Just How Incomplete is the Drake Equation?
And what our lack of imagination means for the Fermi paradox
By MARTIN REZNY
In case you’re not aware of this bit of math, it is a speculative, probabilistic attempt at estimating the number of intelligent technological alien civilizations in our galaxy that we could talk to.
It goes like this:
N = R∗ * fp * ne * fl * fi * fc * L
where:
N = the number of civilizations in our galaxy with which communication might be possible (i.e., which are on our current past light cone);
and
R∗ = the average rate of star formation in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
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
As the equation was discussed in the years since its inception, several modifications have already been proposed. For example, the original model described above is static, ignoring how life, once it develops anywhere, can spread throughout the galaxy.
This is usually considered as a colonization hypothesis, meaning an intelligent technological spacefaring civilization seeding life as it expands, but aimless panspermia could do that as well, only slower. Speed of movement through space is the key variable here.
There’s also the possibility of reemergence of intelligent technological life where it evolved once, which is presumably more likely than the first time around. The lack of both of these considerations in the original Drake equation makes it more valid early in the process of life development.
Then there are potential psychological modifiers. For example, just because the aliens have the technology to communicate or generally show themselves, it doesn’t mean they will want to do that. We could be doing it already, but we don’t consider it to be a priority at the moment, and who knows when we will.
Overall, the possibilities of life spreading and reemerging increase the odds, while psycho-social restrictions decrease the odds, but these modifiers don’t fundamentally undermine any of the underlying assumptions on which the Drake equation is built. For that, we need to think about communication.
Potential Quirks of Interstellar Communication
I understand that most physicists currently can’t think of a way how to communicate faster than light, which is why the Drake equation is focusing on detecting radio or laser signals. However, for starters, the sheer impracticality of that may deter many civilizations from ever expending resources on it.
Secondly, if there is anything faster than light just around the corner, technologically speaking, then virtually nobody would get to doing radio or laser beacons before skipping to the better thing. Given that the better thing is inconceivable to our best physicists today, we wouldn’t be able to detect it.
Well, we do have some ideas, but they’re currently so incredible that they’re uncredible. If the better thing was, for example, anything psi-related like telepathy, then thousands of people could be claiming they’re communicating with aliens all the time and no respectable scientist would believe them.
Alternatively (or concurrently), the better thing could be an FTL drive, which means that you could communicate with anybody anywhere in person, by visiting them in ships. Probably not fleets of ships so as to not scare them shitless, only showing small presence at first. Thousands of people could be claiming to see that all the time, and scientists wouldn’t believe them either.
Of course, these are not hypotheticals. There are many thousands (at least) of such reports every year, which aren’t believed by scientists precisely because we have no idea how such things would work in terms of physics. Sure, maybe all the witnesses are mistaken, but if they aren’t, how would we know?
If we’re unable to determine some reality to be a reality if it were a reality, then we don’t know whether it is a reality or not. Therefore, Drake equation has to be modified by hypotheticals, not be limited to the constraints of current scientific theory, so that we can determine if there is any specific indicator that we could look for that would in any scenario help us narrow down the number of technological species in our galaxy.
In the example of communication, the number of detectable light-speed signals is not a good indicator, given that there are conceivable hypothetical scenarios in which virtually no intelligent species would be using them. In fact, if anything, a notable absence of this mode of communication is an indicator that some of the alternative scenarios may be taking place.
Following the Fermi paradox, maybe there are no communications because there’s nobody around to communicate with. But in this view, Fermi paradox isn’t actually a paradox, it’s a hypothesis. The competing hypothesis is that FTL communication is possible. And while something that we don’t technologically understand is harder to quantify, it’s not impossible.
As I have already mentioned, there are large numbers of people who claim to have been in some form of contact with potential alien beings or craft. Given that what we’re making are probabilistic arguments, the key word is “potential”. Given our potentially significant level of ignorance of the real limits of physics, not all of them can be ruled out with sufficient certainty.
