Are we alone in the universe? Nick Nielsen muses on the nature of the question, for the answer seems to depend on what we mean by being ‘alone.’ Does a twin of Earth’s ecosystem though without intelligent life suffice, or do we need a true peer civilization? For that matter, are we less alone if peer civilizations are widely spaced in time and space, so that we are unlikely ever to encounter evidence of them? And what of non-peer civilizations? SETI proceeds while we ponder these matters, a search that Nick sees as a priority because of the disproportionate value of an exterrestrial signal. Like Darwin in the Galapagos, we push on, collecting data in a quest that is without end. It’s a prospect Nick finds invigorating, and so do I.
by J. N. Nielsen
One of the great questions of our time is, “Are we alone?” Even though it is, for us, an existential question that touches upon our cosmic loneliness, it is, at the same time, a scientific question, as befits our industrial-technological civilization, driven as it is by progress in scientific knowledge. Because it is a scientific question, it hinges upon empirical evidence, but this empirical evidence must be placed in a theoretical context in order to make it meaningful. (Anecdotal evidence is not going to resolve the question.) Empirical evidence provides the observational content of a theory; formal concepts provide the theoretical framework of a theory. Neither in isolation constitutes a science (with the possible exception of the formal concepts of mathematics), but a given science may place more emphasis upon the empirical or the formal aspects of a theory. I will try to show below how Fermi’s paradox can be approached primarily formally or empirically.
Clarke’s tertium non datur
There is an understandable human desire to answer a question as clear as “Are we alone?” with an equally clear yes-or-no answer, but it is not likely that this will be the case. What we discover as we explore the cosmos is likely to be unfamiliar, unprecedented, and perhaps unclassifiable. Or, at least, the unclassifiable will be part of what is found, along with that which fulfills our expectations. It will be what challenges our expectations, however, that will shape the development of our thought and force us to revise our theoretical frameworks.
The yes-or-no formulation of the question of a cosmic loneliness I have elsewhere called Arthur C. Clarke’s tertium non datur, following Clarke’s well-known line that, “Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.”  The logic of this compelling assertion seems undeniable, until one studies logic and one finds that the law of the excluded middle to which Clarke appeals (and which is also known as tertium non datur) is controversial, and that intuitionistic logics do without the law. Making the claim that Clarke makes, then, constitutes a subtle form of Platonism, and a constructivist or an anti-realist will reject this claim. Thus a formal approach to the question “Are we alone?” becomes, in part, a logical question rather than a question of empirical research.
From an empirical point of view, only a little reflection will show that the question “Are we alone?” is not likely to be satisfyingly answered in yes-or-no terms. If we find simple (single-celled) life below the surface of Mars or in the oceans of Europa, will we say that we are no longer alone in the cosmos? Apart from evidence that life can independently emerge in the universe, thus making it all the more likely that a peer civilization exists somewhere in the Milky Way, exobiological bacteria will not satisfy our desire for fellow beings with whom we can communicate as moral equals.
If we find a world of complex life, perhaps even a complex biosphere consisting of multiple diverse biomes, but no sentient, intelligent life, will we say that we are no longer alone? From a biological point of view, a twin of Earth’s ecosystem would mean that Earth is no longer alone, but that still does not rise to the level of finding conscious, communicative beings in the context of a peer civilization. I will admit without hesitation, however, that for some among us such a discovery would carry with it the feeling of cosmic companionship; the feeling of what it means to be alone in the universe is subject to individual variability, and therefore disagreement.
It seems likely to me that most human beings are only going to feel we are not cosmically isolated if we find a peer civilization, that is to say, another civilization roughly technologically equivalent to our own, being the work of biological beings who have converged upon a technology commensurate with our own, or some technology near that level. However, we are not yet prepared to say what a peer civilization is, because we cannot yet say what our own civilization is. We have no science of civilization, and therefore no way to employ scientific concepts to classify, compare, or quantify civilizations.  This does not mean that we have no idea whatsoever what civilization is, or what our civilization in particular is, only that these ideas cannot be called scientific.
