asexual, involves the copying of genetic material (DNA). In all modern organisms the copying process is astonishingly accurate. But it isn't perfect. Occasionally there are copying errors, and these have a random character. In sexually reproducing populations there is another source of randomness: the genetic material of each individual is a random combination of contributions from each parent. The creative factor in biological evolution is natural selection, the tendency of genetic changes that favor survival and reproduction to spread in a population, and of changes that hinder survival and reproduction to die out. From the raw material provided by genetic variation, natural selection fashions new biological structures, functions, and behaviors. A mainstream physicist might reply that the apparent randomness of genetic variation is just a consequence of human ignorance — our inability to understand exceedingly complex but nevertheless completely determinate causal processes — and that evolution is "creative" only in a metaphorical sense. According to this view, evolution merely brings to light varieties of order prefigured in the prebiotic broth. There is an even more fundamental difference between the physical and the biological views of reality: the physicist's picture of reality seems impossible to reconcile with subjective experience. For there is nothing in the neo-Laplacian picture that corresponds to the central feature of human experience, the passage of time. We humans must watch the film unwind, but Laplace's Intelligence sees it whole. Nor is there anything that corresponds to the aspect of reality (as we experience it) that Greek philosophers called becoming, as opposed to the timeless being of numbers, triangles, and circles. The universe of modern physics is an enormously expanded and elaborated version of the perfectly ordered but static and lifeless world we encounter in Euclid's Elements, of which it is indeed a direct descendant. The biologist's world seems entirely different. Life, as we experience it, is inseparable from unpredictability and novelty.
Layzer then examines the role of chance in human freedom and finds that no one has been able to explain what even fundamental quantum mechanical randomness has to do with free choice and moral responsibility.
Freedom and Necessity What is the relation between being and becoming? Is the future as fixed and immutable as the past? What is chance? These questions bear on one of the perennial problems of Western philosophy, the problem of freedom and necessity. Each of us belongs to two distinct worlds. As objects in the world that natural science describes we are governed by universal laws. To Laplace's Intelligence we are systems of molecules whose movements are no less predicable and no more the results of free choice than the movements of the planets around the Sun. but as the subjects of our own experience we see the world differently; not as bundles of events frozen into the block universe of Laplace and Einstein like flies in amber, but as the authors of our own actions, the molders of our own lives. However strongly we may believe in the universality of physical laws, we cannot suppress the intuitive conviction that the future is to some degree open and that we help to shape it by our own free choices. This conviction lies at the basis of every ethical system. Without freedom there can be no responsibility. If we are not really free agents — if our felt freedom is illusory — how can we be guided in our behavior by ethical precepts? And why should society punish some acts and reward others? The Laplacian worldview tends to undermine the basis for ethical behavior. Judeo-Christian theology faces a similar problem. Although Laplace's Intelligence is not the Judeo-Christian God — Laplace's Intelligence observes and calculates; the Judeo-Christian God wills and acts ("Necessitie and chance approach not mee, and what I will is Fate," says the Almighty in Milton's Paradise Lost)— they contemplate similar universes. Nothing is uncertain for an all-knowing God, and the future, like the past, is present to His eyes. But if we cannot choose where we walk, why should those who take the narrow way of righteousness be rewarded in the next life while those who take the primrose path are consigned to the flames of hell? Theologians have not, of course, neglected this question. Augustine, for example, argued that God's foreknowledge (or more accurately, God's knowledge of what we call the future) doesn't cause events to happen and is therefore consistent with human free will. Other theologians have embraced the doctrine of predestination and argued that free will is indeed an illusion. Still others have taken the position that divine omniscience and human free will are compatible in a way that surpasses human understanding. Reconciling the scientific and ethical pictures of the world was a concern of the first scientists. Our scientific picture of the world was foreshadowed by Greek atomism, a theory invented by the natural philosophers Leucippus and Democritus in the fifth century B.C. According to this theory, the world is made up of unchanging, indestructible particles moving about in empty space and interacting with one another in a completely deterministic way. Like modern biologists, Democritus believed that we, too, are assemblies of atoms. Yet Democritus also elaborated a system of ethics based on moral responsibility. He taught that we should do what is right not from fear, whether of punishment or of public disapproval or of the wrath of gods, but in response to our own sense of right and wrong. Unfortunately, the surviving fragments of Democritus's writings don't tell us how or whether he was able to reconcile his deterministic picture of nature with his doctrine of moral responsibility. A century later, another Greek philosopher with similar ideas about physical reality and moral responsibility faced the same dilemma. Epicurus (341-270 B.C.) sought to reconcile human freedom with the atomic theory by postulating a random element in atomic interactions. Atoms, he said, occasionally "swerve" unpredictably from their paths. In modern times, Arthur Stanley Eddington and other scientists have put forward more sophisticated versions of the same idea. According to quantum physics, it is impossible to predict the exact moment when certain atornic events, such as the decay of a radioactive nucleus, will take place. Eddington believed that this kind of microscopic indeterminism might provide a scientific basis for human freedom:It is a consequence of the advent of quantum theory that physics is no longer pledged to a scheme of deterministic laws. . . . The future is a combination of the causal influences of the past together with unpredictable elements. . [S]cience thereby withdraws its moral opposition to free will.But neither Epicurus nor Eddington explained what the "freedom" enjoyed by a swerving atom or a radioactive atomic nucleus has to do with the freedom of a human being to choose between two courses of action. Nor has anyone else.
