A thought about the Fermi Paradox.

My purpose in this post is to ask a serious question that has already been asked and answered to some extent. But I want to ask it given what I think may be new information from an unrelated source. I also hope this isn’t redundant but I’ve haven’t seen this aspect discussed yet. I apologize in advance if it already has.

Let me start out by saying that I’m a serious supporter of SETI but my reasons have changed over the years. Lately I’ve come to think that communicating with another sentient species would allow us to objectively believe we might just yet overcome our problems, even if we can’t get their help. Knowing we’re not alone might be enough. But my question remains: is it possible for any sentient species to achieve this feat? And more importantly, is the silence we hear evidence that it is impossible?

We all know Frank Drake’s formula to estimate the probability that we would contact an alien species includes a single factor, $L$, that describes how long a civilization capable of communicating by electromagnetic radiation will remain in that state. At the time, Drake could not estimate this value. But I’d like to suggest that recent results from climate modeling provide vital information about possible limits on the value of this term.

The problem I’m suggesting we consider is that among the factors that influence the lifetime of civilizations is an exponential increase in the demand of energy at the very same time they presumably start SETI-related activities. This unsustainable energy use far exceeds the renewable energy sources available to the inhabitants of a planet, particularly when SETI-like technology is in its infancy.

Therefore we must consider mechanisms by which energy demand forces nascent alien SETI-civilizations to provide their energy from fossil sources, just as we did. The development of fossil resources drives a transient but self-sustained cycle of global economic growth that is necessarily unprecedented in history of a planet. Fossil resource exploitation also brings about climate change by returning massive geological stores of CO2 to the atmosphere. But this comes with a delayed climate response that limits reactions needed to mitigate negative impacts some decades later than necessary to save the civilization from the consequences.

The result of a sudden atmospheric injection of carbon dioxide is a catastrophic collapse of planetary climate leading to a dystopian post-apocalyptic state of civilization that effectively precludes further development of space-faring endeavors and ends the nascence of an era of interstellar communications before it has any real chance of taking hold. Here on earth it seems the process may complete itself within about one century of the development of radio telescopes: the mean observation for $L$ is about 100 years, albeit with only one data point. The other terms of the Drake equation generally suggest that the number $N$ of civilizations in the galaxy capable of communicating is roughly the same as L. This result implies that the average distance between these civilizations is roughly 10,000 light-years. Since this distance exceeds the lifetime L, each civilization capable of communicating via electromagnetic signals is effectively isolated.

A recent estimate for the value of $L=420$ years is based on human history with a lower number of $L=300$ years for modern societies [1]. Unfortunately, it is hard to see how this estimate can be extrapolated easily to other intelligent species. Nor is there any reason to expect that the communications technology itself would be lost when a civilization reaches its lifespan. Instead it is more reasonable to expect that only an interruption might occur before the technology is rediscovered, adapted, and enhanced provided the event leading to the interruption wasn’t fatal.

At the other end of the spectrum, it is has also been proposed that sufficiently advanced species become effectively immortal societies. The argument is that they can move off the home planet and all but eliminate the risks associated with single-planet residency. Thus $L$ becomes proportional to time where the proportionality constant is the fraction of species that become immortal [2]. One extension to this model suggests that contact with an immortal civilization confers this characteristics through a transfer of knowledge [3], which certainly suggests a strong incentive for a long-term investment in programs like SETI. It is worth noting that such a process would grow, cascade, and eventually result in a dense plethora of such civilizations across the galaxy.

We can think of the problem another way by asking what lifetime $L$ would be necessary to allow a single two-way exchange of information between proximate civilizations. A rough mean distance between communicating civilizations in a galaxy of radius $R$ is given by $D = 1.77 R/\sqrt{L}$. Setting a lower bound on the round-trip signal travel time $2D=L$ tells us that $L>3000$ years is required for a two-way exchange of information. We can call the quantity $C=3000$ the critical time for a civilization to become a member of the “interstellar chat room”.

It would seem that an important consideration for determining whether $L>C$ is whether a sentient species will have evolved in such a way that it has sufficient long-term perspective to overcome the short-term motives that drive it. There are two effects that must be considered, individual species maturation time and planetary environmental volatility.

Individual maturation affects what a species would consider “short-term’’, because the time it takes for their offspring to reach social maturity is an important component in evolution. When maturation time approaches the number of years it takes to release the critical mass of carbon into the atmosphere, a species becomes more likely to consider the impact of carbon a short-term problem that directly and adversely affects its living offspring before they mature, rather than a long-term one that only speculatively affects only future generations. A slow-maturing species is therefore more likely to act in a manner to limit the harm caused by excessive energy demand and therefore more likely to achieve $L>C$.

The second consideration is the volatility of the planetary environment in which the species evolved. Too little volatility and there is nothing to drive species toward sentience. Too much volatility and the environment is incapable of sustaining species long enough to support populations that spread into ecological niches that enable speciation in the first place. On balance we expect species with a dominant short-term response capability to evolve more often because any environment which would give rise to a more long-term response is less able to quickly evolve sentient species. However, the more time goes by, the more likely long-term motivated sentient species are likely to emerge.

We now only need to connect this response to the time it takes for their young to reach social maturity and reason that species with a short maturation time and preferring choices that maximize short-term rewards are more likely to exist than species with a long maturation time that would tend to minimize long-term risks. It’s difficult to come up with a robust model to consider how this trade-off might have played out alternatively, even on Earth. But it does seem reasonable to try to put some numbers to this by defining a ratio $P$ as the number of generations to mature socially between first SETI operations and peak fossil use, assuming a logistic model of fossil energy use. We also define $Q$ as the number of generations between first SETI and failure of the planetary climate system sufficient to preclude interstellar communications. Any species with a $Q>1$ can be expected to be inherently limited with regard to SETI communications and not a likely candidate for overcoming the critical value of $C=3000$.

Consider humans, with a reproductive period of about 25 years and assume the time from first SETI to peak fossil emissions of about 50 years, i.e., $P=2$. Current climate models forecast catastrophic failure of the planetary ecosystem within 50 years of peak fossil, or $Q=4$. Obviously we are far too short-term thinking to overcome $C=3000$. In essence we must argue that only a species that has $Q<1$ is likely to achieve SETI-chat status. This implies that they are exceptionally long-lived relative to their planet’s fossil fuel stores and climatic system inertia, an assumption which seems to argue against their existence, if we are to assume that the evolutionary mechanisms observed here on Earth are universal.

Overall, my conclusion is that we are effectively alone, at least within the horizon of our civilization’s lifetime. That doesn’t mean we shouldn’t search, because the numbers we have are not based on direct observation. They are only averages so there is still a slight chance of success. But I certainly won’t be holding my breath, unless it is to avoid breathing the noxious fumes that occasionally waft over my home from nearby forest fires.

References:

1. M. Shermer, “Why ET Hasn’t Called,” Scientific American, vol. 11, 2002.
2. D. Grinspoon, “Lonely Planets”, 2004.
3. D. Goldsmith and T. Owen, “The Search for Life in the Universe”, 1992.