Simple Probabilities

I’ve written before about Drake’s Equation and the Fermi Paradox. The former suggests the possibility of lots of alien life. The latter asks okay, so where the heck are they? Given that the universe just started, it’s possible we’re simply the first. Maybe the crowd comes later. (Maybe we create the crowd!)

Recently, one of my favorite YouTube channels, PBS Space Time, began a series of videos about this. The first one (see below) talks about the Rare Earth Hypothesis, a topic that has long fascinated me.

The synchronicity in this is that I’d just had a thought about basic probability and how it applies to our being here…

My thought boils down to simply this:

P n

Where P is a probability from 0.0 to 1.0 (inclusive), and n is some small integer larger than, say, three or four.

What P represents is the probability of some event happening that led to intelligent life as we know it.


For example, the rise of eukaryotes seems to depend on the chance occurrence of mitochondria — a separate single-cell organism that invaded and had a symbiotic relationship with some other single-cell organism. Over time, that relationship became permanent, and mitochondria provided energy that allowed multi-cell organisms.

Another such chance involves our Moon, which may have had two crucial effects: Firstly, the iron from Theia ended up in the Earth’s core giving us the strong magnetic field that shields us from solar radiation. Secondly, a large moon creates tidal pools, which may have acted to transition life from the sea to land (where it could use fire).

Possibly thirdly, it may have given us our nice daily rotation period of 24 hours (or so).

[And fourthly, oh, my gosh, the Moon seen from Earth is the same apparent size as the Sun. Eclipses!]

The point is, our history seems to have a number of points where something rather specific (and rather unexpected) had to happen for life to get more complex and ultimately intelligent.


The exponent, n, is meant to represent a rough idea of how many such “improbable” events we might want to consider just for spit-balling purposes. We might figure there were at least five or six such events.

And, also for spit-balling purposes, P is a single value — an averaged probability for these improbable events. Since we’re considering improbable events, P needs to be some like one-in-a-hundred if not more.

The Drake Equation is more nuanced in its factors:

Each of the seven factors vary considerably (see the Wiki article for details).

The proposition here is simply:

The point being that something kind of interesting happens when n is at least five or six.

I think it makes that point better to think of it like this:

(Thinking about it like this is what made me go, “Huh!”)

Ask yourself (as I did), what happens if P = 0.01 (the one-in-a-hundred chance mentioned above).

The equation becomes:

Which makes N equal 0.000000000001 (one-in-a-trillion).

The point being that if we just consider six one-in-a-hundred chances, we’re talking about a one-in-a-trillion chance overall.

We don’t have to make n very big, or P very small, to end up with extremely small chances.


On the other side of this, if we consider the specific chances that had to happen for any single one of us to exist, the odds seem astronomical.

It seems almost impossible that any one of us would exist, yet there are billions of us now (with many billions in our past), and about 360,000 people are born every day.

Each represents astronomical odds for that specific occurrence, but the system constrains results (they’re all human beings). It’s like a random number generator that generates really huge random numbers, but each one contains exactly 400 digits.

The odds of any specific number existing are beyond improbable even knowing they all fall in a range of 400-digit numbers. That holds true even when we generate billions of numbers.

After all, billions is just an eleven-digit number (plus or minus one digit). Just a drop in a bucket compared to 400 digits.


In comparison, a universe with billions of galaxies, and each galaxy containing billions of stars, most of them with planets of some kind.

So there are certainly a lot of chances for a world good for hosting intelligent life — many billions in our galaxy alone.

But the equation above suggests that with just six one-in-a-hundred chances, the odds are one-in-a-trillion (a million-million).

When you consider that nearly all of the planetary systems we’ve seen so far are extremely poor candidates for life, it does make one ponder our place in things.

Granted, our ability to detect exoplanets selects for large worlds, especially ones close to their star. What we’ve seen so far is definitely not a representative sample.

That said, in terms of being livable, pretty much all we’ve seen so far isn’t!

It does seem we might be a bit rare.


Here’s the first of the PBS Space Time videos:

There are two more out (see their channel), and I expect more to come.

For me it was a case of synchronicity because the video came out just a day or two after I’d been thinking about the Drake Equation in terms of what happens when you chain even fairly decent odds.

Stay probable, my friends!

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

14 responses to “Simple Probabilities

    • Wyrd Smythe

      Well, yes, of course. (Although it’s not the time factor so much as the number of opportunities — that’s where odds kick in.)

      There is also that some of these things have time windows. The Moon’s creation, for example, is largely limited to when the Solar system was forming. And that event had many factors that had to be right regarding mass and collision vector.

      Either way, time or opportunities, the point is that long odds actually happening is rare and special.

  • SelfAwarePatterns

    Based on Earth’s history, I think simple microscopic life is probably prevalent in the universe, but complex life is rare. Based on the Fermi paradox, intelligent life is profoundly rare. Our nearest intelligent neighbors may be millions, if not billions, of light years away, possibly beyond our cosmological horizon.

    Alternatively, intelligent life may be more common, but we’ve vastly underestimated the difficulty of interstellar exploration. It might be possible in principle, but so costly in absolute terms that hardly anyone bothers. In that case, SETI may be our only hope.