Layzer reaffirms his 1975 claim about the initial state of the universe lacking significant order or information, but he does not tell us that a theory of the growth of order goes back to the 1960's and is his original contribution.
We need not assume, as Clausius and Boltzmann did in the nineteenth century and - as many modern astronomers and physicists still do, that the Universe started out with a huge store of order that it has been gradually dissipating ever since. If the hypothesis outlined in this chapter is correct, the initial state of the Universe was wholly lacking in order.
In the concluding chapter of Cosmogenesis, Layzer revisits the problem of human freedom and especially creativity. Although he offers no resolution of the free will problem, he places great emphasis on an unpredictable creativity as the basis of both biological evolution and human activity in a universe with an open future.
Strong Cosmological PrincipleThe Strong Cosmological Principle (SCP) is a speculative interpretation of quantum indeterminacy based on Einstein's idea that the probabilities of different experimental results are simply the frequencies of the different results in an "assembly" - a large number of identical experiments. In the Schrödinger's Cat thought experiment, for example, the SCP simply says that in a certain fraction of the experiments the cat is alive, in the remaining fraction, dead. The SCP starts from Einstein's cosmological principle that the properties (and the physical laws) of the universe do not single out any particular place in the universe. Astronomical observations have confirmed that the average properties of the universe are the same everywhere in space and they are the same in all directions from any given point. The universe is statistically uniform and isotropic. Layzer says that his interpretation of quantum theory differs from Einstein's in an important way.
Einstein believed that quantum theory applies to assemblies rather than to individual systems because individual systems are governed by as-yet undiscovered deterministic laws. I have argued that quantum theory applies to assemblies rather than to individual systems because a complete physical reality doesn't refer to individual systems but only to assemblies. The smallest fragment of the Universe we can meaningfully describe is an assembly. If the members of the assembly are in identical microstates, there is no harm in treating them as individuals. But if they are quantal systems coupled to (macroscopic) measuring devices, we run into paradoxes like those we have discussed when we assume that quantum theory applies to them directly as individuals.
Free Will reduxRecently, Layzer imagines that a large assembly of similar situations in different regions of the infinite universe can provide an explanation for the problem of the macroscopic indeterminism needed for free will, without depending on microscopic quantum indeterminism. In each individual system, everything is determined, but in the assembly of all systems, the Strong Cosmological Principle insures there will be a variety of objectively indeterminate outcomes. Layzer says that the fact that we don't know which of the many possible systems we are in means that our future is indeterminate, more specifically that our current state has not been predetermined by the initial state of the universe.
Other Multiple World IdeasIn ancient times, Lucretius commented on possible worlds. In his De Rerum Natura, he wrote in Book V,
for which of these causes holds in our world it is difficult to say for certain ; but what may be done and is done through the whole universe in the various worlds made in various ways, that is what I teach, proceeding to set forth several causes which may account for the movements of the stars throughout the whole universe; one of which, however, must be that which gives force to the movement of the signs in our world also; but which may be the true one,The idea of many possible worlds was also proposed by Gottfried Leibniz, who famously argued that the actual world is "the best of all possible worlds." Leibniz says to Arnauld in a letter from 14 July 1686,
I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God which are distinctive of it, that is, certain primary free decrees (conceived sub ratione possibilitatis) or certain laws of the general order of this possible universe with which they are in accord and whose concept they determine, as they do also the concepts of all the individual substances which must enter into this same universe.Leibniz' notion of a substance was so complete that it in principle could be used to deduce from it all the predicates of the subject (the "bundle" of all properties) to which this notion is attributed. Hugh Everett III's many-worlds interpretation of quantum mechanics is an attempt to deny the random "collapse" of the wave function and preserve determinism in quantum mechanics. Everett claims that every time an experimenter makes a quantum measurement with two possible outcomes, the entire universe splits into two new universes, each with the same material content as the original, but each with a different outcome. It violates the conservation of mass/energy in the most extreme way. The Everett theory preserves the "appearance" of possibilities as well as all the results of standard quantum mechanics. It is an "interpretation" after all. So even wave functions "appear" to collapse. Note that if there are many possibilities, whenever one becomes actual, the others disappear instantly in standard quantum physics. In Everett's theory, they become other possible worlds. The human ignorance of not knowing which universe we are in Layzer calls a macroscopic indeterminism that does solve the free will problem. If Layzer is right, the logically possible worlds of David Lewis and the many worlds of physicist Hugh Everett also solve the free will problem.
