Home Back

The Drake Equation Revisited

Daniel J. Castellano


1. Stars with Terrestrial Planets (R*, fp)
2. Geological Potential for Life (ne)
3. Likelihood of Actual Life (fl)
4. Appearance of Intelligent Life (fi)
5. Advanced Civilization (fc, L)
6. Evaluating the Drake Equation

For decades, Enrico Fermi’s “paradox” about the lack of evidence of extraterrestrial life in our vast and ancient universe has presented a persistent problem for those advocating the likelihood, even near certainty, that there are other intelligent species in the cosmos. Our current failure to encounter these elusive neighbors must be explained by the immense scale involved, or else some behavioral factor accounting for their reticence. Attempts to find life on other planets, intelligent or otherwise, continue undeterred, and in recent years we hear ever more frequent claims that this likelihood is greater than previously estimated. Yet such arguments only sharpen the paradox, for, if life is so probable or common, it is all the more inexplicable that we should not have already encountered advanced civilizations, or even the slightest microbial life.

Frank Drake’s famous equation allows us to subdivide the problem into various probability factors that may account for the presence or absence of intelligent life on other worlds. It is commonly expressed as follows:

N = R* × fp × ne × fl × fi × fc × L

N is the number of civilizations in the galaxy with which we might communicate. R* is the average rate of star formation per year in the galaxy. fp is the fraction of stars that have planets. ne is the average number of planets that can potentially support life, per star with planets. fl is the fraction of such planets that actually develop life at some point. fi is the fraction of planets with life that develop intelligent life. fc is the fraction of civilizations that develop technology releasing signs of their existence. L is the length of time that a civilization sends such signals into space.

To account for the evident difficulty of encountering extraterrestrial intelligence in our galaxy, or anywhere else for that matter, one or a combination of these probability factors must be astronomically low, acting as a bottleneck or “filter” on the generation of contactable life. Until recently, there were far too many unknowns in the Drake equation for us to determine where, if anywhere, the bottleneck is likely to occur. Now, however, our increasing knowledge of extrasolar planetary conditions has allowed us to eliminate several factors, leaving only a few probable explanations of the apparent solitude of the human race.

[Top of page]

1. Stars with Terrestrial Planets (R*, fp)

We can now place some hard numbers into the Drake equation, leaving little excuse for our perplexity about extraterrestrial life. The probable answers are at our disposal, if we are only willing to look. There are 2 x 1011 stars in the Milky Way galaxy, out of 1024 in the entire universe. Our galaxy has had stars in it for about 9 billion years, while the universe is 13.7 billion years old from our reference frame. The galaxy currently forms about seven stars per year, equivalent to four solar masses, while supernovae occur only 1.9 ± 1.1 times per century.[1] Obviously, the rate of formation must have been much greater in the remote past to account for the present number of stars, to give us an average of 22 stars per year over the galaxy’s lifespan.

Recent discoveries have shown that the Galaxy is abundant in stars with planets. 10% of stars in the galaxy are “sun-like” (spectral types F, G or K), and 30% of these sun-like stars have planets. 25% of stars with planets have terrestrial planets (as opposed to just gas giants or ice giants). Combining these probabilities, we find that 0.75% of stars (7.5/1000) have terrestrial planets. This gives us 14 billion stars with terrestrial planets, in agreement with recent direct estimates of 10 billion.[2]

[Top of page]

2. Geological Potential for Life (ne)

If we say that R* = 22 and fp = 0.0075, it remains to determine what fraction of terrestrial planets have the geological potential to support life. For all we know, this could be nearly as high as 1, since we have little concept of what is the range of possible forms of life, nor of life’s potential to inhabit extremely harsh environments. If we limit our discussion to life as we know it, then it is necessary for a planet to be tectonically active and capable of forming a hydrosphere in order for life to be able to originate. The first condition does not eliminate any planets, since all would be tectonically active at least in their period of formation. Water, on the other hand, is present only in some planets. Only Earth has a hydrosphere, yet Mars may have once possessed liquid water early in its geological history. Mercury and Venus have no water, giving us at best a 50% chance of hydrosphere formation, albeit based on an extremely small sample size of four planets. Still, for our purposes, an order of magnitude estimate suffices, and there is little reason to suggest that a given star with one or more terrestrial planets will have much less than a 1 in 10 chance of having a planet with liquid water at some point.

