Can a universal library exist, once that contains all possible books? Centauri Dreams regular Nick Nielsen takes that as just the starting point in his latest essay, which tracks through Borges’ memorable thoughts on the matter to Carl Sagan, who brought the idea of an Encyclopedia Galactica to a broad audience. But are the two libraries one and the same? Nielsen takes the longest possible view of time, exploring a remote futurity beyond the Stelliferous era, to ask when an Encyclopedia Galactica would ever be complete, and who, when civilizations as we know them have ceased to exist, would evolve to read them. If Freeman Dyson’s conception of ‘eternal intelligence’ intrigues you, read on to see how it might emerge. Nielsen authors two blogs of his own, Grand Strategy: The View from Oregon and Grand Strategy Annex, in which a philosophical take on the human future is always at play, but perhaps never so strikingly as in this essay on intellect and its potential to survive.
J. N. Nielsen
1. A Universal Reference Work
2. Civilizations of the Stelliferous Era
3. The End-Stelliferous Mass Extinction Event
4. Eternal Intelligence in the Post-Stelliferous Era
5. Had we but world enough, and time
6. Eternal Intelligence After Dyson
1. A Universal Reference Work
W. V. O. Quine called the idea of a universal library a “melancholy fantasy” , though this admittedly melancholy fantasy was given a beautifully poetic evocation by surrealist writer Jorge Luis Borges in his memorable short story “La biblioteca de Babel.”  The universal library contains all possible books. Here is how Quine puts it: “At 2,000 characters to the page we get 500,000 to the 250-page volume, so with say eighty capitals and smalls and other marks to choose from we arrive at the 500,000th power of eighty as the number of books in the library. I gather that there is not room in the present phase of our expanding universe, on present estimates, for more than a negligible fraction of this collection.” And here is how Borges describes it: “Everything: the minutely detailed history of the future, the archangels’ autobiographies, the faithful catalogues of the Library, thousands and thousands of false catalogues, the demonstration of the fallacy of those catalogues, the demonstration of the fallacy of the true catalogue, the Gnostic gospel of Basilides, the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books.”
[Erik Desmazières, “Salle hexagonale,” From a suite etchings for Jorge Luis Borges, “La Biblioteca de Babel” (The Library of Babel). Boston: Godine, 1998. http://www.loc.gov/pictures/item/2004676845/]
While Borges insisted on the infinity of the universal library, Quine, logician that he was, demonstrates that the universal library is finite. In the same spirit of Quine’s scientific naturalism we might also say that the universal library possesses a high degree of entropy, as most of its volumes are “gibberish.” A somewhat less comprehensive library, and hopefully not nearly as entropic, also has its ultimate origins in fiction, though it has passed from fiction into a durable motif of the future of civilization in the universe. I am thinking of the Encyclopedia Galactica. 
Whether one wishes to consider the Encyclopedia Galactica as another “melancholy fantasy” like the universal library, or as a concrete proposal for an archive of the universe entire, is perhaps a matter of taste, yet like the universal library it is both a poetic and a compelling idea, and one to set the mind thinking. Here is how Carl Sagan formulated the idea of an Encyclopedia Galactica:
“Imagine a huge galactic computer, a repository, more or less up-to-date, of information on the nature and activities of all the civilizations in the Milky Way Galaxy, a great library of life in the Cosmos. Perhaps among the contents of the Encyclopaedia Galactica will be a set of summaries of such civilizations, the information enigmatic, tantalizing, evocative—even after we succeed in translating it.” 
Carl Sagan continued:
“We would discover the nature of other civilizations. There would be many of them, each composed of organisms astonishingly different from anything on this planet. They would view the universe somewhat differently. They would have different arts and social functions. They would be interested in things we never thought of. By comparing our knowledge with theirs, we would grow immeasurably. And with our newly acquired information sorted into a computer memory, we would be able to see which sort of civilization lived where in the Galaxy.” 
Note that Sagan thinks of the Encyclopedia Galactica as an ongoing project, a living record, rather than a finished and finite archive of what was accomplished by the totality of civilization, i.e., astrocivilization, during the period of time in the history of the universe when civilizations were possible. Certainly this is how we would wish to think of our civilization in relation to other civilizations, i.e., as a living legacy, though it seems highly unlikely that these civilizations will ever learn of each other while they are extant.
Today we would be more likely to imagine a huge network or a storage cloud as the medium of an Encyclopedia Galactica, but the particular mechanisms of storage, retrieval, and communication are irrelevant to the central idea of the Encyclopedia Galactica. This has been echoed several times since Sagan introduced it in the context of SETI. For example, by George Basalla:
“Near the end of Cosmos, Sagan estimated the number of advanced technological civilizations thriving in the Milky Way Galaxy. He said there were millions of civilizations scattered throughout our Galaxy and that interstellar space was filled with radio messages sent by extraterrestrial transmitters. The messages constitute an Encyclopedia Galactica, the knowledge and wisdom gathered by millions of civilizations over millions of years of Galactic history.” 
