Tuesday, December 27, 2011

45: The Aliens Among Us

    Is there alien life on other planets?  Are we alone in the
universe?  These are deep questions involving advanced research in
biology, chemistry, physics, astronomy, cosmology, and many related
areas.  But is it really so hard to answer?  In fact, it can be boiled
down to a single equation created by a prominent astronomer in the
1960s, known as the Drake Equation, which will answer all our
questions in one line.   
    So, what is this magical-sounding equation?  It gives us a way to
calculate N, the number of intelligent life forms in our galaxy that
we might possibly communicate with.  Here it is, in all its glory: 
    N = R-star Fp Ne Fl Fi Fc L
    Now you know the answers to all the questions of extraterrestrial
life, and we can end the podcast early for today.  Right?  Well, not
exactly.  Perhaps we should figure out what all those terms we are
multiplying together mean first.
    R-star is the average rate of star formation in the galaxy.
    Fp is the fraction of those stars with planets.
    Ne is the average number of planets for each of
those star systems that could theoretically support life.
    Fl is the fraction of those planets that actually develop life.
    Fi is the fraction of those that develop intelligent life.
    Fc is the fraction of intelligent life forms that actually develop
technology for deep-space communication.
    And finally, L is the average lifetime of this high-tech phase of
those civilizations.
    So, you can see that it's just a common-sense listing of the
things we would have to know in order to calculate the number of alien
life forms.
    It is fun to try to fill in plausible-sounding values and figure
out, based on various assumptions,  the number of alien life forms we
can communicate with.  Naturally, optimists like advocates of SETI
(the Search for Extraterrestrial Intelligence), who believe we should
pour millions of dollars into searching for potentially alien signals
from space, find sets of numbers that give a solution like 5000,
meaning there is an alien lurking around every interstellar corner.
Skeptics, like apparently the author of the Wikipedia article on this
topic, plug in numbers that get an answer closer to 2, which means
that maybe, somewhere out there, there is just one alien civilization
that we might hear from someday.  And perhaps we should save our SETI
money to spend on math podcasts.
    If you are now somewhat underwhelmed by the power of this
equation, join the club.  While it is a neat, concise expression, it
is essentially just listing all the probabilities, for some of which
we just have wild guesses, that we would have to string together to
answer the question of alien life.  In a sense, it just begs the
question.  But begs it in an authoritative-sounding way.  It has been
pointed out that we do have one data point:  whatever values one
substitutes in, we would expect N to be at least 1, since we are
pretty sure that *we* exist.  But beyond that, I think the biggest
lesson out of this is that just because you can put something in an
equation, doesn't mean you actually know anything useful.  On the
other hand, equations do sound very convincing, regardless of how
little information they contain.  Perhaps one day an alien life form
will land here and tell us what the real values are.
    And this has been your Math Mutation for today.

  • The Drake Equation at Wikipedia
  • SETI at Wikipedia
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