The Fermi Paradox and Are We Alone in the Universe?

The Fermi paradox is something like this. The Universe is enormous, and there are an astronomical number of planets. Accordingly, the potential for intelligent life somewhere should be enormous, but we find no evidence of anything. The Seti program has been searching for decades and has found nothing. So where are these aliens?

What is fascinating about this is an argument from Daniel Whitmire, who teaches mathematics at the University of Arkansas and has published a paper in the International Journal of Astrobiology (doi:10.1017/S1473550417000271 ). In it, he concludes that technological societies rapidly exterminate themselves. So, how does he come to this conclusion. The argument is fascinating relating to the power of mathematics, and particularly statistics, to show or mislead.

He first resorts to a statistical concept called the Principle of Mediocrity, which states that, in the absence of any evidence to the contrary, any observation should be regarded as typical. If so, we observe our own presence. If we assume we are typical, and we have been technological for 100 years (he defines being technological as using electricity, but you can change this) then it follows that our being average means that after a further 200 years we are no longer technological. We can extend this to about 500 years on the basis that in terms of age a Bell curve is skewed (you cannot have negative age). To be non-technological we have to exterminate ourselves, therefore he concludes that technological societies exterminate themselves rather quickly. We may scoff at that, but then again, watching the antics over North Korea can we be sure?

He makes a further conclusion: since we are the first on our planet, other civilizations should also be the first. I really don’t follow this because he has also calculated that there could be up to 23 opportunities for further species to develop technologies once we are gone, so surely that follows elsewhere. It seems to me to be a rather mediocre use of this principle of mediocrity.

Now, at this point, I shall diverge and consider the German tank problem, because this shows what you can do with statistics. The allies wanted to know the production rate of German tanks, and they got this from a simple formula, and from taking down the serial numbers of captured or destroyed tanks. The formula is

N = m + m/n – 1

Where N is the number you are seeking, m is the highest sampled serial number and n is the sample size (the number of tanks). Apparently this was highly successful, and their estimations were far superior to intelligence gathering, which always seriously overestimated.

That leaves the question of whether that success means anything for the current problem. The first thing we note is the Germans conveniently numbered their tanks, and in sequence, the sample size was a tolerable fraction of the required answer (it was about 5%), and finally it was known that the Germans were making tanks and sending them to the front as regularly as they could manage. There were no causative aspects that would modify the results. With Whitmire’s analysis, there is a very bad aspect of the reasoning: this question of whether we are alone is raised as soon as we have some capability to answer it. Thus we ask it within fifty years of having reasonable electronics; for all we know they may still be asking it a million years in the future, so the age of technological society, which is used to base the lifetime reasoning, is put into the equation as soon as it is asked. That means it is not a random sample, but causative sample. Then on top of that, we have a sample of one, which is not exactly a good statistical sample. Of course if there were more samples than one, the question would answer itself and there would be no need for statistics. In this case, statistics are only used when they should not be used.

So what do I make of that? For me, there is a lack of logic. By definition, to publish original work, you have to be the first to do it. So, any statistical conclusion from asking the question is ridiculous because by definition it is not a random sample; it is the first. It is like trying to estimate German tank production from a sample of 1 and when that tank had the serial number 1. So, is there anything we can take from this?

In my opinion, the first thing we could argue from this Principle of Mediocrity is that the odds of finding aliens are strongest on earth-sized planets around G type stars about this far from the star, simply because we know it is at least possible. Further, we can argue the star should be at least about 4.5 billion years old, to give evolution time to generate such technological life. We are reasonably sure it could not have happened much earlier on Earth. One of my science fiction novels is based on the concept that Cretaceous raptors could have managed it, given time, but that still only buys a few tens of millions of years, and we don’t know how long they would have taken, had they been able. They had to evolve considerably larger brains, and who knows how long that would take? Possibly almost as long as mammals took.

