Emergent Complexity, Teleology, and the Arrow of Time

P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 10 Emergent Complexity, Teleology, and the Arrow of Time Paul Davies 1. the dying universe In 1854, in one of the bleakest pronouncements in the history of science, the German physicist Hermann von Helmholtz claimed that the universe must be dying. He based his prediction on the Second Law of Thermody- namics, according to which there is a natural tendency for order to give way to chaos. It is not hard to find examples in the world about us: peo- ple grow old, snowmen melt, houses fall down, cars rust, and stars burn out. Although islands of order may appear in restricted regions (e.g., the birth of a baby, crystals emerging from a solute), the disorder of the envi- ronment will always increase by an amount sufficient to compensate. This one-way slide into disorder is measured by a quantity called entropy. A state of maximum disorder corresponds to thermodynamic equilibrium, from which no change or escape is possible (except in the sense of rare statisti- cal fluctuations). Helmholtz reasoned that the quantity of entropy in the universe as a whole remorselessly rises, presaging an end state in the far future characterized by universal equilibrium, following which nothing of interest will happen. This state was soon dubbed the “heat death of the universe.” Almost from the outset, the prediction of cosmic heat death after an ex- tended period of slow decay and degeneration was subjected to theological interpretation. The most famous commentary was given by the philosopher Bertrand Russell in his book Why I Am Not a Christian, in the following terms: 1 All the labors of the ages, all the devotion, all the inspiration, all the noonday bright- ness of human genius are destined to extinction in the vast death of the solar system, and the whole temple of man’s achievement must inevitably be buried beneath the debris of a universe in ruins. All these things, if not quite beyond dispute, are yet so nearly certain that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built. 191 P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 192 Paul Davies The association of the Second Law of Thermodynamics with atheism and cosmic pointlessness has been an enduring theme. Consider, for example, this assessment by the British chemist Peter Atkins: 2 We have looked through the window on to the world provided by the Second Law, and have seen the naked purposelessness of nature. The deep structure of change is decay; the spring of change in all its forms is the corruption of the quality of energy as it spreads chaotically, irreversibly and purposelessly in time. All change, and time’s arrow, point in the direction of corruption. The experience of time is the gearing of the electrochemical processes in our brains to this purposeless drift into chaos as we sink into equilibrium and the grave. As Atkins points out, the increase in entropy imprints upon the universe an arrow of time, which manifests itself in many physical processes, the most conspicuous of which is the flow of heat from hot to cold; we do not encounter cold bodies getting colder and spontaneously giving up their heat to warm environments. The irreversible flow of heat and light from stars into the cold depths of space provides a cosmic manifestation of this simple “hot to cold” principle. On the face of it, it appears that this process will continue until the stars burn out and the universe reaches a uniform temperature. Our own existence depends crucially on a state of thermodynamic disequilibrium occasioned by this irreversible heat flow, since much life on Earth is sustained by the temperature gradient produced by sunshine. Microbes that live under the ground or on the sea bed utilize thermal and chemical gradients from the Earth’s crust. These too are destined to diminish over time, as thermal and chemical gradients equilibrate. Other sources of energy might provide a basis for life, but according to the Second Law, the supply of free energy continually diminishes until, eventually, it is all exhausted. Thus the death of the universe implies the death of all life, sentient and otherwise. It is probably this gloomy prognosis that led Steven Weinberg to pen the famous phrase, “The more the universe seems comprehensible, the more it also seems pointless.” 