The key numbers here are therefore the number of incidents of alien contact and the percentage of such incidents that cannot be attributed to any known natural or man-made phenomena. The estimates for this percentage, at least in terms of unexplained UFO sightings, range anywhere between 3-25%, with many leaning toward 5%, like famous theoretical physicist Michio Kaku.
The number of unexplained incidents of alien contact can be further refined by how many different alien species or overall distinct technologies or languages are described in them. However, given the possibility of genetic engineering, cultural divergence, and technological convergence, it would be hard to probabilistically disentangle a species from a nation or class, etc.
Definition of alien species is not really entertained in the original Drake equation and related discussions, so I guess I would propose to treat the term “intelligent technological alien species we can communicate with” as a “distinct alien society” (less biologically speciesist, more cultural definition).
For example, in this sense, the Vulcans and Romulans from Star Trek would be considered to be different alien species, even though *SPOILERS* they are biologically speaking two branches of the same species as defined by DNA and historical origin. After all, we wouldn’t be talking to DNA, but to cultures.
This is however still a too reductionist view of what aliens are, if what we want to have is an equation that’s able to calculate with all of our known unknowns. “Aliens” that people can have contact with are not necessarily all “space aliens”. There are other conceivable dimensions where life can exist.
In terms of numbers, the alien lore, speculation, and testimonies aren’t too incoherent and are definitely not boundless. If one focuses on the number of consistent distinct alien descriptions, one will get a number somewhere between half a dozen and low tens. You got your grays, lizardmen, hairy wildmen, little people, mantises, human-like nordics, and then the incidence of descriptions sharply declines. Based on the overall body of descriptions, each of these can easily have several variations, or convergent evolutions.
Other Omitted Hypotheticals
The number of distinct alien cultures can be further subdivided into space alien cultures, ancient alien cultures (pre-human intelligent technological civilizations that evolved on Earth), future alien cultures, ultraterrestrial alien cultures (parallel to us), and supernatural (or interdimensional, if you prefer) alien cultures, at least. There can also be combinations of these.
However Rick-and-Morty it might sound, you could hypothetically have aliens who, from our point of view, are supernatural beings from other planet’s parallel time-line’s future’s ancient past. Then again, you could disregard this whole level of distinction, as all of such cultures are sufficiently alien from us, while dimensions like space, time, or parallel universes are all part of reality.
Why it matters from the point of view of the Drake equation is that each additional dimension where life can be and from where it can travel to our here and now changes how the spreading of life, whether through panspermia or colonization, needs to be calculated. Let’s consider it.
Space aliens bring the FTL travel possibility, which should still have a velocity or range cap (how much of a gap can be jumped). Naturally occurring wormholes or (potentially extradimensional) corridors of faster travel would allow panspermia to occur faster than light and potentially change the geometry of spread from a sphere to seemingly discontinuous networks.
Ancient aliens are the least exotic option, being essentially part of the reemergence variable. The only modifier special to them would be the number of civilizations that are effectively hiding deep underground or underwater where they fled from an apocalypse. Which would be very hard to detect, especially if we assume that most civilizations are surface ones and only look for signs of life through radiation and atmospheric composition.
Future aliens, depending on how real-time travel would actually work, could bring the possibility that once life develops arbitrarily late in the history of the universe, it can be seeded back in time, starting from a much earlier point. Or it could dramatically increase the number of parallel timelines, resulting in a far greater number of different ultraterrestrial alien civilizations. Or it could be used to eliminate life by preemptively stopping its evolution. Time travel, as usual, is possibly the hardest to narrow down, until we understand it better.
As for the ultraterrestrial aliens versus the supernatural (interdimensional) aliens, they both bring the ability of life to travel between what amounts to different universes. The difference is that ultraterrestrials could be considered as following the same or sufficiently similar laws of physics (being only a result of a split in timeline), while “supernatural” beings may be able to interact with our physical world, but ultimately aren’t limited to our physics.
