After men persuaded themselves, that everything which is created is created for their sake, they were bound to consider as the chief quality in everything that which is most useful to themselves, and to account those things the best of all which have the most beneficial effect on mankind. Further, they were bound to form abstract notions for the explanation of the nature of things, such as goodness, badness, order, confusion, warmth, cold, beauty, deformity, and so on; and from the belief that they are free agents arose the further notions praise and blame, sin and merit. Baruch Spinoza, The Ethics, Part I: "Concerning God," Appendix, translated by R.H.M. Elwes (1883), color added -- order and disorder, warmth and cold, are all, of course, physical quantities with units of measure -- unknown to the science of Spinoza's day.
Every mathematician knows it is impossible to understand any elementary course in thermodynamics.
Vladimir Arnold, Владимир Арнольд (1937-2010), 1989
No one knows what entropy really is.
John von Neumann (1903–1957), 1949
ὅτε ἤμην νήπιος, ἐλάλουν ὡς νήπιος, ἐφρόνουν ὡς νήπιος, ἐλογιζόμην ὡς νήπιος·
ὅτε γέγονα ἀνήρ, κατήργηκα τὰ τοῦ νηπίου.
Cum essem parvulus, loquebar ut parvulus, sapiebam ut parvulus, cogitabam ut parvalus; quando factus sum vir, evacuavi quae erant parvuli.
When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things. 1 Corinthians 13:11 In Arthur C. Clarke's classic science fiction novel, Childhood's End [1953], the Earth is visited by powerful aliens, the Overlords. These beings, however, turn out not to be conquerors or Lords of the Universe, simply babysitters. They know that life on earth will undergo a transformation, unavailable, for unknown reasons, to them. In the end, the last generation of humans develops telekinetic powers, ceases requiring ordinary nutrition, and finally vanishes in a translation to another existence, whose terms, as energy, spirit, or transcendence, are left obscure, even to the Overlords.
This kind of apocalypse is not of a kind familiar from existing religions, but to the non-religious it probably would also seem unlikely, especially when we learn that the Overlords are directed by a being, the Overmind, whose purposes and nature are really unknown to them. Nevertheless, we must consider that, however unlikely such a development seems, we cannot anticipate what is liable to emerge in the universe with increasing levels of development and complexity. At each level of organization in nature, it would be difficult or impossible for us to predict what emerges at the next level.
The forces of nature likely imply the existence of sub-atomic particles, and sub-atomic particles atoms and molecules. Atoms, however, exhibit irregularities. Why gold and copper are colored, and no other elementary metals, may be explicable in some obvious way some day, but not yet. What comes next, however, the stunning complexity of minerals, rocks, and especially the variety of organic substances based on carbon, creates a level of reality apparently different in kind from particles and atoms. Amino acids clump into proteins and, with DNA and RNA, explode into an infinite variability of life. As life develops, we get creatures who begin manipulating objects for their own use. Then we get a creature, us, who does this on a planetary, and extra-planetary, scale and lives day to day in structures that are not only artifacts but often use materials that are not even found in nature. The beginning of this seems to coincide with something else, the development of human language. Unfortunately, we know little about the early stages of linguistic evolution, though Derek Bickerman reasonably speculates that language without grammar, like attested Pidgin languages, probably dates back to the Pithecanthropines, while language as it is now familiar, with elaborate grammatical systems (even providing a default grammar, a universal grammar, for attested Creole languages), is a phenomenon of modern humans or, at best, Neanderthals.
What is then extraordinary about this is that we have fully formed modern humans as much as 30,000 years ago. Then, for 25,000 years, not much changes. We get a continuous paleolithic culture whose terms are not much different over the millennia, though much of what we would like to know about it (the languages, religions, history) we likely will never know. Then comes a Revolution, or perhaps a couple of them. The Neolithic Revolution makes artificial agriculture the principal basis of human nutrition. Then, as Neolithic cultures become ever more organized and urban, and begin (in the Old World) replacing stone tools with copper ones, another Revolution in its own right, we get writing, the most fateful Revolution of all. History begins. In Ancient History, however, there are considerable regularities, things that are constant even in comparison to surviving Neolithic and preliterate cultures, like the Incas of the New World. They all have their gods, their kings, their temples, their laws, their legends. And they have their characteristic views of the universe. They do not know that the earth is a finite body floating in space, or that the sun, moon, and stars are natural objects, like the Earth itself -- and not gods.
That begins to change with the Greeks and with Israel. In the latter, the gods disappear and the one God withdraws from nature. In the former, we get a messier process, by which the gods withdraw step by step and lose their mythic personae, as the Greeks come to explain natural events in naturalistic and mechanistic terms. The gods gradually fade away, until the projects of Greece and Israel, Athens and Jerusalem, unify in Christianity (and then in Islâm). That produces a level of culture characteristic of the Middle Ages. Now people know that the Earth is a finite body floating in space, and that the sun and the moon are natural objects, but they do not know that the earth (though Greeks had at least thought of it) is moving, or that the stars are other suns and the universe vast beyond imagining. Another Revolution was needed for that. They also knew that the Earth was round and that Europe, Asia, and Africa were the major land masses. The discovery that there were four other continents required enough of a technological Revolution to make transoceanic voyages possible. Curiously, the Chinese may have achieved this first, but then withdrew.