Possible Worlds and Free WillIn our two-stage model of free will, we can imagine the alternative possibilities for action generated by an agent in the first stage to be "possible worlds." They are counterfactual situations in Kripke's sense, involving a single individual. Note that Kripkje's possible worlds are extremely close to one another. The quantification of information in each case shows a very small number of bits as the difference between them, especially when compared to the typical examples given in possible worlds cases. In the case of Humphrey winning the election, millions of persons must have done something different. Such worlds are hardly "nearby." For typical cases of a free decision, the possible worlds require only small differences in the mind of a single person. By comparison, the possible worlds of Hugh Everett, David Lewis, and David Layzer in general may bear very little resemblance to one another. But note that they all include Layser's solution to the problem of free will, at least in those worlds with thinking beings, because the inhabitants do not know which of all the possible worlds they are in.
Other I-Phi pages on Layzer's work
Layzer's papersA Preface to Cosmogony, 1963 (PDF) Cosmic Evolution and Thermodynamic Irreversibility, 1965 (PDF) The Strong Cosmological Principle, Indeterminacy, and the Direction of Time, 1967 The Arrow of Time, 1971 The Arrow of Time, 1975 (PDF) The Arrow of Time, 1976 (PDF) Quantum mechanics, thermodynamics, and the strong cosmological principle, 1982 (PDF) Cosmology, initial conditions, and the measurement problem, 2010(PDF) Naturalizing Libertarian Free Will, 2010 (Word doc) Free Will as a Scientific Problem, 2010 (PDF)
Brooks, Daniel R., and E.O.Wiley, 1988, Evolution as Entropy, Univ. Chicago Press, p.11 + Chaisson, Eric, 2001. Cosmic Evolution, Harvard University Press, p.129-30 Decadt, Yves, 2000, The Average Evolution (De Gemiddelde Evolutie) Frautschi, S. 1982. "Entropy in an Expanding Universe," Science v.217, pp.593-599 __________, 1988. "Entropy in an Expanding Universe." in Entropy, Information, and Evolution, , MIT Press, p.12 Layzer, David, 1963, "A Preface to Cosmogony," Astrophysical Journal. v.138, p.174. ______, 1967, "The Strong Cosmological Principle, Indeterminacy, and the Direction of Time" in The Nature of Time, Cornell University Press, 1967 [the first presentation of SCP?, in 1963] ______, 1970. "Cosmic Evolution and Thermodynamic Irreversibility," in Pure and Applied Chemistry 22:457. (Presentation in Cardiff, Scotland, 1965?) ______, 1971, "Cosmogonic Processes," in Astrophysics and General Relativity, two volumes, edited by Max Chrétien, Stanley Deser, and Jack Goldstein, Gordon and Breach, NY. [Summer institute at Brandeis, 1968 - the first appearance of Growth of Order?] ______, 1971, "The Arrow of Time," unpublished manuscript, June 24, 1971 ______, 1975. "The Arrow of Time," Scientific American, December, pp.56-69. ______, 1976. "The Arrow of Time," Astrophysical Journal. v.206, p.559. ______, 1980. American Naturalist. v.115, p.809. ______, 1982. "Quantum mechanics, thermodynamics, and the strong cosmological principle," in Physics as Natural Philosophy, A. Shimony and H. Feshbach, eds., MIT Press ______, 1984. Constructing the Universe. Scientific American Illustrated Library, chapter 8. ______, 1988. "Growth of Order in the Universe," in Entropy, Information, and Evolution, MIT Press, pp.23-39. ______, 1990. Cosmogenesis: The Growth of Order in the Universe. Oxford University Press. pp.140-45. ______, 2010. "Cosmology, Initial Conditions, and the Problem of Measurement." (arXiv) ______, 2010. "Naturalizing Libertarian Free Will" 2010 (Word doc) [submitted to Mind and Matter] ______, 2010. "Free Will as a Scientific Problem" (PDF) Lestienne, Rémy, 1990. The Children of Time. U. Illinois Press, p.123. _______________, 1993. The Creative Power of Chance. U. Illinois Press, p.108. Roederer, Juan., 2005. Information and Its Role in Nature, Springer, p. 227. Salthe, Stanley, 2004. "The Spontaneous Origin of New Levels in a Scalar Hierarchy," Entropy 2004, 6, 327-343 Wicken, Jeffery S., 1987. Evolution, Thermodynamics, and Information, Oxford University Press, p. 39.