Matematics is alien

Do aliens exist? The evidence is varied across time and across the globe. But mathematicians who study aliens always impress me. These are individuals who firmly stand on the pillar of logical reasoning- mathematics, that is. And yet, they are considering one of the most contested ideas of humankind… Are we alone?

Mathematicians (along with a lot of other really smart people) sometimes appear crazy. Their ideas are too advanced and so, as Arthur C. Clark once coined, the ideas indistinguishable from magic. And everyone knows that magic doesn’t exist.  You can’t make something move without touching it. Except… my garage door opens every day and I’ve never touched that thing! Honestly, I enjoy viewing the world as though every scientific thing is actually magical. A new line of code that makes my life simpler? Magic! Internal combustion engines? Magic! Hot Water?!  You get the idea.

Alien_1But while I love attributing scientific advances to magic, I don’t enjoy attributing non-scientifically proven theories (or magic) as science. Unlike the scientists who founded the Jet Propulsion laboratory (as told by this Cracked Podcast), who believed in and cast spells on a regular basis, I don’t actually believe in magic. And similarly, I don’t actually believe in aliens. Not seriously anyways. Not until it’s proven.

And while all the green alien paraphernalia in Area 51 cannot convince me, mathematics might… Woodruff Sullivan and Adam Frank recently published a paper summarized in the NY Times article, “Yes, There Have Been Aliens,” which described how mathematics show that intelligent life probably existed in our universe at some point. It employs the Drake Equation which is basically the multiplication of a bunch of different probabilities. Let’s take a quick look at the details of that equation:

N=R_* \cdot f_p \cdot n_e \cdot f_l \cdot f_c \cdot L

where

R_* \; = rate of star formation. (known)
f_p \; = fraction of stars that have habitable planets (current research)
n_e \; = number of planets/star that has habitable planets (current research)
f_l \; = fraction that develop life (unknown)
f_c = fraction of life that is intelligent (unknown)
L = length of time to release communications (we could make a guess)
For a while f_p and n_e were expected to be the limiting factor(s) in this equation. However, as scientists discover more and more stars and planets, it seems this f_p is very close to 1 and n_e at least 1. At this point, the biggest unknown is the probability that life is formed and the probability that this life is intelligent.

Universe1

The authors plug in some values into the equation to get a sense of what the values of f_l and f_c would need to be to make intelligent life unlikely.  This is kind of like saying: “If I know how many lottery tickets are winners, how many are printed, how many people play and how many tickets each player buys, then I can tell you the likelihood that you’ll win the lottery.”  In this case, the authors are say, “I can tell you the likelihood that someone won the lottery at some point in history.”  And, certainly the chances of someone winning the lottery over the entire history of the lottery’s existence are higher than the chances of me winning the lottery. (and if you want to know more about winning the lottery and how to game this system, check out Planet Money‘s episode on the subject.)

So, Sullivan and Frank are trying to show the limiting values of f_l \cdot f_c. Historically, the probability of getting a civilization on a habitable planet was pessimistically considered at one in 10 billion per planet. Sullivan and Frank show that unless f_l \cdot f_c is less than one in 10 billion trillion, life is likely to have existed. This means that even if you take the pessimistic number of 1/10 billion, then 1 trillion civilizations existed across the universe. Magic!

Before I close this inquiry into alien life, I have to point out the counter argument. The Atlantic recently posted a rebuttal article. The core of the rebuttal is that while 1/10 billion was seen as pessimistic, we don’t have any idea what the real number is.  Like, 1/10 billion trillion is really small, but it’s possible that we are the only planet with humans on it. This argument is factual, we don’t actually know the value of f_l \cdot f_c…

But, wouldn’t it be cool if we did? Or maybe we should be willing to believe (in the face of scientific argument) that f_l \cdot f_c could be large enough to make intelligent life probable. Or maybe not?  I guess it depends what kind of mathematician you are.  Are you willing to believe that magic is just science we haven’t solidified yet? Or are you a mathematician who believes is magic worthless until the moment when it is definitively proved and can be reproduced ad nauseam?