Again, we get modern culture through nearly simultaneous Revolutions, that of science, that of exploration, and that of emancipation -- the liberal politics of individual freedom. The former began with Copernicus and Galileo, the next with Columbus and da Gama, the latter in the Netherlands, then Britain, and finally and especially with the United States. As before, change is often resented and resisted. Many now think science a kind of fraud; it is common to deny that Columbus discovered America, because there were people there already (although, strictly speaking, they didn't know where they were); and millions of people were murdered in the 20th century by political ideologies (Fascism and Communism) that despised individualism and the liberal order, and we are presently seeing a powerful and violent movement of Islamic Fascism -- which nevertheless derives its intensity and violence largely from its own realization of the weakness, poverty, and failure of Islamic societies in comparison to the West (or, for that matter, the Far East) [note].
It is hard to have the science without the individualism, as the Soviet Union learned to its undoing. And science, meanwhile, has profoundly altered our vision and knowledge of the universe. Nothing else in history has made the truth so plain that we don't know what comes next. No Newtonian predicted Einstein. Einstein himself was alarmed at the tendencies of quantum mechanics. The more we know, the more mysterious some things get. Cosmology, which promised to become rather tidy thirty years ago, has become messier instead. One of the most important and growing mysteries is over the systems of order, and especially of emerging order, that I have been discussing here.
Modern philosophy begins with some confident ideas, expressed by Spinoza in the epigraph above, that order is a subjective judgment and not part of objective facts about nature. As beauty is in the eye of the beholder, so is order. This holds up rather well in general opinion, but the informed scientist must admit, even if grudgingly, that it doesn't quite agree with the results of science. There is, as it happens, a scientific measure of order. It is called "entropy," a term from Greek, ἐντροπία, suggested by Rudolf Clausius (1822-1888). In Greek ἐντροπία actually means "a trick, dodge," while ἐντροπή is "a turning towards." Both are from the verb ἐντρέπω, "to turn about, to alter." Clausius wanted it to mean "transformation."
Like all hard science, entropy can be expressed in equations and in physical units: S = k ln W. This is Boltzmann's Law (see also the "Stefan-Boltzmann Law"). It says that entropy (S) is equal to a constant (Boltzmann's Constant = 1.3806503(24) x 10-23 J/K) times the natural logarithm of W -- which is "the number of possibilities to realize any distribution appropriate to any body of many individual elements" [Entropy, edited by Andreas Greven, Gerhard Keller, and Gerald Warnecke, Priceton University Press, 2003, p.25]. This is the "statistical" meaning of entropy.
Entropy is quantified in units of Joules/Kelvin, i.e. units of energy per units of temperature. Low entropy is high order; high entropy is low order and high disorder. If there is just one possibility, the logarithm will be zero, low entropy indeed. The equation, which Boltzmann never wrote, is nevertheless engraved on his tomb.
Yet I have seen college physics books that have discussed entropy without giving any equations or physical units for it. This may leave the impression with many that entropy, along with the concept of "order," is not a properly scientific matter. Perhaps more metaphysics than physics. I find this puzzling. It enables people, including correspondents to this website, to repeat Spinoza's assertions, as though they are still relevant to the science of thermodynamics. And it may not be just "rocks for jocks" college students who have this problem. Nobel Laureate physicist Frank Wilczek ignores entropy, order, and thermodynamics in his entire book about the "fundamentals" of physics. One might suspect that something about it disturbs him.
The original meaning of entropy, and the explanation for its units, was not the statistical one. It was originally a simple characteristic of thermodynamics, the study of heat and temperature.
The Second Law of Thermodynamics begins with a very simple observation: Heat does not flow from colder objects to warmer objects. This is already pregnant with all the implications of entropy. Why does heat not flow from colder objects to warmer objects? Because entropy (S) in a closed system always increases, which means that disorder increases. If a colder object grew colder by exporting heat to a warmer object, which then becomes warmer, the two objects become more distinct and thus more ordered. As a colder object actually warms up and the warmer object cools, they become alike and eventually indistinguishable, and thereby less ordered and more chaotic. From this basic feature of thermodynamics, the phenomenon of entropy generalizes into a vast array of statistical, informational, and other applications.
The phenomenon of entropy, however, is more perplexing and controversial than most other principles of established science. Everyone wants to know why the Second Law should be true. This is mainly because it imposes a condition on time that is not found in other laws of physics. Galileo's equations, Newton's equations, Maxwell's equations, Einstein's equations and other fundamental equations of physics work just the same whether one is going ahead in time, or backwards in time. The familiar feature of macroscopic life, that time goes forwards and not backwards, is not evident in the fundamental equations of physics. Because of this, many physicists like the idea that time actually does not have an intrinsic "arrow" and that our commonsense understanding of time as directional is naive, subjective, an illusion, or merely speculative metaphysics.
