The fascination with finding habitable planets — and perhaps someday, a planet much like Earth — drives media coverage of each new, tantalizing discovery in this direction. We have a number of candidates for habitability, but as Andrew LePage points out in this fine essay, few of these stand up to detailed examination. We’re learning more all the time about how likely worlds of a given size are to be rocky, but much more goes into the mix, as Drew explains. He also points us to several planets that do remain intriguing. LePage is Senior Project Scientist at Visidyne, Inc., and also finds time to maintain Drew ex Machina, where these issues are frequently discussed.
by Andrew LePage
The past couple of years have been eventful ones for those with an interest in habitable extrasolar planets. The media have been filled with stories about the discovery of many new extrasolar planets that have been billed as being “potentially habitable”. Unfortunately follow-up observations and new insights into the properties of planets larger than the Earth have cast doubts on some of these initial optimistic proclamations that have been largely ignored by the media and other outlets. With all the new information available, I figured it was a good time to make an objective reevaluation of the potential habitability of a number of extrasolar planets that have made the headlines in recent years.
Basic Habitability Criteria
A thorough assessment of the habitability of any extrasolar planet would require a lot of detailed data on the properties of that planet, its atmosphere, its spin state and so on. Unfortunately, at this very early stage, the only information typically available to scientists about extrasolar planets is basic orbit parameters, a rough measure of its size or mass and some important properties of its sun. Combined from theoretical extrapolations of the factors that keep the Earth habitable, the best we can hope to do at this time is to compare the known properties of extrasolar planets to our current understanding of planetary habitability to determine if an extrasolar planet is “potentially habitable”. And by “habitable”, I mean habitable in an Earth-like sense where the surface conditions allow for the existence of liquid water on the planet’s surface. While there may be other worlds that might possess environments that could support life (e.g. Mars or the tidally heated moons Europa and Enceladus), these would not be Earth-like habitable worlds of the sort being considered here.
One of the key pieces of information we have available for extrasolar planets to assess their potential habitability is their effective stellar flux (or Seff where Earth’s value is defined as 1). This can be readily calculated using information about a planet’s orbit and the luminosity of its sun. If this effective stellar flux falls within a range corresponding to the limits of a sun’s habitable zone (HZ), this planet has met one of the basic criteria for potential habitability.
One of the more better known definitions for the limits of the habitable zone as defined by the work of James Kasting (Pennsylvania State University) starting over two decades ago is based on an extrapolation of our knowledge of the processes that have kept our own planet habitable over the last several billion years despite a 30% increase in the Sun’s luminosity. The latest refinements of this work by Ravi Kopparapu (Pennsylvania State University) and his collaborators define the inner limit of the HZ to correspond to the Seff where a moist runaway greenhouse effect sets in. At higher effective stellar flux values, skyrocketing surface temperatures and the loss of a planet’s allotment of water in a geologically brief period of time will result. For an Earth-size planet orbiting a Sun-like star, this limit corresponds to an Seff of about 1.11. The Seff corresponding to this inner limit of the HZ would be slightly higher for planets more massive than the Earth and slightly lower for stars cooler than the Sun.
There have been models proposed over the past decade and more with higher effective stellar flux values for the inner limit of the HZ in cases of synchronous rotation (which would be common for planets orbiting in the HZs of red dwarfs) and a range of other special circumstances. Such definitions have been attractive to some hoping to maximize the chances that a new find might be considered to be habitable. However, these sometimes involve extreme extrapolations from conditions here on Earth or contrived special circumstance. In general, these definitions require more study and some reliable empirical observations to be on a firmer theoretical footing like the work by Kopparapu et al.. In a recent paper by Kasting and Kopparapu et al., it is argued that while there is certainly genuine uncertainty on the precise inner limit of the HZ as a result of limitations of the simple models used to date, some of the most optimistic inner limit definitions involve scenarios that are physically unrealistic. As result, I personally tend to favor the more conservative definition of the inner limits of the HZ.
The outer limit of the HZ, as defined by Kopparapu et al., corresponds to the maximum greenhouse limit beyond which a CO2-dominated greenhouse is incapable of maintaining a planet’s surface temperature. The latest work suggests an Seff value of about 0.36 for a Sun-like star with cooler stars having slightly lower values. As with the inner limit of the HZ, there are some slightly more optimistic definitions of the outer edge of the HZ such as the early-Mars scenario or evoking some sort of super-greenhouse where gases other than just CO2 contribute to warming a planet. But these more optimistic definitions do not change the Seff for the outer limit of the HZ significantly.