3 The fundamental basis for the Second Law is the inexorable logic of chance. To illustrate the principle involved, consider the simple example of a hot body in contact with a cold body. The heat energy of a material substance is due to the random agitation of its molecules. The molecules of the hot body move on average faster than those of the cold body. When the two bodies are in contact, the fast-moving molecules communicate some of their energy to the adjacent slow-moving molecules, speeding them up. After a while, the higher energy of agitation of the hot body spreads across into the cold body, heating it up. In the end, this flow of heat brings the two bodies to a uniform temperature, and the average energy of agitation is the same throughout. The flow of heat from hot to cold arises entirely because chaotic molecular motions cause the energy to diffuse democratically among all the participating particles. The initial state, with the energy distributed P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 Emergent Complexity, Teleology, and the Arrow of Time 193 in a lopsided way between the two bodies, is relatively more ordered than the final state, in which the energy is spread uniformly throughout the system. One way to see this is to say that more information is needed to describe the initial state – namely, two numbers, the temperatures of the two bodies – whereas the final state can be described with only one number – the common final temperature. The loss of information occasioned by this transition may be quantified by the entropy of the system, which is roughly equal to the negative of the information content. Thus as information goes down, entropy, or disorder, goes up. The transition of a collection of molecules from a low to a high entropy state is analogous to the shuffling of a deck of cards. Imagine that the cards are extracted from the package in suit and numerical order. After a period of random shuffling, the cards will very probably be jumbled up. The transition from the initial ordered state to the final disordered one is due to the chaotic nature of the shuffling process. So the Second Law is really just a statistical effect of a rather trivial kind. It essentially declares that a disordered state is much more probable than an ordered one – for the simple reason that there are numerically many more disordered states than ordered ones, so that when a system in an ordered state is randomly rearranged, it is very probably going to end up less ordered than it was before. Thus blind chance lies at the basis of the Second Law of Thermodynamics, just as it lies at the basis of Darwin’s theory of evolution. Since chance – or contingency, as philosophers call it – is the opposite of law and order, and hence of purpose, it seems to offer powerful ammunition to atheists who wish to deny any overall cosmic purpose or design. If the universe is nothing but a physical system that began (for some mysterious reason) in a relatively ordered state, and is inexorably shuffling itself into a chaotic one by the irresistible logic of probability theory, then it is hard to discern any overall plan or point. 2. reaction to the bleak message of the second law of thermodynamics Reaction to the theme of the dying universe began to set in the nine- teenth century. Philosophers such as Henri Bergson 4 and theologians such as Teilhard de Chardin 5 sought ways to evade or even refute the Second Law of Thermodynamics. They cited evidence that the universe was in some sense getting better and better rather than worse and worse. In Teilhard de Chardin’s rather mystical vision, the cosmic destiny lay not in an inglorious heat death but in an enigmatic “Omega Point” of perfection. The progressive school of philosophy saw the universe as unfolding to ever greater richness and potential. Soon after, the philosopher Alfred North Whitehead 6 (curi- ously, the coauthor with Bertrand Russell of Principia Mathematica) founded the school of process theology on the notion that God and the universe are evolving together in a progressive rather than a degenerative manner. P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 194 Paul Davies Much of this reaction to the Second Law had an element of wishful think- ing. Many philosophers quite simply hoped and expected the law to be wrong. If the universe is apparently running down – like a heat engine run- ning out of steam, or a clock unwinding – then perhaps, they thought, nature has some process up its sleeve that can serve to wind the universe up again. Some sought this countervailing tendency in specific systems. For example, it was commonly supposed at the turn of the twentieth century that life somehow circumvents the strictures of thermodynamics and brings about increasing order. This was initially sought through the concept of vitalism – the existence of a life force that somehow bestowes order on the material contents of living systems. Vitalism eventually developed into a more sci- entific version, what became known as organicism – the idea that complex organic wholes might have organizing properties that somehow override the trend into chaos predicted by thermodynamics. 