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:
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!