What are the Odds?

I can’t remember not liking science fiction, particularly those that visit other worlds and encounter different forms of life. To gaze up at the starts and envisions worlds upon worlds, maybe with someone looking up at ours and wondering the same. It’s an ancient concept, beginning first with the planets of our own solar system, and later extending to the stars themselves. The assumption that there was life, including intelligent life, on other worlds was so strong that it came as a shock to discover that the other planets of our solar system were uninhabited.

It’s something most of us science fiction fans just accept and go on. That’s a good thing for writers who dream up these worlds. What most science fiction fans can’t tolerate are poorly created worlds. They must be consistent with science, or have a story so good that we overlook it.

World building was the subject of a recent Mad Genius Club post. Author Pam Uphoff examined the science behind habitable worlds and the potential of life. This happened to hit an itch I’ve had of late concerning probabilities, which can be surprising. I was dashing off a comment to address it in-depth, and it ran so long that I decided to post it here. What it all boils down to is that the probabilities are steep. Really steep. So steep that, from a strictly scientific point of view, it’s a possible (and recognized) answer Fermi’s Paradox. Fermi’s Paradox is simply the question, if there’s intelligent life out there, where are they?

This gets into a speculative area. We only know of one inhabited world – ours – and we don’t know if that’s average or not. There are some things we do know. Such as, as best as we can tell, the first stars were made up only of hydrogen, because that’s all there was. When gravity pulls enough together, though, and it starts to fuse into helium. This goes on until the hydrogen is gone, and then the helium starts to fuse, and, if the start is large enough, this goes on all the way to iron. When these massive stars go supernova, the resulting explosion makes elements from iron all through the elements of the periodic table.

This means that the only planets possible for the first stars would have been hydrogen gas giants. It’s only after there’s more elements that we can have rocky planets, chemicals, and other interesting stuff. Our sun is either a second or third generation star, so either it’s in the age range of when the first interesting stuff happens or maybe interesting stuff had been going on for some time. The oldest known second generation star is almost as old as the universe (13.8 billion years for the universe; 13.2 billion years for the start) and nearly three times older than the sun. Plenty of time for “Old Ones,” right?

Well, that’s gets into something that’s bothered me about all this, and oddly it involved typewriters and monkeys. We’ve all hears of the proverbial monkeys and the works of Shakespeare. Infinite monkeys banging at infinite typewriters could produce all the works of Shakespeare because, well, we’re dealing with infinities. But what would be the odds of randomly generating just one work? Like Sonnet 18. Sonnet 18 is short, with only 625 characters; 639 with carriage returns; 653 with computer style line feed and carriage return sequence (two different ASCII commands to accomplish what one swipe of the old manual typewriter carriage return accomplished). I had originally assumed a 30 character keyboard, but this is too low: One actual typewriter I looked at had 53, not including special keys for that particular model. Including both computer style line feed and carriage returns, that typewriter was capable of 70 characters. With 70 characters, the odds of randomly generating Sonnet 18 is about 1 to 7.063 5 x 101,204. In comparison, there’s only been about 4.354 9 x 1017 seconds since the Big Bang. As Fred Reed observed, we’re talking about the spontaneous generation of a cloud of hydrogen into all the works in the British Museum – and then some.

My itch isn’t philosophical. There’s a possibility that a random sequence that could lead to intelligent life is more rare than randomly generating Sonnet 18. That means if life randomly arose around a second generation star that gave birth to ours and somehow survived the process, then it could be limited to the stars in the stellar nursery that birthed our own, and likely the life on those worlds aren’t writing an equivalent to Shakespeare or much of anything at all. If life randomly arose only on our world, then we don’t have even than.

If, on the other hand, the components of life are more or less self-ordering, like growing sugar crystals, then that means that given second or third generation elements you’re likely to end up with the necessary molecules. But then those molecules have to order themselves in such a way as to self-replicate and to keep themselves intact and then work their way up to musing about how life could begin spontaneously. It starts to look like an extremely lucky night at the casino, and we know from extinctions that the house doesn’t favor the player.

Surely there’s enough stars, though. Or is there? There’s an estimated 7 x 1022 stars in the universe. Another estimate puts the number of stars with a habitable zone as 1 in five. So there should be about 1.4 x 1022 possible stars in the entire universe that could support life.