7 Others imagined that order could come out of chaos on a cosmic scale. This extended to periodic resurrections of the cyclic universe theory, according to which the entire cos- mos eventually returns to some sort of pristine initial state after a long period of decay and degeneration. For example, during the 1960s it was suggested by the cosmologist Thomas Gold 8 that one day the expanding universe may start to recontract, and that during the contraction phase, the Second Law of Thermodynamics would be reversed (“time will run backwards”), returning the universe to a state of low entropy and high order. The speculation was based on a subtle misconception about the role of the expanding universe in the cosmic operation of the Second Law (see the following discussion). It turns out that the expansion of the universe crucially serves to provide the necessary thermodynamic disequilibrium that permits the entropy in the universe to rise, but this does not mean that a reversal of the expan- sion will cause a reversal of the entropic arrow. Quite the reverse: a rapidly contracting universe would drive the entropy level upward as effectively as a rapidly expanding one. In spite of this blind alley, the hypothesis that the directionality of physical processes might flip in a contracting universe was also proposed briefly by Hawking, 9 who then abandoned the idea, 10 calling it his “greatest mistake.” Yet the theory refuses to lie down. Only this year, it was revived yet again by L. S. Schulman. 11 The notion of a cyclic universe is, of course, an appealing one, and one that is deeply rooted in many ancient cultures; it persists today in Hinduism, Buddhism, and Aboriginal creation myths. The anthropologist Mircea Eliade 12 termed it “the myth of the eternal return.” In spite of detailed scrutiny, however, the Second Law of Thermodynamics remains on solid scientific ground. So solid, in fact, that the astronomer Arthur Eddington felt moved to write, 13 “if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” Today, we know that there is noth- ing anti-thermodynamic about life. As for the cyclic universe theory, there is P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 Emergent Complexity, Teleology, and the Arrow of Time 195 no observational evidence to support it (indeed, there is some rather strong evidence to refute it). 14 3. the true nature of cosmic evolution In this chapter I wish to argue, not that the Second Law is in any way sus- pect, but that its significance for both theology and human destiny has been overstated. Some decades after Helmholtz’s dying universe prediction, as- tronomers discovered that the universe is expanding. This changes the rules of the game somewhat. To give a simple example, there is good evidence that 300,000 years after the Big Bang that started the universe off, the cos- mic matter was in a state close to thermodynamic equilibrium. This evidence comes from the detection of a background of thermal radiation that per- vades the universe, thought to be the fading afterglow of the primeval heat. The spectrum of this radiation conforms exactly to that of equilibrium at a common temperature. Had the universe remained static at the state it had reached after 300,000 years, it would in some respects have resembled the state of heat death described by Helmholtz. However, the expansion of the universe pulled the material out of equilibrium, allowing heat to flow and driving complex physical processes. The universe cooled as it expanded, but the radiation cooled more slowly than the matter, opening up a tempera- ture gap and allowing heat to flow from one to the other. (The temperature of radiation when expanded varies inversely in proportion to the scale fac- tor, whereas the temperature of nonrelativistic matter varies as the inverse square of the scale factor.) In many other ways too, thermodynamic dise- quilibrium emerged from equilibrium, most notably in the formation of stars, which radiate their heat into the darkness of space. This direction- ality is the “wrong way” from the point of view of a na¨ıve application of the Second Law (which predicts a transition from disequilibrium to equilib- rium), and it shows that even as entropy rises, new sources of free energy are created. I must stress that this “wrong way” tendency in no way conflicts with the letter of the Second Law. To see why this is so, an analogy may be helpful. Imagine a gas confined in a cylinder beneath a piston, as in a heat engine. The gas is in thermodynamic equilibrium at a uniform temperature. The entropy of the gas is at a maximum. Now suppose that the gas is compressed by driving the piston forward; it will heat up, as a consequence of Boyle’s Law. If the piston is now withdrawn again, restoring the gas to its original volume, the temperature will fall once more. In a reversible cycle of contraction and expansion, the final state of the gas will be the same as the initial state. What happens is that the piston must perform some work in order to compress the gas against its pressure, and this work appears as heat energy in the gas, raising its temperature. In the second part of the cycle, when the piston is withdrawn, the pressure of the gas pushes the piston out and returns exactly P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 196 Paul Davies the same amount of energy as the piston had injected. The temperature of the gas therefore falls to its starting value when the piston returns to its starting position. However, in order for the cycle to be reversible, the piston must move very slowly relative to the average speed of the gas molecules. If the pis- ton is