Most terrestrial planets will have the requisite diversity of chemical composition to make the building blocks of life: carbon, oxygen, hydrogen, nitrogen, and sometimes phosphorus and sulfur. The supposition of silicon-based life is unnecessary, since carbon is sufficiently ubiquitous. The more critical element is sulfur, which is necessary to most known forms of life, yet is also toxic to life when over-abundant. Thus Mars, with its high sulfur content, was unable to support life, notwithstanding the presence of water.[3]

So-called organic molecules are now known to be far more prevalent throughout the galaxy than previously thought. Further, we know that some bacteria can use sulfur instead of oxygen, and may conjecture that liquid ammonia might serve as a substitute for water. Still, these grounds for optimism about the likelihood of extraterrestrial life must be checked by two considerations: (1) a necessary condition is far from a sufficient condition; and (2) extreme conditions impose limits on the development of life. In the sensationalist media, any discovery of extra-terrestrial water or an “organic” compound is hailed as evidence that such an environment is capable of supporting life. Yet the presence of the requisite building blocks of life is but a bare minimum requirement, and does nothing to advance the thesis that these could ever be combined in a way to develop even the simplest organisms. For all we know, countless other special geological conditions might be necessary for the appearance of life to be possible.

As for the supposedly invincible adaptability of life to extreme environments, we see limits to this capacity even in our own planet. At 8 km (5 mi) below the ocean’s surface, immense pressures allow for only small swimmers, jellyfish and protists. At 10.5 km, there are no more swimmers, only jellyfish and amoebas several centimeters across. At the deepest point on earth, over 11 km deep, there is nothing but a barren wasteland. There are similar limits on temperature, as no lifeform can survive with a body temperature below -20 degrees without suspending its life functions and reviving later. No microbes except for some bacteria living in permafrost can have functions below minus 2 degrees Celsius. Larger organisms such as penguins have heat insulation enabling survival at -40 degrees C for brief periods, still well short of the temperatures of the Antarctic interior (-60 to -80 C).[4] Life does not always “find a way;” there are physical limits to the adaptability of organisms, even given geological time scales.

Our inability to assess the probability of a planet being capable of supporting life currently depends more on ignorance of biology than of geology. As long as we cannot fix the parameters within which life may develop and survive, we cannot define the geological and orbital criteria necessary for supporting life. Notwithstanding this difficulty, there is an emerging consensus that the necessary geological and chemical pre-conditions are much more abundant than previously thought, so that there should be no lack of planets in the galaxy physically capable of supporting life.

We might at least make a rough order of magnitude estimate of ne, the number of life-capable planets per star with one or more terrestrial planets. The frequency of terrestrial planets in the habitable zones of sun-like (FGK) stars with planets is (34 ± 14)% [5] This is based on extrapolation from the distribution of observed exoplanets, since habitable zone terrestrial planets are difficult to observe directly. Using the previously mentioned estimate that 25% of FGK stars with planets have at least one terrestrial planet, we find that, given an FGK star possesses one or more terrestrial planets, on average it will have 0.34/0.25 = 1.4 such planets in a habitable zone. This is somewhat less than Drake’s original conjecture of ne = 2, based on the sole data point of our solar system (counting Earth and Mars as habitable). Still, a value of 1.4 remains quite high.

Presently, there are no strong grounds for reducing this value of ne, mainly because we do not know enough about the criteria necessary for life. The probability of a planet having a hydrosphere is practically built into the habitable zone (HZ) criterion, given the newfound prevalence of water in the cosmos. HZ planets may have masses four to five times that of Earth, but we cannot on that account definitely exclude the possibility of life. On the other hand, too small a mass would preclude life, since there would be no atmosphere to prevent the first complex molecules from being destroyed by solar radiation. Additionally, the carbon dioxide partial pressure must not be so high as to cause a runaway greenhouse effect, as on Venus. Modern computations of the habitable zone range must also take into account that the HZ boundaries may shift over time. For example, the HZ of our solar system might have included Mars from 3.5 billion to 500 million years ago. A higher CO2 content would have been needed in the outer HZ, limiting the possibility of developing complex aerobic life.[6]

[Top of page]

3. Likelihood of Actual Life (fl)

Retaining our value of ne = 1.4 as an order of magnitude estimate, we can defer all other questions of habitability to the discussion of the origin of life. After all, the determination of these factors depends more on biology than on geology as such, so it is fitting that we should build them into our value of fl.

