Basics

Basics

Population-Consumption Model

This mathematical model relating world population and consumption of resources has gone through several versions. Most of the content on this site relates to Version 2. The implications of the latest, Version 3 (May 2011) are in the early phase of being fleshed out.

Version 3

Consumption = M_t * P² / 2 + M_e * P

Cmax = M_t * Pmax² / 2 + M_e * Pmax

Poprate = Ratemag * P / Pmax * (1 - P / Pmax)

where:

Cmax is maximum consumption
P is population
Pmax is maximum population based on Cmax
Poprate is the population rate (fractional change per year)
Ratemag is the maximum normal population rate
M_t is transaction mass
M_e is extraction mass

Version 2

Consumption = A * (r₂/r₁)^F * t^{B*EXP(C*t^D+E*t^(D-1))}

Population = G * Consumption^0.5

Speed = H * Consumption

where:

r₂ is the previous year's resources
r₁ is the resources two years earlier
t is the year
The rest are constants

Happiness, Consumption, and Life Expectancy

Happiness = a * LN(Consumption) + b

Lifespan = c * LN(Consumption) + d

Where a, b, c, d are constants.

Good World

For each species s with population P_s and life expectancy L_s:

W_s = P_s * L_s

Where V is the total number of species, the total amount of good W in the observable universe is:

W = ∑_s=1^s=V(P_s * L_s)

If we integrate W over the entire lifetime of the universe, it should ideally be at large as possible.

Climate Change

Emissions = f * Consumption^1.5

Temperature = g * Consumption³ + InitialTemperature

Where f and g are constants.