moved suddenly, the gas will lag behind in its response, and this will cause a breakdown of reversibility. This is easy to understand. If the piston moves fast when it compresses the gas, there will be a tendency for the gas molecules to crowd up beneath the piston. As a result, the pressure of the gas beneath the piston will be slightly greater than the pressure within the body of the gas, and so the piston will have to do rather more work to compress the gas than would have been the case had it moved more slowly. This will result in more energy being transferred from the advancing piston to the gas than would otherwise have been the case. Conversely, when the piston is suddenly withdrawn, the molecules have trouble keeping pace and lag back somewhat, thus reducing the density and pressure of the gas adjacent to the piston. The upshot is that the work done by the gas on the piston during the outstroke is somewhat less than the work done by the piston on the gas during the instroke. The overall effect is a net transfer of energy from the piston to the gas, and the temperature, hence the entropy, of the gas rises with each cycle. Thus, although the gas was initially in a state of uniform temperature and maximum entropy, after the piston moves the entropy nevertheless rises. The point is, of course, that to say the entropy of the gas is a maximum is to say that it has the highest value consistent with the external constraints of the system. But if those constraints change – because of the rapid motion of the piston, for example – then the entropy can go higher. During the movement phase, then, the gas will change from a state of equilibrium to a state of disequilibrium. This comes about not because the entropy of the gas falls – it never does – but because the maximum entropy of the gas increases, and, moreover, it increases faster than the actual en- tropy. The gas then races to “catch up” with the new constraints. We can understand what is going on here by appreciating the fact that the gas within a movable piston and cylinder is not an isolated system. To make the cycle run, there has to be an external energy source to drive the piston, and it is this source that supplies the energy that raises the temperature of the gas. If the total system – gas plus external energy source – is considered, then the system is clearly not in thermodynamic equilibrium to start with, and the rise in entropy of the gas is unproblematic. The entropy of the gas cannot go on rising forever. Eventually, the energy source will run out and the piston and cylinder device will stabilize in a final state of maximum entropy for the total system. The confusion sets in when the piston-and-cylinder expansion and con- traction is replaced by the cosmological case of an expanding and (maybe, one day) contracting universe. Here the role of the piston-and-cylinder P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 Emergent Complexity, Teleology, and the Arrow of Time 197 arrangement is played by the gravitational field. The external energy supply is provided by the gravitational energy of the universe. This has some odd features, because gravitational energy is actually negative. Think, for exam- ple, of the solar system. One would have to do work to pluck a planet from its orbit around the sun. The more material concentrates, the lower the gravi- tational energy becomes. Imagine a star that contracts under gravity; it will heat up and radiate more strongly, thereby losing heat energy and making its gravitational energy more negative in order to pay for it. Thus the principle that a system will seek out its lowest energy state causes gravitating systems to grow more and more inhomogeneous with time. A smooth distribution of gas, for example, will grow clumpier with time under the influence of gravitational forces. Note that this is the opposite trend from the case of a gas, in which gravitation may be ignored. In that case, the Second Law of Thermodynamics predicts a transition toward uniformity. This is only one sense in which gravitation somehow goes “the wrong way.” It is tempting to think of the growth of clumpiness in gravitating systems as a special case of the Second Law of Thermodynamics – that is, to regard the initial smooth state as a low-entropy (or ordered) state, and the final clumpy state as a high-entropy (or disordered) one. It turns out that there are some serious theoretical obstacles to this simple characterization. One such obstacle is that there seems to be no lower bound on the energy of the gravitational field. Matter can just go on shrinking to a singular state of infinite density, liberating an infinite amount of energy on the way. This fundamental instability in the nature of the gravitational field forbids any straightforward treatment of the thermodynamics of self-gravitating systems. In practice, an imploding ball of matter would form a black hole, masking the ultimate fate of the collapsing matter from view. So from the outside, there is a bound on the growth of clumpiness. We can think of a black hole as the equilibrium end state of a self-gravitating system. This interpretation has been confirmed by Stephen Hawking, who proved that black holes are not strictly black, but glow with thermal radiation. 