Exoplanets, 4 billion-year-old life, Fermi’s paradox and zero-one laws

What do exoplanets, four-billion-year-old life, Fermi’s paradox and zero-one laws of probability theory have to do with each other? Quite a bit, actually. Let us review these developments, one by one:

New exoplanet discoveries

Depiction of the seven exoplanets of the TRAPPIST-1 system. Courtesy NASA.

Depiction of the seven exoplanets of the TRAPPIST-1 system. Courtesy NASA.

On 22 February 2017, a consortium of NASA and European astronomers announced that there are not just one but seven planets that potentially could harbor life, all orbiting a yellow dwarf star named TRAPPIST-1, about 40 light-years (235 trillion miles or 378 trillion km) from earth. This is clearly a remarkable discovery, adding seven to the staggering number (over 3400) of exoplanets currently known, and, more importantly, adding seven to the list of planets (over 30) that are potential habitable homes of life as we know it.

These discoveries were made by carefully analyzing the transit of these planets in front of the host star; conveniently, the planets are in a plane that is in a direct line between the star and earth. What’s more, by careful data analysis the astronomers were even able to deduce the size and mass of these planets, confirming that all seven are roughly the size of earth. While all seven are possible harbors for life, three seem particularly plausible, namely e, f and g in the figure.

Four-billion-year-old life

Iron-rich chert, containing ancient fossils. Courtesy D. Papineau and NY Times.

Iron-rich chert, containing ancient fossils. Courtesy D. Papineau and NY Times.

In another remarkable development, on 1 March 2017 an international (U.K., U.S., Canada, Australia) team of researchers announced discovery of what appear to be primitive fossilized microorganisms that are at least 3.77 billion and possibly up to 4.28 billion years old. These were likely deposited in hydrothermal vents, which are known to be habitats for microbes and may have been the original cradles for the origin of life on earth.

Some researchers dispute these findings. But earlier studies have already confirmed the existence of life 3.5 billion years ago. So either way it is clear that life formed on earth almost “immediately” after its surface solidified, or, in other words, within a few million years (an eye-blink in cosmic time) after the earliest epoch that life possibly could have arisen.

Fermi’s paradox

If life formed so quickly here on earth, surely it has also formed on many of the estimated 100 billion other planets surrounding stars in the Milky Way. And if life has arisen on numerous other planets, surely, after several billion years of evolution, at least some of these planets are now homes to full-fledged technological civilizations, at least as advanced as ours; in fact, almost certainly they are far more advanced, since it is highly unlikely that after billions of years that they are exactly at our level. With their advanced technology, surely they have been able not only to witness the rise of life and civilization on our planet, but also to contact us or otherwise disclose their existence, deliberately or inadvertently. Yet decades of determined high-tech searches by the SETI project and other groups have come up empty-handed. WHERE IS EVERBODY?

Fermi’s paradox, as this conundrum is known, has been analyzed in great detail by many writers since 1950 when Fermi first posed it. Astronomer Frank Drake, for example, proposed his now-famous Drake Equation:

N = R* fp ne fl fi fc L

which estimates the number of technological civilizations in the galaxy. For additional information on the scientific debate, see our previous blogs (Blog A and Blog B), or books by Stephen Webb (2002), John Gribbin (2011) and Paul Davies (2011).

The bottom line is that there are no good answers. Here is a quick summary of some of the proposed explanations and common rejoinders:

  1. They are under strict orders not to disclose their existence to a civilization such as ours. Rejoinder: In numerous vast, diverse ET civilizations (or even in just one ET civilization), each spanning multiple planets and stars and very likely billions of individuals, it is hardly credible that a galactic society could impose a global ban on communication to Earth that is absolutely 100% effective. Note that once a signal has been broadcast and is on its way to Earth, there is no way to call it back, within known laws of physics.
  2. They exist, but have lost interest in research, exploration and expansion. Rejoinder: Given that Darwinian evolution strongly favors organisms that think, explore and expand, it is hardly credible that every individual in every ET civilization has lost interest in research, exploration and expansion, or that a global ban on such activities is absolutely 100% effective. What’s more, a society’s long-term existence hinges on an in-depth understanding of potential perils in its stellar environment, such as asteroids, supernovas, gamma ray bursts, neutron star mergers and potentially hostile neighbors.
  3. They exist, but have no interest in a primitive, backward society such as ours. Rejoinder: Perhaps 99.999% of a society is not interested in primitive societies such as ours — perhaps to them, we are ants. But it is hardly credible that every individual in every ET civilization has no interest. By analogy, in our society perhaps 99.999% of the public has no interest in ants. But some do. There is even a full-fledged scientific field (myrmecology) to study ants, and researchers have meticulously catalogued every known species.
  4. They are calling, but we do not yet recognize the signal. Rejoinder: While SETI still has much searching to do, it is very reasonable to assume that at least some signals are targeted to societies such as ours, in a form (e.g., light or microwaves) that could be readily recognized by a newly technological society. Again, it is hardly credible that a galactic society could enforce a global ban on communication targeted to emerging technological civilizations such as us that is absolutely 100% effective. And as noted before, once a signal is on its way to Earth it cannot be called back, within known laws of physics.

    A similar diversity argument defeats a wide range of other proposed explanations:

    • Diversity is a fundamental, inescapable law of Darwinian evolution, and even applies to cosmic evolution via the anisotropy in the cosmic microwave background.
    • Copying DNA is 99.9999% accurate, but “errors” drive evolution.
    • Highly conformist societies, organizations and firms inevitably fail.
    • All great figures of recent history were nonconformists: Albert Einstein, Martin Luther King, Susan B. Anthony, Nelson Mandela, Steve Jobs.

