Drake, SETI, and why the Fermi Paradox isn't a Paradox

There is a popular concept called the "Fermi Paradox" which basically asks the question: Given some simple math, it is possible to estimate that there must be a huge number of civilizations that have developed radio in this galaxy, yet we haven't heard their transmissions; Why not? Science fiction authors and philosophers have imagined all sorts of answers to this question. But there is no need to assume that there are aliens out there exterminating intelligent species the moment they start advertising their presence with radio waves. Rather, a universe that looks devoid of civilizations, despite the best efforts of SETI, is exactly what one would expect if one takes more than a few minutes to think about it.

We'll start where most people do with the Drake Equation. The Drake equation is meant to be an estimate of the number of existing alien civilizations in the galaxy. In it's most common form, it looks like this:

• Ng = Sg x Fp x Ne x Fl x Fi x Fc x L

Where:

• Ng = the number of civilizations in our galaxy.
• Sg = Number of stars in the Galaxy.
• Fp = the fraction of those stars that have planets.
• Ne = the average number of planets that can potentially support life.
• Fl = the fraction of planets that could support life that actually develop life at some point.
• Fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations).
• Fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
• L = the length of time for which such civilizations release detectable signals into space.

Sg, Fp, and Ne can be estimated from astronomical observations. Unfortunately, the remaining variables are hard to estimate... we have only one example of a planet with life, with intelligent life, or with civilization that emits radio waves... our own... and we have no idea how long we will continue to be such a civilization, to say nothing of how long the average radio-capable civilization lasts. Thus, discussing the Drake equation inevitably becomes a guessing game.

Unfortunately, the Drake equation is often used as an argument by SETI (the Search for Extra Terrestrial Intelligence) proponents for funding to listen for radio messages from the stars. They inevitably try and assume "conservative" choices for Fl, Fi, Fc, and L... but the truth is we have no idea what constitutes a conservative value for any of these variables. However, there is a far greater problem with using the Drake equation to justify SETI: Regardless of what numbers you plug into it, the Drake equation can NOT support such arguments since the number of contactable civilizations in the galaxy is not closely related to the number of existing civilizations in the galaxy.

As a measure of the number of contactable alien civilizations, the Drake equation is fundamentally flawed. Non-directional radio signals are hampered by the inverse-squared law. As this article explains very well, a normal UHF TV signal, for example, would be undetectable relative to the cosmic background static even from the closest solar system to Earth, even with an antenna the size of the whole Earth on the receiving end. Further, every time you double the distance, you quadruple the difficulty of detecting the signal. So detecting that TV signal from, say, a few hundred light years away instead of the nearest star (four and a half light years away) is tens of thousands of times more difficult, even with a planet sized antenna. (And remember, we can't assume alien technology will come to the rescue here... WE are the ones with the difficult problem of detecting the signal and WE are the ones who do NOT have a planet sized Antenna!) Therefore, to apply the Drake equation to the problem of SETI, we must acknowledge that considering all the stars in the galaxy as contactable is grossly inaccurate. Rather we must modify the Drake equation to replace certain terms:

Ng (the number of civilizations in the whole galaxy, a disk 51,000 light years across) must be replaced with Nc which is the number of alien civilizations close enough to Earth that communication might be possible.

Similarly, Sg representing the number of stars in all the galaxy (about 3x10^11), must be replaced with Sc the number of Stars in communications range of Earth. So now our modified drake equation is:

• Nc = Sc x Fp x Ne x Fl x Fi x Fc x L

For non-directional signals, because Sc is zero (that is there are NO stars close enough for non-directional signals to work; see above link), Nc must also be zero.

The only way to overcome the problem that no stars are within range of non-directional signals is to assume directional signals instead. Using directional signals, the number of stars in communication range becomes greater than 0, but is still a tiny fraction of the whole galaxy (rather than being in the hundreds of billions for all the stars in the galaxy(Sg), the contactable stars (Sc) might be as much as the tens of thousands because even the best directional signals still spread out and lose power with distance). In addition to accepting a penalty of being able to detect civilizations from a region incredibly smaller, the modified Drake equation has to have a new term, Cc, to account for the cost of using directional signals rather than omni-directional broadcasts. The alien civilization must be specifically trying to transmit to US... not the star next to us, not the whole sky, just us. AND we have to be listening to THEM, not the star next to them, not the whole sky, just them. AND both civilizations must be doing this, light-speed-delay taken into account, at exactly the SAME TIME. Our modified Drake equation needs to represent this probability that both civilizations will happen to focus their radio gear on each-other at the same time... we'll call this variable Cc (the Chance of this coincidence).

So an estimate of the number of contactable civilizations (more SETI-relevant, but still not perfect) is this modified version of the Drake equation:

• Chance of Communication Being Possible = Sc x Fp x Ne x Fl x Fi x Fc x L Cc

The only basis for guessing a value of Cc is to look at our own behavior. We listen to a lot of stars, so it's fairly reasonable to assume that an alien civilization might also. Unfortunately, based upon the number of directional transmissions WE CHOOSE to send out, the chances that another civilization will send out signals AT ALL, to say nothing of often enough that it will be detected by us when we happen to be listening to them is pretty astronomically low. In the decades since we've had radio transmitters of non-trivial power, we've only sent 28 messages divided over 13 projects. I will assume that we are typical, and therefore Cc is very close to zero: We aren't sending, so they are likely not sending, so it doesn't matter if anyone is listening to say nothing of doing so at the right time to the right star.