15 The Hawking radiation has exactly the form corresponding to thermodynamic equilibrium at a characteristic temperature. If we sidestep the theoretical difficulties of defining a rigorous notion of entropy for the gravitational field and take some sort of clumpiness as a measure of disorder, then it is clear that a smooth distribution of matter represents a low-entropy state as far as the gravitational field is concerned, whereas a clumpy state, perhaps including black holes, is a high-entropy state. Returning to the theme of the cosmic arrow of time, and remem- bering the observed fact that the universe began in a remarkably smooth state, we may conclude that the matter was close to its maximum entropy state, but that the gravitational field was in a low-entropy state. The expla- nation for the arrow of time that describes the Second Law of Thermody- namics lies therefore in an explanation of how the universe attained the P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 198 Paul Davies smooth state it had at the Big Bang. Penrose 16 has attempted to quantify the degree of surprise associated with this smooth initial state. In the case of, say, a normal gas, there is a basic relationship between the entropy of its state and the probability that the state would be selected from a ran- dom list of all possible states. The lower the entropy, the less probable would be the state. This link is exponential in nature, so that as soon as one departs from a state close to equilibrium (i.e., maximum entropy), the probability plummets. If one ignores the theoretical obstacles and just goes ahead and applies this same exponential statistical relationship to the grav- itational field, it is possible to assess the “degree of improbability” that the universe should be found initially in such a smooth gravitational state. In order to do this, Penrose compared the actual entropy of the universe to the value it would have had if the Big Bang had coughed out giant black holes rather than smooth gas. Using Hawking’s formula for the entropy of a black hole, Penrose was able to derive a discrepancy of 10 30 between the actual entropy and the maximum possible entropy of the observable uni- verse. Once this huge number is exponentiated, it implies a truly colossal improbability that the universe should start out in the observed relatively smooth state. In other words, the initial state of the universe is staggeringly improbable. What should we make of this result? Should it be seen as evidence of design? Unfortunately, the situation is complicated by the inflationary uni- verse scenario, which postulates that the universe jumped in size by a huge factor during the first split second. This would have the effect of smoothing out initial clumpiness. But this simply puts back the chain of explanation one step, because at some stage one must assume that the universe is in a less-than-maximum entropy state, and hence in an exceedingly improbable state. The alternative – that the universe began in its maximum entropy state – is clearly absurd, because it would then already have suffered heat death. 4. the cosmological origin of time’s arrow The most plausible physical explanation for the improbable initial state of the universe comes from quantum cosmology, as expounded by Hawking, Hartle, and Gell-Mann. 17 In this program, quantum mechanics is applied to the universe as a whole. The resulting “wave function of the universe” then describes its evolution. Quantum cosmology is beset with technical mathematical and interpretational problems, not the least of which is what to make of the infinite number of different branches of the wave function, which describes a superposition of possible universes. The favored resolu- tion is the many-universes interpretation, according to which each branch of the wave function represents a really existing parallel reality, or alternative universe. P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 Emergent Complexity, Teleology, and the Arrow of Time 199 The many-universes theory neatly solves the problem of the origin of the arrow of time. The wave function as a whole can be completely time- symmetric, but individual branches of the wave function will represent uni- verses with temporal directionality. This has been made explicit in the time- symmetric quantum cosmology of Hartle and Gell-Mann, 18 according to which the wave function of the universe is symmetric in time and describes a set of recontracting universes that start out with a Big Bang and end up with a big crunch. The wave function is the same at each temporal extremity (bang and crunch). However, this does not mean that time runs backward in the recontracting phase of each branch, `a la Gold. To be sure, there are some branches of the wave function in which entropy falls in the recon- tracting phase, but these are