Another important parameter we have available today to gauge the potential habitability of an extrasolar planet is its mass (or MP) derived from precision radial velocity measurements or its radius (or RP) calculated from observations of planetary transits. In the case of the radial velocity measurements, we actually only know the planet’s MPsini value where i is the inclination of the orbit with respect to our line of sight. Since the inclination can not be determined directly from radial velocity measurements alone, we can only know the planet’s minimum mass or the probability that the actual mass is in some range of interest. By definition, the actual mass of a planet with an unconstrained orbit inclination is most likely larger than this minimum mass – in some case it can be much larger.
A series of analyses of Kepler data and follow-up observations published over the last year have shown that there are limits on how large a rocky planet can become before it starts to possess increasingly large amounts of water, hydrogen and helium as well as other volatiles making the planet a Neptune-like world with no real prospect of being habitable. Work performed by Leslie Rogers (a Hubble Fellow at the California Institute of Technology) has shown that planets with radii greater than no more than 1.6 times that of the Earth (or RE) are most likely mini-Neptunes. This and other recent work suggests that this transition corresponds to planets with masses greater than about 4 to 6 times that of the Earth (or ME). As a result, planets larger or more massive than these empirically-derived thresholds are unlikely to be rocky planets never mind habitable. On the other hand, recent work submitted for publication by a team led by Courtney Dressing (Harvard-Smithsonian Center for Astrophysics) strongly suggests that worlds smaller than this threshold will usually have an Earth-like composition. For a more thorough discussion of this work, see The Composition of Super-Earths and my earlier Centauri Dreams post The Transition from Rocky to Non-Rocky Planets.
Image: This diagram illustrates how the boundaries of the HZ as defined in the work of Kopparapu et al. vary as a function of star temperature and planet mass. Several potentially habitable extra solar planets are included. Credit: Chester Harman/PHL/NASA/JPL.
With these basic criteria available, it is possible to start to gauge the potential habitability of an extrasolar planet. For this review, I wanted to use a well-regarded catalog of potentially habitable planets. The University of Puerto Rico at Arecibo Planetary Habitability Laboratory maintains a web site which currently lists 28 extrasolar planets in 23 systems in their Habitable Exoplanets Catalog along with many more currently unconfirmed planets that will not be considered here. The reviews that follow use this list of confirmed extrasolar planets and the data it contains except where noted.
EPIC 201367065d: RP=1.5 RE, Seff=1.51
This extrasolar planet is among the first new worlds found during Kepler’s extended “K2” mission with its discovery just announced by Crossfield et al. in a paper submitted for publication. As I write this, it has yet to make it into the “Habitable Exoplanet Catalog” but I am including it here because it is bound to be added shortly since it seems to have properties similar to other worlds already in the catalog.
With a radius of 1.5 RE, this EPIC 201367065d is just below the threshold dividing rocky and Neptune-like planets making it more likely to have an Earth-like composition. Unfortunately, its high effect stellar flux places it well beyond the inner boundary of the HZ as it is more conservatively defined for a red dwarf star. But given the uncertainties in its properties, I estimate that there is still about a one in eight chance of it actually orbiting inside even the conservatively defined HZ. While I consider EPIC 201367065d to be a poor candidate for being potentially habitable at this time, its sun is relatively nearby and bright making it a good candidate for follow up observations that can provide some hard data about the properties of worlds like this.
GJ 163c: MPsini=7.3 ME, Seff=1.40
GJ 163c was discovered in 2012 using precision radial velocity measurements. As a result, we only know that its minimum mass is 7.3 ME. Given that this value is already exceeds the 6 ME threshold that seems to divide large rocky planets from mini-Neptunes and that this planet’s actual mass is probably higher still, it is unlikely that GJ 163c is a rocky planet. Combined with its high effective stellar flux that is larger than the more conservative definitions of the HZ, it seems improbable that GJ 163c is a potentially habitable, Earth-like world.