Supernatural therefore doesn’t mean “magical” in a sense of having no rules, but “magical” in a sense of being able to transcend our rules, while retaining the requirement that any entity that exists can only do so on the basis of some physics. The multiverse hypothesis does allow for universes with laws of physics dramatically different from ours, in infinite variations, so maybe some are at least compatible enough for a life based on them to briefly visit us.
The level of divergence of life across the scope of all possible physics could dramatically complicate calculations like the Drake equation, but not very differently from our inability to know what and how many different types of life can emerge even within our own physics. It would be mostly an issue of being unable to define what life or living being is in the first place, without which we obviously will not be able to count it. While we should count it, as intelligence able to interfere in our universe is plenty alive to mess with us.
The Where Are All the (Now Even More) Aliens Problem
As you can probably imagine, if life can travel not only faster than light, but also through time and across universes, the Fermi paradox only gets more intense. If everything is allowed, it would pretty much guarantee that intelligent life has always been everywhere, even if it only evolved a few times across the vast swaths of reality. Well, unless there are counteracting forces.
As I already mentioned, psychology is one such “force” that can potentially counteract any technological capability, as well as make us able to reject any evidence of alien life always being everywhere around here. The denial scenario is simple enough and requires little more explanation. The ways in which psychology may prevent a technology from being used, not so much.
Let’s look at a big example of us developing a god-like technology and then barely using it — nuclear weapons. The nation that developed it used it only twice, the minimum amount to prove to an enemy that it works. So, even when USA was a unilateral nuclear power, it didn’t use it to destroy everyone else. In fact, it rushed to develop it first precisely so that nobody does that.
Ever since then, these awesome weapons were only “used” for deterrence, and the first bunch of countries who developed them made sure further proliferation was prohibited. The trend since then has been, if anything, disarmament, to decrease the number of nuclear weapons (that are not being used). There are some rogue states with other plans, but that’s because of how comparatively weak they are to the established early adopters.
From this strategic, geopolitical point of view, which is fueled by self-preservation and rationality (the two likely most common basic motivations of intelligent technological powers), easier travel through space, time, or universes could paradoxically cause the apparent lack of sprawling empires.
Which is to say, not necessarily a lack of alien civilizations, but a lack of our ability to easily see them — through some early higher power’s version of non-proliferation and disarmament treaties, in space, time, or other dimensions. With only sub-light travel, cosmic non-proliferation wouldn’t be enforceable. If you can do it, confining everyone to their local area is both rational and relatively benevolent. The other approach would be to eradicate all others.
As for an alternative scenario without a dominant power, much like if we were to start a hot nuclear war with more than one side firing nukes, an open FTL, time, or interdimensional war could easily erase most civilizations pretty much everywhere and essentially forever. This may make advanced life sustainable only in (FTL+) universes with a cold war-like scenario.
It seems that the only scenario in which there would be a sprawling empire is the one with an absolutely dominant malevolent power eradicating everyone else. But then we wouldn’t have a way to know it, unless we were it. Especially if you factor in FTL+ tech and the concept of berserker drones, we would already have been wiped out by such an advanced power, or even preempted. Then again, it’s not clear that such a scenario is particularly viable.
Ideologically-driven eugenic expansionists like the Nazis may certainly try to accomplish a cosmocide every once in a while, but maybe whenever they do, they motivate someone more benevolent and with greater potential, like a coalition of everyone else, to prevent that. I guess that such a race could have a major evolutionary head-start, but why would they then become fervent eradicators of life, when there isn’t much of it and it’s non-threatening?
What does this all mean for the Drake equation and similar probabilistic arguments? For starters, it affects the speed of the expansion variable, as the ultimate limit is not how fast you can move, it is how much everyone is allowed to expand by the dominant power that can move fast enough across the universe to enforce the limit on expansion. Until we have more data, this variable also cannot be separated from the enforced limits on other forms of travel and therefore spreading of life, like time travel or dimensional travel.