The fraction of “habitable” planets (for our purposes, HZ planets) that actually produce life is designated fl in the Drake equation. This is the most mysterious factor of all, since no one knows how life arose, and there is not even a well-defined model or theory for the origin of life. All our discoveries of extra-terrestrial “organic” material pertain only to precursors of life, that is, necessary but perhaps not sufficient conditions for life. In fact, we cannot know what the sufficient conditions are because we do not have a well-defined model of how life arises.

We only know of one planet where life actually did originate: our own. All the hype about discovering precursors—such as water and organic molecules—obscures the fact that there is evidently a vast gap between these precursors and the actual appearance of life. In fact, the more widespread these precursors prove to be, the more remarkable it becomes that life, as far as we know, only ever appeared on this one planet. This suggests that the processes leading to life—assuming they can be modeled stochastically—involve a series of highly improbable events. Corroborating the idea that fl is extremely low is the consideration that all life on earth has a common origin, so abiogenesis likely occurred but once (at least successfully), and it has not been repeated in the eons that followed.

We will set aside any attempt to quantify fl, for want of hard evidence. It may well be the case that this is the bottleneck or filter accounting for the absence of extraterrestrial intelligence.

[Top of page]

4. Appearance of Intelligent Life (fi)

Once life does arise some way, somehow, with genetic matter and biochemistry, is it a matter of inevitability that organisms should eventually—barring some planetary catastrophe—develop into intelligent beings? Once again, the incompleteness of our knowledge makes this impossible to determine. There are many conflicting hypotheses as to why or how humans developed their intelligence, but these are extremely speculative, to say the least. At any rate, they do not help us to quantify the probability that a planet with life will develop intelligent beings.

In our case, it took 550 million years after the Cambrian explosion, or 1.5 to 2 billion years after the earliest eukaryotic life, for organisms to acquire rational intelligence. We have no way of knowing if this phylogenetic path was near optimal or far from optimal, having no other worlds with which to compare. However, given the observed volume and diversity of life in all periods since the Paleozoic era, it would seem that the odds of life finding a way to attain ever increasing sophistication are good, especially as evolution seems to be biased in favor of increasing complexity. This guess is consistent with our observations so far, which are all-or-nothing: either a planet becomes rich with life, or it never develops life at all (or perhaps life fails in its early infancy).

One possible adverse factor to the development of intelligent life is the duration required. If a planet ceases to be in the habitable zone after a billion years or so, the unintelligent organisms may not be able to adapt to the new extremes, resulting in planetwide extinction before intelligent life appears. This concern is applicable to borderline HZ planets such as Mars. If we conservatively eliminate all the borderline HZ planets, we reduce the probability of developing complex, intelligent life by a factor of 0.73.[7]

Planetary cataclysms are geologically infrequent once the period of formation has been completed. When they do occur, they are not so comprehensive as to exterminate life directly. The mass extinction events on Earth have been the result of an adjustment period to dramatic climactic shifts, sometimes initiated by meteorite impact. Even the K-T event did not directly exterminate macroscopic life, but created an environment to which the great reptiles could not adapt in the millennia that followed. There were no long-term setbacks, on a geological time scale, in Earth’s evolutionary history, as each mass extinction was followed by new adaptations that opportunistically exploited the change in conditions. This says something more than the truism that life on our planet was never extinguished, giving us reason to think that planetary cataclysm is not a significant factor in offsetting the prospects of the development of advanced life. We may further guard against the charge of selection bias by noting that even our neighboring planets did not suffer impacts that could have annihilated life on Earth. The probability of such an event is low, given the fact that life arises after the period of planetary formation, and that any planet with life will have an atmosphere to diminish greatly the impact of whatever few asteroids or meteors remain.

In sum, then, there is little reason to assign a value of fi that is dramatically lower than 0.73, if we accept that intelligent life, or at least an organism physically capable of receiving the faculty of intelligence, arises from naturalistic evolution.

