*What can we say about the possible appearance and spread of civilizations in the Milky Way? There are many ways of approaching the question, but in today’s essay, Dave Moore focuses on a recent paper from Robin Hanson and colleagues, one that has broad implications for SETI. A regular contributor to Centauri Dreams, Dave was born and raised in New Zealand, spent time in Australia, and now runs a small business in Klamath Falls, Oregon. He adds: “As a child, I was fascinated by the exploration of space and science fiction. Arthur C. Clarke, who embodied both, was one of my childhood heroes. But growing up in New Zealand in the ‘60s, such things had little relevance to life, although they did lead me to get a degree in biology and chemistry.” Discovering like-minded people in California, he expanded his interest in SETI and began attending conferences on the subject. In 2011, he published a paper in JBIS, which you can read about in Lost in Time and Lost in Space*.

**by Dave Moore**

I consider the paper “If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare,” by Robin Hanson, Daniel Martin, Calvin McCarter, and Jonathan Paulson, a significant advance in addressing the Fermi Paradox. To explain exactly why, I need to go into its background.

## Introduction and History

In our discussions and theories about SETI, the Fermi paradox hangs over them all like a sword of Damocles, ready to fall and cut our assumptions to pieces with the simple question, where are the aliens? There is no reason not to suppose that Earth-like planets could not have formed billions of years before Earth did and that exosolar technological civilizations (ETCs) could not have arisen billions of years ago and spread throughout the galaxy. So why then don’t we see them? And why haven’t they visited us, given the vast expanse of time that has gone by?

Numerous papers and suggestions have tried to address this conundrum, usually ascribing it to some form of alien behavior, or that the principle of mediocrity doesn’t apply, and intelligent life is a very rare fluke.

The weakness of the behavioral arguments is they assume universal alien behaviors, but given the immense differences we expect from aliens—they will be at least as diverse as life on Earth—why would they all have the same motivation? It only takes one ETC with the urge to expand, and diffusion scenarios show that it’s quite plausible for an expansive ETC to spread across the galaxy in a fraction (tens of millions of years) of the time in which planets could have given rise to ETCs (billions of years).

And there is not much evidence that the principle of mediocrity doesn’t apply. Our knowledge of exosolar planets shows that while Earth as a type of planet may be uncommon, it doesn’t look vanishingly rare, and we cannot exclude from the evidence we have that other types of planets cannot give rise to intelligent life.

Also, modest growth rates can produce Kardeshev III levels of energy consumption in the order of tens of thousands of years, which in cosmological terms is a blink of the eye.

In 2010, I wrote a paper for JBIS modeling the temporal dispersion of ETCs. By combining this with other information, in particular diffusion models looking at the spread of civilizations across the galaxy, it was apparent that it was just not possible for spreading ETCs to occur with any frequency at all if they lasted longer than about 20,000 years. Longer than that and at some time in Earth’s history, they would have visited/colonized us by now. So, it looks like we are the first technological civilization in our galaxy. This may be disappointing for SETI, but there are other galaxies out there—at least as many as there are stars in our galaxy.

My paper was a very basic attempt to deduce the distribution of ETCs from the fact we haven’t observed any yet. Robin Hanson et al’s paper, however, is a major advance in this area as it builds a universe-wide quantitative framework to frame this lack of observational evidence and produces some significant conclusions.

It starts with the work done by S. Jay Olsen. In 2015, Olson began to bring out a series of papers assuming the expansion of ETCs and modeling their distributions. He reduced all the parameters of ETC distribution down to two: (α), the rate at which civilizations appeared over time, and (v) their expansion rate, which was assumed to be similar for all civilizations as ultimately all rocketry is governed by the same laws of physics. Olsen varied these two parameters and calculated the results for the following: the ETC-saturated fraction of the universe, the expected number and angular size of their visible domains, the probability that at least one domain is visible, and finally the total expected fraction of the sky eclipsed by expanding ETCs.

In 2018, Hanson et al took Olsen’s approach but incorporated the idea of bringing in the Hard Steps Power Law into modeling the appearance rate of ETCs, which they felt was more accurate and predictive than the rate-over-time models Olsen used.