Since there are older stars out there, why haven’t we found evidence? That question should be rephrased into, how would we? The Seti program assumes that aliens would try to send us messages, but why would they? Unless they were directed, to send meaningful signals over such huge distances would require immense energy expenditures. And why would they direct signals here? They could have tried 2,000 years ago, persisted for a few hundred years, and given us up. Alternatively, it is cheaper to listen. As I noted in a different novel, the concept falls down on economic grounds because everyone is listening and nobody is sending. And, of course, for strategic reasons, why tell more powerful aliens where you live? For me, the so-called Fermi paradox is no paradox at all; if there are aliens out there, they will be following their own logical best interests, and they don’t include us. Another thing it tells me is this is evidence you can indeed “prove” anything with statistics, if nobody is thinking.

Planets for alien life

In my novel, “A Face on Cydonia”, an alien message was finally intercepted. That raises the question, what is the probability of alien life? Frank Drake answered that question with the Drake equation, which involved the product of the number of potentially suitable stars, the probability such a star has a suitable planet, the probability that life will evolve on such a planet, and the probability that it will develop to a civilization. (There is a little more to it, relating to communications, but we leave that.)

In my ebook, “Planetary Formation and Biogenesis” I tried to put some numbers on these, or at least the conditions that have to be met. I should add that what I put forward is NOT in accord with most astronomical thinking. Most astronomers and physicists believe that planets form through gravitational attraction of planetesimals (Bodies of the 100 km size) into embryos (bodies about Mars size) then these accrete into planets by gravitational collisions. While this theory has been around for 60 years, nobody has any real idea how planetesimals form. My concept is that the initial bodies accrete through chemistry that differs at different temperatures, and that means you do not get a uniform distribution of planetesimals. Unfortunately, if I am correct, there are a number of different types of solar system that can evolve.

For life to evolve, it is usually considered the planet must be in what is called the “habitable zone”, which is usually defined by a zone in which planets have liquid water. Venus is usually considered to be too hot, and Mars too cold. The distance from the star for the habitable zone depends on the luminosity of the star, which in turn depends on the stellar mass to a power of approximately four. Thus if we require the planet to be in the habitable zone, for very small stars the planet has to be very close to the star. The smaller the star, the more common it is. If the star is very big, it burns so much faster and does not last. For these reasons, it is usually thought that stars have to be roughly the same size as the sun, i.e. G-type stars (our sun is a G-type, but one of the smaller ones) or K-type (the next size range down). The next problem for a planet is whether the star is a single star, and if so, do they come close enough to gravitationally throw the planets away. Double stars are more common than single stars. Further, stars have to have sufficient elements heavier than helium. You cannot have rocky planets without silicon! Finally, for life to evolve very far, the star has to be old enough.

None of the closest stars to Earth seem particularly promising. The most promising is Alpha Centauri, which also happens to be the closest, at a little over 4 light years, and has two stars that approach about as close as the Sun-Saturn distance. One star is slightly bigger than Sol, and the other is a smaller star. Neither star could hold a gas giant, but rocky planets might be possible, and the smaller star appears to have a small planet. A star like Sirius or Procyon is simply too big and will not last long enough to let animal-type life evolve. The two closest single stars that seem big enough have their problems. Epsilon Eridani is known to have a Jupiter-type planet, but is only 900 million years old, so any planets will not have had time to evolve advanced life. Tau ceti is probably old enough, but it has a low fraction of heavy elements, and may not be able to form rocky planets.

There are only 2 G-type stars (our sun is a G-type star) within ten light years, and about 18 within thirty light years, however K-type stars might also be adequate, and there are about 38 of them within 30 light years. Unfortunately, the heavier G-type and the lighter K-type are probably not suitable, so we may have a lot of space to ourselves. On the other hand, our galaxy is huge, and by my count it probably contains something like a hundred billion suitably sized stars. Those near the centre of the galaxy probably have to be discounted (the region is too violent) and we may have to eliminate about half of the rest for various reasons, nevertheless, it is almost certain that there are plenty of suitable stars. It is just that they are rather far away both from us and from each other. How many will have planets? That is for a later post.