Stats On Extra-Terrestrial Life

From the mailbag comes this question.

Dear Professor Briggs,

Thanks for your astutely iconoclastic posts. I’m very interested on your opinion as regards the “there’s an infinite number of planets so there must be more intelligent life” meme. Disclosure: I am an Anti-Dawkins, “meme”-hating big fan of the late Stephen J. Gould, who thought the odds were greatly against anything like us on other planets, based upon the unlikelihood of so many crucial events in our evolutionary history. Thanks.

Michael Felong

Hey, me too! I also think memes are stupid, except as synonyms for “goofy ideas du jour“. As a scientific explanation for human behavior, they are at best asinine and useless and at worst a scurrilous, unjustified attack on human intelligence.

And I too enjoyed Stephen Gould’s writing and was with him all the way in his criticisms of the risible just-so stories “evolutionary psychologists” tease each other with.

But to your question. If there were an infinite number of planets, and given what we know about physics and biology as it pertains to evolution and so forth, then there would indeed be an infinite number of planets with life. Whether that life is “intelligent” is a separate question requiring the additional premise that all we (a sample of intelligent life) are is the result of “blind” forces. However, suppose that premise is true for the sake of this argument. Then given the other premises, there would be an infinite number of other planets with intelligent life, with “many” (by which I mean an infinite number) of these planets having life that looks and acts like us.

Depressing, no?

All this follows easily from simple probability calculus. Let the chance human-like beings evolve from scratch be some number, and let that number be as small as you like as long as it’s greater than zero. (It cannot be infinitesimally small given we already see us.) Then as long as we’re multiplying this small number against an infinite number, we must end up with infinity.

That means we must have an infinite number of planets that look just like ours (but are not ours) which contain beings who look us, who speak and act as we do, who are our doppelgangers in every respect, even to the point that there must exist at least one (other) plant where a being named “Felong” writes to another being named “Briggs” asking him questions about infinity.

There: An argument only a multi-worlds physicist could love. But also a demonstration that infinities are dangerous creatures not to be trifled with.

Anyway, there are not an infinite number of planets; in this universe there are not a infinite number of anything. I leave open the question whether there really are an infinite number of universes (with which no communication is possible). But inside this one, everything is finite. All is countable and limited.

This being so, it becomes crucial to nail the probability with which sentient life evolves. With an infinite number of planets, its size was irrelevant; here, it is everything. We can still say this probability is non-zero, and we can say this because we can say this. It is here that Gould’s observation that we are highly complex becomes relevant.

And we are complex; I’d say indescribably so, or at least incomprehensibly so. By which I mean that no one person can understand all that it is to be human, or can delineate the exact processes which were the causes of our evolution (an event which I do not deny). The best we can say is that there is nothing else like us; no other animal is even similar to us, especially with regards to thinking—and how that thinking relates to our ability to make tools which would make other intelligent life aware of our existence.

Since even identifying the premises which give us the probability our of evolution is difficult (or impossible), we can’t say with any certainty how many other planets with intelligent species exist. This remains true even if we could unambiguously say how many other planets there were which could support life and can support it for some identifiable length of time (for the universe is also finite in time).

The best we can do is to make the numbers up whole cloth, à la the Drake equation and its variants. This of course makes for a certain amount of fun, and for innumerable Star Trek episodes. But that’s about it.


  1. William Sears

    I believe that you have made a mathematical error, Briggs. There are different orders of infinity. The probability of planetary life might be infinitesimally small (i.e. not finite) and when multiplied by an infinite number of planets the result could be finite or even one.

    I think that you are too harsh on Dawkins and too easy on Gould. I have read most of Gould’s books and have greatly enjoyed his smooth writing style. But, I have also read the rebuttals of many of his intellectual opponents, and gradually come to the conclusion that Gould was too often full of it and addicted to an ad hominem style of attack. Dawkins has recently strayed into poorly thought out attacks on religion but his writing on evolutionary biology is still, in my mind, superior to that of Gould. Better than both is the late Ernst Mayr.

  2. Bill S

    coincidentally I just read
    Alone in the Universe by john Gribben.
    I’d say he did a decent job trashing the Drake equation.

  3. Doug M

    I always liked Fermi’s paradox — if there were intelegent life in the unverse they would have found us by now.

  4. Briggs

    Doug M,

    Yeah, but ask my uncle and he says they have found us already. Watch the skies!

  5. revGDright

    Didn’t Frank Tipler touch on some of this in The Physics of Immortality? It was one of those long stuck-on-an-airplane reads I got halfway through many years ago….

  6. Milton Hathaway

    “. . . no one person . . . can delineate . . . the causes of our evolution (an event which I do not deny)”

    I’m not sure how to interpret this statement, since I’m not used to thinking of evolution as an event. Nevertheless, I shall comment anyway.

    If you think of designing a human as an engineering problem, and Mother Nature as an analog computer, then if evolution explains humans, Mother Nature accomplished this engineering task using some sort of an optimization algorithm. Last I heard, which admittedly is years-old info, the optimization algorithm was still being only vaguely described as a combination of “natural selection”, “random mutations”. A quick look at Wikipedia yields some unfamiliar (to me) terms such as “genetic drift”, “gene flow”, “RNA interference”, “genetic hitchhiking”, etc, etc, etc. All this strikes me as just fancy words to say, basically, “and then a miracle occurs”, and the optimization algorithm converges to a human.