exceedingly rare among the total ensemble of universes. The overwhelming majority of branches correspond to universes that either start out with low entropy and end up with high entropy, or vice versa. Because of the overall time symmetry, there will be equal proportions of universes with each direction of asymmetry. However, an observer in any one of these universes will by definition call the low-entropy end of the universe the Big Bang and the high-entropy end the big crunch. Without the temporal asymmetry implied, life and observers would be impossible, so there is an anthropic selection effect, with those branches of the universe that are thermodynamically bizarre (starting and ending in equilibrium) going unseen. Thus the ensemble of all possible universes shows no fa- vored temporal directionality, although many individual branches do, and within those branches observers regard the “initial” cosmic state as exceed- ingly improbable. Although the Hartle–Gell-Mann model offers a convinc- ing first step in explaining the origin of the arrow of time, it is not without its problems. 19 To return to the description of our own universe (or our particular branch of the cosmological wave function), it is clear that the state of the universe in its early stages was one in which the matter and radiation were close to thermodynamic equilibrium, but the gravitational field was very far from equilibrium. The universe started, so to speak, with its gravitational clock wound up, but with the rest in an unwound state. As the universe expanded, there was a transfer of energy from the gravitational field to the matter, simi- lar to that in the piston-and-cylinder arrangement. In effect, gravity “wound up” the rest of the universe. The matter and radiation started out close to maximum entropy consistent with the constraints, but then the constraints changed (the universe expanded). Because the rate of expansion was very rapid relative to the physical processes concerned, a lag opened up between the maximum possible entropy and the actual entropy, both of which were rising. In this way, the universe was pulled away from thermodynamic equi- librium by the expansion. Note that the same effect would occur if the universe contracted again, just as the instroke of the piston serves to raise the entropy of the confined gas. So there is no thermodynamic basis for P1: JRQ-IRK/kab-kaa P2: JzL 0521829496c10.xml CY335B/Dembski 0 521 82949 6 March 10, 2004 1:21 200 Paul Davies supposing that the arrow of time will reverse should the universe start to contract. The history of the universe, then, is one of entropy rising but chasing a moving target, because the expanding universe is raising the maximum possible entropy at the same time. The size of the entropy gap varies sharply as a function of time. Consider the situation one second after the big bang. (I ignore here the situation before the first second, which is complicated but crucial in determining some important factors, such as the asymmetry between matter and antimatter in the universe.) The universe consisted of a soup of subatomic particles – such as electrons, protons, and neutrons – and radiation. Apart from gravitons and neutrinos, which decoupled from the soup well before the first second owing to the weakness of their interactions, the rest of the cosmic stuff was more or less in equilibrium. However, all of this changed dramatically during the first 1,000 seconds or so. As the tem- perature fell, it became energetically favorable for protons and neutrons to stick together to form the nuclei of the element helium. All of the neu- trons got gobbled up in this way, and about 25 percent of the matter was turned into helium. However, protons outnumbered neutrons, and most of the remaining 75 percent of the nuclear matter was in the form of iso- lated protons – the nuclei of hydrogen. Hydrogen is the fuel of the stars. It drives the processes that generate most of the entropy in the universe to- day, mainly by converting slowly into helium. So the lag behind equilibrium conditions is this: the universe would really “prefer” to be made of helium (it is more stable), but most of it is trapped in the form of hydrogen. I say “trapped” because, after a few minutes, the temperature of the universe fell below that required for nuclear reactions to proceed, and it had to wait un- til stars were formed before the conversion of hydrogen into helium could be resumed. Thus the expansion of the universe generated a huge entropy gap – a gap between the actual and the maximum possible entropy – during the first few minutes, when the equilibrium form of matter changed (due to the changing constraints occasioned by the cosmological expansion and the concomitant fall in temperature) from a soup of unattached particles to that of composite nuclei like helium. It was this initial few minutes that effectively “wound up” the universe, giving it the stock of free energy and establishing the crucial entropy gap needed to run all the physical processes, such as star burning, that we see today – processes that sustain interesting activity, such as life. The effect of starlight emission is to slightly close the entropy gap, but all the while the expanding universe serves to widen it. However, the rate of increase of the maximum possible entropy during our epoch is modest compared to what it was in the first few minutes after the Big Bang – partly because the rate of expansion is much less, but also because the cru- cial nuclear story was all over in a matter of minutes. (The gap-generating processes occasioned by the expansion of the universe today are all of a less significant nature.) I haven’t done the calculation, but I suspect that today [...]