## The Hard Steps Power Law

The Hard Steps power law was first introduced in 1953 to model the appearance of cancer cells. To become cancerous an individual cell must undergo a number of specific mutations (hard steps i.e. improbable steps) in a certain order. The average time for each mutation is longer than a human lifetime, but we have a lot of cells in our body, so 40% of us develop cancer, the result of a series of improbabilities in a given cell.

If you think of all the planets in a galaxy that life can evolve on as cells and the ones that an ETC arises on being cancerous, you get the idea. The Hard Steps model is a power law, so the chances of an outcome happening in a given period of time is the inverse of the chance of a step happening (its hardness) to the power of the number of steps. Therefor the chance of anything happening in a given time goes down very rapidly with the number of hard steps required.

In Earth’s case, the given period of time is about 5.5 billion years, the time from Earth’s origin until the time that a runaway greenhouse sets in about a billion years from now.

## The Number of Hard Steps in our Evolution

In 1983 Brandon Carter was looking into how likely it was for intelligent life to arise on Earth, and he thought that due to the limitations on the time available this could be modeled as a hard step problem. To quote:

This means that some of the essential steps (such as the development of eukaryotes) in the evolution process leading to the ultimate emergence of intelligent life would have been hard, in the sense of being against the odds in the available time, so that they are unlikely to have been achieved in most of the earth-like planets that may one day be discovered in nearby extra-solar systems.

Carter estimated that the number of hard steps it took to reach our technological civilization was six: biogenesis, the evolution of bacteria, eukaryotes, combogenisis [sex], metazoans, and intelligence. This, he concluded, seemed the best fit for the amount of time that had taken for us to evolve. There has been much discussion and examination of the number of hard steps in the literature, but the idea has held up fairly well so Hanson et al varied the number of hard steps around six as one of their model variables.

## The Paper

The Hanson paper starts out by dividing ETCs into two categories: loud aliens and quiet aliens. To quote:

Loud (or “expansive”) aliens expand fast, last long, and make visible changes to their volumes. Quiet aliens fail to meet at least one of these criteria. As quiet aliens are harder to see, we are forced to accept uncertain estimates of their density, via methods like the Drake equation. Loud aliens, by contrast, are far more noticeable if they exist at any substantial density.

The paper then puts aside the quiet aliens as they are, with our current technology, difficult to find and focuses on the loud ones and, in a manner similar to Olsen, runs models but with the following three variables:

i) The number of hard steps required for an ETC to arise.

ii) The conversion rate of a quiet ETC into a loud, i.e. visible, one.

iii) The expansion speed of a civilization.

In their models, (like the one illustrated below) a civilization arises. At some point, it converts into an expansive civilization and spreads out until it abuts a neighbor at which point it stops. Further civilizations in the volume that is controlled are prevented from happening. Results showing alien civilizations that are visible from our point of view are discarded, narrowing the range of these variables. (Note: time runs forward going down the page.)

## Results

In a typical run with parameters resulting in them not being visible to us, expansive civilizations now control 40-50% of the universe, and they will finish up controlling something like a million galaxies when we meet one of them in 200 million year’s time. (Note, this paradoxical result is due to the speed of light. They control 40-50% of the universe now, but the electromagnetic radiation from their distant galaxies has yet to reach us.)

From these models, three main outcomes become apparent:

## Our Early Appearance

The Hard Step model itself contains two main parameters, number of steps and the time in which they must be concluded in. By varying these parameters, Hanson et al showed that, unless one assumes fewer than two hard steps (life and technological civilizations evolve easily) and a very restrictive limit on planet habitability lifetimes, then the only way to account for a lack of visible civilizations is to assume we have appeared very early in the history of civilizations arising in the universe. (In keeping with the metaphor, we’re a childhood cancer.)

All scenarios that show a higher number of hard steps than this greatly favor a later arrival time of ETCs, so an intelligent life form producing a technological civilization is at this stage of the universe is a low probability event.

## Chances of other civilizations in our galaxy

Another result coming from their models is that the higher the chance of an expansive civilization evolving from a quiet civilization, the less the chance there is of there being any ETCs aside from us in our galaxy. To summarize their findings: assuming a generous million year average duration for a quiet civilization to become expansive, very low transition chances (p) are needed to estimate that even one other civilization was ever active anywhere along our past light cone (p < 10^{−3}), or existed in our galaxy (p < 10^{−4}), or is now active in our galaxy (p < 10^{−7}).

