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FERMI'S PARADOX

In the discussion about (potential) alien life, there's been a lot of discussion of Fermi's Paradox. If you try to calculate the likely numbers of technological civilizations in this galaxy alone, it's pretty easy to come up with numbers in the thousands or maybe even millions. Ok – so if there are all these civilizations out there, why aren't they visiting us?

I believe I can answer the question, in the remainder of this page, along with the next.

First let's try it out with a few simple numbers. There are about two hundred billion stars in the Milky Way galaxy. Let's suppose there is a technological civilization (one with space travel) on one out of every ten star systems (probably a ridiculously high estimate). That would leave twenty billion planets with intelligent life in the galaxy. Suppose those planets range in level of advancement from about where we are to a billion years more advanced than we are. If the 20 billion planets are evenly spread over that billion-year interval, that would mean there are about twenty planets per year of advancement. (In other words, there would be 20 planets about a year more advanced than we are, another 20 two years more advanced, another 20 three years more advanced, and so on.)

Now I've played pretty fast and loose with the "level of advancement", and what it means, and how it might be measured. It doesn't matter, because it won't affect the final argument.

So the number of planets – ranging in level of advancement equivalent to us, up to a thousand years more advanced than us – would be about 20 thousand. Now let's assume further that these planets are evenly distributed throughout the galaxy. Since there are 200 billion stars, the odds of finding one of the 20 thousand – when examining a particular star – would be 20,000 divided by 200 billion. That's one in ten million.

So, when we examine a particular star, the odds of it being home to a technological civilization no more than a thousand years ahead of us are about one in ten million.

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Now let's generalize. Suppose there are N stars in the galaxy (we think we know N, it is about 200 billion). Let P_I be the probability that a star has intelligent life, with a civilization able to travel in space, on one of its planets (or a moon of a planet). If we apply a Drake equation type of argument, then

(1) P_I = f_P * n_E * f_L * f_I * f_T

Carl Sagan seemed to think this number might be fairly high; the Rare Earth crowd thinks it's pretty low. Let the level of advancement of a civilization, in years, be anywhere from zero to some upper limit, say U. U might be a billion years or more, who knows?

I ignore for the moment that different civilizations will probably advance at different rates. I also ignore the fact that Western civilization appears to be advancing much more rapidly now than a hundred years ago. I also focus on technological advancement – not cultural, social, or moral. But this might not be a bad assumption. Take a society that's not particularly morally advanced, give it technology like the atom bomb, and it won't last long.

Finally – and this is the crux of the argument – if one civilization is at a certain level of advancement A (in years), and another is at a level B, assume they will be interested in communicating with each other only if the difference between A and B is less than some limit Y. (Or perhaps I should say, even able to communicate with each other.) For example, would we be interested in contacting a civilization that was just moving from the hunter-gatherer phase (a civilization that was about 8,000 years behind us)? If this were 1492 instead of 2019, the answer would be "yes – if only to kill them and take their land." The answer today is probably "no – leave them alone until they become more advanced" – sort of the Prime Directive of the Star Trek franchise. Likewise, any civilization thousands of years more advanced than we are would probably not be interested in contacting us. This all assumes, of course, that advanced civilizations are relatively benign, or at least not malevolent. If they're like the The Borg of Star Trek, all bets are off.

This is an interesting subject for speculation that I'm not going to pursue further at the moment, except to state the issue. There are two aspects to this. First, if an advanced civilization – that has the ability to travel between stars – is malevolent, what could we provide them that they couldn't more easily get themselves? It would seem they would have no incentive to visit us. The second aspect – is it inevitable that advanced civilizations be benign? As I mentioned above, it seems likely that a civilization that has advanced technology, that's not benign, would destroy itself. The problem with these types of arguments is that the cost of being wrong is unacceptably high.

In other words, if we discover an advanced alien civilization that doesn't know of our existence, should we contact them? All the arguments above seem to say "yes". But if that civilization is NOT benign, the same thing could happen – to the entire human race – that happened to the American Indian after Columbus "discovered" America for the Europeans. The probability that those aliens are malevolent might be very small, but the consequences are very great.