... March 10, 2004 Emergent Complexity, Teleology, and the Arrow of Time 1:21 207 and otherwise left alone, life rides an escalator of complexity growth Another caveat concerns the ultimate fate of the universe So long as there is an entropy gap, the universe can go on creating more and more complexity However, in some scenarios of the far future, matter and black holes eventually decay and evaporate,... complicate the traditional “order into chaos” theme Moreover, the discovery of self-organizing and self-complexifying processes in nature suggests that alongside the degenerative arrow of time there exists a creative arrow, pointing in the direction of increasing richness, diversity, and potential There is no conflict between these two arrows The ultimate fate of the universe remains open Notes 1 Bertrand... Laflamme, and G W Lyons, The Origin of Time Asymmetry,” Physical Review D47 (1993): 5342 10 S W Hawking, The No Boundary Condition and the Arrow of Time, ” in Physical Origins of Time Asymmetry, ed J J Halliwell, J Perez-Mercader, and W H Zurek (Cambridge: Cambridge University Press, 1994), p 346 11 L S Schulman, “Opposite Thermodynamic Arrows of Time (forthcoming) 12 M Eliade, The Myth of the Eternal... Emergent Complexity, Teleology, and the Arrow of Time 1:21 203 was purchased at an entropic price As I have explained, the rapid expansion of the universe just after the Big Bang created a huge entropy gap, which has been funding the accumulating complexification ever since, and which will continue to do so for a long while yet Thus the history of the universe is not so much one of entropic degeneration and. .. something that augments the laws of nature or follows from them If it augments them, whence comes this higher-level law? If it is a consequence of the laws of nature, then will such a principle follow from a random set of natural laws, or is there something special about the actual laws of the real universe that facilitates the emergence of nonzero sum interactions? Whatever the answers to these difficult questions,... heat death I have summarized these many and varied scenarios in my book The Last Three Minutes.22 6 a law of increasing complexity? Clearly, modern cosmology paints a far more complicated picture of the fate of the universe than the simple heat death scenario of the nineteenth century But leaving this aside, the question arises as to the relevance of the Second Law of Thermodynamics to cosmic change... 2004 Emergent Complexity, Teleology, and the Arrow of Time 1:21 201 starlight emission generates more entropy than the rise in the maximum entropy caused by the expansion, so that the gap is probably starting to close, although it has a long way to go yet, and it could start to open up again if the dominant processes in the universe eventually proceed sufficiently slowly that they once more lag behind the. .. end of space, time, and matter The universe will not have reached equilibrium before the big crunch, so there will be no heat death, but rather death by sudden obliteration Some theological speculations about the end state of a collapsing universe have been made by Tipler.21 In the case of an ever-expanding universe, the question of its final state is a subtle matter The outcome depends both on the. .. in entropy Indeed, the time irreversibility introduced into macroscopic processes by the Second Law of Thermodynamics actually provides the opportunity for a law of increasing complexity, since if complexity were subject to time- reversible rules, there would then be a problem about deriving a time- asymmetric law from them (This is a generalized version of the dictum that death is the price that must... 1:21 Emergent Complexity, Teleology, and the Arrow of Time 205 number wall of minimal complexity 1 2 3 humans microbes complexity number (a) 2 1 (b) 3 complexity figure 10.1 Ladder of progress? Biological complexity increases over time, but is there a systematic trend or just a random diffusion away from a “wall of simplicity”? The diffusion model, supported by Gould, is shown in (a) Curves 1, 2, and . 1:21 Emergent Complexity, Teleology, and the Arrow of Time 199 The many-universes theory neatly solves the problem of the origin of the arrow of time. The. irreversibly and purposelessly in time. All change, and time s arrow, point in the direction of corruption. The experience of time is the gearing of the electrochemical