Drake Equation

An equation used to estimate the number of technological civilizations that may exist in the galaxy. There is no exact answer to Frank Drake's famous equation, but it nonetheless a tool for the scientific community, and the force "behind every project at the SETI Institute."

N = R_* x f_p x n_e x f_l x f_i x f_c x L

Where:

N = The number of civilizations in the Milky Way whose radio emissions are detectable.

R_* = The rate of formation of stars with a large enough "habitable zone" and long enough lifetime to be suitable for the development of intelligent life.

f_p = The fraction of Sun-like stars with planets is currently unknown, but evidence indicates that planetary systems may be common for stars like the Sun.

n_e = Number of earths per planetary system. All stars have a habitable zone where a planet would be able to maintain a temperature that would allow liquid water. A planet in the habitable zone could have the basic conditions for life as we know it.

f_l = The fraction of those planets where life develops. Although a planet orbits in the habitable zone of a suitable star, other factors are necessary for life to arise. Thus, only a fraction of suitable planets will actually develop life.

f_i = The fraction life sites where intelligence develops. Life on Earth began over 3.5 billion years ago. Intelligence took a long time to develop. On other life-bearing planets it may happen faster, it may take longer, or it may not develop at all.

f_c = The fraction of planets where technology develops. The fraction of planets with intelligent life that develop technological civilizations, i.e., technology that releases detectable signs of their existence into space.

L = The length of time that communicative civilizations release detectable signals into space.

     Source: SETI

A very silly equation to estimate the number of civilizations in our galaxy with detectable radio emissions. The "math" behind it is solid, sure. So it's a tautology. But it's still meaningless: in order to be able to use the equation, we have to know the values of the parameters appearing in it. And we don't have a clue.

I might just as well propose the Scolnicov Equation:

N = N_* * p_radio * p_detect

where N is the same as in Drake's equation, N_* is the number of stars in the Milky Way, p_radio is the probability of radio emissions from a given star, and p_detect is the probability of detecting such emissions.

So let's go over the parameters in the Drake equation. Remember, to use it you have to be able to get good estimates on all of them!

R_*

Nope. We've only one instance of life, so the best we can do is hope for a Sol-like star. And we don't really know how many of these there are in our galaxy (we don't really know the total number of stars). But let's say we know it up to a factor of 10.

f_p

No Sol-like stars are known to have planets. It is entirely plausible that our solar system is extraordinary and not a typical system. After all, it's highly unlikely to get life on a system with no planets at all, is it? So the 2 events (life and planets) are highly correlated.

Estimate this one at any number you like, really. 10^-7? 10^-10? 10^-30? You pick! Note also that at such low values it's essential to have a good definition of your sample space (e.g. consider a case where the Earth is the only place in the universe with life; will you be arranging your numbers to get N=1?).

n_e

Again, unknown. Note that the solar system only has one, and no other solid planets are known, Earth-like or otherwise. All comments for f_p apply here, only more so.

f_l

Now we're getting to the weak points of the argument. This is even less known than the previous points, for which astronomical evidence is at least imaginable. What should we call it? 1/3? 1/10? 1/100? 10^-10? 10^-100?

f_i

Now we're leaving the realm of science fiction and entering that of second-grade fantasy. Does anyone seriously think they can estimate this? Perhaps I should just take all evidence into account, and set f_i=1. After all, all planets I know of that have life also have intelligent life. Or maybe I should make up some other number, like 10^-20. Is one of these numbers less plausible than the other?

f_c

OK, here we just need an expert on alternative history. You can set any value here too, but presumably you're not going to be using the incredibly tiny numbers of the previous section. Say anywhere between 1/10 and 1/10000.

L

More alternative history. We've been emitting radiation for over a century now! Not a lot of time, is it? This number includes the probability of a nuclear war, the probability of a slide back into barbarism, the average length of time before we get bored and think of something better to do with our time, the average length of time before we invent warp communications which are undetectable to primitive civilisations, and other easily-estimable numbers

All Drake's equation does is replace our ignorance with a list of meaningless letters. Thanks, but I prefer to state my ignorance out front.

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In response to Mr. Frog

What are these "extremely conservative numbers"? How were they calculated? How did these "scientists" get around the obstacles I show? Perhaps by guessing and then proclaiming themselves as scientists using extremely conservative numbers?

Responding "scientists said it, so it must be true" is hardly convincing. I hope.