When put together, the variable could be called something along the lines of “enforced expansion limit”, or, when flipped, “non-proliferation enforcement failure rate”. It wouldn’t really help us identify whether we are in this scenario or not, this cannot be determined yet between the FTL+ hypothesis and the Fermi hypothesis, but assuming it is one of the more consistent scenarios, maybe thinking about it can give us some new things to look for.
How to Look for Life More Advanced Than You
I have already mentioned some examples, like the number of alleged alien contact incidents, the percentage of how many of them remain unexplained, and the number of frequently reported distinct types of alien entities. However, these are admittedly soft, social-sciency numbers, which will never be satisfactory to some of the more hard science-oriented skeptics. Even though many UFOs are demonstrably objective, non-imaginary phenomena.
If you want something more tangible, then the first step is to stop looking for signs of expansion, which would be stalled, or the byproducts or non-FTL technologies being applied on a large scale, like waste heat. We can get lucky an catch some conventional megastructure some day or some civilization around our current level, but if there is something better around the corner, then this technological phase is incredibly brief, so unlikely to be observed.
If you think about it, in an FTL+ universe, our current pre-FTL technological level is destined to be extremely short-lived already because of the FTL+ technologies being used essentially all over creation by someone ever since their discovery. This means that all other intelligent life will see them being used, which should speed up their development, and you have a good chance to eventually get a crashed ship dropped into your lap to reverse engineer.
What would also be happening despite any non-proliferation enforcement, which can likely never be perfect, would be some smaller-scale activities, like crime or minor military skirmishes. Admittedly, these will be hard to detect across vast distances, but remember, in an FTL+ universe, distance is almost irrelevant. If anything is going on anywhere, there’s a good chance it’s going on everywhere, including here, where we should be able to observe it.
However, there would still be some difficulty to spotting alien skirmishes, crime, or even sanctioned local activities. Given the fact that the inevitable nature of (intelligent) crime is stealth (to avoid being detected by the law-enforcing authorities), and given that the sanctioned activities like scientific observation would likely be hidden to begin with or covered up after the fact by aliens or us to avoid causing a planetary panic, it gets tricky.
Let’s start with skirmishes. While very advanced ships may be undetectable to us while fully functional, they should become much more easily spotted once they’re disabled in a fight or suffer a major accident. The tangible variable here obviously are ship crashes, any single one of which in theory should be a smoking gun proving alien life. Which creates a big problem, however, because that makes them a prime target for government cover-up. The only number we’re left with is of testimonies of witnessing a crash or cover-up.
As for either crime or sanctioned scientific experiments (on us), the number of reported alien abductions seems an obvious choice, however it is much softer than even the UFO sightings. A better, more objective figure would be that of people who have gone missing and potentially reappeared under mysterious or inexplicable circumstances. So, essentially a subset of Missing 411 cases, of which there are currently thousands documented worldwide. The number of unexplained mutilations of livestock fits here as well.
In any version of FTL+ scenario, there’s also a good chance that there’s some kind of permanent alien presence on Earth. So, maybe instead of looking into deep space, we should probe our own backyard more thoroughly. This should include mainly oceans, cave systems, deep forests, deserts, Antarctica under ice, and, based on ancient lore and modern accounts alike, lone mountains and mountain ranges. Essentially everywhere where we don’t settle, but where you could conceivably build a permanent base, away from us.
You still should be able to find something in space, though, but again, much closer to home. In an FTL+ universe, there most likely will be some kind of evidence of intelligent life, at least ancient, somewhere in our own solar system. If you want pointers, our Moon is very weird, Phobos (one of the moons of Mars) is very weird, Saturn with its rings keeps popping up in UFO discussions, ISS keeps shutting down their feed from orbit all the time for apparently no reason, and the immediate vicinity of the Sun had some UFOs.
