Longevity Function (Version 1)

The time for a fixed population to deplete its resources ("depletion time") is a function of the speed that the resources can be moved and the total amount of resources.

Where "v" is the speed as a fraction of the speed of light and "R" is the amount of resources in Earth masses, the depletion time "T" in years is represented by the following "longevity function" (based on the combined population model):

T = 4.58E5 R / v ; where a = 4.58E5 (where "E" means "times 10 raised to the following exponent")

Values for these variables are projected to be the following at the end of 2008:

R = 8.02E-11; v = 5.57E-07

Projections indicate that by the population peak in 2037, they will be

R = 2.41E-11; v = 1.15E-6

On the other hand, population size "P" (people) and per-capita consumption "U" (in Earth masses) are each proportional to the square root of speed:

P = 9.29E12 v^.5

U = 2.35E-19 v^.5

According to the Second Law of Consumption, where "Lgen" is generation time, "Umin" is minimum per-capita consumption, and "Lmin" is the life expectancy when U = Umin:

L = Lgen Log(U/Umin)+ Lmin = 21 Log(1.32E+23 U) + 40

As a corollary, life expectancy (in years) is related to the natural logarithm of speed:

L = 4.56 Ln(v) + 134 = 10.5 Log(v) + 134

Happiness (as a fraction of the maximum, 1) is poroportional to L:

H = L/134

In terms of "U" the longevity function can be written as:

T = b R / U^2 ; b = 2.53E-32

Relating T and L:

L = 21 Log(R/T)+525.5