Back at Charlie Stross' "Mediocrity," commenter Rick York

pointed to an

interesting new approach to the question of where extraterrestrial civilizations are, in the arXiv-hosted paper

"Where is everybody? -- Wait a moment ... New approach to the Fermi paradox".

*[T]here is another take on the problem thanks to a new approach by Igor Bezsudnov and Andrey Snarskii at the National Technical University of Ukraine.*

Their approach is to imagine that civilisations form at a certain rate, grow to fill a certain volume of space and then collapse and die. They even go as far as to suggest that civilisations have a characteristic life time, which limits how big they can become.

In certain circumstances, however, when civilisations are close enough together in time and space, they can come into contact and when this happens the cross-fertilisation of ideas and cultures allows them both to flourish in a way that increases their combined lifespan.

Bezsudnov and Snarskii point out that this process of spreading into space can be easily modelled using a cellular automaton. And they've gone ahead and created their own universe using a 10,000 x 10,000 cell automaton running over 320,000 steps.

The parameters that govern the evolution of this universe are simple: the probability of a civilisation forming, the usual lifespan of such a civilisation and the extra bonus time civilisations get when they meet.

The result gives a new insight into the Fermi Paradox. Bezsudnov and Snarskii say that for certain values of these parameters, the universe undergoes a phase change from one in which civilisations tend not to meet and spread into one in which the entire universe tends to become civilised as different groups meet and spread.

Bezsudnov and Snarskii even derive an inequality that a universe must satisfy to become civilised. This, they say, is analogous to the famous Drake equation which attempts to quantify the number of other contactable civilisations in the universe right now.

The

Drake equation is a famous equation developed by physicist Frank Drake to define the parameters governing the possibility of communicative extraterrestrial civilizations. See below for the cut and paste from Wikipedia.

*The Drake equation states that:*

N = R* * fp * ne * fl * fi * fc * L

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R* = the average rate of star formation per year 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 the above that actually go on to develop life at some point

fi = the fraction of the above that actually go on to develop intelligent life

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time such civilizations release detectable signals into space

Bezsudnov and Snarskii present their modification to the Drake equation in this way.

*Civilizations are born with the probability *n* and have the initial life time (time of expansion) *T*0 set in advance after which they die (disappear or cease to show itself). Contact of developing Civilizations increases actual life time for everyone contacted on a certain extra time, named further a time bonus Tb . We will refer to this model as a Bonus Stimulated model (BS-model).*

Further we will use terminology adapted for discussion of Fermi paradox even though the offered model can describe and another phenomena. It is possible to offer the analogy to economy, and in this instance the initial lifetime 0 T is a seed capital of the new formed company. Also this capital defines time of company’s independent life, while association process of this company with other companies stimulate the further development, increasing stability of existence of association by b T value etc.

Arguably, the Bezsudnov-Snarskii thesis is hopeful: we might just have to wait. (Definitions of "we" have to vary.)

*Modern, certainly, not indisputable, estimations for N are the values of an order of 1, (more precisely (10) from 0.05 to 5000). The same estimation is also true for any other Civilization in our Universe, hence, Intellect should extend on all of the Universe. While this fact did not happened yet, unfortunately, or to be more precise we are not included yet in this global process which, probably, already going on!*

[. . .]

Fermi paradox: proposed and investigated BS-model is moderately optimistic. It is shown that there exists a scenario when at the given moment almost all Civilizations are lonely– «there is nothing», however after some, sufficiently prolong time Civilizations will get into a contact and the Universe as a whole becomes civilized. Conclusion is that it is necessary to wait!

This thesis appeals to my liking for non-zero sum solutions.