How about our own galaxy? There is estimated to be up to 400 billion stars in the Milky Way. That gives us 80 billion stars with habitable zones. We know from Venus and Mars that just because a planet is in the habitable zone doesn’t mean it will be habitable, so the number of actual habitable worlds in our galaxy is likely less. One-third, like our own? That would give us about 27 billion habitable planets. NASA estimates it much lower, to 1 billion. No one knows for sure.

Let’s say, though, that there’s 27 billion habitable planets. Doesn’t that mean the odds favor not only life but intelligent life?

Not necessarily. Successive odds are multiplies. Let’s go back to our randomly generated Sonnet 18. There’s a 1 in 70 chance of getting the first character correct by picking a character at random. To get the first and second characters correct is 70 x 70 = 4,900, or 1 in 4,900. Of three, 1 in 343,000, and so on. By the time we get to the end of the sonnet, we reach our odds of about 1 in 7.063 5 x 101,204. So whatever odds they are of having the right chemicals is multiplied by the odds of having the right conditions, and this is multiplied by each successive odds of developing all the parts of a working cell, and then of a multicellular organism, on up to intelligent life. We don’t know what those odds are, but consider the odds of generating just Sonnet 18 with 70 characters.

To be fair, there’s more than one chance per planet. If we want our random chance to occur at a smoker (undersea geyser), then the chance is not only for each smoker time each world, but the amount of time for the process to take place. Here what little I know of probability theory ends, and I’m not sure of the odds that two random sonnet generators would produce Sonnet 18. I do know that it could never reach 100%, and we can see this with a simple analysis of coin flips: Odds 1 coin flipper will produce heads is 1 to 2; odds of 2 are 1 to 3 to 4; odds of 3 are 7 to 8; odds of 4 are 15 to 16; odds of 5 are 31 to 32; and even at 1,000 coin flippers the odds are (1.071 5 x 10301 – 1) / 1.071 5 x 10301. It approaches a certainty but never gets there.

My pathetic attempts to calculate how many random generators it would take to get to 50% probability of generating Sonnet 18 met with both the mathematical and computer versions of “TILT.” The problem is the size of the numbers. I’m sure there’s a way to calculate it, but I don’t know it. It’s certainly more than two random generators.

Now consider the problem of the spontaneous generation (abiogenesis) of life. Even though there’s evidence for life existing just 430 million years after a Mars-sized object slammed into the earth, that doesn’t mean it’s a matter of “Just add water.” Even if the molecules used by life could form, it’s not the same as it automatically coming together into a functioning package. We’re once again looking at long odds.

Just what those odds are is unknown because no one knows exactly how life could spontaneously arise. Simply saying it might have happened in such-and-such manner isn’t the same as knowing, and how chemicals could form a self-replicating package remains a topic of debate.

From the debate, though, it’s still more than just add water: maybe it was at a smoker; maybe it was along shore; maybe it was on a shore sprinkled with uranium; maybe it formed in volcanic ash and blew in to the sea; maybe it formed in a drying puddle. Each of these maybes describes something limited in scope, and, in turn, means long odds. By each theory, consider all the places where life could have arose and didn’t; maybe the smoker stopped spewing chemical rich hot water, as smokers tend to do; maybe the beach dried out or didn’t dry out enough; maybe radioactivity was too high or not enough; maybe the compounds formed and didn’t blow out to sea; maybe the puddle never saw water again. What it all comes down to is long odds regardless. And we haven’t even gotten life to the level of bacteria, or to the extinction events yet.

What it all comes down to is that either the Earth won the lottery less than 500 million years after the Earth and Moon were molten blobs, or something else was going on. Personally, I think something else was going on. When a guy keeps winning at craps, you get suspicious about the dice.

What this means for abiogenesis is that life is rarer than commonly assumed. It means that if life came about by random means, then if it exists elsewhere in our solar system, it likely came from a single source. Given that big meteors can blast things from planet to planet, that’s not outrageous. For panspermia fans, that could mean it arose about the star that went supernova and formed the stellar nursery that gave birth to our star and others. That would also mean that if there’s life elsewhere, the best place to look would be around the other stars that came from the same source.

Or not. If life came about purely as random chance, odds are there is nothing there at all.

Fun time: This post is about 10,588 characters long. Using the same method we did to calculate the odds of randomly generating Shakespeare’s Sonnet 18, what are the odds of randomly generating this useless bit of fluff?