Even physicists who understand the paradox or absurdity of believing that time can simply run backwards, and who grasp onto entropy as the place in science were the directionality of time comes in, nevertheless are left with a chicken or egg dilemma. Is time directional because of entropy, or is there entropy because time is directional? Unfortunately, answering the question either way ends up being unsatisfactory; for if time is directional because of entropy, why does entropy have to be that way? And if there is entropy because time is directional, why is time directional? The problem is that directionality, either of entropy or of time, probably requires metaphysical answers, which are neither amenable to scientific method nor to the taste of scientists.
One view is that entropy, and time, cannot run backwards because chaos is in terms of probablility much more likely than order. There may be only one ordered state, but large, sometimes vastly large, numbers of disordered states. So the sharp betting money is on disorder. Thus, if a glass falls off the table and breaks on the floor, it's not impossible that the glass would reassemble itself, just very unlikely. This is counter-intuitive. We would tend to think that time would need to run backwards for the glass to reassemble itself. Indeed, something else about that case seems impossible. The falling glass, even before it hits the floor, cannot just return to the tabletop.
The argument from probability wants to trace even the directionality of time back to statistics. A hot substance and a cold substance placed so that the heat can flow would encompass many possibilities. The heat could distribute itself in all sorts of ways, and, as it happens, there are vastly more possibilities for even distribution than there are for the hot substance to only draw heat from the cold one. Thus, the statistician says that it is possible for the cold substance to get colder, but in large samples, say trillions of atoms in macroscopic objects, the chances for that are infinitessimal. However, this presupposes that the heat will spread out in all the statistically possible combinations. This begs the question, for we have stipulated that the heat can flow in all possible ways. That itself relies on the Second Law of Thermodynamics. Who is to say that the heat cannot flow in idiosyncratic ways, so that it avoids "spreading out"? Well, the Second Law says that it cannot flow in idiosyncratic ways. And, of course, if we derive the effects of the Second Law from an application of the Second Law, then we should not be surprised that we end up with the Second Law. And time flows in the way stipulated by the Law, directionally. Order collapses into chaos.
Despite Classical physics often being said to allow time to go in either direction, it does forbid the glass from spontaneously returning to the tabletop, leaping up against gravity. That is not like the random flow of heat. The fall itself turns the potential energy of gravity into the kinetic energy of the fall, energy which is then expended, as work, as the glass hits the floor. It is too easy to think of Classical physics simply saying that the Earth might run backwards in its orbit, rather than forwards. The math works the same way. But the math doesn't work that same when the glass falls to the floor. Getting the glass back to the tabletop, like getting the glass put back together, takes an input of new energy -- low entropy energy. We supply that to fix the glass, although I have never properly repaired broken dishes or glasses to my satisfaction. Otherwise the energy expended would need to just spontaneously return whence it came. Perhaps that is just unlikely, but it sounds like it should be a stronger physical impossibility. But it is easier for me to pick up the glass, especially if unbroken, and put it back up on the table.
Postquam homines sibi persuaserunt, omnia quae fiunt propter ipsos fieri; id in unaquaque re praecipuum iudicare debuerunt quod ipsis utilissimum, et illa omnia praestantissima aestimare, a quibus optime afficiebantur. Unde has formare debuerunt notiones, quibus rerum naturas explicarent scilicet bonum, malum, ordinem, confusionem, calidum, frigidum, pulchritudinem et deformitatem etc.; et quia se liberos existimant, inde hae notiones ortae sunt, scilicent laus et vituperium, peccatum et meritum.
The First Law of Thermodynamics is an energy conservation law. In the equation at far left, given in an elementary physics textbook (Physics, The Foundation of Modern Science, by Jerry B. Marion, John Wiley & Sons, Inc., 1973), we see that changes in internal energy (U) are equal to heat (Q) minus work (W). In other words, you heat something up, like steam, and it both gains energy and does work (pushes a piston), but it only gains the energy from the heat that is not expended in the work. Since energy, heat, and work can call be expressed in the same units ("Joules" in the S.I., but calories are traditional units of heat energy, where 1 Cal = 4186 Joules), the terms of the equation are all ultimately about the same thing. The equation at right for the same law is from Greven, Keller, and Warnecke: It gives us a derivative for internal energy plus kinetic energy (K) with respect to time (t), where heat and work (A) are shown as derivatives with respect to time also, indicated with conventional overdots.
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| Newton's Cannon, which, if powerful enough, will launch a projectile into orbit. Principia, Vol. II, The System of the World, University of California Press, translated by Andred Motte, 1729, revised, Florian Cajori, 1966, p.551; nothing was actually put into Earth orbit until 1957. |
What it would mean for time to "run backwards" is easy. Make a video recording of the glass falling off the table and breaking. Then run the video backwards. That's time running backwards. It violates the laws of physics; but, hey, that's what we're asking about. Time really running backwards is going to violate both entropy and Newtonian mechanics, regardless of everyone's fantasy about time easily running in either direction. To even get the glass back on the table, we need the equivalent of Newton's Cannon, which applies a force to get it back up.