For SETI to be successful, there needs to be a loud ETC close by, and for one to be close by, the conversion rate of quiet civilizations to expansive, loud ones must be in the order of one per billion. This is not a good result pointing to SETI searches being productive.

## Speed of expansion

The other variable used in the models is the speed of expansion. Under most assumptions, expansive civilizations cover significant portions of the sky. However, when taking into account the speed of light, the further distant these civilizations are, the earlier they must form for us to see them. One of the results of this relativistic model is that the slower civilizations expand on average, the more likely we are to see them.

This can be demonstrated with the above diagram. The orange portion of the diagram shows the origin and expansion of an ETC at a significant proportion of the speed of light. We—by looking out into space are also looking back in time—can only see what is in our light cone (that which is below the red line), so we see the origin of our aliens (say one billion years ago) and their initial spread up to about half that age. After which, the emissions from their spreading civilization have not yet had time to reach us.

The tan triangle represents the area in space from which an ETC spreading at the same rate as the orange aliens would already have arrived at our planet (in which case we would either not exist or we would know about it), so we can assume that there were no expansive aliens having originated in this portion of time and space.

If we make the spread rate a smaller proportion of the speed of light, then this has the effect of making both the orange and tan triangles narrower along the space axis. The size of the tan exclusion area becomes smaller, and the green area, which is the area that can contain observable alien civilizations that haven’t reached us yet, becomes bigger.

You’ll also notice that the narrower orange triangle of the expansive ETC crosses out of out of our light cone at an earlier age, so we’d only see evidence of their civilization from an earlier time.

The authors note that the models rely on us being able to detect the boundaries between expansive civilizations and unoccupied space. If the civilizations are out there, but are invisible to our current instruments, then a much broader variety of distributions is possible.

## Conclusions

We have always examined the evolution of life of Earth for clues as to the distribution alien life. What is important about this paper is that it connects the two in a quantitative way.

There are a lot of assumptions build into this paper (some of which I find questionable); however, it does give us a framework to examine them and test them, so it’s a good basis for further work.

To quote Hanson et al:

New scenarios can be invented and the observable consequences calculated immediately. We also introduce correlations between these quantities that are obtained by eliminating dependence on α [appearance rate], e.g. we can express the probability of seeing at least one domain as a function of v [expansion velocity] and the currently life-saturated fraction of the universe based on the fact we haven’t see or have encountered any.

I would point out a conclusion the authors didn’t note. If we have arisen at an improbably early time, then there should be lots of places (planets, moons) with life at some step in their evolution, so while SETI searches don’t look promising from the conclusions of this paper, the search for signs of exosolar life may be productive.

This paper has given us a new framework for SETI. Its parameters are somewhat tangential to the Drake Equation’s, and its approach is to basically work the equation backwards: if N=0 (number of civilizations we can communicate with in the Drake equation, number of civilizations we can observe in this paper), then what is the range in values for f_{i} (fraction of planets where life develops intelligence), f_{c} (fraction of civilizations that can communicate/are potentially observable) and (L) length of time they survive. The big difference is that this paper factors in the temporal distribution of civilizations arising, which is not something the Drake Equation addressed. The Drake equation, for something that was jotted down before a meeting 61 years ago, has had a remarkably good run, but we may be seeing a time where it gets supplanted.

## References

Robin Hanson, Daniel Martin, Calvin McCarter, Jonathan Paulson, “If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare,” *The Astrophysical Journal*, 922, (2) (2021)

Thomas W. Hair, “Temporal dispersion of the emergence of intelligence: an inter-arrival time analysis,” *International Journal of Astrobiology* 10 (2): 131–135 (2011)

David Moore, “Lost in Time and Lost in Space: The Consequences of Temporal Dispersion for Exosolar Technological Civilizations,” *Journal of the British Interplanetary Society*, 63 (8): 294-302 (2010)

Brandon Carter, “Five- or Six-Step Scenario for Evolution?” *International Journal of Astrobiology*, 7 (2) (2008)

S.J. Olson, “Expanding cosmological civilizations on the back of an envelope,” arXiv preprint arXiv:1805.06329 (2018)