Let’s resume our discussion on the implications of the Fermi paradox on superintelligence. As I said in my previous article, any civilization that masters space travel and achieves the possibility of building megastructures, must have developed superintelligence as a prerequisite. This consideration is based on an extrapolation of our current technological level and on reasonable projections for the near future. In this post, I will discuss an alternative scenario that is compatible with the hypotheses 1-4 discussed in the previous article. These hypotheses were:

1. Intelligence and advanced civilizations are common in the Universe
2. A space-faring civilization develops super-intelligence before being capable of performing interstellar travels or able to build megastructures
3. Super-intelligence leads to the quick development of technologies that allow interstellar travel and/or the construction of megastructures
4. Super-intelligence can be controlled and does not lead to the self-destruction of the civilization that develops it

Let’s now consider the following minimal scenario: a civilization tries to avoid space colonization as long as it can (which includes the avoidance of any interstellar communication attempt), while still growing and prospering. How long do we need to
wait before the civilization is forced to find new resources beyond its home planet? This question is important because it can provide a crude estimate of the timescale needed before a civilization needs to move to outer space. In my previous post, I discussed the lack of evidence for the presence of megastructures around any of the about 1 million stars observed so far. I posited that a civilization-building one megastructure around one star every million years — and doubling this rate every million years — would have become detectable by us in just 20 million years. Since this number is tiny compared to the age of our galaxy, we should have long detected something.

Question: Is one million years a reasonable estimate when considering the time it will take a civilization to leave its host planet?

First of all, we need to determine how a civilization grows over time. Let’s begin by taking as an example our civilization and calculate what is the world’s capacity for the human population. The current world population (2017) amounts to 7.2 billion individuals, whereas in the year 2000 we were about 6 billion people.  Projections of the growth rate estimate a population of about 11.2 billion in the year 2100 (so 83 years from now).

A good proxy to measure the growth rate of the population is the so-called logistic differential equation, which corrects the exponential growth model by introducing a constant K, called the capacity of the environment. In short, the logistic equation
corrects an exponentially growing population by limiting its growth as a consequence of the saturation of the environment. The model can be written as:

$latex P(t) = P_0\frac{K}{(1+A\,e^{-kt})}$

where $latex A=(K-P_0)/P_0$, $latex P_0$ is the population at time $latex t=0$, and $latex k$ is the growth rate. Let’s start with $latex P =P_0\cdot\,e^k(t-t_0)$ where $latex P_0 = P(0) = 6$ billions, where we set $latex t=0$ as the year 2000. From this equation we can easily find $latex k\approx\,0.01$ since $latex P(17) = P_0\cdot\,e^{17\cdot\,k}$. The constant $latex k$ is the growth rate, i.e., there is an increase of about 1% in the human population per year. Using our logistic equation model we can find the maximum capacity of Earth as $latex K\approx 8$ billion people. This means that the Earth is already very close to its maximum capacity. More sophisticated models, that consider the available resources of our planet in more detail, revise the number $latex K$ to slightly larger values of 9-10 billion individuals, which is not too far off from our very crude empirical estimate.

Two differing predictions discuss very different outcomes for our future. In the first scenario, the human population will keep growing even well beyond its maximum capacity (with consequential environmental disasters, exhaustion of resources, and so forth) whereas the second scenario predicts that the human population will level off
at around 10-11 billion individuals and then stall. Indeed the population in developed countries is currently slightly shrinking or it is growing only because of massive immigration. The fertility rate drops dramatically in basically all wealthy countries for a variety of reasons. This trend might thus reasonably extend to the developing countries once they reach a similar level of wealth as the most developed countries.

In the first scenario, our civilization will be under enormous pressure to find new resources, perhaps beyond our planet, whereas in the second case our civilization might have reached a stable equilibrium. In the latter scenario what will presumably keep growing will be the power consumption per capita, rather than a combination of an increase in energy expenditure and the growing size of the population. The reason why increasing power consumption is expected is easy to understand if we postulate that the wealth of the overall human population will keep increasing over time. The power consumed by human civilization across millennia has kept increasing, but its growth
has become exponential after the industrial revolution and there is no reason why this trend should stop in the near future. Humans use a total of about $latex 10^{21}$ joules of energy every year which corresponds to about 30 TW of power. The energy comes primarily from coal, oil, and natural gas, with renewable energy playing an increasingly important role — solar power for example shows exponential growth.

The Sun provides about 1 kW of power per square meter here on Earth. If humans were able to harness 100% of the incident solar power, then we would have something of the order of $latex 10^5$ TW available. This is about 4 orders of magnitude larger than we currently use, so there seems no shortage of resources for the future.

Let’s now call the amount of power we currently consume $latex pow_0$ and let’s call this time $latex t_0$. We begin by assuming an exponential growth for the power consumption so that $latex pow(t) =pow_0\cdot\,e^c(t-t_0)$ where c is a constant. The constant c is the power consumption increase rate, which we take like 1% (one can estimate it from empirical data by looking at the historical records as done with the world population). With a growth of 1%, we will need $latex 10^5$ TW of power in about 800 years. Of course, the amount of solar power that can be effectively harnessed is much less than estimated above, since the surface area that can be covered with solar panels is a small fraction of the total land area and there must be also an efficiency factor in converting the incident energy and the one effectively usable. A more realistic (but still wildly optimistic) estimate that considers something like 1% of the incident Solar energy would place the saturation energy limit at 100-200 years from now rather than 800.

