I am a reader of your articles on extraterrestrial technologies and I am surprised by what you are doing: Calculations on concrete data that tell us new things about probable structures. (sorry for the mistakes; I don't understand English; I use a translator).

One of the data involved is the duration of these structures. But to determine the longevity of a technological civilization, one must reason on questions far removed from astronomy, the same ones that we must consider to determine whether humanity will survive. Economic, ecological, political, ethical considerations ... To live with a post-self-destructive technology it is necessary for a species to adapt its behavior and this implies the development of adequate genetics.

I have found that tech civilizations that adapt to self-destructive technology (I call them Stable Tech Civilizations, or CiTE) can meet two conditions:

1. Accumulation. If post-self-destructive technological civilizations colonize and spread, I find nothing that has killed them from their birth until now.

2. Conditional probability. If the CiTEs must colonize to have a long life, they are forced to explore and intervene in the space around them. One of the possible results of exploration is the discovery of another world with less technology or even at an earlier stage. If the first civilization increases the chances that the second civilization passes the self-destructive phase and constitutes another CiTE, then the probability of the appearance of stable forms of technology would depend on the existence of previous CiTEs.

Specifically, point 1 states that CiTEs are born but do not die and point 2 says that some CiTEs increase the probability of occurrence of others (note that in that case, the rare earth theories would only impact 100% on the pioneer CiTE)

In an approximate calculation, assuming that 8,000 My after BB arises the first CiTE and then, every 10 My increases by 1% the previous amount, I reach 13,800 My with 321 CiTEs. But when I do the math with 5%, the number is over 2 million million (2 * 10 ^ 12). Obviously, the number of habitable worlds limits the function, but still the number of CiTE is astronomical.

I am amazed at the amount of this second case, because I am only assuming the natural origin of the first CiTE, a subsequent accumulation and an increase in the natural probability of CiTEs of 5% every 10 million years.

I have studied the conditions for a potentially self-destructive technological civilization to pass through the danger zone and become stable and durable, but I have turned away from the math. Can more precise calculations be made on assumptions 1 and 2?