Here the signals employed for SETI and METI themselves constitute the archive that is the Encyclopedia Galactica, which echoes the familiar idea within SETI circles that SETI communication, if it does occur, is likely to be a one-way messaging enterprise, so we can imagine aging supercivilizations, aware of their own impending mortality, sending out the whole of their collected knowledge of their civilization into the universe in a grand gesture of generosity to be received by some unknown heir who may profit from this cosmic beau geste.
Another perspective on the Encyclopedia Galactica is that of a valuable record hoarded by a “Galactic Club” to which aspirant civilizations are only given access once they have demonstrated the requisite measure of civilizational maturity. But even if a civilization is found to measure up, it may not find the perusal of the Encyclopedia Galactica particularly interesting, as suggested by Albert Harrison:
“We hope for an Encyclopedia Galactica that will, in effect, become available on our joining the Galactic Club. However, this reference work is likely to be incomplete for two reasons: (1) extraterrestrials may not ask the same questions that we do and hence may not have ready answers for us; and (2) at least at first the encyclopedia will have little to say about life on Earth, and other societies may want information about us.” 
Harrison makes the assumption that the accounts of civilizations contained in Encyclopedia Galactica will be studied by peer civilizations, so that this is a reference work consulted by simultaneously extant civilizations—a record extended only to peer civilizations deemed worthy of the honor. This is probably unrealistic, and it points to an obvious ellipsis in peer interpretations of civilizations: the record is incomplete because it does not yet account for the decline and extinction of the peers so engaged in interpretation. The Encyclopedia Galactica can’t have much that is definitive to say about terrestrial civilization until that civilization has run its course, and we hope that we would have access to the Encyclopedia Galactica before our civilization has run its course so that we might have the benefit of the knowledge and experience contained therein. 
There is a relation between Basalla’s implication that the Encyclopedia Galactica will only consist of one-way messages between civilizations that can never engage in a dialogue, and Harrison’s concern that the Encyclopedia Galactica might say little about terrestrial civilization, and what it says may not be very helpful and have few answers for us (which implies that it does not, and cannot, include the whole scope of human civilization). No encyclopedic account, despite its pretensions to comprehensivity and completeness, can be complete until the object of knowledge is complete, and no historical object of knowledge is complete until its history is complete. Thus, as Hegel said, the owl of Minerva takes flight only with the setting of the sun. Or, in another poetic image, the ancient advice to count no man happy until he is dead presumably holds for civilizations as well: count no civilization as happy (or as existentially viable, for that matter) until that civilization is no more (in which case that civilization has ceased to be existentially viable).
2. Civilizations of the Stelliferous Era
The incompleteness of the Encyclopedia Galactica is a reflexive problem only, i.e., a problem of civilization for civilization, affecting only contemporaries and peer civilization, and this incompleteness need not compromise the final edition, as it were, which would ideally outlast the civilizations that produced it. What I want to suggest in this context is that the Encyclopedia Galactica, like the universal library, if it were brought into existence, would be finite, though enormous beyond human comprehension, and that it would consist of the total record of civilizations of the Stelliferous Era once those civilizations are all extinct and have left a complete record of themselves (or as complete as is possible) for a posterity that could no longer be considered civilizations in anything like the same sense.
In order to explain the strange claim I am making, I will employ an approach to the long term history of the universe formulated by Fred Adams and Greg Laughlin in their book The Five Ages of the Universe: Inside the Physics of Eternity. The authors adopt the convention of a cosmological decade, such that, “If ? is the time in years, then ? can be written in scientific notation in the form ? = 10? years, where ? is some number.”  This is a logarithmic time scale that makes it possible to handle the enormous spans of cosmological time from the big bang through the dissolution of the known universe. Adams and Laughlin divide the history of the universe into five major divisions: the Primordial Era (defined as -50 < ? < 5), the Stelliferous Era (6 < ? < 14), the Degenerate Era (15 < ? < 39), the Black Hole Era (40 < ? < 100), and the Dark Era (? > 101, which could also be expressed as 101 < ? < ?).
For obvious and anthropocentric reasons, we focus on the Stelliferous Era of the universe (“stelliferous” literally meaning “full of stars”), which is why I above referred to “civilizations of the Stelliferous Era,” even though the Stelliferous Era is but a small slice of time in the history of the universe. It is during the Stelliferous Era when there are brightly burning stars collected in vast galaxies that civilizations, such as we are capable of recognizing them, can exist. While the many forms of civilization that have been present on Earth can be classified under several distinct heads, and moreover this taxonomy of civilizations would need to be extended if we find other civilizations elsewhere in the universe, from the perspective of cosmology understood over the long term, however, all these civilizations may be classed as civilizations of the Stelliferous Era. Even Kardashev civilizations would all be artifacts of the Stelliferous Era; the furthest extrapolations of the Kardashev scale, beyond KI, KII, and KIII to KIV and Kn, still yield civilizations of a recognizable stelliferous type.