    Thus in a vast, diverse society, there will be exceptions to any rule: “All ET are like X” has no credibility, no matter what X is. It is ironic that while most scientists would reject any suggestion that all members of some sector of the world society (religious, political, national, regional) have some particular characteristic, yet many seem willing to hypothesize sweeping stereotypes on extraterrestrial societies.

  5. They exist, but are not aware of our existence yet — our microwave signals have only passed 80 light years distance. Rejoinder: Evidence of an emerging technological civilization on Earth has been on display for much longer:
    • Our atmosphere has contained methane, oxygen and other chemical signs of life for at least three billion years.
    • Images of Earth would have shown dinosaurs and countless other large species for at least 300 million years.
    • Images of Earth would have shown bipedal hominin creatures for at least 5 million years.
    • Images of Earth would have shown large human structures (China, Egypt, Rome) for at least 3,000 years.
    • Urban lights have been on display for at least 2,000 years.
  6. They exist, but are too far away. Rejoinder: Such arguments ignore the potential of rapidly advancing technology. For example, once a civilization is sufficiently advanced, it could send “von Neumann probes” to distant stars, which could scout out suitable planets, land, and then construct additional copies of themselves, using the latest software beamed from the home planet. In one recent analysis, researchers found that 99% of all star systems in the Milky Way could be explored in only about five million years, which is an eye-blink in the multi-billion-year age of the Milky Way [Nicholson2013]. Already, scientists are planning to send fleets of nanocraft to visit nearby stars such as Alpha Centauri [Billings2016]. And astronomers hope to soon be able to detect signatures of life on nearby exoplanets [Johnson-Groh2017].
  7. Civilizations like us invariably self-destruct. In 200 years of technological adolescence, we have not yet destroyed ourselves through a nuclear, environmental or biological catastrophe. Thus it is hardly credible that societies such as ours invariably self-destruct, without any exceptions whatsoever. In any event, within a few years human civilization will spread to the Moon, Mars and elsewhere, and then its long-term survival will be largely impervious to calamities on the home planet.
  8. Earth is a unique planet with characteristics fostering a long-lived biological regime leading to intelligent life. Rejoinder: All recent discoveries point in the opposite direction, namely that Earth-like regimes are common:
    • The universe contains at least 100 billion galaxies.
    • The Milky Way contains at least 100 billion stars.
    • Thousands of exoplanets have been discovered.
    • More than 40 exoplanets have been identified in the habitable zone — several around a single star.

    Along this line, recent work in biogenesis indicates that the origin of life was not a particularly unlikely event. This is also indicated by the fact that life arose almost immediately (over 3.8 billion years ago) after the formation of the Earth. See Origin.

  9. WE ARE ALONE, within the Milky Way galaxy if not beyond. Rejoinder: It hardly seems credible that we are unique even in the Milky Way (with 100 billion stars and planets), much less the entire universe (with 100 billion galaxies). This solution may be consistent with Occam’s razor, but it is an extreme violation of the “Copernican principle,” namely the hypothesis that there is nothing special about Earth or humanity. Many recoil at this “solution,” but what is the alternative?

Zero-one laws of probability

Those who have studied probability theory will recall various “zero-one” laws. Colloquially speaking, if an event has nonzero probability, then eventually, under independent repetitions, it certainly will occur (i.e., it will occur with probability one). Conversely, if an event has zero probability, then no matter how many independent repetitions are performed, it will never occur (i.e., it will occur with probability zero). There is no other logical probability other than zero or one.

Other specific examples of zero-one laws include the Borel-Cantelli lemmas and the Hewitt-Savage law. The first Borel-Cantelli lemma says (under appropriate conditions) that if the sum of the probabilities of a sequence of events is finite, then the probability that infinitely many of them occur is zero. The second Borel-Cantelli lemma says (again, under appropriate conditions) that if the sum of the probabilities diverges and the events are independent, then the probability that infinitely many of them occur is one.

Zero-one laws seem to be analogous to Fermi’s paradox. If, as seems reasonable, there are many alien civilizations (or even just one), each with billions of individuals (as with the human species), having arisen from Darwinian evolution and thus imbued with a drive to expand and explore, then it seems exceedingly improbable that not a single individual or group of individuals from even one of these civilizations has visited the earth, attempted to make contact, or has even merely disclosed their own existence, deliberately or inadvertently. In other words, with billions of possibilities, the probability should be unity that one or more would contact us or at least permit their existence to be disclosed to a civilization such as ours.

The other possibility is, of course, rather disquieting: For reasons we evidently cannot yet fathom, we represent the end of a long string of exceedingly unlikely events (possibilities include the origin of life, the origin of complex multicellular life, the origin of intelligent life, the avoidance of various planetary catastrophes, the maintenance of a hospitable environment over billions of years, etc.), whose probability of simultaneously occurring is virtually zero. For example, there may be some great filter (e.g., a gamma-ray burst or the like) that invariably ends societies such as ours before they advance to the technology level or venture to the stars or colonize the galaxy, and we somehow have miraculously avoided this common fate so far. Either way, we are alone — the first and only technological civilization in the Milky Way if not beyond.

So which is it, probability one or probability zero? Is intelligent life pervasive in the universe, or is humanity a highly improbable freak of nature?


What is the answer to Fermi’s paradox? The present author certainly does not know. But it is clear that the research topics behind Fermi’s paradox (exoplanets, origin of life, SETI, etc.) are among the most significant scientific questions that our species has addressed.

I, for one, hope that I live to see the day that this question is finally resolved.

[This appeared on the Math Scholar blog.]

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