But, we are able, not only to imagine it, but we've got the video on top of that. Film at Eleven. And Hume's criterion was that anything we can imagine is possible. So, in those terms, time can run backwards, violating laws of physics along the way. So that would tend to mean that the directionality of time, far from being a function of probability or any physical law, is part of the fundamental ontology of time. The only way to actually run time backwards would be with.... a miracle. Or superpowers. It's in the movies.
The directionality of entropy is a matter that is more difficult than one might think to express mathematically. Familiar algebraic notation does not include symbols to indicate temporal irreversibility. How this is dealt with we can see in two versions of an equation for the Second Law. At right (in the image at left) is the Boltzmann statistical equation for entropy, which says nothing about time. 
At left are two equations given at different places in Greven, Keller, and Warnecke. At far left is an equation (p.1) that, again, has nothing about time in it and doesn't say either how entropy might change or how it is related to order (T is temperature in Kelvins). 
At center left is another equation (p.21) that includes time and is expressed as an inequality, so we get some notion that over time entropy will increase. If we set that equation as an equality rather than inequality, then the two equations are equivalent, multiplying out the dt term -- as we can see at right where the Q overdot term is unpacked. It also ends up that temperature is equivalent to the derivative of heat with respect to entropy.
On the other hand, in a way we don't really want an equation in which time or entropy are irreversible, because in open physical systems entropy can indeed decrease. Which brings us back to order. If the Second Law is the way that the directionality of time enters fundamental physics, it is also where what might otherwise be thought to be metaphysical questions about order enter fundamental physics. The Second Law is often used by people with religious objections to evolution as an argument why evolution cannot occur from only natural causes, since the organization of living organisms clearly involves a decrease in entropy from inorganic nature -- violating the Second Law. Unfortunately for them, this proves too much. If the prevention of increases in entropy requires supernatural intervention, then life itself, not just the evolution of life, would require such intervention, since all living things maintain, as long as they live, levels of organization that defeat, apparently, the Second Law. This, indeed, is what people used to believe, when the soul was thought to be the principle of life. The soul as a transcendent or supernatural object became less popular in science, but then for a good while the doctrine of "vitalism" in chemistry was that organic substances could not be synthesized from inorganic. This notion was overthrown when organic substances were indeed synthesized, but some people, not so much in science, still seem to believe that life requires some kind of vital principle added to even the organic chemistry. This, again, might prove too much, since grasses and trees would need a vital principle as much as people, a notion more familiar in Buddhism than in Western religion. Indeed, traditional religious belief in Christianity is that animals do not have souls; but if it is the soul that staves off entropy and makes life possible, then all animals, as well as grasses and trees, must have souls.
For many years, 
I did not see revealing discussions of this issue. But then Roger Penrose supplied the key point in The Emperor's New Mind (diagram from page 319 in Oxford University Press, 1990, edition). The Earth is an entropy pump. The sun is a point source in the sky. This imposes a geometrical order on the energy it radiates. That energy itself consists of specific wavelengths of photons, generated according to Planck's Law of Black Body radiation by the hot atoms and molecules in the sun's atmosphere. However, the Earth, absorbing that energy from that particular direction, radiates energy in all directions, with a lack of geometrical order, in the form of all the wavelengths radiated chaotically by various warm substances on the earth. Thus, what goes out has higher entropy than what comes in, reducing the overall entropy of the Earth. A living organism like the human body exists on similar terms. What we eat, what goes in, is much more orderly than what comes out. Indeed, in the most delicate terms, what comes out usually looks like whatever else comes out -- though different foods can produce some identifiable differences. But most of the structure and variety of what we eat has been lost.
We can see a very practical example of Penrose's point in something that made for the industrial revolution. Heat is the most chaotic and highest entropy form of energy. Other forms of energy, following the Second Law of Thermodynamics, will migrate to heat. The usefullness of the energy then seems to be lost, even as heat radiates from the Earth. But this is not necessarily so. Heat is deliberately generated in a boiler. This heats water, which converts into steam. Steam itself is pretty chaotic; and, unless you want to get warmed up in a steam bath, it does not obviously seem like something to convert into a low entropy form of energy. But you can do precisely that, with a steam engine. The steam is piped into a piston, and the steam pressure pushes the piston. The piston drives a rod, and the rod can turn a wheel. The turning wheel sends you down the tracks, doing a lot of very focused and organized, i.e. low entropy, kind of work. So how did that work? Like Penrose's sun in the sky, the steam engine works through bits of geometry. Of course, you have built the geometry; and it is a very organized, i.e. low entropy, kind of thing. And, of course, a lot of very high entropy heat escapes from the engine. It can be more or less efficient, i.e. the output of low entropy energy is balanced or offset by the dispersal of very high entropy heat. But, meanwhile, you've got your moving train, doing all sorts of useful work -- a force applied over a distance (F=ma, E=mv2). So a steam engine, after a fashion, is just geometry, but not in a naturally occurring form -- it is an artifact of James Watt's own very low entropy brain.