The familiar motif of a million year old supercivilization is still a civilization of the stelliferous era, and all (or at least most) of the problems of SETI remain—finding other technological civilizations and communicating with them within a time frame during which meaningful communication is possible. Indeed, as millions of years pass, like grains of sand through a cosmic hourglass, these problems will only be magnified. Time lag between communication would be compounded by technology lag. Entire interstellar civilizations could rise and fall, and their technologies with them, in the time it took for an EM spectrum message to travel across a single galaxy.
Even if today there is but one technological civilization in the universe, this will not necessarily be the case throughout the Stelliferous Era. Given the existence of our civilization, other civilizations may follow from it. The time before us is sufficient that many civilizations might be descendants of terrestrial civilization, lose contact with their origins (as the occlusion of the past is a common event), evolve into an entirely distinct civilizations that do not know themselves to be terrestrial in origin, and eventually rediscover each other in the cosmos in the same way that human beings discovered each other living in separate geographically isolated groups around Earth in an earlier age. In this way, many civilizations may come to populate the Stelliferous Era even if life has no origin other than that on Earth.
Moreover, in so far as the Stelliferous Era will endure for approximately another hundred trillion years until hydrogen has been exhausted and star formation ceases, many other worlds will have a chance at life and civilization. Given that our solar system is less than five billion years old, there is time enough for several solar systems like our own to form and come to maturity with life and civilization before the Stelliferous Era has run its course.
For the time being it must remain an open question whether anything that could meaningfully be called a civilization could exist after the Stelliferous Era; even if the Degenerate, Black Hole, and Dark Eras are not without intelligent beings related in some kind of society, it seems likely that this form of society must be a variety of non-civilization, such as a post-civilizational institution. That being said, we will keep an open mind on the question of post-stelliferous civilizations, even as we attempt to clarify the parameters of civilization during the Stelliferous Era.
We could characterize the civilizations of the Stelliferous Era in rough, general terms as socially and technologically organized communities of complex organic life naturally emergent from a biosphere, or the artificial successors of such organic life, in the context of successor institutions having their origins in the social and technological organization of their biological predecessors. This is an admittedly awkward characterization, and not at all definitive, but it captures some of the salient features of the civilizations we expect to find in the universe in its present state of development and for the foreseeable future.
Conditions of the universe can change radically and yet still be consistent with the existence of large scale spacefaring civilization, with these civilizations taking a form something like that outlined above. After the Milky Way and the Andromeda galaxies are combined into one enormous elliptical galaxy, and the local group is reduced to a single galaxy and some satellites, and all other galaxies, groups, and clusters have passed beyond the cosmic horizon leaving each massive galaxy isolated, a spacefaring civilization of the Stelliferous Era would still be possible. 
As long as stars shine, warming small, rocky planets in their habitable zones with atmospheres and sufficient heavy elements (which metallicity will only increase over time), civilizations emergent from organic life are possible.  After the Stelliferous Era, however, the universe will be a very different place in which the kind of civilizations that existed during the Stelliferous Era could no longer exist. There will no longer be biospheres, and therefore no longer any complex organisms such as are dependent upon biospheres heated by stars. There will no longer be suns (i.e., stars) as we know them today, and no brightly lit galaxies constituting a network of stars and planetary systems in which an interstellar civilization would be comfortably at home.
3. The End-Stelliferous Mass Extinction Event
Intelligence and civilization that had its origins during the Stelliferous Era, as these have originated on Earth (assuming that panspermia is false), may go on to perpetuate itself in the post-stelliferous universe, but if such intelligence and civilization does so, it must do so under radically changed conditions. Indeed, these conditions will be so radically changed that I would no longer call the successor institutions to civilization in the post-Stelliferous Era civilizations, though I would call the possibility of ongoing intelligence something that we could recognize and identify as intelligence. When the last stars burn out, the last of the recognizable civilizations will die with them. This we may call the upcoming End-Stelliferous mass extinction event, with the extinction being not only biological organisms depending upon solar radiation, but also the civilizations depending upon such biological organisms.
Our civilization, then, no matter how vibrant, vital, and robust, has its outer limit in time not fixed by the habitable lifespan of Earth (as was once assumed, and is still occasionally asserted ), but rather by the habitable lifespan on all stars with planetary systems in the observable universe. Our civilization, like ourselves, is mortal, though its lifespan is so potentially long that the prospect of extinction is set so far in the distant future that it cannot be contemplated with any sense of urgency. Nevertheless, we know that the potential lifespan our of civilization is finite, and certain consequences follow from this.
There is a poignant passage by Eugene Wigner I am reminded of, which describes the last days of John von Neumann: “When von Neumann realized that he was incurably ill, his logic forced him to realize also that he could cease to exist, and hence cease to have thoughts. Yet this is a conclusion the full content of which is incomprehensible to the human intellect and which, therefore, horrified him. It was heart-breaking to watch the frustration of his mind, when all hope was gone, in its struggle with the fate which appeared to him unavoidable but unacceptable.”  Much the same could be said of civilizations: at some point in the development of civilization the realization becomes unavoidable that even a civilization cannot endure indefinitely, and then that civilization must struggle with a fate that is both unavoidable and unacceptable—its own annihilation.