    In terms of rare Earth, I think it’s definitely true that for humans, Earth is rare. We’re unlikely to be able to survive in the vast majority of other biosphere that might exist, at least with our current biology.

    • Wyrd Smythe

      “Based on Earth’s history, I think simple microscopic life is probably prevalent in the universe”

      I suspect that’s right. The caveat is that Earth’s history really is only a single example. It does seem clear that once life starts, it’s robust and ubiquitous.

      I do wonder about probabilities for abiogenesis, though. The evolution of RNA from organic chemistry seems one of those improbable events — I’m not sure anyone has a mechanism for how that happened yet. (I did read a good account of how cell membranes may have evolved.)

      As for intelligent life, it wouldn’t surprise me at all that we’re it in the Milky Way.

      “It might be possible in principle, but so costly in absolute terms that hardly anyone bothers.”

      And who’s to say a species has the same exploratory nature we do.

      The flip side might be the von Neumann machine idea of sending out robots that find resources to make more robots. If you stick with asteroids or other little objects, you don’t even have to worry about launching out of a gravity well.

      “In terms of rare Earth, I think it’s definitely true that for humans, Earth is rare.”

      We can probably extend that to include any lifeform that uses water as a chemical solvent, although it’ll be really interesting to see what we find on Europa or Enceladus. (Heh. Never thought about it; they both start with ‘E’.)

      The question I have is whether life might not need a greater energy source than likely on those moons. Maybe you need a lot of free energy to overcome entropy enough to kick-start life.

      • SelfAwarePatterns

        In terms of Earth history, definitely, we’re dealing with a sample of one. But it’s all we have to go on so far. If we find life anywhere else in the solar system, even the most primitive variety, it will confirm that viewpoint.

        On the other hand, if we find out that the oceans in various moons have ideal environments for life, but ones where it never started, that in itself will tell us that you might be right about RNA being one of those rare events.

        On the von Neumann probes, even they may turn out to be far more difficult than we currently imagine. Maybe getting to any appreciable percentage of the speed of light in a manner where we can slow down again at the destination, is profoundly difficult. And engineering a probe to work for centuries or millenia might present equally daunting challenges.
        I don’t see that as likely, but since we don’t yet have engineering solutions to the challenges, we can’t know for certain.

        On life on Europa and Enceladus, you might be right. Or biological processes in those environments might simply be slower as a result of the low energy, meaning that evolution takes a lot longer there. But it might be that it takes a lot of energy to get life started, energy similar to Earth’s hadean era.

      • Wyrd Smythe

        “In terms of Earth history, definitely, we’re dealing with a sample of one.”

        There’s been some recent talk about the possibility of life originating in deep sea vents. (Which turned into science writer headlines screaming: “Darwin Was Wrong About Life’s Origin!” [sigh])

        But if there were true, it gives hope for places like Europa or Enceladus. Interesting thing about moons, some of them get energy merely from tidal forces!

        (Did you ever see Europa Report? I didn’t care for it (don’t like the found footage thing), but it had some good points.)

        “On the von Neumann probes, even they may turn out to be far more difficult than we currently imagine.”

        It does seem more viable if you don’t care at all about return results. It only takes a few launched from the asteroid belt to start the process.

        Slowing down isn’t too bad if you don’t care about time. Enduring for many centuries is a serious engineering challenge, though, that’s a good point. If it were me, I’d convert entire asteroids to semi-self-sustaining probes. Load’m up with ice for fuel (H and O).

        But it would require a mindset involving a major desire to seed the galaxy, wouldn’t it. Or a civilization mature enough and confident enough to have research programs lasting millennia.

        “Or biological processes in those environments might simply be slower…”

        Even chemical processes might be inhibited depending on temperature. Life eats life, so you need an environment capable of spawning and maintaining a food chain. (Or some form of complex life that lives directly on some basic form of energy. Just seems like complex life involves a food chain, but, again, we only have the one example.)

      • SelfAwarePatterns

        I did see Europa Report, and mostly enjoyed it. But I know what you mean about the found footage genre.

        “Life eats life, so you need an environment capable of spawning and maintaining a food chain.”

        That’s why I think complex life is very unlikely there. We’re more likely to find simple autotrophic single celled type organisms, with a very shallow to non-existent food chain.

      • Wyrd Smythe

        As you say, it’ll be telling what we find (or don’t) in places like Europa.

        Mars sometimes seems to have what people hope is evidence of ancient (or even current) life. There is that methane business, for example. But so far it seems Mars became dry and dead too long ago for life to have had much chance. (OTOH, we’ve hardly scratched the surface of Mars. I don’t have much hope for it, though. It does seem like “Let’s Colonize Mars!!” fever has died down thankfully.)

      • SelfAwarePatterns

        I think Mars has a hold on people because it seems like the next place to go after the moon, and is the least inhospitable place in the solar system (after the Earth). But most people don’t seem to understand that least inhospitable is still very inhospitable, with Antarctica the Garden of Eden by comparison.

        Still, finding evidence of life, either ancient or current, would be a major discovery. But like you, I’m really not holding out much hope for it.

      • Wyrd Smythe

        Yeah, living on Mars would be pretty much like living on the Moon, but much further from your support systems.

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