GJ 180b: MPsini=8.3 ME, Seff=1.23
GJ 180c: MPsini=6.4 ME, Seff=0.79
GJ 180 is a system thought by some to contain a pair of potentially habitable planets. While GJ 180c appears to orbit comfortably inside the inner part of the HZ of this system, GJ 180b seems to orbit just a little too close to be considered habitable using the more conservative definition of the HZ. Unfortunately, with measured minimum masses of 8.3 ME and 6.4 ME for GJ 180b and c, respectively, it is highly unlikely that either of these planets have rocky compositions. Given that these planets’ actual masses are probably much higher than this, it is more likely they are mini-Neptunes or larger with little prospect of being potentially habitable.
GJ 442b: MPsini=9.9 ME, Seff=0.70
GJ 442b is yet another example of a planet that seems to orbit inside the HZ of its sun no matter how it is defined but it is too massive to likely be a rocky planet. Radial velocity measurements indicate that this planet has a minimum mass of 9.9 ME which makes it much more likely to be a mini-Neptune. In fact, given the uncertainty in the inclination of its orbit to our line of sight, there are better than even odds that GJ 442b is Neptune-size or even larger. As a result, GJ 442b is highly unlikely to be a potentially habitable planet.
GJ 667Cc: MPsini=3.8 ME, Seff=0.88
GJ 667Ce: MPsini=2.7 ME, Seff=0.30
GJ 667Cf: MPsini=2.7 ME, Seff=0.56
GJ 667C has been in the news a lot recently because of the belief that it contains as many as seven planets discovered using precision radial velocity measurements. Initial assessments hinted that three of the planets in this packed system might be potentially habitable – GJ 667Cc, e and f. Unfortunately, follow-up work performed on this promising planetary system now strongly suggests that it does not contain any potentially habitable planets at all.
A series of independent analyses of the radial velocity data for GJ 667C culminating in the work by Paul Robertson and Suvrath Mahadevan (Pennsylvania State University) now indicates that the radial velocity variations originally interpreted as being the result of as many as seven planets are in fact caused by only two planets. It now seems likely that surface activity on GJ 667C modulated by its 105-day rotation period is responsible for mimicking the subtle radial velocity signature of the other supposed planets including the potentially habitable GJ 667Ce and f. A similar situation was encountered last year with the habitable planets of GJ 581 which these same investigators also found to be the result of stellar activity masquerading as planets. While more follow-up work is required, it now seems likely that GJ 667C and f do not exist.
While the existence of GJ 667Cc seems to be secure, unfortunately its potential habitability appears to have been overstated. Based on its Seff value, GJ 667Cc seems to be safely inside the inner portions of this star’s HZ. However, since this planet was discovered using radial velocity measurements, we currently only know that its minimum mass is about 4.1 ME based on the work by Robertson and Mahadevan. Given the currently unconstrained inclination of its orbit to our line of sight, there is only a one in three chance that this world has a mass less than the 6 ME threshold dividing predominantly rocky worlds from mini-Neptunes. It is much more probable that GJ 667Cc is a mini-Neptune with little chance of being potentially habitable.
If GJ 667Cc beats the odds and is a rocky planet after all, it is still unlikely to be a promising habitable planet candidate. Investigation of the spin state of GJ 667Cc performed by Valeri Makarov and Ciprian Berghea (US Naval Observatory) strongly suggests that this world is experiencing excessive tidal heating due to the high eccentricity of its small orbit around its primary. Makarov and Berghea estimate that if GJ 667Cc has an Earth-like composition, tidal heating would generate about 300 times the heat flow as the Earth experiences melting its mantle and crust in the process. Given the two most likely possibilities, it seems highly improbable that GJ 667Cc is a potentially habitable world. For a more detailed discussion of this system, see Habitable Planet Reality Check: GJ 667C.
GJ 682c: MPsini=8.7 ME, Seff=0.37
Based on an analysis of the radial velocity of GJ 682, it appears that GJ 682c orbits near the outer limits of the HZ of this system. But once again, with a minimum mass of 8.7 ME and an actual mass that is probably much higher, it is highly unlikely that GJ 682c is a rocky planet. Given an unconstrained orbit inclination, it has about an even chance of being Neptune-size or larger. It is therefore very unlikely that GJ 682c is potentially habitable.
