The missing E.T. denominator

There's a mathematical fallacy in the argument that life exists outside of Earth just because the universe is so vast.

I don't have any philosophic objections to the existence of extraterrestrial life, but what does bug me is when people claim that simply because the universe is so big, that somehow makes it not only likely but practically certain that life has developed on other planets or in other solar systems or galaxies.

That kind of thinking presumes some very important information that we just don't have. We are currently unable to enter any coherent value into the portion of the Drake Equation that pertains to how frequently life arises from non-life.

First, let's talk about abiogenesis. That's a term scientists use to describe how life arises from non-living matter. We have an admittedly very limited knowledge of events outside of our own planet, but so far as we know, abiogenesis has occurred only once, and from that one event, all life on Earth proceeded. (It's possible that abiogenesis occurred independently multiple times during the beginning of life on Earth, but I don't think we yet have a compelling argument that it must have happened more than once.)

Despite many attempts, no one has been able to reproduce this process, creating new life from non-living matter. So we're pretty confident that it's not easy to do, but as I understand it we have only a very foggy idea about just how improbable it is.

Next, let's talk about frequency and prevalence. Frequency describes how often an event happens, and prevalence describes how numerous a given thing is within some group or area. So, if there are 99 burglaries in a city in a 3-year period, we might describe the frequency as 99/3 = 33 burglaries a year. And if there are 18 left-handers with a graduating class of 180, we might describe their prevalence as 18/180 = 10% lefties.

Notice how both frequency and prevalence require a numerator and a denominator in their calculations?

Well, how do you construct the numerator and denominator with regard to how often abiogenesis happens?

If I know that a certain volcano has erupted approximately once every two years for the past century, I can use that information to describe the eruption frequency. The numerator would be 50 (the number of times it has erupted in the past century) and the denominator would be 100 (the number of years in the past century).

But suppose I know only that a certain volcano has erupted this year. I don't know whether it has ever erupted in any year before this year, and I don't know how likely it is to erupt at any time in the future. I have my numerator (1), but how can I possibly know what the denominator is?

Maybe it's 10 years. Maybe it's 1,000 years. Or maybe it's an unfathomably large number of years — meaning that throughout the entire existence of the universe, for however long that lasts, this one eruption is the only eruption the volcano will ever have.

Let's consider another example. Suppose you see a number with this pattern:

.1001000101001000101001000___

What would you say is the likelihood that a 1 is the next number in the sequence? I'd say it's somewhat likely, because within the 25 numerals that preceded it, the number 1 appeared 8 times, so just going by random chance, the odds are roughly 1-in-3 that the next number will be a 1. If you observe that there is a repeating pattern to the sequence, you might be able to predict the next number with even greater accuracy.

But suppose you see a number with this pattern:

.1000000000000000000000000___

What is the likelihood that a 1 is the next number in the sequence? You could say the odds are 1-in-25, but that doesn't takes into account the clear pattern we see in the sequence. Unless and until we start to see some more ones pop up, it's reasonable to assume that this is a sequence of infinite zeroes, or at the very least that it could perfectly well be a sequence of infinite zeroes. Suppose the sequence goes on for many trillions of numerals. No one's going to say, "Well, if there are trillions of 0s, it's highly unlikely that there won't be some 1s sprinkled in there somewhere."

Similarly, no matter how large the universe is, no matter how many other stars or planets are out there, no matter how many of them could support life as we know it ... unless we know how often abiogenesis happens, we cannot say how likely it is that extraterrestrial life exists.

I'll leave you with a little food for thought: If we identify or generate just one other instance of abiogenesis, do we now have enough information to estimate how prevalent extraterrestrial life might be?

Read the sequel to this post:
Fermi's Pair o' Decks: Card-trick math reveals odds of alien life