Monday, June 24, 2013

The Alien Contact Probability Boundary

The Drake Equation, as we all know, purports to determine the potential number of intelligent civilizations that share our Milky Way galaxy. Obviously, it makes a number of far-reaching assumptions. But, upon hearing yet another reference to it again, one that indicated it predicts millions of other civilizations, I had to think - there has to be an upper limit, or boundary, to that number based on one sheer fact: we have not heard from any of them, at least not just yet.

Now, of course I'm not the first to proffer this question (why haven't we heard from anyone yet?). What I am suggesting is that the possible number of civilizations is bounded by our not having heard from them to date. And, as time goes by without a signal, that number declines. 

Now, by intelligent life, my only assumption is that it is one that is capable of communication and it only needs to communicate, say, the value of Pi, the ratio of a circle's circumference to its diameter, since that it a universal constant and it seems the most obvious one, to me. (I believe this was actually part of a 1950's era sci-fi movie.) Furthermore, SETI notwithstanding, let's say we've had radio receivers around for nearly a hundred years. Note that I will not be dividing this number in half since I'm not assuming a signal is in response to our own transmissions.

So, if we assume a sphere with a radius of a hundred light years, how many such spheres are contained within the Milky Way Galaxy? Perhaps we should exclude the central portion of the galaxy on the assumption it is uninhabitable. But, we could make any number of such assumptions. I think that is the question since if the population density of life (previously defined) is greater than that, we should have picked up a signal from them, intentional or not.

To make this calculation, we'll use an ellipsoid volume calculator , and eliminate the central bulge, assuming that is uninhabitable. 

For the outer ellipsoid, I very wildly assumed dimensions of 100,000 x 100,000 x 10,000 light years (major axis x minor axis x vertical axis). For the inner ellipsoid, I assumed 20k x 20k x 5k light years. The net volume of the supposed inhabitable zone is then 51,313 billion light years. Dividing that by our 100 light year radius sphere of communication yields 513 billion such spheres.

What that number then represents, fraught with the assumptions as it may be, is the number of civilizations in the galaxy there would have to be in order for us to have heard from them by now (the bottom line number of the Drake Equation).

Now, I'm certainly not saying there is no other intelligent life, however you wish to define it, in the galaxy. But whenever I hear the galaxy is "teeming with life", I have to wonder, up to what point? Oh, I suppose we will hear a signal at some point, say in a couple or three hundred years or so. But, I'm betting the message won't be, "We'll get right back to you".

William Shaheen
Superstition Mountain Astronomical League

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