Maybe they are all gone

Earlier this year, I wrote an article about the 1961 Drake Equation. This is the equation which is used to estimate the number of advanced civilisations in the Milky Way galaxy. That article, entitled ‘Where is everyone’ was in part driven by new estimates of some of the parameters used in the equation. That title was like the phrase used by the Nobel Prize winning Italian physicist, Enrico Fermi, when, back in 1950, during a discussion of sightings of Unidentified Flying Object, he asked ‘Where is everybody’. It alluded to the fact that the universe is so huge, stars so numerous and presumably planets so numerous, but we only know of life on one planet? This was known as the Fermi Paradox¹. Coincidentally, Enrico Fermi died in 1954, on the same date I started writing this, the 28^th of November²  (there have been many interruptions; it’s that time of year). A recent paper (Wong & Bartlett 2022) has been published which may explain why we haven’t had any visitors, or detected any telltale radiation (e.g. radio waves) from advanced civilisations³. However, the terminology is a bit difficult for me and, I suspect, many others to understand. So, we have to go back a bit to understand ‘superlinearity’ and to get a bit of background.

Bettencourt et al. (2007) proposed a different way of looking at how exceptional cities are. Looking at a city using a ‘linear’ scale you would expect that the per capita rate of wealth, productivity, innovation, energy use and crime would remain about the same as the city grew. However, that is not so. They have shown, in fact, that with each doubling of city population, each inhabitant is, on average, 15% wealthier, 15% more productive, 15% more innovative, uses 15% more energy, and 15% more likely to be a victim of violent crime, regardless of the city’s geography or from what time the data comes. This phenomenon is termed “superlinear scaling”⁴. 

One of the authors, Luis Bettencourt, said: “Almost anything that you can measure about a city scales nonlinearly, either showing economies in infrastructure or per capita gains in socioeconomic quantities. … This is the reason we have cities in the first place”^5. This superlinearity is attributed to the social nature of cities³.

What Bettencourt et al. (2007) showed, is that many properties of cities (e.g. GDP, patents, wages, disease and crime) are power law functions of population size with a superlinear scaling exponent termed β which is greater than 1 (β>1) rendering increasing returns with increasing size. Their analysis showed that when β>1, unbounded growth will occur, tending towards infinite population (and hence towards infinite demand on resources) in a finite amount of time. If such a ‘singularity’ is approached unchecked, the system will eventually exceed its energy supply and collapse (or significantly regress). However, Bettencourt et al. (2007) suggested that singularities can be avoided by major qualitative changes, or ‘innovations’, that reset the initial conditions and parameters of the growth equation and set the city on a new trajectory. However, if the underlying dynamics remain, i.e. β>1 still holds true, then the city will be on a trajectory towards a new singularity later in time³. These ‘innovations’ simply postpone the system’s collapse.

Wong & Bartlett (2022) hypothesise that with the interconnectedness granted by the internet, a planetary civilisation transitions to a state akin to a global city, and it too will face what they term an ‘asymptotic burnout’; an ultimate crisis where the singularity-interval time scale becomes shorter than the innovation time scale. However, if such a global civilisation develops the capability to understand this trajectory, it will have a window of time in which to undertake fundamental change to prevent that collapse. To do this it will have to head toward long-term homeostasis* and ‘well-being’ instead of unyielding growth. Wong & Brtlett use this to propose a new resolution to the Fermi paradox: civilisations either collapse from burnout or redirect themselves to prioritising homeostasis, a state where continued expansion is no longer a goal, making them difficult to detect remotely³. This may be why we haven’t had any visitors.

*Homeostasis: This is any self-regulating process by which biological systems tend to maintain stability while adjusting to conditions that are optimal for survival. If homeostasis is successful, life continues; if unsuccessful, death ensues. The stability attained is actually a dynamic equilibrium, in which continuous change occurs yet relatively uniform conditions prevail⁶.

Sources

1. https://blotreport.com/2023/02/15/where-is-everyone/
2. https://www.britannica.com/biography/Enrico-Fermi
3. https://royalsocietypublishing.org/doi/10.1098/rsif.2022.0029
4. https://www.pnas.org/doi/10.1073/pnas.0610172104
5. https://www.santafe.edu/news-center/news/city-ranking-bettencourt
6. https://www.britannica.com/science/homeostasis