Yet annihilation need not mean the annihilation of all legacy. What legacy will civilizations of the Stelliferous Era leave for any future beings in the universe? One conception of legacy is to leave something of value to posterity, when “posterity” is understood to mean the continuing tradition of one’s own civilization, and even more narrowly understood to mean one’s own biological heirs. A further conception of legacy is to leave something that can be of value to another civilization, so that it survives the annihilation of one’s own civilization. Beyond this, one can posit leaving as a legacy something of value even to non-civilization, so that when the epoch of civilizations has passed, and only post-civilizational institutions remain, i.e., non-civilizations, something of the epoch of civilizations will be preserved and will enter into the permanent history of the universe.
In the context of post-stelliferous intelligence, when the civilizations of the Stelliferous Era are no longer extant, and therefore no longer adding to their historical record (and we have truly reached the end of history, i.e., humanistic history, though not of natural history), the large but finite record of civilizations of the Stelliferous Era will constitute a remarkable archive. We can imagine an Encyclopedia Galactica as a legacy of the Stelliferous Era cosmos, and one of the interesting consequences to follow from the finitude of civilization of the Stelliferous Era is that the Encyclopedia Galactica constitutes a finite record that could, in principle, be mastered by our successors. Who could these successors possibly be?
I should have titled this “Who (or what) will read the Encyclopedia Galactica?” as there will no longer be a niche in the cosmos for the sentient-intelligent species that populate the civilizations of the Stelliferous Era, and what follows them, if anything, may not be anything we can regard as a “who” but rather would appear as a “what” to us. Presumably these successors would not be what I above attributed to the civilizations of the Stelliferous Era, namely: socially and technologically organized communities of complex organic life naturally emergent from a biosphere, or the artificial successors of such organic life, in the context of successor institutions having their origins in the social and technological organization of their biological predecessors. The negation of any of the terms of this characterization of Stelliferous Era intelligence and civilization would yield a possible successor in the Degenerate Era that could supply the reader or readers of the Encyclopedia Galactica.
4. Eternal Intelligence in the Post-Stelliferous Era
For some time following the End-Stelliferous mass extinction event there will be sufficient harvestable energy in the universe for sophisticated post-Stelliferous intelligences to maintain a significant infrastructure. For example, it is possible to imagine exotic beings such as a matrioshka brain powered by a spinning black hole, powering the entire surface of a planet, or even the entire surface of a Dyson sphere dedicated to a single computational entity.  However, I would like to focus on the farthest and least accessible future, and the idea for continuing intelligence into the farthest future that was first formulated by Freeman Dyson—that of eternal intelligence.  Dyson’s approach has the great merit of being both scientific and quantitative without being reductivist, and is therefore of the greatest interest. 
Dyson in his paper on eternal intelligence set himself the task of investigating, “…the constraints set by the laws of physics upon the possible growth of life and intelligence in the universe.” He went on to add that, “It turns out that the constraints upon the spread and survival of life are much weaker than I anticipated.”  However, Dyson was also especially concerned to legitimize cosmological eschatology as a branch of study and knowledge. Dyson makes several nods to epistemic humility in urging the study of the far future: “If our analysis of the long-range future leads us to raise questions related to the ultimate meaning and purpose of life, then let us examine these questions boldly and without embarrassment. If our answers to these questions are naive and preliminary, so much the better for the continued vitality of our science.” And, “I do not expect everybody to agree with the answers. My purpose is to start people thinking seriously about the questions.” 
After an initial discussion of the physics of the universe in the far future, Dyson takes up biology and asks a fundamental question that philosophers would call the mind-body problem: “whether the existence of my consciousness depends on the actual substance of a particular set of molecules or whether it only depends on the structure of the molecules.” In J. N. Islam’s exposition of Dyson’s eternal intelligence Islam notes that if conscious life is unique to the particular molecular substance of the brain, “Life can then continue to exist only so long as warm environments exist, with liquid water and a free supply of energy to support a constant rate of metabolism. In this case, since a galaxy has only a finite supply of free energy, the duration of life is finite.”  The same can be said, mutatis mutandis, for civilization. What Islam has laid out here are the conditions of civilization during the Stelliferous Era. Not only will this condition be finite, but it will not outlast the Stelliferous Era (a condition we might call strongly finite). Civilization is but a mayfly in the life of the universe.
Dyson applied well known scaling laws that hold for life on Earth  and extrapolates this scaling principle to postulate an intelligence that can scale its temperature and energy usage to take advantage of what little usable energy remains in the post-Stelliferous Era.  Dyson suggests that life might not only slow itself down, but could also hibernate, and with these two strategies can continue indefinitely. “This example shows that it is possible for life with the strategy of hibernation to achieve simultaneously its two main objectives. First… subjective time is infinite; although the biological clocks are slowing down and running intermittently as the universe expands, subjective time goes on forever. Second… the total energy required for indefinite survival is finite.” 
