Probabilities in the Galaxy
A Distribution Model for habitable Planets
Copyright © Klaus Piontzik Claude Bärtels

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German Version    


13.5.5 - Total Number of humanoid Civilizations

Derived from equation 12.2.2, the total number of humanoid civilizations in the galaxy is the sum of all spectral classes:

  NHumZivGal = ∑ Nzx = A·∑ (Fx · Fph · Fk · FLiz· Fm)
   
13.5.5.1 Equation


Then the equation can be written like this:

13.5.5.2 Equation


This results in the number of humanoid civilizations of
one civilization level in the galaxy:

13.5.5.3 Equation


According to equation 6.2.4, the following probability for a civilization level can be established :

 


The total probability results from the sum of the individual probabilities when a set of civilization levels is considered.

 


Technological civilizations are levels 6, 7 and 8, so the probability of a humanoid technological civilization is:


F
z = 14.400/7.301 · (1:36+1:49+1:64)
F
z= 405.225/3.218.741 = 1:7,943 ¤ 1:8
F
z= 1:8

If you want to know how many humanoid civilizations exist in total, then you have to look at levels 3 - 8, i.e. the human development time. Therefore, the probability of a humanoid civilization


F
z = 14.400/7.301 · (1/9 + 1/16 + 1/25 + 1:36+1:49+1:64)
F
z= 0,547,168 = 1:1,82759 ¤ 1:2
F
z= 1:2

If you want to know how many humanoid civilizations and precursors exist in total, then you have to look at levels 2 - 8, i.e. the actual human development time. Therefore, the probability of a humanoid civilization:


F
z = 14.400/7.301 · (1/4 + 1/9 + 1/16 + 1/25 + 1:36+1:49+1:64)
F
z= 1,04025 ¤ 1
F
z= 1

It was to be expected that across all levels of civilization, at least 1 existed, i.e.
Fz= 1:

So for the number of humanoid civilizations in the galaxy:

13.5.5.4 Equation


Adapted to the model used so far:

 


 

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