[Top of page]

5. Advanced Civilization (fc, L)

Given the existence of human-caliber intelligence on a planet, we might say with the benefit of hindsight that advanced technology is an eventual inevitability. However, we should note that there were many periods in human history and prehistory of stagnation and decline. Yet once man is capable of verbalization and conceptualization, it is only a matter of time before someone makes the necessary breakthroughs, if the human population can be sustained. The first conquests of man were other hominids, likely driven to extinction by being out-competed by their more intelligent cousins. Tiny australopithecines might have faced the danger of extinction by predation, but Homo sapiens, and likely even Homo erectus, had little to fear as a species except other hominids. When one creature has rational intelligence and the other does not, the advantage is as great as that of a sighted person over the blind.

Since the laws of physics are the same everywhere, and any planet that can support life will have the metals and fossil fuels necessary for technological advancement at least to an age of electronics and low orbit rocketry, it is a given that an intelligent species will eventually develop such technology, barring a freak planetary catastrophe. Mankind has made such progress in only a ten thousand year period, following a 100,000 year period of minimal progress. It is conceivable that other intelligent beings would take longer, but not by more than an order of magnitude, and certainly not by many orders, so this is not a significant factor in the Drake equation. Thus fc is close to 1, as an order of magnitude estimate.

Lastly, we need to consider the duration that a technological civilization is able to persist. During the Cold War, it was often suggested that most civilizations, or even all of them, ended in wars of self-destruction. This all-too-pat explanation of why we might not hear from extraterrestrial civilizations seems less plausible now, having seen that the Cold War lasted only a few decades, an historical eyeblink. The nuclear standoff now seems an absurd anomaly, driven in part by the pretension of the historically ill-fated Communist movement, which proved to be a deviation from the mainstream of historical progress. When nations are mature enough to act in their mutual interest, even the most irrational will acknowledge the need to avoid a war of total annihilation. It turns out that even the Communist regimes were not at all anxious for such a war, and so they were soon cooperative in bilateral arms reductions. While a global apocalypse is a possibility, it is hardly plausible that such holocausts occur with regularity, as if it were a rule of nature that creatures should use their rational will for their own total destruction.

Although we hardly appear to be an optimally rational species, we nonetheless have managed to overcome our most destructive tendencies, and now are limited only by our planet’s resources, which should last at least a century. As we turn toward renewable resources, we should be able to continue for thousands of years. If at least some races are able to establish long-term sustainability, they should be able to last millions of years, driving up the average duration of advanced civilization (L) into tens of thousands of years. If spacefaring is possible, some may even outlast the lifespan of their planets, continuing for hundreds of millions, or conceivably billions of years.

[Top of page]

6. Evaluating the Drake Equation

The product of all other factors computed so far (R*, fp, ne, fi, fc) is about 0.015. Thus, even on the conservative assumption that advanced civilizations typically last only 1000 years, there should be about 15 detectable civilizations in our galaxy. Using the more likely assumption that such civilizations last tens of thousands of years (as Drake himself supposed), there should be hundreds of detectable civilizations. If, as many futurists suppose, spacefaring is possible, there should be thousands of worlds with detectable intelligent life. Our inability to find any evidence of such life becomes increasingly perplexing as we spend more years of fruitless search, while at the same time lowering the Drake factors discussed.

The most likely explanation of the Fermi paradox is the unmeasured factor fl, the probability of a habitable planet actually developing life. Even the simplest life is far too complex for us to reverse engineer into a coherent model of development from chemical constituents. Some stage or combination of stages in the early development of life must have required a highly improbable sequence of occurrences or local conditions. This remarkable happening may have been in the origin of life, or in pre-Cambrian development, or in the mysterious Cambrian explosion. There is no lack of sun-like stars or earth-like planets, yet there is a staggering dearth of even the simplest microbial life. The simplest explanation is that life is something of a freak occurrence, even when conditions are favorable.

Assuming a modest 10,000 year average lifespan for advanced civilizations, fl would have to be about 1/1000 or less to account for our solitude in the galaxy. If we allow that spacefaring is possible, then life would have to be an extremely rare phenomenon, since a race from an earlier generation of stars ought to have colonized the galaxy by now. If we insist that the occurrence of life on a habitable planet is not astronomically improbable, we would have to accept the near certainty that long-range interstellar travel is hopelessly impossible forever. One or the other dream must die: extraterrestrial life in this galaxy or a human destiny among the stars.