GJ 832c: MPsini=5.4 ME, Seff=1.00
In 2014, a team led by Robert Wittenmyer (UNSW Australia) announced the discovery of a planet orbiting GJ 832 using precision radial velocity measurements. Given the properties of this world, Wittenmyer et al. specifically stated in their discovery paper that they did not believe that their find was a potentially habitable planet and it was more likely to be a uninhabitable super-Venus instead. This candid assessment was ignored by some who argued that GJ 832c is among the most Earth-like planets known. The effective stellar flux of GJ 832c places this world just inside the inner edge of this system’s conservatively defined HZ. Even if we were to expand the HZ limits based on more optimistic definitions of the HZ, the 5.4 ME minimum mass of GJ 832c gives it a 90% probability of exceeding the 6 ME mass threshold dividing Earth-like and Neptune-like planets. As a result, it is improbable that GJ 832c is a rocky planet never mind a potentially habitable one. For a more detailed discussion of this planet, see GJ 832c: Habitable Super-Earth or Super Venus?.
GJ 3293b: MPsini=8.6 ME, Seff=0.60
GJ 3293b is yet another example of a world that seems to orbit comfortably inside the HZ but has almost no chance of being habitable due to its excessive mass. Based on precision radial velocity measurements, GJ 3293b has a minimum mass of 8.6 ME which already exceeds the 6 ME mass threshold where it is more likely that a planet is a mini-Neptune instead of a rocky planet. With an unconstrained orbit inclination, there are about even odds that this planet is actually Neptune-size or larger. As a result, it is highly improbable that GJ 3293b is potentially habitable.
HD 40307g: MPsini=7.1 ME, Seff=0.68
The situation with HD 40307g is comparable to that of GJ 442b, GJ 682c and GJ 3293b: the planet seems to orbit comfortably inside the HZ but it is most likely a mini-Neptune or larger planet. With a minimum mass of 7.1 ME derived from radial velocity measurements and an unconstrained inclination, it is unlikely that HD 40307g is a potentially habitable planet.
Kapteyn b: MPsini=4.8 ME, Seff=0.43
Kapteyn’s Star is an ancient, nearby red sub-dwarf only 12.8 light years away. Last year’s announcement of the discovery of two planets orbiting this star promises important insights into the planet formation process during the earliest history of our galaxy. One of those two planets, Kapteyn b, was widely claimed to be the oldest potentially habitable planet yet discovered. Looking at this world’s effective stellar flux, it seems to be comfortably inside the outer part of this star’s HZ. But since it was discovered using precision radial velocity measurements, we only have a minimum mass value of 4.8 ME. With an unconstrained orbit inclination, there is an 80% probability that its actual mass exceeds 6 ME making it more likely to be a mini-Neptune rather than a rocky planet. As a result, it is unlikely that Kapteyn b is a potentially habitable planet. For a more detailed discussion of this planet, see Habitable Planet Reality Check: Kapteyn b.
Kepler 22b: RP=2.4 RE, Seff=1.11
Like so many planets found using radial velocity measurements, there have also been worlds discovered by NASA’s Kepler mission that were initially considered potentially habitable by some but turn out to be too large after more detailed analyses of planet properties have become available. The effective stellar flux of Kepler 22b places it just beyond the inner edge of a conservatively defined HZ. But with a radius measured to be 2.4 RE, which easily exceeds the 1.6 RE threshold where planets are no longer likely to be rocky, it is very unlikely that Kepler 22b is a potentially habitable planet and more likely to be a volatile-rich mini-Neptune instead.
Kepler 61b: RP=2.2 RE, Seff=1.27
Kepler 61b is in a similar situation as Kepler 22b: its effective stellar flux appears to be a bit too high to be considered inside the conservative definition of the HZ and its large radius of 2.2 RE makes it unlikely to be a rocky planet. As with Kepler 22b, Kepler 61b is very unlikely to be a potentially habitable planet and more likely to be a mini-Neptune.
Kepler 62e: RP=1.6 RE, Seff=1.10
Kepler 62f: RP=1.4 RE, Seff=0.39
After reading one disappointing review after another so far, the reader might begin to think there are no potentially habitable planets currently known. Fortunately, there is the multi-planet system of Kepler 62. Kepler 62e appears to orbit just beyond the inner edge of this star’s HZ and with a radius of 1.6 RE, it has about even odds of actually being a rocky planet. Taking into account the uncertainty of the actual inner limit of the HZ, it seems that Kepler 62e is a fair candidate for being a potentially habitable planet.