Penrose also sees cosmological implications for entropy. As stars die, some of them are massive enough to collapse into Black Holes. In Black Holes, most of the information about the bodies falling into them is lost -- they have very high entropy. However, the Big Bang is more like a White Hole, with matter coming out of it rather than falling in. The Big Bang is the opposite of Black Holes in another respect: It had very, very low entropy, otherwise Black Holes would have formed quickly in the history of the Universe. Stephen Hawking famously predicted that there would be small Black Holes left over from the Big Bang, but these (or their radiation signatures) have never been observed. One might, indeed, expect that the Universe as a cosmos, as a place of order, would begin with low entropy.
A correspondent once wrote to The Proceedings of the Freisian School about this page, protesting and insisting that order is a completely subjective business and that, apparently, the Second Law of Thermodynamics is not really a scientific law. For years, I might have given some credit to this argument, when all the discussions I ever saw about entropy were conceputal rather than quantitative. If something is physical, it should be possible to measure it. And so, if entropy is a physical quantity, there should be units of it that can be measured. I don't know why generally accessible discussions of entropy do not mention that it is a physical quantity that can be measured. Because it is. As we have already seen, the units of entropy are Joules/Kelvin, or units of energy per units of temperature. Heat is energy, but temperature is something else. Temperature is physically related to energy by way of entropy. Low entropy means that a small amount of energy corresponds to a unit of temperature, while high entropy means that a large amount of energy corresponds to a unit of temperature. Entropy is thus about efficiency, as we might expect, since order is more efficient than disorder, and producing a given temperature with less energy than otherwise is more efficient. Temperature itself can be very low entropy or very high entropy, e.g. the high temperature of the Big Bang were low entropy while the low temperatures in the future "heat death" of the expanding universe will be very high entorpy.
It is noteworthy that as the universe expands and cools, entropy necessarily increases. Because of the conservation of energy (or Einsteinian mass-energy), the sum of energy (or mass-energy) in the universe is a constant. The young universe, after the Big Bang, is very hot. With a high temperature, the amount of energy per degree of temperature is going to be relatively low -- the hotter the lower. Thus, the young universe has relatively low entropy. As the universe cools, now down to about 3 Kelvins (the temperature of the black body radiation of the Cosmic Background Radiation), the energy per degree of temperature necessarily increases greatly. So entropy increases. The Second Law of Thermodynamics does not say why entropy increases, and there may be an ontological reason more fundamental than the cooling of the universe, but the expansion and cooling of the universe alone would account for it [note].
The phenomena of life and the universe itself thus curiously have something in common, low entropy. But out of mere life comes something else: 
language, consciousness, art, science, etc. This is the level of organization that Pierre Teilhard de Chardin (1881-1955) would have called the noösphere, the realm of "mind" (nóos, noûs). Orthodox science tends to react negatively to Teilhard, since his ideas are strongly teleological (with mind and matter, consciousness and the universe, becoming unified at the "Omega Point"), but the teleology is hardly necessary to appreciate the situation [note].
Orthodox science is slow to acknowledge how different the phenomena of consciousness are from the rest of life or matter. Some recent philosophers have built careers around reductionistic and naturalistic explanations of consciousness -- most of which, as John Searle might say, succeed simply by leaving out consciousness altogether. It is not surprising that an evolutionary biologist like Stephen Jay Gould (1941-2002) would object to the teleology in Teilhard ("orthogensis" is the name for teleological evolution), but Gould also objected to the very notion that evolution produces progress over time, generating higher levels of organization. "Progress" and "higher" organization sounded too much like value judgments.
Indeed, but each of them can simply and precisely mean lower levels of entropy, which is what we would expect from the Earth as an entropy pump. If Gould's notion is that nature hits a certain level of organization and then that's it, there is no evidence for this and, in the evident levels of increasing organization over time, considerable evidence against it -- if we are entitled make reasonable extrapolations from attested developments in nature -- as we are. Is there the slightest hint of evidence that no further levels of organization are likely to emerge, comparable to molecules, minerals, life, consciousness, civilization, etc.? Of course not. And it is the radical difference between consciousness and previous organic life that someone like Gould is reluctant to admit. In this, Teilhard was more right, and someone like Gould is really applying a metaphysical (materialistic) dogma, not honestly arguing in the terms of good science. Whatever the metaphysical preferences of scientists, entropy, with its profound implications, fairly evident to Penrose, is here to stay.