This brings us to an interesting contradiction: Proponents of SETI, believe that Earth and humans are typical so that the values of Fl, Fi, Fc can be assumed to be high and therefore the number of civilizations in the galaxy is also high. But, if we believe that we are typical, then we must assume that each of these civilizations, like us, is unwilling to bother sending many/any signals to the stars. So, either we are typical and there are no messages to recieve, or we are not typical and there are no civilizations to send them. So, either Fl, Fi, and Fc are close to zero, or Cc is close to zero.. Regardless, the product of our modified Drake equation must be close to zero.

The Drake equation was never really intended to estimate the probability of successfully contacting aliens, but merely how likely they are to exist, and even our modified drake equation above only predicts the chance of communications being possible. To turn the Drake equation into a full estimate of SETI's ability to succeed, we need to add still MORE variables! I have detailed these new variables, along with the final version of the SITE-relevent-Drake-inspired equation below:

• SITE-Success-Probability = Sc x Fp x Ne x Fl x Fi x Fc x L Cc x Mc x Se

The second new variable: Mc. This is necessary to address the problem of message format and recognition. Look at the Arecebo message as a text-book example of how to do this wrong. It is damn near unintelligible, even to humans. It changes formats: including symbolic, numeric, and physical representations of wildly different subjects. The physical representations are stylized and simplified to the point of being almost unrecognizable even with foreknowledge of what they depict, and are not drawn even remotely to-scale relative to each other (including things as small as molecules and as large as solar systems). One is forced to wonder, even if such a message were received by aliens, what are the chances that they would even recognize it as a message, much less actually understand the message?

Since the Arecebo message, more sophisticated message designs have been considered. However, people who claim that mathematics is a "universal language", are in my opinion, living in a fool's paradise. Look at something as simple as prime numbers: Think 2, 5, and 17 are prime number? Think again: the complex integers (1-i) and (1+i) are factors of 2, the complex integers (2-i) and (2+i) are factors of 5, and the complex integers (4-i) and (4+i) are factors of 17; so, if you number theory includes complex and imaginary numbers, the list of primes changes. Similarly, our current number theory does not include 1 as prime, but that is a basically arbitrary choice, and indeed at one time it was listed amongst the prime numbers. Imagine the aliens send a message that was: 1, 3, 7, 11, 13, 19... someone naive enough to think that math is a universal language would be wondering why 1 is on the list and 2, 5, and 17 aren't!

The idea that an alien mind, shaped by the needs of an alien environment, will have alighted upon anything like our concept of mathematics is laughable. One can easily imagine a concept of mathematics that treats numbers as strictly locations on a continuum, or fractions of the whole, and thus has no concept of integers. Without the concept of integers, the concept of primes doesn't even exist. Because it is not digital, such a mathematics would acknowledge no distinction between transcendental numbers and rationals. As a result, a species might send a message based upon what they consider to be elementary basic mathematics, but have it be indistinguishable from noise from the point of view of the receiving species. To address this, our modified Drake equation includes the term: Mc, Mental compatibility, the probability that our transmissions or their transmissions will be sufficiently within each others frame of reference that it will be recognized as a message, understood, and ideally replied to.

I have no way of guessing what value Mc has, but I do know that a awful lot of misunderstandings happen between humans who already speak the same language, so an argument can be made that Mc would also be very close to zero.

The last new variable: Se. Se represents Systematic errors... or the probability that because of our unavoidably human-centric approach, we are systematically failing to look for signals in the right way. (With values near one representing a high probability that we are looking in most or all of correct ways, and numbers near zero representing a high probability that we have failed to look in the right ways).

One way in which we might be failing in this regard is built right into the Drake equation's terms: solar systems with planets. Looked at from a sheer size point of view, planets represent a tiny fraction of the universe... especially if we only limit our concern to their surfaces. Conversely, the largest potential class of habitats in the universe is small icy bodies, or proto-comets such as populate the Oort cloud of our solar system and are theorized to drift between most stars. That is, by looking at star systems, and planets, and especially star systems with planets in the "habitable zone", we may be excluding from our search the very thing we are looking for. But there are other aspects of Se that extend beyond just looking in the wrong place: Something as simple as timing could be thwarting us, it might be that aliens are transmitting one microsecond long messages at a rate of ten or twenty messages a year at our planet and can't understand why we are not receiving them. Or perhaps the modulation of most alien messages is on the order of one bit every 50-100 years. The degrees of freedom in this space of possible systematic errors that we might be making are near infinite, but the number of ways we are looking for signals is not, leading us to the face the fact that the value of Se is also almost certainly close to zero, that is we're not really looking for ALIENS, just creatures almost identical to humans, but from other planets.

Thus, we are forced to conclude that because new and necessary terms in the Drake equation to make it relevent to the SETI project (Cc, Mc, and Se) are all probably very close to zero, combined with the fact that only a tiny fraction of the galaxy is remotely close enough to be considered contactable, the probability of contacting such species is also very close to zero regardless of the probability of those aliens actually existing somewhere or not. This is why the Fermi-Paradox is no paradox at all. Rather, seeming silence from the stars is EXACTLY what a reasonable person would expect, almost perfectly regardless of the number of alien civilizations in the universe.