Nuclear fusion is another excellent source of energy that could become a game-changer for our civilization. It might indeed provide an enormous amount of power if we will really become able to master this technology. Fusion energy requires that hydrogen is converted (fused) into helium. This reaction has an efficiency (set by nuclear physics) of 0.7% in converting mass into energy. The total amount of hydrogen in the Earth’s crust is about 0.75% of its weight. The crust mass is 1% of the total Earth’s mass. Therefore there are about $latex 4.5\times10^{20}$ grams of hydrogen available. If all of it is fused into helium (an unrealistic assumption since most of the hydrogen is bound in water molecules) then we have a total of $latex 3\times10^{35}$ joules available. For how immensely large this amount of energy might seem, if we keep the power consumption growth at the 1% rate, we will have exhausted this energy source within a few thousand years. And considering the caveats above (amount of hydrogen truly available) this timescale will be most likely of the order of a few hundred years.  Extrapolating to the distant future is of course a complicated (if not impossible) task, resulting in inaccurate predictions most of the time. However, if no other source of energy is discovered in the meanwhile, there is no way to increase the power consumption beyond this limit.

Another important consideration to make is that using a huge amount of power produces also an enormous waste of heat. Indeed from fundamental principles of thermodynamics, we know that no thermodynamic process can exceed the efficiency of a Carnot cycle. The efficiency of a Carnot cycle can be calculated as

$latex \eta=1-\frac{T_{C}}{T_{H}}$

where the C and H subscripts refer to the temperature $latex T$ of the cold and hot body in the thermodynamic cycle. If in the near future (near because as we have seen we will reach an energy limit within, at most, a few hundred years) we will be able to reach an efficiency of 99% — which is probably extremely optimistic and unrealistic — then we will inject an amount $latex (1-\eta)\,pow_0 e^c(t-t_0)$ of heat into the environment as heat waste. Since infrared radiation is absorbed by atmospheric gases like CO2 and H2O, there is no way to get rid of this heat without having a substantial increase in atmospheric temperature. This imposes another physical limit on the amount of energy that can be realistically used by our civilization. One can think of a way to release this heat into space, by using for example special beaming devices made of mirrors, but at the current stage, this seems overly speculative.

In summary, both the human population increase, energy expenditure, and the limits imposed by the laws of thermodynamics, suggest that humanity will not be able to keep the current growth rate for more than a few hundred years. After this amount of time, we need to either level off in population & power consumption or start colonizing space. This seems a quite hard limit based on simple considerations. It appears therefore that the time window of one million years is probably a much longer time than would be necessary to exhaust the resources of a typical Earth-like planet, and our estimate of 20 million years can be considered a safe upper limit. This is a problem, as we have already discussed since it leads to some tension with the observations (Fermi paradox).

However, the amount of time elapsed before exhausting all planetary resources depends also on the number of individuals that will start the new colony. This number might be initially very small, although it needs to be larger than the so-called minimum viable population. This number is a lower bound on the number of individuals required to avoid extinction because of, among others, genetic stochasticity. The use of advanced genetic techniques or other ways of reproduction different than sexual might affect these considerations. It is therefore difficult to speculate on the possible way a new colony will grow since it might be possible to keep the number of individuals at an absolute minimum in order to provide the highest share of resources per capita. If a new colony is guided by a superintelligent agent, then keeping the number of individuals at its absolute minimum might be the most desirable option to achieve the best possible outcome. If this decision is employed, it would prolong almost indefinitely the amount of time the colony will spend on a host planet, and it might strongly reduce the need to create new daughter colonies.

By analogy with our civilization, it follows that for an initial population of, say, 10 billion individuals, there are as many as 100 million potential first-generation daughter colonies. The true numbers might be much smaller than this because the original planet could retain a large fraction of its original individuals. However, as we have seen before, a small growth rate in a group of 10 billion individuals quickly takes off, and the excess individuals might have no other choice than to leave the host planet. This again creates tension with the observations. Since there are 40 billion potentially habitable planets, then one in 400 of these planets should be already colonized, so again the question is why we haven’t seen any so far. However, if the colonies are very small there might be no need to build megastructures since the amount of power that can be extracted from the host planet might be sufficient to sustain the small colony for extremely long times. We set aside for the moment the question of how such a tiny society might work.

We reach now the following conclusion: if a civilization becomes space-faring, then the daughter colonies — guided by a putative superintelligence — need to be composed of a very small number of individuals. This is required because, in this way, they can power their (micro-)society with the resources of the host planet, without needing extra energy harnessed with megastructures. The optimization of the energy resources of a host planet might be the best strategy — perhaps suggested by a superintelligent agent — that maximizes the expected value of the colony utility function. In a certain sense, this conclusion could be very useful to set constraints on what a superintelligent agent might look like, although the risk of having made some wrong assumption during the above reasoning is high and the temptation of assigning specific properties to the superintelligent agent should be taken cum grano salis. In summary: if our hypotheses 1-4 are correct, and if we add the fifth hypothesis that a civilization needs to leave its host planet in a time shorter than 1 million years, then we reach the conclusion that many small colonies need to be present in our galaxy in this very moment.