    My experience with optimization algorithms is that it’s very hard to define a cost function that doesn’t get hopelessly bogged down getting stuck in local minima that aren’t anywhere near an acceptable solution. And the design problems I was addressing were many, many orders of magnitude simpler than designing even the most humble creature. It’s absolutely critical to find a suitable cost function, since it doesn’t take many variables before a brute-force search would require orders of magnitude more computing effort than a universe jammed full of computers hammering away on the problem for the current age of the universe.

    My point: It appears to me that the theory of evolution presents an intractable optimization algorithm. Until I start reading about testable optimization algorithms that can produce evolution, I see very little practical difference between the theory of evolution and creation science. Both are not disprovable, and are therefore not truly science. And I’m not at all swayed by the argument that it must be one or the other. How can one possibly say that the only choices are the unfathomably complicated and the unfathomably mysterious?

  7. JH

    The universe seems to have no boundary and is infinitely big. ^_^

    All conjectures about ET life are interesting. Why people want to trash others’ ideas is beyond me… as if they have the right answer.

  8. Dr K A Rodgers

    “In the beginning was nothing which exploded”. T Pratchett (1992)

  9. ad

    And that was your first mistake Milton, thinking of designing a human as an engineering problem. There was no design, there is no optimization, there are no definable cost functions. We may well be a local minima. We certainly do not seem particularly optimal for anything. We do manage to get in a wide range of circumstances, so certainly seem adequate.

  10. Bob

    ” Why people want to trash others’ ideas is beyond me… ”

    I think that may be part of the optimization algorithm mentioned by Milton. It makes us better in the evolutionary hunger games.

    Has anybody else noticed that the History Channel has gone overboard with UFO and space alien shows?

  11. I thought it’s still unknown if this universe is finite or infinite.

    On the other hand, I suppose the past light cone of any given point must be finite.

  12. JH


    I am not sure if it’s part of the optimization algorithm Milton mentioned and if trashing others makes us better. This does remind me of an very informative post on evolution here. One of my favorite blogs. Be aware that this post could vacuum up a lot of your time if you become too curious.

  13. The biggest paradox of the all is that Enrico Fermi fervently believed in extraterrestrial life!

  14. Bob Ludwick

    Buried late in this column:

    Fred Reed provides this: “If something looks implausible, it probably is. Evolution writ large is the belief that a cloud of hydrogen will spontaneously invent extreme-ultraviolet lithography, perform Swan Lake, and write all the books in the British Museum.”

    And of course I just had to get into the act with: A. In the beginning there was absolutely nothing. At all. Then there was around 1e55 kg of stuff and a universe to put it in. 1.5e10 years and a bunch of evolving later, here we are. B. “In the beginning, God created the heavens and the earth……..” One statement represents the pinnacle of current cosmology, and plausible as all get out; the other is primitive religious superstition. You pick.

  15. Bob Ludwick

    As we stand now, Fermi’s Paradox isn’t. There could be a one to one correspondence between stars and intelligence races on planets in orbit around them, but unless they are aware of actual physics which exist for us exclusively in fantasy and science fiction, they have not visited us and will not. Ever.

  16. Mmm, one little quibble — if we were the only “intelligent” life in countably infinite planets, then the frequentist probability of intelligent life would be infinitesimal. A Bayesian, of course, would observe that the existence of one planet with intelligent life increases one’s believe that intelligent life can happen….

  17. Rob

    ” Why people want to trash others’ ideas is beyond me… ”

    A good argument for this is carried on Judith Curry’s blog where she quotes someone who says that arguing is not a way to find the truth, but to show you are better than your opponent. Sounds like a good answer – even if it is rather depressing!

    On Dawkins vs Gould I think what turned out is just this kind of argument – they agree on probably 95-99%, but they (and their supporters) got so stuck on what they disagree about that it seems as though they are complete opposites and now both sides just want to win the argument. Dawkins in particular has got crotchety and way too dogmatic as he has got older, but that doesn’t make everything he has written wrong. Stephen Gould may well have died just young enough to have missed this stage (or maybe not quite young enough, if you disagree with him), but I am quite happy to let older people have their quirks (heck, I am getting that way myself!).

    Back to the argument on alien intelligence – I think an even bigger issue is that it would take only a slightly different timing of the development of this intelligence to render us completely oblivious to each other. How long has mankind been able to even see beyond our very close neighbours? Barely the blink of an eye in terms of the age of the universe. And how will be communicating another few hundred (thousands?) of years in the future? Would we still be able to recognize ourselves from now?

  18. cb

    Eh, I do not think you are correct. If you were to accept that evolution is true, then there is probably life elsewhere:

    If evolution is true, then ‘life’ is probability-busting: consider the very wide range of living things found on this world; consider how rapidly humans came into being from old-apes (as an example).

    Evolution means probability gets busted, and complexity becomes irrelevant. Reason cannot encompass the awesomeness that is evolution… 😉

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