The law of trichotomy for exocivilizations
Elsewhere I have discussed what I called the law of trichotomy for exocivilizations, which is the straight-forward observation that another civilization, presumably a peer civilization, must, in relation to our own civilization, appear before our civilization, during the period of our civilization, or after our civilization.  The dichotomy between being alone or not alone in the cosmos, and the trichotomy of another civilization coming before, during, or after our own civilization, are formal ideas based on conceptual distinctions. In other words, they are not ideas based on empirical evidence, and so they derive from the theoretical context employed to interpret empirical evidence.
While the law of trichotomy for exocivilizations is ideally applicable, in practice it runs into relativistic problems. Relativity means the relativity of simultaneity, so that the absolute simultaneity implied by an ideal interpretation of the law of trichotomy (as when we apply the law to real numbers) does not work if the simultaneity in question is the punctiform present . If, however, we allow a little leeway, and grant some temporal “width” to the present, we could define a broad present in which peer civilizations exist simultaneously, but this width would rapidly exceed the age of industrial-technological civilization as we attempt to expand this broadly-defined present in the galaxy (much less the universe). Thus, what we will not find are peer or near-peer civilizations existing simultaneously with our own, unless scientific discoveries force major changes in relativity theory or something like the Alcubierre drive proves to be a practicable form of interstellar transportation.
The act of traveling to the stars in order to seek out peer civilizations involves a lapse of time both on our home planet and on the homeworld of a peer civilization. The kind of temporally-distributed civilization that I described in Stepping Stones Across the Cosmos could constitute one form of temporal relations holding among mutual exocivilizations: the overlapping edges of two or more temporally-distributed civilizations may come into contact, but given that both civilizations are temporally distributed, the home world of these civilizations can never be in direction contact, and any radio communication between them might require hundreds, thousands, or millions of years—periods of time probably well beyond the longevity of our present civilization.
Using formal concepts in the absence of observation
The examples given above of Arthur C. Clarke’s tertium non datur and the law of trichotomy for exocivilizations seem to point to the limitations of formal conceptions in the face of the stubborn facts of empirical observation, but formal concepts can prove to be a powerful tool in the absence of empirical observation, when these observations require technologies that do not yet exist, or which have not been built for institutional or financial reasons.
One of the most obvious ways in which we are now limited in our ability to make empirical observations is that of imaging exoplanets. We know that this technology is possible, and in fact we could today build enormous telescopes in space, such as a radiotelescope on the far side of the moon, shielded from the EM spectrum radiation of Earth, and possibly sufficiently sensitive to detect the passive EM radiation of an early industrial-technological civilization. That we do not do so is not a matter of scientific limitations, and not even a matter of technological limitations. We have the technology now to do this, though there would be many engineering problems to be resolved. The primary reason we do not do so is lack of resources.
Because of our inability at present to see or to visit other worlds, we have no empirical data about life or civilization elsewhere in the universe. It is sometimes said that we have only a single data point for life, and scientific extrapolation from a single data point is unreliable, if not irresponsible.
While a merely formal grasp of life and civilization may seem a pale and ghostly substitute for actual empirical data, in the absence of such empirical data a formal understanding may allow us to extract from our own natural history, and the history of our civilization, not one data point but many data points. If we can take a sufficiently abstract and formal view of our own world, that is to say, if we can rise to the level of generality of our conceptions that attends only to the structure of life and civilization on Earth, we may be able to derive a continuum of historical data points from the single instance of life on Earth and the single instance of human civilization.
Credit: Wikimedia Commons.
Spatio-temporal distribution of life in the universe
Life on Earth taken on the whole constitutes a single data point, but the natural history of life on Earth reveals a continuum of data points. The temporal distribution of the natural history of life on Earth – if this is at all representative of life simpliciter – can be roughly translated into the spatial distribution of life on Earth-like planets in the universe, on the assumption that Earth-like planets are continuously in the process of formation.