Dyson noted that, “If life tries to survive for an infinite subjective time in a closed cosmology, speeding up its metabolism as the universe contracts and the background radiation temperature rises, the relations (56) and (59) still hold, but physical time t has only a finite duration… biological clocks can never speed up fast enough to squeeze an infinite subjective time into a finite universe.”  This suggests an interesting way of thinking about Dyson’s eternal intelligence. There is a philosophical thought experiment known as a supertask, which is the idea of performing some infinite action or series of actions in a finite period of time. In other words, there is at least one finite constraint upon a supertask, as there is at least one finite constraint—available energy—for some intelligence pursuing an infinitude of subjective moments of time in the indefinite future.
There are at least two ways that we can think of infinite tasks being completed with finite resources, Dyson’s proposal for eternal intelligence and the philosophical thought experiment of supertasks. The two conceptions are interestingly complementary. In Dyson’s account, intelligence adapted to the cold conditions of a future universe, thermodynamically running down to a “heat death,” both slows itself down and periodically hibernates in order to conserve what resources remain to it. One may think of Dyson’s eternal intelligence as an embodied supertask, as it seeks to demonstrate the conditions under which an infinite subjective life span can be experienced under conditions of finite constraint. This suggests the possibility of a distinction between what I will call extensive supertasks and intensive supertasks.
In the thought experiment of supertasks, an infinite task (such as thinking an infinite thought, which Dyson’s eternal intelligences would be able to do over a future infinity of the universe) is divided into a convergent series and the first portion of the task is completed in a finite period of time, the next portion is completed in half that time, and so on, until the entire infinite task is completed in only twice the time required for the first portion of the task. This I will call an intensive supertask. The completion of an infinite task or series of tasks over an infinite period of time I will call an extensive supertask, as it still involves an infinite task, but in extenso.
Given this distinction, Dyson’s eternal intelligence constitutes an attempt to demonstrate the physical possibility of extensive supertasks, and the possibility of experiencing infinite subjective time in a finite and closed universe would constitute an embodied intensive supertask. While Dyson implicitly rules out the possibility of intensive supertasks on physical grounds, here Dyson has neglected his own frequently referenced philosophical bias of optimism. If Dyson is correct that, “life is free to evolve into whatever material embodiment best suits its purposes,” (in the event that consciousness is not unique to the particular molecular makeup of organic minds), consciousness need not be tied to biological limitations and some non-biological substrate for consciousness may make it possible to realize intensive supertasks.  Our incomplete knowledge of physics ought to make us hesitant to rule out this possibility.
It is Dyson’s philosophical optimism that led him to focus on scenarios of an open universe, in which there is at least a chance for life to continue, whereas in a closed universe we would seem to condemned to a fiery end. It is this same interest in an open and incomplete universe that led Dyson to analogize between the consequence of Gödel’s incompleteness theorem for formal thought and the possibility of an open universe that is physically inexhaustible as Gödel’s mathematical universe is inexhaustible. This analogy is particularly compelling in relation to Dyson’s speculation on eternal intelligence, as the far future universe that Dyson describes may be considered a physical embodiment of a state of affairs explicitly described by Gödel:
“Turing … gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive. What Turing disregards completely is the fact that mind, in its use, is not static, but is constantly developing, i.e., that we understand abstract terms more and more precisely as we go on using them, and that more and more abstract terms enter the sphere of our understanding. There may exist systematic methods of actualizing this development, which could form part of the procedure. Therefore, although at each stage the number and precision of the abstract terms at our disposal may be finite, both (and, therefore, also Turing’s number of distinguishable states of mind) may converge toward infinity in the course of the application of the procedure.” 
Dyson’s eternal intelligence is a particular example of how the development of precision, abstraction, and distinguishable states of mind may converge toward infinity. This in turn is particularly compelling in relation to Paul Davies’ exposition of Dyson’s eternal intelligence. Davies wrote of Dyson’s conception:
“True immortality, however, demands more than the ability to process an infinite amount of information. If a being has a finite number of brain states, it can think only a finite number of different thoughts. If it were to endure forever, this would mean that the same thought would be entertained over and over again. Such an existence seems as pointless as that of a doomed species.” 
I think this objection is misconceived, partly for the reasons given by Gödel, and partly due to a conflation. I note that Davies’ formulation employs “brain states” rather than conscious states. Dyson explicitly proposes his account of eternal intelligence in terms of conscious life measured in subjective temporal increments, and for this reason we should not seek to reduce Dyson’s quantitative measure of intelligence to computation. (As I noted earlier, Dyson’s conception of mind is non-reductive.) While we may tend to think of any future non-biological substrate for consciousness as a digital computer, there is nothing inevitable about this. Just as the human mind supervenes upon a physical brain with both biochemical and electrical processes, so too a future non-biological substrate for consciousness that could perpetuate the mind into the post-Stelliferous Era could be similarly mixed in its constitution, operating both in digital and analogue modes in parallel.
