# 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.

# World’s fastest bicycle

University of Toronto Engineering Science  alumni and students construct the world’s fastest human powered vehicle.  Link here. (In case you were wondering, I’m EngSci 8T5).

# Selection of the week

Famed Northern Irish flautist Sir James Galway (the man with the golden flute) and pianist Phillip Moll play the first movement of  Sergei Prokofiev’s Flute Sonata in D, Op 94, composed in 1943.

# Selection of the week

Canadian clarinet sensation Eric Abramovitz playing Francis Poulenc’s Clarinet Sonata in B-flat, FP 184.

# The blurry line between human and ape

Primate researcher extraordinaire, Frans de Waal, pens an excellent commentary in the New York Times on the recent discovery of Homo Naledi. His thesis that the distinction between human and nonhuman is not clear cut is something I wholeheartedly subscribe to. No matter what we look at, the difference between humans and other species is almost always quantitative and not qualitative.

Here are some excerpts and I recommend you read the whole thing:

The fabulous find, named Homo naledi,has rightly been celebrated for both the number of fossils and their completeness. It has australopithecine-like hips and an ape-size brain, yet its feet and teeth are typical of the genus Homo.

The mixed features of these prehistoric remains upset the received human origin story, according to which bipedalism ushered in technology, dietary change and high intelligence. Part of the new species’ physique lags behind this scenario, while another part is ahead. It is aptly called a mosaic species.

We like the new better than the old, though, and treat every fossil as if it must fit somewhere on a timeline leading to the crown of creation. Chris Stringer, a prominent British paleoanthropologist who was not involved in the study, told BBC News: “What we are seeing is more and more species of creatures that suggests that nature was experimenting with how to evolve humans, thus giving rise to several different types of humanlike creatures originating in parallel in different parts of Africa.”

This represents a shockingly teleological view, as if natural selection is seeking certain outcomes, which it is not. It doesn’t do so any more than a river seeks to reach the ocean.

News reports spoke of a “new ancestor,” even a “new human species,” assuming a ladder heading our way, whereas what we are actually facing when we investigate our ancestry is a tangle of branches. There is no good reason to put Homo naledi on the branch that produced us. Nor does this make the discovery any less interesting…

…The problem is that we keep assuming that there is a point at which we became human. This is about as unlikely as there being a precise wavelength at which the color spectrum turns from orange into red. The typical proposition of how this happened is that of a mental breakthrough — a miraculous spark — that made us radically different. But if we have learned anything from more than 50 years of research on chimpanzees and other intelligent animals, it is that the wall between human and animal cognition is like a Swiss cheese…

… It is an odd coincidence that “naledi” is an anagram of “denial.” We are trying way too hard to deny that we are modified apes. The discovery of these fossils is a major paleontological breakthrough. Why not seize this moment to overcome our anthropocentrism and recognize the fuzziness of the distinctions within our extended family? We are one rich collection of mosaics, not only genetically and anatomically, but also mentally.

# Abraham Bers, 1930 – 2015

I was saddened to hear that my PhD thesis advisor at MIT, Professor Abraham Bers, passed away last week at the age of 85. Abe was a fantastic physicist and mentor. He will be dearly missed by his many students. I showed up at MIT in the fall of 1986 with the intent of doing experimental particle physics. I took Abe’s plasma physics course as a breadth requirement for my degree. When I began, I didn’t know what a plasma was but by the end of the term I had joined his group. Abe was one of the best teachers I have ever had. His lectures exemplified his extremely clear and insightful mind. I still consult the notes from his classes from time to time.

Abe also had a great skill in finding the right problem for students. I struggled to get started doing research but one day Abe came to my desk with this old Russian book and showed me a figure. He said that it didn’t make sense according to the current theory and asked me to see if I could understand it. Somehow, this lit a spark in me and pursuing that little puzzle resulted in my first three papers. However, Abe also realized, even before I did I think, that I actually liked applied math better than physics. Thus, after finishing these papers and building some command in the field, he suggested that I completely switch my focus to nonlinear dynamics and chaos, which was very hot at the time. This turned out to be the perfect thing for me and it also made me realize that I could always change fields. I have never been afraid of going outside of my comfort zone since. I am always thankful for the excellent training I received at MIT.

The most eventful experience of those days was our weekly group meetings. These were famous no holds barred affairs where the job of the audience was to try to tear down everything the presenter said. I would prepare for a week to get ready when it was my turn. I couldn’t even get through the first slide my first time but by the time I graduated, nothing could faze me. Although the arguments could get quite heated at times, Abe never lost his cool. He would also come to my office after a particularly bad presentation to cheer me up. I don’t ever have any stress when giving talks or speaking in public now because I know that there could never be a sharper or tougher audience than Abe.

To me, Abe will always represent the gentleman scholar to which I’ve always aspired. He was always impeccably dressed with his tweed jacket, Burberry trench coat, and trademark bow tie. Well before good coffee became de rigueur in the US, Abe was a connoisseur and kept his coffee in a freezer in his office. He led a balanced life. He took work very seriously but also made sure to have time for his family and other pursuits. I visited him at MIT a few years ago and he was just as excited about what he was doing then as he was when I was a graduate student. Although he is gone, he will not be forgotten. The book he had been working on, Plasma Waves and Fusion, will be published this fall. I will be sure to get a copy as soon as it comes out.

2015-9-16: Here is a link to his MIT obituary.

# Selection of the week

Samuel Barber’s Adagio for Strings.  Appropriate for this sad day.  Leonard Slatkin conducts the Detroit Symphony Orchestra.