The situation for Kepler 62f appears even better. With a radius of 1.4 RE, which is comfortably below the 1.6 RE dividing line between Earth-like and Neptune-like planets, there is a good chance that Kepler 62f is a rocky planet. Combined with its effective stellar flux that places it in the outer part of even a conservatively defined HZ, it appears that Kepler 62f is among the better potentially habitable planet candidates currently known.
Kepler 174d: RP=2.2 RE, Seff=0.43
Like so many other planets initially considered to be potentially habitable by some, Kepler 174d seems to orbit well inside the HZ but it appears to be too large to be a rocky planet. With a radius of 2.2 RE, it is much more likely that Kepler 174d is a volatile-rich mini-Neptune with poor prospects of being potentially habitable.
Kepler 186f: RP=1.2 RE, Seff=0.29
When its discovery was announced last year, Kepler 186f generated much attention because of its Earth-like size and its orbit inside the HZ of its red dwarf sun. Recently published refinements of its properties by a team led by Guillermo Torres (Harvard-Smithsonian Center for Astrophysics) in the same paper where they just announced the discovery of eight new habitable zone planets has only reinforced the case for the potential habitability of Kepler 186f. Its effective stellar flux places it towards the outer edge of the HZ of this system. Its radius of 1.2 RE, which is comfortably below the 1.6 RE limit that divides Earth-like planets from Neptune-like planets, makes it probable that it is a rocky planet. So long as no major impediments to habitability of planets orbiting red dwarfs are revealed, Kepler 186f is one of the best habitable planet candidates currently known. For a more detailed discussion of this world, see Habitable Planet Reality Check: Kepler 186f.
Kepler 283c: RP=1.8 RE, Seff=0.90
Kepler 283c is one of those planets that is frustratingly close to being potentially habitable but just doesn’t quite make it. The effective stellar flux of Kepler 283c places it near the inner edge of its sun’s HZ. But with a radius measured to be 1.8 RE, it is more likely to have a volatile-rich instead of rocky composition. Kepler 283c only has a fair chance at being potentially habitable.
Kepler 296e: RP=1.5 RE, Seff=1.22
Kepler 296f: RP=1.8 RE, Seff=0.34
When the discovery of planets in this system was first announced in 2014, Kepler 296f was considered by some to be a good habitable planet candidate. But follow-up observations of this star soon revealed that instead of it being a single star, it consisted of a pair of red dwarf stars instead that appear blended together as viewed by Kepler. As a result, the properties of its planets which had been derived assuming a single star were no longer valid. Additional work by Torres et al. has been able to resolve this issue and they derived properties that would make both Kepler 296f and e habitable planet candidates.
A closer look at this work, however, casts some doubt on this assessment. With a radius of 1.5 RE, which is smaller than the 1.6 RE size limit for rocky planets, Torres et al. calculated that there is 50.7% probability of Kepler 296e being a rocky planet. While they calculated a high probability that Kepler 296e orbits inside the HZ, they were using a very optimistic definition of the HZ that placed the inner edge of the HZ where the effective stellar flux was 50% higher than Venus experiences today. Given the uncertainties in this world’s derived orbital properties, I estimate that there is only one chance in four that it actually orbits inside the HZ as it is more conservatively defined. Unless the predictions of models of a more optimistic definition of the inner limit of the HZ are borne out, it seems more likely that Kepler 296e is a larger but cooler version of Venus and is only a fair habitable planet candidate.
The situation for the more distantly orbiting Kepler 296f is a bit more promising in some ways. The effective stellar flux for this planet places it comfortably inside the outer part of its sun’s HZ. However, with a radius of 1.8 RE, Torres et al. estimate that there is only a 30.6% probability that Kepler 296f is a rocky world. Because of this, Kepler 296f is only a fair potentially habitable planet candidate
Kepler 298d: RP=2.5 RE, Seff=1.29
This world’s high effective stellar flux places it well outside the conservative definition of the HZ. But even if more optimistic limits prove to be true, its large radius of 2.5 RE makes it much more likely that it is a mini-Neptune. As a result, Kepler 298d has a very low probability of being a potentially habitable planet.