5. Had we but world enough, and time
The measures of time that make EM spectrum communications between civilizations emergent in distinct solar systems unrealistic for beings like ourselves, i.e., peer species, are no longer relevant to an eternal intelligence, whose condition approximates what I recently called infinitistic cosmology. By this measure, the familiar motif of a million year old supercivilization is a mere upstart in terms of the potential cosmological scope of intelligence. What would intelligences of such temporal scope, with the potential ability to think infinite thoughts, do with their time?
Paul Davies has noted that, “…some commentators have suggested that super-advanced intellects of this sort would spend most of their time proving ever more subtle mathematical theorems.”  While some intelligences may find themselves fascinated with proving ever more complex mathematical theorems, other intelligences, antiquaries among post-stelliferous intelligences, may be no less fascinated by studying the legacy of the Stelliferous Era as communicated to the future through the Encyclopedia Galactica.
Here at last we meet the readers of the Encyclopedia Galactica. In the vast stretches of time available during the post-stelliferous universe, intelligences of these eras may not only study, analyze, and interpret the legacy of the Stelliferous Era, as an exercise in metahistorical inquiry into civilizations of the Stelliferous Era, but may also formulate ever more exacting simulations of the history of the Stelliferous Era. There is, after all, time enough to perform real time simulations of all the civilizations of the Stelliferous Era several times over, perhaps in each case changing a single variable in order to reenact the whole of history under controlled conditions. Here we come to the problems suggested by the simulation hypothesis, but to pursue these problems is an inquiry for another time.
6. Eternal Intelligence After Dyson
Several of Dyson’s formulations in this paper no longer appear to be tenable, but he can nevertheless be said to have attained his end, in that many researchers have subsequently taken up the questions he posed, and it is only due to this subsequent research that we are able to identify the points at which Dyson’s argument may not work.
Steven Frautschi took up Dyson’s idea in his paper “Entropy in an Expanding Universe.” Frautschi reaches a mixed conclusion:
“Although we have failed to find a viable scheme for preserving life based on solid structures, other forms of organization may be possible, as emphasized by Dyson. It stands as a challenge for the future to find dematerialized modes of organization (based on dust clouds or an e+ e– plasma?) capable of self-replication. If radiant energy production continues without limit, there remains hope that life capable of using it forever can be created.” 
Lawrence M. Krauss (previously mentioned in connection with the “end of cosmology” thesis and cited in note ) and Glenn D. Starkman also took up Dyson’s eternal intelligence in their paper “Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe.” Like Frautschi, their analysis casts further doubt on a truly infinite future for life in the universe:
“…a cosmological constant dominated universe is permeated by background radiation at a constant temperature… [which] is the minimum temperature at which life can function. It is then impossible to have both infinite subjective lifetime and consume a finite amount of energy. Life must end, at least in the sense of being forced to have finite integrated subjective time.” 
Indeed, Krauss and Starkman couple their argument for the finitude of life with the “end of cosmology” thesis, yielding a world in which both life must end and knowledge must be curtailed:
“If, as the current evidence suggests, we live in a cosmological constant dominated universe, the boundaries of empirical knowledge will continue to decrease with time. The universe will become noticeably less observable on a time-scale which is fathomable. Moreover, in such a universe, the days—either literal or metaphorical—are numbered for every civilization. More generally, perhaps surprisingly, we find that eternal sentient material life is implausible in any universe. The eternal expansion which Dyson found so appealing is a chimera.” 
While I concede the force of later arguments and new evidence, I am not yet prepared to entirely abandon Dyson’s eternal intelligence.
It is often said that the laws of physics “break down” in the vicinity of a singularity. A singularity is massive and exerts a strong gravitational attraction, so it should be describable in terms of general relativity, which we use to describe the largest structures in the cosmos shaped by gravity; but a singularity is also very small, perhaps even dimensionless, and so should be describable in terms of quantum theory, which we use to describe the smallest events in nature. This is a problem, because there is as yet no testable physical theory that fully integrates general relativity and quantum theory. It is a problem that is not limited to singularities.
Science has gotten very good at describing the macroscopic features of our world, and has pushed this account downward as far as the subatomic level and upward as far as galaxies, groups of galaxies, and clusters of galaxies. But our understanding of the world at the extremes—the extremely large and the extremely small in terms of space, and the extremely short-lived and extreme long-lived in terms of time—leaves much to be desired. It could even be said that our understanding of nature breaks down at the extremes of space and time.
At the furthest limits of our knowledge, at the largest scales of space and time such as we have here been considering, we have much to learn and much to discover. Because we do not yet know the large scale structure of the cosmos, we are not yet in a position to dismiss the eternal futurity of intelligence. The various theories proposed to account for dark matter and dark energy have difference consequences for the long-term, large-scale fate of our universe—and anything that might lie beyond our universe. So while cosmologists are today converging upon a consensus of an open universe (one of the conditions of Dyson’s argument for eternal intelligence), there remain many crucial questions upon which there is as yet no consensus in the scientific community.
