Basics
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 4 (January 2014), are in the early phase of being fleshed out.
h = Ppop / Epop = F / (a_{h} * F + b_{h})
Epop = a_{e} * Ppop^{2} + b_{e} * Ppop + c_{e} for Epop < Emax
F * Ppop = a_{m} * Emax^{2}+ b_{m} * Emax + c_{m} for Epop < Emax
L = F / (a_{L} * F + b_{L} )
where:
Version 3 (for a detailed overview, see Population, Consumption, and the Future of the World)
Consumption = M_{t} * P^{2} / 2 + M_{e} * P
Cmax = M_{t} * Pmax^{2} / 2 + M_{e} * Pmax
Poprate = Ratemag * P / Pmax * (1 - P / Pmax)
where:
Consumption = A * (r_{2}/r_{1})^{F} * t^{B*EXP(C*t^D+E*t^(D-1))}
Population = G * Consumption^{0.5}
Speed = H * Consumption
where:
Happiness, Consumption, and Life Expectancy
Happiness = a * LN(Consumption) + b
Lifespan = c * LN(Consumption) + d
Where a, b, c, d are constants.
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.
Emissions = f * Consumption^{1.5}
Temperature = g * Consumption^{3} + InitialTemperature
Where f and g are constants, Consumption is proportional to the Global Ecological Footprint.
© Copyright 2011-2012 Bradley Jarvis. All rights reserved.