Human evolution certainly took an extraordinary turn. Our bodies and brains are more or less what they were 30,000 years ago, but what we do with them is something that people from that era, or even from as little as 3000 years ago, would have found incomprehensible. Human evolution vaulted into the evolution, not of organs, but of tools, and then into the evolution, not just of tools, but of ideas. In a way, this has opened up the Universe itself like a can of tuna. What more can we expect? Well, there is no telling -- though science fiction writers try every day. It truly is reasonable to expect that human life and human knowledge in a century may in some ways be as different from what they are now as what they are now is different from the life and knowledge of Tutankhamon. That there will be higher levels of organization is reasonably predictable, but what they will be and what it will all mean is radically unpredictable. Is there a teleology here? That depends on what increasing levels of organization have to do with the fundamental nature of the universe. Are levels of organization like minerals, life, and consciousness implicit in the seed of the basic laws of physics? Not in any obvious way, but their possibility must be contained in there somehow. And we also must wonder what the alternatives are. Life means many things. There are many languages, though they all have something in common. It would be nice to know how many possibilities there are as entropy gets lower and lower, but this is probably as unpredictable as any particular new form of emerging order.
The new forms of order, however, which follow upon consciousness, necessarily have their teleological aspect just because consciousness itself is purposive. This has been discussed elsewhere. Consciousness turns the world inside out. Usually the universe is thought of as blind, causal, and deterministic, but these conceptions themselves only arise in consciousness, which is not blind and is both purposive and free. The determinist uses the freedom and purposiveness of consciousness to deny that very freedom and purposiveness. This is, to say the least, paradoxical. But a metaphysics of materialism stands in the way of a better understanding. At the very least, ontological undeciability can allow equal standing to causal nature and teleological consciousness. Increasing order thus leads to a radically different perspective on reality, for which the "noösphere" is by no means an inflated characterization.
We cannot know what comes next, and certainly not whether some change as radical as life or consciousness is possible, but we can consider what people would like to have happen. Childhood's End is itself an example of this. People acquire (apparently) supernatural powers and are translated to a different existence. I doubt it is a coincidence that this sounds, despite the differences, like some kind of religious apocalypse. Similarly with Robert Heinlein's Stranger in a Strange Land, where Michael Valentine Smith is a Savior figure with supernatural powers who, planning his own martyrdom, is translated to a different plane of existence. And one hardly needs science fiction for such examples. There is no (traditional) religion that is free of supernatural and miraculous events. To the rational and the secular, however, there hardly seems any possibility in life more discredited than miracles. The classic argument against miracles is often taken to be Hume's. However, Hume's argument against miracles is that they violate laws of nature, while most recent philosophers read Hume to argue that there is no good reason to believe that there are laws of nature. Hume is actually more coherent than these enthusiasts, since Hume believes that there are reasons to believe things (laws of nature) with some subjective certainty, even when there is no rational (objective) certainty to this and it cannot be said to constitute knowledge in the traditional sense -- which is why Hume regards himself as a Skeptic (no knowledge), but of the Academic (reasonable belief) rather than the Pyrrhonian (suspend all judgment) variety. It is a common mistake for philo-Humean Analytic philosophers to embrace the Skepticism to a Pyrrhonian degree, or at least with a dose of subjective uncertainty that Hume does not allow, while inconsistently retaining the certain rejection of miracles.
Hume's argument that miracles are things that suspiciously we usually hear about rather than see can be well taken. Indeed, in an age of live and instantaneous television coverage, we don't get video of miracles on the evening news. At the same time, more skeptically than Hume, we are justified in wondering about the necessity of natural law, especially when miracles, while violations of laws of nature, are not at the same time violations of causality -- the point of most religious miracles is that they are caused, since the nature of their origin is testimony to the religion involved. Hume may not have realized there was that difference; but then it doesn't matter much for him, since he would not believe there would be any notion of causality in general without experience of natural laws in particular. What is noteworthy is that historically we do not find people who did not believe in causality, while particular laws of nature mostly awaited the convoluted discovery process of modern science.
We might begin to wonder whether miracles are things that actually have happened or whether they are something that can happen. All human hopes and beliefs about miracles may be premonitions or anticipations of what can happen in the future. How it would happen, of course, is beyond anticipation. If it did happen, however, if people began walking on water, flying, raising the dead, everyone would immediately know what this was. We have the categories for it. And the fundaments of nature would be opened up in a way radically different from what science itself was able to do.
Well, is there any evidence that miracles might begin to happen, that we might get Childhood's End or Michael Valentine Smith, or, for that matter, Jesus Christ or Siddhartha Gautama? No, not a shred. What we should be ready for, however, is that whatever the future holds, there is an excellent chance that it will be all but incomprehensible in terms of what we already think we know. Almost every generation thinks that its understanding of the universe is just about complete, that everything that can be invented or thought of has already been invented or thought of. But we are continually surprised even in small ways. In Stranger in a Strange Land, Heinlein imagined people going to Mars, but he didn't think that radio communication with the astronauts on Mars was possible. Now we know that communication is a snap, but getting people there is still the problem. Science fiction rarely anticipated the miniaturization of computers, that there would be hand held calculators (Heinlein had slide rules far into the future), personal desktop computers, or the array of "smart" technology that ranges from cellphones to televisions and automobiles. But this is small potatoes compared to the more radical innovations in order that have occurred geologically and historically -- life, consciousness, civilization, writing, etc. In their own way, these things are already miracles. Whether one thinks there will simply be a better mousetrap, or a galactic civilization, or miraculous suspension of the laws of nature, the lesson is simply to expect miracles.