 Quine, W. V. O., Quiddities: An Intermittently Philosophical Dictionary, Cambridge: Harvard University Press, 1987, “Universal Library,” p. 223.
 Borges, Jorge Luis, “The Library of Babel,” available in many translations and collections.
 According to Wikipedia, the idea of the Encyclopedia Galactica first appeared in Isaac Asimov’s short story “Foundation” (Astounding Science Fiction, May 1942). I first encountered the idea in Carl Sagan’s Cosmos (cf. note  below).
 Carl Sagan, Cosmos, Chapter XII, Encyclopaedia Galactica.
 Basalla, George, Civilized Life in the Universe: Scientists on Intelligent Extraterrestrials, Oxford et al: Oxford University Press, 2006, p. xi.
 Harrison, Albert A., After Contact: The Human Response to Extraterrestrial Life, New York and London: Plenum Trade, 1997, pp. 116-117.
 Granted the zoo hypothesis, advanced alien civilizations might have a more complete record of human civilization than we ourselves possess, and that would be of great interest to us, so Harrison’s item (2) may not hold, but even under these conditions Harrison’s item (1) would still be valid.
 Adams, Fred and Laughlin, Greg, The Five Ages of the Universe: Inside the Physics of Eternity, New York: The Free Press, 1999, p. xxiii. Greg Laughlin notes on his blog The Five Ages (in Cosmology in the middle-stelliferous era) that, “The discovery that the expansion of the universe is accelerating came just about the time that my book with Fred Adams, The Five Ages of the Universe, was going to press. So we were significantly out-of-date right from the start. Some of the bigger-picture details in our narrative, such as gravitationally-based computation, almost certainly won’t occur if all of the other galaxies are all accelerated out beyond our causal horizon, but all the events dealing with stars and planets are unaffected by the presence of dark energy.”
 This is the scenario described in Sherrer and Kraus’ “The end of cosmology” scenario, which two published both as a research paper (“The Return of a Static Universe and the End of Cosmology,” Lawrence M. Krauss and Robert J. Scherrer, Journal of General Relativity and Gravitation, Vol. 39, No. 10, pages 1545–1550; October 2007. www.arxiv.org/abs/0704.0221) and as a popularized account in Scientific American (“The End of Cosmology? An accelerating universe wipes out traces of its own origins,” Lawrence M. Krauss and Robert J. Scherrer, Scientific American, March 2008, pp. 46-53). Cf. note  below.
 Greg Laughlin notes on his blog The Five Ages (in Degenerate Era plate tectonics): “There are plenty of potentially habitable planets orbiting low-mass M-dwarf stars which have staggeringly long main-sequence lifetimes. The long-term habitability hitch for the planets orbiting these stars is not the loss of stellar radiation, but rather cooling of the planetary interior and the attendant shut-down of mantle convection. A cold planet like Mars doesn’t maintain a dynamo, it has no magnetic field to speak of, and its atmosphere is therefore subject to the ravages of solar coronal mass ejections. It’d really be quite nice if WIMP annihilation could keep things ticking long after the heat of formation and the heat of radioactive decay have e-folded into oblivion.”
 In a previous Centauri Dreams post, How We Get There Matters, post I cited Ward and Brownlee on civilization likely being confined exclusively to the Earth.
 Wigner, Eugene P., Symmetries and Reflections: Scientific Essays, Bloomington and London: Indiana University Press, 1967, Chapter 21, “John von Neumann,” p. 261. Of von Neumann Wigner is supposed to have said, “only he was fully awake,” and, “There are two kinds of people in the world: Johnny von Neumann and the rest of us.”
 Davies, Paul, The Eerie Silence: Renewing Our Search for Alien Intelligence, Boston and New York: Haughton Mifflin Harcourt, 2010, p. 162.
 Although Dyson himself does not use the phrase “eternal intelligence” in the paper “Time Without End,” I will adopt the convention and refer to Dyson’s idea in this way.
 That is, Dyson never says, “consciousness is nothing but x” (a formulaic instance of reductivism), but is only concerned to ask what kind of consciousness might still be possible in the far future of the universe with, as Paul Davies put it, “…resources renting to zero and time tending to infinity.” (The Last Three Minutes: Conjectures about the Ultimate Fate of the Universe, Basic Books, 1994, p. 111) Krauss and Starkman in the paper cited in note  introduce a reductive formulation as a hypothetical: “…if consciousness can be reduced to computation, life, at least life which involves more than eternal reshuffling of the same data, cannot be eternal.”
 Dyson, Freeman, Selected Papers of Freeman Dyson with Commentary, American Mathematical Society, 1996, p. 45.
 “Time Without End: Physics and Biology in an Open Universe,” Freeman J. Dyson, Reviews of Modern Physics, Vol. 51, No. 3, July 1979.
 Islam, J. N., The Ultimate Fate of the Universe, Cambridge et al.: Cambridge University Press, 1983, p. 110.