Which all makes sense, for the most part. You can probably observe us very well from a tidally locked Moon, you can recharge even a massive ship very well close to the Sun, there could be a bunch of alien satellites in our orbit to keep tabs on us or to keep our WMDs in check, smaller moons like Phobos would be great for mining, and creating rings is an extremely cool (mega) art project, which we would totally make happen ourselves if we could.
New Equation Adventure Time
When taken together, there’s certainly no shortage of what to look for or take into account when considering and FTL+ version of Drake equation. As long as one gets over the logical fallacy of “I’m preemptively not willing to entertain any evidence for theories that contradict my pet model”. I’m not sure what the best way is to mathematically reformulate the current version of the equation, but let’s at least throw something out there:
Na = ((ic*fu)*sa)+af
Where:
Na = Number of distinct, locally active alien cultures;
and
ic = Number of reported incidents of alien contact, including UFO sightings and potential alien abductions
fu = Average of the fractions of unexplained UFO sightings, of credible abduction testimonies (with enough evidence by court of law standards), and of unexplained disappearances
sa = Average fraction of reported alien contact incidents ascribed to a single alien appearance type
af = Number of alien artifacts or specimen found with distinct biological, technological, or cultural markers
Not very complicated, is it? You may be wondering how this equation connects to the original Drake equation. To put it simply, the number of aliens active here, coupled with the colonization speed variable, would be an indicator of how many more species there probably are beyond our local area of space. Without knowing the speed limit, we could still only guess. Though speed limit in space may not be enough in an FTL+ universe — speed of colonization also relates to limits of time travel and dimension hopping.
The number of planets, or at least solar systems, where new life can evolve, and how frequently it happens, should still be an important part of the equation as well, but maybe in a somewhat altered sense. Given that FTL+ civilizations may be able to live in huge space habitats or interdimensional bubbles powered by who knows what, and that they’re definitely able to seed life and terraform or even build worlds, it becomes more about matter itself.
Insofar as the number of stars and planets correlates with how much free energy and stuff there is to live from, it will set limits just fine on how much advanced life there can be at any given point in time. It may not look like a lot of our galaxy’s mass is being used by huge technological civilizations, but as I hinted at earlier, assuming geopolitics and environmentalism are a thing among successful space empires, we may not be able to notice anything.
For all we know (which in the grand scheme of things is almost nothing), our whole solar system could have been artificially constructed or altered on mega-scale and we would have no idea. Maybe no one is allowed to build Dyson spheres or swarms because those are obvious cosmic weapons of ultimate destruction that take a long time to build and can’t be hidden. Maybe there are better power sources than stars. Maybe the grownups feel that stealing the stars from newborn civilizations is a douche move.
Whatever the reasoning, this real possibility would require one variable added somewhere to the original Drake equation, let’s make it ce = cap on cosmic expansion. For simplicity, let’s think of it as the average number of planets that a spacefaring civilization is allowed, or ultimately able, to colonize, or how much naturally occurring mass or energy it is allowed to exploit. It’s one of those variables that will probably only become useful once we gather some data about alien life, but we can already tell that either there are essentially no aliens around, or this number isn’t very large, or advanced alien civilizations are very good at hiding from our view, and possibly space.
This is a starting point of many other considerations, for example, if this is an FTL+ universe, what will be the ratio of naturally evolved versions of life or intelligence versus the seeded ones? Maybe if all life we find is very convergent, the seeding is more likely, and vice versa. What is a more likely general policy of a galactic empire for natural worlds without intelligent life? Are they kept as biosphere preserves, or is intelligent life helped along?
Well, I guess I have wasted enough of your time, so I’ll leave you to entertain such considerations as you see fit. As a political scientist, I personally find the question of exopolitics (geopolitics in space between spacefaring species) very intriguing, but it deserves an article, or a series of books, of its own. Let me know what you think about my modification of the Drake equation and the whole idea of looking for intelligent life in our own backyard in an FTL+ universe. Or, if you’re an alien yourself, feel free to tell me how it really is.