At right we have been seeing a diagram of half-spheres stacked on each other. This display is suggested by Buddhist and Hopi cosmology, where the sky we see above is, 
of course, a solid sphere (in the Bible a "firmament," steréôma in Greek), upon which there are other spheres, which are other worlds. Below us the stack continues down. In Buddhism, the worlds below us are hells, while those above are heavens. We get from one to the other by rebirth. In the Hopi cosmology, however, we have the interesting idea that we have come from the worlds below us, and will eventually migrate to the ones above. This happens because we eventually ruin the world we are in, as evil and corruption take over. A worthy remnant, as with Noah's Ark, are selected by the gods to climb up to a new world. They are given the rules by which they will prosper as they live in the new world. Neglecting those rules will result in the same evils, but hopefully the same migration, as before. We are currently supposed to be in the Fourth World. The Kiva, the particular ceremonial structure found in the American Southwest, used by the ancient Anasazi and by modern Hopi and Pueblo Indians, reproduces the form of our world, with a spherical dome above, topped with an opening for access -- although there are variations with flat roofs, lateral access, and even square walls.
Emerging levels of order as entropy decreases in the history of the Earth can be compared to migrating upward into one of the new Hopi worlds. Of course, the others are not left behind but continue to be present. I have labeled each world in terms of its level of natural structure, the science that studies that structure, or both. It is noteworthy that the sciences do tend to sort themselves in this way. Some areas of inquiry remain confused or primitive as sciences, such as morality and politics. On the other hand, something that is reasonably scientific in its form and history, economics, is nevertheless muddied by moral and political disagreements -- e.g. the persistence of Keynesianism, let alone Marxism. This is properly a matter for philosophy to address, even as the sciences themselves ultimately derive from (Greek) philosophy; but in the 20th century philosophy did this job very poorly and rarely had a constructive contribution to the issues. For instance, with the two individuals often said to be the greatest philosophers of the 20th century, Ludwig Wittgenstein and Martin Heidegger, the former had no moral or political philosophy, since he did not think such things could exist, while the later was an enthusiastic member of the Nazi Party. This does not inspire confidence in the tradition.
Whose Blunder? Entropy: The Greatest Blunder in the History of Science, by Arieh Ben-Naim
The only hope of this movement for any success has been to borrow technology from the West to use against it, like hijacking airliners to fly them into buildings on 9/11/01. Nothing could be more revealing than this act -- Islamic kamikaze pilots who don't even have their own airplanes, while Palestinians dance in the streets in celebration (for innocent civilian deaths, including Arab and Muslim victims). Every such act bespeaks a moral degradation that would have been shocking to the noble exemplars of Mediaeval Islam like Saladin.
I think that Paul Sen is confused about this. He says:
I find this passage extraordinary in a number of ways. I have never seen anyone else claim that the laws of physics were different in the early universe, that space and time were different, and that energy was not conserved. Noether's Theorem is, indeed, that energy and momentum will be conserved if the laws of mechanics do not change across space and time. So Paul Sen has only come up with these extraordinary statements because he thinks we must admit that energy was not conserved in the early universe. That it cooled down like a pottery kiln. This ignores the expansion of the universe, and also that the wavelenth of light in the Cosmic Background Ratiation is simply red shifted, thanks to the expansion and the distance now between the surface of the radiation and us. All we need is Hubble's Law, which Sen doesn't mention. Thus, he has not taken them into consideration.
And, of course, if space is infinite but the universe is finite, as we seem to find Frank Wilczek saying, then the universe does have "surroundings" into which it can lose heat. Sen doesn't consider the cosmological alternatives there; and in fact he doesn't even explain to us, in this respect, what he is talking about.
He has not noticed, of course, that temperature can drop, and energy can remain constant, just by entropy increasing. Indeed, in Sen's book about thermodynamics, I don't see a discussion such as I have given about the physical units of entropy and the relationship between entropy, temperature, and energy. He devotes considerable attention to the role of statistics and probability in understanding entropy, but nothing to entropy as something quantifiable as Joules/Kelvin.
Other curiosities about this passage are perhaps simply nit picking. In his book, Sen has written about Lord Kelvin and the scale of absolute temperature in Kelvins. But he doesn't use Kelvins here, where it is most appropriate. Instead, he uses degrees Celsius, which involves nothing fundamental about cosmology.