 The Santa Fe Institute has in particular of late entered into a study of scaling laws, which has been described in the recent article Scaling: The surprising mathematics of life and civilization by Geoffrey West. West’s work on the structure of cities, related to his work on scaling, has garnered significant attention, being featured in a New York Times article, A Physicist Solves the City.
 Dyson formulates what he calls the Biological Scaling Hypothesis: “If we copy a living creature, quantum state by quantum state, so that the Hamiltonian of the copy is
Hc = ? U H U?1,
where H is the Hamiltonian of the creature, U is a unitary operator, and ? is a positive scaling factor, and if the environment is similarly copied so that the temperatures of the environments of the creature and the copy are respectively T and ? T, then the copy is alive, subjectively identical to the original creature, with all its vital functions reduced in speed by the same factor ?.” This has subsequently come to be abbreviated DBSH.
 “Time Without End” Ibid. This seems outrageously counter-intuitive, but there is a geometrical parallel that can make the idea intuitively tractable by way of geometrical intuition: take a finite two dimensional manifold and cut it in half, placing the halves next to each other. Then cut half of either half and place it next to the first two pieces. Iterated infinitely, this yields infinite geometrical length from finite geometrical area. This instance is itself a supertask (cf. the discussion that follows above), but if time and energy can be treated in parallel to geometry, infinite conscious awareness could follow from finite energy resources. However, it seems likely that in some point of the halving we would pass below the physical threshold necessary to the maintenance of conscious awareness, and thought would end. Nevertheless, by this method consciousness might be perpetuated into a distant futurity in which civilization as we know today has long since ceased to be possible.
[A notebook sketch showing the supertask of constructing infinite length from finite volume]
 Ibid. (56) and (59) refer, respectively, to “the appropriate measure of time as experienced subjectively by a living creature” (as expressed by Dyson as an equation), and the energy dissipation rate of a creature or a society with a given complexity of molecular structure as involved in a single act of human awareness, expressed by Dyson in the equation m = k f Q ?2, where m is metabolism, k is Boltzmann’s constant, f is the coefficient from the previous equation, and ? is the temperature.
 Given the possibility of intensive supertasks, no limit could be placed on what consciousness might achieve in the realm of the mind, whether in a finite and closed universe or an infinite and open universe, since intensive supertasks would presumably be possible in either context. If an advanced intelligence can formulate a method for realizing extensive supertasks (i.e., if Dyson’s eternal intelligence is possible), it might set itself (as a potential extensive supertask) the aim of formulating a method to achieve intensive supertasks, in which case it may be possible for infinite subjective time to be realized in a finite universe, but only after an initial elapse of time converging on infinity.
 “Some remarks on the undecidability results” (Italics in original) in Gödel, Kurt, Collected Works, Volume II, Publications 1938-1974, New York and Oxford: Oxford University Press, 1990, p. 306. I previously wrote about this passage from Gödel in Gödel’s Lesson for Geopolitics and Addendum on Technological Unemployment.
 Davies, Paul, The Last Three Minutes: Conjectures about the Ultimate Fate of the Universe, Basic Books, 1994, p. 111. Note the resemblance between Davies’ scenario and the Nietzschean idea of the eternal recurrence of the same. For Davies, the eternal recurrence of the same is utterly pointless; for Nietzsche, accepting the eternal recurrence of the same is amor fati, the love of fate, and, in Shakespearean terms, a consummation devoutly to be wished.
 Davies, Paul, The Eerie Silence: Renewing Our Search for Alien Intelligence, Boston and New York: Houghton Mifflin Harcourt, 2010, pp. 166-167.
 “Entropy in an Expanding Universe,” Steven Frautschi, Science, New Series, Vol. 217, No. 4560 (Aug. 13, 1982), pp. 593-599.
 “Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe,” Lawrence M. Krauss and Glenn D. Starkman, Astrophys. J. 531 (2000) 22-30, arXiv:astro-ph/9902189v1. There is much more to Krauss and Starkman’s argument than I have quoted here.
 Ibid. If an intergalactic civilization is established before Krauss and Sherrer’s “end of cosmology” thesis is realized (whether or not it is impossible to converge upon cosmology’s standard model under these changed observational conditions), then the other galaxies that have disappeared beyond the cosmic horizon will have carried with them a civilization once held in common among the later separated and isolated galaxies, now lying outside the light cones of each other. Such an intergalactic civilization would represent the high point of the integration of our universe, unifying life and civilization into a grand intergalactic synthesis, after which time each representative galaxy would go its own way of necessity as it loses touch with every other galaxy. This eventuality would be obvious for ages to come—is obvious now in the very distant future—and the need to prepare for this eventuality would be foreseen for at least as long. Copies of the Encyclopedia Galactica would be distributed to other galaxies before they disappeared from sight, although these copies would, sadly, be incomplete. Thus if an eternal intelligence is possible, it would have a complete record only of its own galaxy. The Encyclopedia Galactica would not be an Encyclopedia Universalis.