In more detail:
1. The universe is about 13.7 billion years old.
2. The Milky Way galaxy may be nearly as old as the universe itself – 13.2 billion years, by one estimate , which means that, in one form or another, the Milky Way has persisted for about 96 percent of the total age of the universe.
3. Population I stars, with higher a metallicity consistent with the formation of planetary systems with small, rocky planets are as much as 10.0 billion years old , or have existed for about 73 percent of the total age of the universe – almost three-quarters of the age of the universe.
4. The Earth formed about 4.54 billion years ago, so it has been around for 33% of the age of the universe, or about a third.
5. Life is thought to have started at Earth about 4.2 to 3.8 billion years ago, so life has been around for 28 percent of the age of the universe, or more than a quarter. Life started at Earth almost as soon as Earth cooled down enough to make life possible. Although life started early, it remained merely single-celled microorganisms for almost two billion years before much more of interest happened.
6. Eukaryotic cells appeared about 2 billion years ago, for a comparative age of 15% of the age of the universe.
7. Complex multicellular life dates from about 580 million years ago (from the Cambrian explosion), so it has been around for 4 percent of the age of the universe.
8. The mammalian adaptive radiation following the extinction of dinosaurs (and thereby giving us lots of animals with fur, warm blood, binocular vision, sometimes color vision, proportionally larger brains necessary to process binocular color vision, and thus a measure of consciousness and sentience) began about 65 million years ago, and thus represents less than a half of one percent of the total age of the universe.
9. Hominids split off from other primates somewhere in the neighborhood of five to seven million years ago, and thereby began the journey that resulted in human beings, which possess a greater encephalization quotient than any other terrestrial species. This period of time represents about half of a thousandth of one percent of the age of the universe. 
10. The earliest forms of civilization emerged about 10,000 years ago, roughly simultaneously starting in the Yellow River Valley in China, the Indus River Valley, Mesopotamia, and what is now Perú (with a few other scattered locations). Industrial-technological civilization – the kind of civilization that can (potentially) build spacecraft and radiotelescopes – is a little more than 200 years old, which is too small of a fraction of one percent to bother calculating. This is the proverbial needle in the cosmic haystack.
We can recalculate these percentages specific to the age of the Earth (rather than to the age of the universe entire), so that 88 percent of the Earth’s age has included life, 44 percent has included eukaryotic cells, 13 percent has included complex multicellular life, 1.4 percent has included mammals of the post-K-Pg extinction event, 1.5 thousandths of a percent has included hominids, and a miniscule fraction of a percent of the total age of Earth has included civilization of any kind whatever.
Given a small, rocky planet in the habitable zone of its star (i.e., given an Earth twin, which recent exoplanet research suggests are fairly common), such a planet is 88 percent likely to have reached the developmental stage of rudimentary life, 44 percent likely to have reached the stage of eukaryotes, 13 percent to have progressed to something like the Cambrian explosion, and a little more than one percent may have produced animal life of a rudimentary degree of sentience and intelligence.  If we take current estimates of Earth twins of 8.8 billion in the Milky Way galaxy alone , only somewhat more than a million would have advanced to the stage corresponding to early hominids on Earth – and these million must be found within the 300 billion star systems in the galaxy.
The data points that we can extract from our own natural history leave us almost completely blind as to our future, and therefore equally blind in regard to civilizations more technologically advanced than our own. We have no experience of the collapse of industrial-technological civilization, so we have no evidence whatsoever that would speak to the longevity of such a civilization. 
Image: Stromatolites in Shark Bay, photograph taken by Paul Harrison. Is this what most habitable planets in the galaxy look like? Credit: Wikimedia Commons.
A universe of stromatolites
Of course, it is misleading to speak of taking an Earth twin at random. The universe is not random.  Like the Earth itself, it exhibits a developmental trajectory (sometimes called “galactic ecology” or “cosmological ecology”), so that any particular age of the universe is going to yield a different percentage of Earth twins among the total population of planets in the universe. Someone versed in astrophysics could give you a better number than I could estimate, and could readily identify the period in the development of the universe when Earth-like planets are likely to reach their greatest number, though we know from our own existence that we have at least passed the minimal threshold.