Similarly, I don't see why he uses expressions like "millionth of a meter" or "1.9 millimeters" rather than giving us powers of 10 or using appropriate SI units. A "millionth of a meter" is 10-9 meters, or a nanometer. In talking about the electromagnetic spectrum, we do see discussion of "millimeter wavelengths" for a band of microwave radiation, but we don't get that kind of background with Sen's usage. Indeed, such usage persists throughout Sen's book. So I wonder a little about what goes on here.
In the late 1970's I used to attend a charming event at the University of Texas, the "Thursday Nights at the Physics Movies." These were science films, usually, that were introduced by physics professors. Many of the films, like some on quantum mechanics, were quite good -- to the point that I still wish I had a copy of them or had taken detailed notes. We also got some jokes, such as that, while engineers revered basic equations of their discipline, evident in one of the films, "they would never dream of writing one themselves." I notice this needling of engineers in the popular "The Big Bang Theory" television show.
Sometimes, however, the good physicists didn't quite know what they were dealing with. One film -- I think it was called "Omega" -- was an impressionistic presentation of Pierre Teilhard de Chardin's cosmology. Without narrative or explanations, but just with images and music, like Koyaanisqatsi, the film looked like it had something to do with the universe and with science; but what it was all supposed to add up to was not in the least bit evident, unless one already knew about Chardin's ideas, particularly the "Omega Point." The physics professors didn't, and so they could only express puzzlement over what the film was really all about.
They might have had a similar challenge with the more recent What the (Bleep) Do We Know!? [2004], which does have narrative and explanations, and superficially looks like an exploration of some of the strange consequences of quantum mechanics. However, the movie is actually a propaganda piece promoting the view of "Natural Law" found in the Transcendental Meditation (TM) system of the Guru Maharishi Mahesh Yogi (1914-2008). Spotting John Hagelin in the movie was a good clue. Hagelin, who actually is a professional physicist, has been the Presidental Candidate for the TM based "Natural Law Party" three times and promotes his interpretation of quantum mechanics at the Maharishi International University (now the Maharishi University of Management) in Iowa.
This movie does pose a nice intellectual challenge to identify the point were it leaves the tracks of orthodox science and goes off into Transcendental Meditation. That point comes where the collapse of the The idea that the collapse of the wave function is something that can be consicously controlled we also find in Science Set Free, 10 Paths to New Discovery, by science dissident Rupert Sheldrake.
The Pierre Teilhard de Chardin movie I saw at Texas at least was not actively obscuring what it was all about. It just presented no explanation whatsoever. It was nice to look at, and at least it left the uninitiated confused rather than deceived.
The "Thursday Nights at the Physics Movies" were presented in a lecture hall in what used to be the physics building at the university. There was a new physics building, and the old one was then actually used by the Home Economics Department. At the top of the building, however, was something unavoidably out of place for home economics: a large telescope in its own nicely constructed observatory. At various times, the telescope was open for public viewing.
I was doing some astronomical viewing at the time with my own telescope, but on one night I saw something through the observatory telescope that I could never have seen through my own small instrument. Globular Clusters, which are great balls of stars that orbit the Galaxy, look like no more than fuzzy patches of light in the sky through a small telescope. Through the large refractor in the observatory, however, I seemed to see individual stars in a Globular Cluster I was looking at. And they sparkled. This made the object look like a living jewel. It was not possible for anything of the sort to be visible in photographs. Today, it should be possible to show the effect from a live video signal of a modern telescope, but I still have not seen anything quite like what that looked like live to my eye.
Childhood's End,
the Mystery of Order, Note 2Think of the universe as a giant kiln, which, a long time ago, glowed orange-red. This light energy was most intense at a short wavelength of around a millionth of a meter, meaning its temperature was high, at around 2,700oC. Now this same light energy is considerably cooler -- the wavelength of the glow is most intense at a long wavelength of 1.9 millimeters, which means its temperature has fallen to -270oC. Now when an actual kiln cools down, it loses heat to its surroundings. No heat is destroyed. But the universe has no surroundings to which it can lose heat. For it to cool down, heat disappears, which means energy is not being conserved. But this is what [Emmy] Noether's theorem predicts. In the early universe, the fabric of space and time were different than how they are now, and so the laws of mechanics, for example, were different than the way they are now. And that means in turn that energy is not conserved. In summary, Noether's theorem predicts that energy is conserved only when space and time remain unchanged. [Einstein's Fridge, How the Differnce Between Hot and Cold Explains the Universe, Schribner, 2021, pp.158-159]
Childhood's End,
the Mystery of Order, Note 3
wave function is described, not as a purely random event (which is the most characteristic thing about quantum reality), but as something that can be consciously controlled -- by implication through TM. This is subtly done, and the non sequitur can easily escape the attention of anyone not alerted to the tendency of the movie. I don't see it described, for instance, in the reviews of the movie at Amazon.com, none of which seem to make the connection between the movie and TM. This dissimulation of the movie with respect to its true agenda was also characteristic of the political rhetoric of the Natual Law Party, which, even when Hagelin himself was the candidate, never honestly explained its background and inspiration from the Maharishi.