Recent claims of evidence of life on other planets fail to distinguish precursors of life from actual life, and do not consider the likelihood that these precursors are widely distributed among worlds that never have had nor will have life. To insist that the galaxy must be teeming with life would force us to shift the improbability factor elsewhere, and say that most planets with life do not go beyond the bacterial stage, or at least not to intelligent life.

Today’s extraterrestrial enthusiasts remain undeterred by the galaxy’s radio silence, for they ardently desire there to be intelligent life elsewhere. Yet Fermi’s question, “Where are they?” holds more force today than ever. As we find that there are plenty of Earth-like planets, and plenty of the raw materials needed for organismal life, there is less and less excuse for the fact that no one has contacted us. After all, there should be hundreds, if not thousands of civilizations immeasurably more advanced than that of our young solar system. It is becoming glaringly obvious that life is a miracle, if not in a properly supernatural sense, at least in the colloquial sense of a wildly improbable occurrence. For all we know, the events that led to life were so freakish, that we needed at least 1013 stars in order to get so lucky, if not the full 1024 of the whole universe.

I do not presume to declare that there is no life anywhere else in the universe. Rather, life is a highly infrequent occurrence, so much so, that it is highly unlikely for two civilizations to contact each other within the same galaxy, perhaps at all. For all intents and purposes, those other civilizations might as well exist in other universes. While this is not very gratifying, as it is contrary to our conceit that some day mankind will know all that is to be known (or at least all that is of interest), it seems to best comport with the facts.

Many contemporary thinkers like to dismiss religious beliefs as wishful thinking, yet even atheists indulge in this attitude, as they continue to dream of extraterrestrials, undeterred by all the negative evidence, clinging to every circumstantial datum and confusing mere possibility with likelihood. Perhaps it is too depressing to consider that man may be alone in the universe, if not in fact then at least for all practical purposes. There will be no extraterrestrials to come to us as benevolent angels, whether to positively aid us or at least to personify the ideals of superior rationality that those who await them expect.

Science fiction of the 1950s and 60s conveyed the idea that there was no limit to human progress, and that man’s destiny would be in space. Yet hard physical reality has put a damper on manned space exploration, and those who appreciate the magnitude of the distance even to the nearest star will realize what a hopeless dream it is to communicate meaningfully, much less physically meet with other civilizations. For now, at least, our resources and attention are better spent on the civilization we know than on ones that exist only in imagination.

[Top of page]

See also: The Chimera of Life on Mars | Number of Humans in Space


[1] Diehl et al. “Radioactive 26Al from massive stars in the Galaxy,” Nature 439, 45-47 (2006).

[2] X. Bonfils et al. “The HARPS search for southern extra-solar planets XXXI. The M-dwarf sample” http://arxiv.org/abs/1111.5019 (2011).

[3] Benton Clark, “Death by Sulfur: Consequences of Ubiquitous S Before and After the Biotic Transition, for Mars and Other S-Rich Planets,” Astrobiology 8, no. 2 (April 2008): 433.

[4] There are bacteria in the South Pole snow, but these only have metabolic activity at around -15 degree C, a temperature reached briefly in the warmest months. See: Stephen G. Warren and Stephen R. Hudson. “Bacterial Activity in South Pole Snow is Questionable” Applied and Environmental Microbiology, vol. 69, no. 10 (October 2003), 6340-6341.

[5] Wesley A. Traub. “Terrestrial, Habitable-Zone Exoplanet Frequency from Kepler” http://arxiv.org/abs/1109.4682 (2011).

[6] S. Franck et al. “Planetary habitability: is Earth commonplace?” Naturwissenschaften (2001) 88:416-426.

[7] This number comes from taking the ratio of Traub’s op. cit. “narrow ” HZ planet frequencies (average of 0.27, 0.25, 0.22 = 0.246) to the “ nominal” HZ average frequency of 0.34).

Back Top

© 2012 Daniel J. Castellano. All rights reserved. http://www.arcaneknowledge.org