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Back to the main argument. Then in the galaxy, the number of civilizations will be

(2) N * P_I Their level of advancement will be from zero to U, and if they are evenly distributed across that spectrum (a potentially big assumption), there will be, in each year of advancement:

(3) N * P_I/U The number within Y years of us (ahead of us) will be:

(4) Y * [N * P_I/U] Those behind us in advancement don't count; they won't be spacefaring. And we will see that, even if we want to include those, it's not going to alter the conclusions. If we look at a particular star, the probability that it will contain a civilization up to Y years ahead of us, in technological advancement, is the number in (3), divided by the number of stars N:

(5) Y * [N * P_I/U]/N = Y * P_I/U This assumes that there are no "clusters" of stars with civilizations all about the same age – another potentially big assumption.

Perhaps civilizations, once they reach the spacefaring stage, colonize large parts of the galaxy near them, much like the Europeans colonized the New World. And then, later they evolve into different cultures of approximately equal technological development, much like Europe and the New World countries are now evolving. This shows how this "field" of SETI is susceptible to rampant speculation, and how little we really know.

Now recall that P_I is the probability that a star has intelligent life, with space travel, U is the maximum number of years of technological advancement that other civilizations could have, and Y is the maximum number of years of advancement that a civilization could have, from us, and still be able and willing to communicate with us. (Note that I have tacitly assumed that WE are a spacefaring civilization – but we are not. At least, we don't have the ability to travel between stars.)

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So here's the punchline: It generally doesn't matter what N (the number of stars in the galaxy) is! In (4) N appears in both numerator and denominator, so it divides out. Even if P_I is one (so that every star has a spacefaring civilization – clearly an unreasonable assumption) – if U is much bigger than Y, the probability is very small that a spacefaring civilization will find another civilization of interest. If Y is a thousand years and U a billion, even if P_I is one, the probability of finding a civilization of interest, when examining one star, is ONE IN A MILLION. If P_I is a tenth of a percent (the Rare Earth advocates would probably make it much smaller than this), the probability becomes one in a BILLION. A spacefaring civilization would have to look at an extremely large number of stars before it finds a civilization that it wishes to contact.

As I mentioned earlier, one could argue that a civilization far in advance of us would use 2Y in the calculation, since they could look ahead and look behind – but that's not going to change the conclusions.

And I haven't even examined the possibility that any civilization, in order to reach us from another star, has to be so far ahead of us that they wouldn't be interested (in contacting us) from the get-go. (In other words, any civilization that has the ability to travel between stars – is truly spacefaring – might be so far ahead of us that they would be unwilling or unable to communicate with us.)

If a civilization is more than Y ahead of us, what's to keep us from contacting them, even if they aren't interested in contacting us? Presumably they could conceal themselves from us, so we would not even be aware of their existence, even if we discovered the solar system(s) where they lived.

Now this line of reasoning doesn't explain why, apparently, no aliens have ever visited us. Presumably they could have visited millions of years ago, then left when they saw no signs of civilization. But no aliens have ever left any trace of their presence here – at least that we're able to detect. But there may be an explanation for this as well.

But there seem to be good reasons to believe that advanced aliens would not, or could not, communicate with us. I lay out those arguments in the next page.

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Before I go there, I want to do one other thing. How likely is the universe imagined in the Star Trek franchise, created by Gene Roddenberry? How likely is that to happen? Suppose that – in another centrtury or two – we develop the ability to travel between stars. Then what is the probability that there is at least one other such civilization in the galaxy?

Not quite. What is the probability that there are at least two such civilizations in the galaxy – that are wtithin a few decades of each other, technologically?

Above, I "derived" the following:

(5) P_D = Y * P_I/U

where P_I is the probability of spacefaring, intelligent life; U is the maximum number of years that a civilization could be technologically ahead of a spacefaring one; Y is the number of years that a spacefaring civiliazation could be ahead of another and still be able to communicate, and P_D is the probability that a given star has a spacefaring civilization that could communicate with another.

It should be clear that we can make Y the number of years that one spacefaring civilization is advanced over another and still be part of the Star Trek universe. Then we can follow the same reasoning (?) that I did when I derived (5). Then some reasonable (?) numbers are, for Y, 10 to 50, for U, a billion, so that (5) becomes, even if P_I is one, roughly one in a hundred million.

So here is NO CHANCE of the Star Trek iniverse happening. (Assuming all of the numerous assumptions I've made are correct; otherwise this is all highly speculative; it is anyway.) It's not because of the technology involved; it's simply because:

It's taken over four billion years for a technological cvilization to evolve on Earth. When we become spacefaring, the odds of another civilization, anywhere in the galaxy, reaching that level, within a few decades of when we do, are essentially zero.

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