Despite the fact that my estimates are admittedly misleading and probably inaccurate, as a rough-and-ready approach to what we are likely to see when we have the technology to observe or to visit Earth twins, these percentages give us a little perspective. We are more likely than not to find life. Life itself seems likely to be rather common, but this is only the simplest life. We may live in a universe of stromatolites – i.e., thousands upon thousands of habitable worlds in the Milky Way alone, but inhabited only by rudimentary single-celled life . Maybe a tenth of these worlds will have seas churning with something like the equivalent of trilobites, and possibly one percent will have arrived at the stage of development where many species have relatively large brains, precise vision (something like binocular color vision), and limbs capable of manipulating their environment. In other words, possibly one percent of worlds will have produced species capable of producing civilization. The chance of finding the tiny fraction of a percent of these species that go on to create an industrial-technological civilization (and therefore could be considered a peer civilization to our terrestrial civilization) remains vanishingly small.
In a universe of stromatolites, are we alone or are we not alone? The answer is not immediately apparent, and that is why I said that the tertium non datur form of the question, “Are we alone?” is not likely to be given a satisfying answer.
Image: A caricature of Darwin collecting beetles by fellow young naturalist Albert Way. Credit: The Darwin Project. Credit: The Darwin Project.
A journey to distant worlds
From the above considerations, I consider the search for a peer civilization to be like the proverbial search for a needle in a haystack. But it is still a search that is well worth our while – as well as being worth our investment. If you are personally invested in a search for a particular needle in a haystack, you are likely to continue the search despite the apparently discouraging odds of being successful. We are, as a civilization, existentially invested in the search for a peer civilization, as a response to our cosmic loneliness. For this reason if for no other, the search for a peer civilization is likely to be pursued, if only by a small and dedicated minority.
Far from suggesting that the difficulty of a successful SETI search means that we should abandon the search, I hold that the potentially scientifically disruptive effect of a SETI search that finds an extraterrestrial signal would be so disproportionately valuable that SETI efforts should be an integral part of any astrobiological effort. The more unlikely the result, the greater would be the falsification of existing theories upon a successful result, and therefore the more we would have to learn from such a falsification. This is the process of science. A single, verifiable extraterrestrial signal would give a satisfying answer to the “Are we alone?” question, since a single counter-example is all that is needed.
Anticipating responses that I have encountered previously, I should mention that I do not find this point of view to be in the least depressing or discouraging. A universe of stromatolites, with the occasional more complex biosphere thrown into the mix, strikes me as an exciting and worthwhile object of exploration and scientific curiosity. With so many worlds to explore, it is easy to imagine the re-emergence in history of the gentleman amateur natural historian, which is how Darwin began his career, and some future Darwin collecting the extraterrestrial equivalent of beetles might well make the next major contribution to astrobiology. Darwin wrote, “…it appears to me that nothing can be more improving to a young naturalist, than a journey in distant countries.”  He might as well have written, “…nothing can be more improving to a young naturalist, than a journey to distant worlds.”
If we add to this prospect (to me a pleasant prospect) the possibility of a few extraterrestrial civilizations lurking among the stars of the Milky Way, at a pre-industrial level of development and therefore unable to engage with us until we stumble upon them directly , I cannot image a more fascinating and intriguing galaxy to explore.
 Quoted in Visions: How Science Will Revolutionize the Twenty-First Century (1999) by Michio Kaku, p. 295.
 I take these three kinds of scientific concepts – classification, comparison, and quantification – from Rudolf Carnap’s Philosophical Foundations of Physics, section 4; cf. my post The Future Science of Civilizations. We can classify, compare, and quantify energy usage, and it is this approach that gives us Kardashev civilization types; we can also classify, compare, and quantify information storage and retrieval, which gives us the metric proposed by Carl Sagan for giving a numerical value to civilization, but I take these to be reductive approaches to civilization, and therefore inadequate.
