# The Drake equation and the Cambrian explosion

This summer billionaire Yuri Milner announced that he would spend upwards of 100 million dollars to search for extraterrestrial intelligent life (here is the New York Times article). This quest to see if we have company started about fifty years ago when Frank Drake pointed a radio telescope at some stars. To help estimate the number of possible civilizations, $N$, Drake wrote down his celebrated equation,

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

where $R_*$ is the rate of star formation, $f_p$ is the fraction of stars with planets, $n_e$ is the average number of planets per star that could support life, $f_l$ fraction of planets that develop life, $f_i$ fraction of those planets that develop intelligent life, $f_c$ fraction of civilizations that emit signals, and $L$ is the length of time civilizations emit signals.

The past few years have demonstrated that planets in the galaxy are likely to be plentiful and although the technology to locate earth-like planets does not yet exist, my guess is that they will also be plentiful. So does that mean that it is just a matter of time before we find ET? I’m going to come on record here and say no. My guess is that life is rare and intelligent life may be so rare that there could only be one civilization at a time in any given galaxy.

While we are now filling in the numbers for the left side of Drake’s equation, we have absolutely no idea about the right side of the equation. However, I have good reason to believe that it is astronomically small and that reason is statistical independence. Although Drake characterized the probability of intelligent life into the probability of life forming times the probability it goes on to develop extra-planetary communication capability, there are actually a lot of factors in between. One striking example is the probability of the formation of multi-cellular life. In earth’s history, for the better part of three and a half billion years we had mostly single cellular life and maybe a smattering of multicellular experiments. Then suddenly about half a billion years ago, we had the Cambrian Explosion where multicellular animal life from which we are descended suddenly came onto the scene. This implies that forming multicellular life is extremely difficult and it is easy to envision an earth where it never formed at all.

We can continue. If it weren’t for an asteroid impact, the dinosaurs may never have gone extinct and mammals may not have developed. Even more recently, there seem to have been many species of advanced primates yet only one invented radios. Agriculture only developed ten thousand years ago, which meant that modern humans took about a hundred thousand years to discover it and only in one place. I think it is equally plausible that humans could have gone extinct like all of our other australopithecus and homo cousins. Life in the sea has existed much longer than life on land and there is no technologically advanced sea creature although I do think octopuses, dolphins and whales are intelligent.

We have around 100 billion stars in the galaxy and let’s just say that each has a habitable planet. Well, if the probability of each stage of life is one in a billion and if we need say three stages to attain technology then the probability of finding ET is one in $10^{16}$. I would say that this is an optimistic estimate. Probabilities get small really quickly when you multiply them together. The probability of single cellular life will be much higher. It is possible that there could be hundred planets in our galaxy that have life but the chance that one of those is within a hundred light years will again be very low. However, I do think it is a worthwhile exercise to look for extracellular life, especially for oxygen or other life emitting gases in the atmosphere of exoplanets. It could tell us a lot about biology on earth.

2015-10-1: I corrected a factor of 10 error in some of the numbers.

## One thought on “The Drake equation and the Cambrian explosion”

1. My view is most of the terms on the rt side of the drake equation may be well known. Its discussed in a youtube presentation called ‘space oddity’ by the famous scientist david bowie. one of the astronauts also did a version of this video when he was in outer space looking for intelligent life—it turned out there wasnt any, anywhere in the universe. if one considers newton’s simple variant of general relativity, f=Gm1m2/r**2 where G is is the shockley-Hsu general intelligence of the universe, its about zero—same as energy of the universe and mass of the photon.

intelligent life has been shown to be an oxymoron see https://johncarlosbaez.wordpress.com/2015/07/20/the-game-of-google (from quanta mag, also on youtube as ‘numberphile’)

many of those terms may not be fractions but fractals ( a la chaos, solitons, and fractals journal—the only place i would publish besides http://www.vixra.org .
eg http://www.arxiv.org/abs/1306.4311
Lee Smolin, who seems to have decided that time does exist (despite julian barbour’s timeless universe’) thinks cosmology is similar to evolution—-universes evolve via natural selection, and maybe might cluster into something worthwhile like dinosaurs, in terms of GNP (discussed in economics as the ‘clustering illusion’ on wikipedia—eg the tendency of economists like herman daly and robert solow to count things like dollars, when physicists know the basic quanta of the universe are tulips—discovered by spinoza in the netherlands, though he called them monads after dr pangloss, and now they are grown or mined in kenya on large plantations of it for bitcoins. .

there are actually a small remnant population of dinosaurs in the local park.

i actually didnt know that aubrey drake of toronto, ontario also had an equation. (see wikip—and i am not a fan for some reason. i can think of only 2 canadian bands i like apart from indigenous music—neil young (‘sugar mountain’—i was going to go this weekend up there in west virginia but due to weather i think my ride has canceled) and slakah the beatchild who i see has a youtube video with drake

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