Kepler 438b: RP=1.1 RE, Seff=1.38
Kepler 438b is one of the eight extrasolar planets recently announced by Torres et al. as orbiting inside the HZ. While they estimate that there is a very high 69.6% probability of being a rocky planet owing to its small 1.1 RE radius, their assessment of the potential habitability of this world is based on the very optimistic definition of the HZ they adopted in their paper that would comfortably include Venus in our own solar system (which is most definitely not a habitable planet). Assuming a more conservative definition of the HZ limits and taking into account the large uncertainties in its properties, I roughly estimate that there is only one chance in four that Kepler 438b actually orbits inside the HZ. Given this, it appears that Kepler 438b is a poor candidate for being potentially habitable and is more likely to be a slightly larger and cooler version of Venus than an Earth-like planet.
Kepler 440b: RP=1.9 RE, Seff=1.43
Another one of the new discoveries announced by Torres et al. is Kepler 440b. Given its rather large radius of 1.9 RE, Torres et al. estimate that there is only a 29.8% probability that Kepler 440b is a rocky planet making it more likely to be a mini-Neptune instead. While they calculate a high probability that this planet orbits inside the optimistic definition of the HZ they used, I estimate that there is less than even odds of this planet orbiting inside the HZ as it is more conservatively defined. Taken together, it appears that Kepler 440b is a poor candidate for being a potentially habitable planet.
Kepler 442b: RP=1.3 RE, Seff=0.70
By far, the most promising candidate for a potentially habitable planet recently announced by Torres et al. is Kepler 442b. The sun of this system, Kepler 442, is a relatively young K-dwarf star about 1,100 light years away with 61% of the mass of the Sun and 12% of its luminosity. With a radius of 1.3 RE, Kepler 442b is estimated by Torres et al. to have a 60.7% probability of being a rocky planet. Even assuming a conservative definition for the outer limit of the HZ, this world seems to have a very high probability of orbiting comfortably inside this zone. When all the current observations are considered, it appears that Kepler 442b is one of the best candidates found to date for being a potentially habitable planet.
Kepler 443b: RP=2.3 RE, Seff=0.89
Kepler 443b was the last of the eight newly confirmed planets announced by Torres et al. that appear in the “Habitable Exoplanet Catalog”. While its effective stellar flux is certainly in a range that places it inside the HZ with a high probability no matter how it is defined, it seems to be too large to be potentially habitable. With a radius of 2.3 RE, Torres et al. calculate that there is only a 4.9% probability of Kepler 443b being a rocky planet. Since it is much more probable to be a mini-Neptune, Kepler 443b is unlikely to be a potentially habitable planet.
KOI 4427b: RP=1.8 RE, Seff=0.24
One of the planets studied by Torres et al. that still remains unconfirmed is a planet currently designated KOI 4427.01. Although its detection has a 99.16% confidence level, it did not quite meet the 3-sigma detection threshold set by Torres et al. but it still seems significant enough to likely be a bona fide planet. Based on the radius of 1.8 RE, Torres et al. estimate that there is only a 27.3% probability that this is a rocky world. Combined with less than even odds of this world orbiting inside the conservatively defined outer limit of the HZ, KOI 4427b appears to be a poor candidate for being a potentially habitable planet.
Tau Ceti e: MPsini=4.3 ME, Seff=1.51
The Sun-like star Tau Ceti has generated much interest over the decades among scientists looking for habitable planets. Unfortunately its relatively high level of activity has complicated efforts to find verifiable planets orbiting this star using precision radial velocity measurements. Despite the outstanding issues, one of the purported planets of Tau Ceti announced two year ago has been claimed by some to be potentially habitable. Tau Ceti e was discovered using precision radial velocity measurements but remains unconfirmed. Ignoring this issue for the moment, the analysis of the available data yields a minimum mass of 4.3 ME which appears to be near the lower end of the mass range where rocky planets transition to volatile-rich planets. Factoring in the unconstrained inclination of this planet’s orbit, there is a two in three chance that its mass exceeds the 6 ME threshold mass making it more likely to be a mini-Neptune. Its effective stellar flux also exceeds by a fair margin that for the conservative definition of the HZ. Taking all this information together, it seems that Tau Ceti e is more likely to be a hot mini-Neptune than a potentially habitable planet. These facts along with the questionable existence of this world make Tau Ceti e to be a very poor habitable planet candidate.