 The law of trichotomy for exocivilizations is simply a particular example of the law of trichotomy for real numbers, though applied to civilizations in time – time being a continuum that can be described by the real numbers.
 The idea of the punctiform present is that of the present moment as a durationless instant of time that is the unextended boundary between past and present. Note that the idea of the punctiform present is an idealization, like Clarke’s tertium non datur and the law of trichotomy of exocivilizations; as such it is a formal conception of time, and not an empirical claim about time. Like the distinction between pure geometry and physical geometry, we can distinguish between pure time, which is a formal idea parallel to pure geometry, and physical time.
 Cf. the Wikipedia entry on metallicity: http://en.wikipedia.org/wiki/Metallicity
 “Populations of Stars” http://www.astronomynotes.com/ismnotes/s9.htm
 I am employing the older distinction between primates and hominids. It has become commonplace in recent anthropological thought to introduce a new distinction between hominids and hominims, according to which hominids are all the great apes, including extinct species, and hominims are all human species, extinct and otherwise; This new distinction adds nothing to the older distinction. Moreover, from a purely poetic point of view, “hominim” is an unattractive word with an unattractive sound, with a series of insufficiently contrasting consonants (especially in contradistinction to “hominid”), so I prefer not to use it. I realize that this sounds eccentric, but I wanted my readers to be aware, both of the distinction and my reasons for rejecting it.
 I leave it as an exercise to the reader to reformulate my developmental account of the emergence of industrial-technological civilization on Earth into the more familiar terms of the developmental account implicit within the Drake equation.
 A recent study was widely publicized as predicting that 8.8 billion Earth-like planets are to be found in the habitable zones of sun-like stars in the Milky Way galaxy. “Prevalence of Earth-size planets orbiting Sun-like stars,” Erik A. Petigura, Andrew W. Howard, and Geoffrey W. Marcy doi: 10.1073/pnas.1319909110 (http://www.pnas.org/content/early/2013/10/31/1319909110)
 I wrote, “almost completely blind,” instead of, “completely blind,” as there obviously are predictions that can be made about the future of industrial-technological civilization, and some of these are potentially very fruitful for SETI and related efforts. More on this another time.
 The universe is neither random nor arbitrary; Earth is not random; life, intelligence and civilization are not random. Neither, however, are they planned; the order that that exhibit is not on the order of conscious construction anticipating future developments. It is one of the great weaknesses of our conceptual infrastructure that we have no (or very little) terminology and concepts to describe or explain empirical phenomena that are neither arbitrary nor teleological. We have, perhaps, the beginnings of such a conceptual infrastructure (starting with natural selection and moving on to contemporary conceptions of emergentism), but this has not yet pervasively shaped our thought, and it remains at present sufficiently counter-intuitive that we must struggle against our own cognitive biases in order to consistently and coherently think about the world without reference to teleology.
 According to Wikipedia, stromatolites are, “layered bio-chemical accretionary structures formed in shallow water by the trapping, binding and cementation of sedimentary grains by biofilms (microbial mats) of microorganisms, especially cyanobacteria. Stromatolites provide the most ancient records of life on Earth by fossil remains which date from more than 3.5 billion years ago.” I employ stromatolites merely as an example of early terrestrial life sufficiently robust to endure up to the present day; no weight should be attached to this particular example, as any number of other examples would serve equally as well. I could have said, perhaps with greater justification, that we may live in the universe of extremophiles.
 Charles Darwin, Journal of researches into the natural history and geology of the countries visited during the voyage of H.M.S. Beagle round the world, under the Command of Capt. Fitz Roy, R.N. 2d edition. London: John Murray, 1845, Chap. XXI (http://darwin-online.org.uk/content/frameset?itemID=F14&viewtype=text&pageseq=1)
 Our galaxy may host hundreds or thousands of civilizations at a stage of pre-electrification, prior to any possibility of technological communication or travel, and therefore beyond the possibility of observation until we can send a probe or visit ourselves. But keep in mind that a thousand civilizations unable to communicate by technological means, and distributed throughout the disk of the Milky Way, may as well be so many needles in a haystack.