Unfortunately, an objective assessment of the known properties of the planets in the Planetary Habitability Laboratory’s “Habitable Exoplanets Catalog” casts grave doubts about the potential habitability of the majority of the planets on this list. Most of them are likely too large to be habitable Earth-like planets and are much more likely to be mini-Neptunes or even larger volatile-rich planets with very poor prospects of being habitable. In all fairness, this fact has only just become appreciated by the scientific community over this past year based on analyses like those conducted by Rogers. As a result of this, Torres et al. actually calculated the probability that their new finds were rocky planets and gave refreshingly honest assessments of their finds’ prospects in their recent discovery paper. Hopefully we will see more of this welcome practice in the future.
In three cases, it appears that the potentially habitable planets do not exist. Especially in the case of GJ 667C, the radial velocity variations that had been interpreted as being the result of orbiting planets now appear to be “false positives” caused by previously unrecognized and very subtle forms of stellar activity modulated by the star’s rotation. The unconfirmed planets believed to orbit Tau Ceti are also strongly suspected to be false positives at this time.
Among the 28 planets in the “Habitable Exoplanets Catalog”, only three appear to be genuinely good candidates for being potentially habitable: Kepler 62f, Kepler 186f and Kepler 442b. Fair candidates worthy of further consideration include Kepler 62e, Kepler 283e, Kepler 296e and f as well as Kepler 438b. In the case of these latter five worlds, they might be too large or too hot to be potentially habitable. Further observations and theoretical work on planetary habitability should help resolve their status.
Unfortunately, all of these promising candidates for potentially habitable planets orbit dim K- and M-dwarf stars that present possible issues with their habitability such as synchronous rotation, stellar flare activity and high luminosity early in their diminutive suns’ lives to name just a few. But all hope for finding better candidates is certainly not lost. Besides the likely prospects of finding more habitable planet candidates orbiting dimmer stars, the continued analysis of Kepler data is sure to uncover more Earth-like planets orbiting in the HZ of Sun-like stars as well. In addition to the recently announced discovery by Torres et al. of eight planet HZ planets, there was the much quieter announcement of two Kepler planet candidates found in the HZ of two Sun-like stars (see Earth Twins on the Horizon?). While these and similar finds still require follow-up observations to confirm their planetary nature, they provide a foretaste of the bona fide Earth-like habitable planets yet to come.
Ian J.M. Crossfield et al., “A Nearby M Star with Three Transiting Super-Earths Discovered by K2”, arVix 1501.03798 (submitted for publication in The Astrophysical Journal), January 15, 2015 (preprint).
Courtney D. Dressing et al., “The Mass of Kepler-93b and the Composition of Terrestrial Planets”, arVix 1412.8687 (accepted for publication in The Astrophysical Journal), December 30, 2014 (preprint).
James F. Kasting, Ravi K. Kopparapu et al., “Remote life-detection criteria, habitable zone boundaries, and the frequency of Earth-like planets around M and late K stars”, Proceedings of the National Academy of Sciences, Vol. 111, No. 35, pp. 12641-12646, September 2, 2014 (full text).
R. K. Kopparapu et al., “Habitable zones around main-sequence stars: new estimates”, The Astrophysical Journal, Vol. 765, No. 2, Article ID. 131, March 10, 2013 (full text).
Ravi Kumar Kopparapu et al., “Habitable zones around main-sequence stars: dependence on planetary mass”, The Astrophysical Journal Letters, Vol. 787, No. 2, Article ID. L29, June 1, 2014 (preprint).
Valeri V. Makarov and Ciprian Berghea, “Dynamical evolution and spin-orbit resonances of potentially habitable exoplanet. The Case of GJ 667C”, The Astrophysical Journal, Vol. 780, No. 2, article id. 124, January 2014 (preprint).
Paul Robertson and Suvrath Mahadevan, “Disentangling Planets and Stellar Activity for Gliese 667C”, The Astrophysical Journal Letters, Vol. 793, Article ID. L24, October 1, 2014 (preprint).
Leslie A. Rogers, “Most 1.6 Earth-Radius Planets are not Rocky”, arVix 1407.4457 (submitted to The Astrophysical Journal), July 16, 2014 (preprint).
Guillermo Torres et al., “Validation of Twelve Small Kepler Transiting Planets in the Habitable Zone”, arVix 1501.01101 (submitted to The Astrophysical Journal), January 6, 2015 (preprint).
Robert A. Wittenmyer et al., “GJ 832c: A super-Earth in the habitable zone”, The Astrophysical Journal, Vol. 791, No. 2, Article id. 114, August 2014 (preprint).
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.