Limit-Seeking Case

Note that this page was updated on 10/5/2015.

The following graph shows normalized values for key variables based on limit-seeking with historical parameters:

This case uses the following assumptions:

Values	Conditions and Descriptions
Start Year = 2015	Start Year = year that variables begin to apply to projections (reflected in next year)
Fprog = ( F_year - F_year-1) / ( Flimit_year-1 - F_year-1) Fprogpref = A * Fe_year-1	Fprog = footprint progress Fprogpref = preferred footprint progress Fe + 2 * FeMin < FeTotal Flimit = ( FeTotal - P * Fmin ) / P A = 0.003497308 Fmin = 7.23E-11 Earth/person/year
Pprog = ( P_year - P_year-1) / ( Plimit_year-1 - P_year-1) Pprogpref = B1 * Fe_year-1^B2	Pprog = population progress Pprogpref = preferred population progress Fe + 2 * FeMin < FeTotal Plimit = FeTotal / ( F + Fmin ) B1 = 0.01613707 B2 = 1.448977982
( P_year - P_year-1) / P_year-1 <= Maximum [ ( P_year - P_year-1) / P_year-1]_{year = 1950 to 2015}	P_year - P_year-1> 0
Total Resources = FeTotal_year = Rrate * (year - year₀) + FeTotal₀	FeTotal₀ = 2.783331687 Earth/year year₀ = start year Rrate = annual rate of change = 0
FeMin_adj = FeMin_proj - [ FeTotal_year - (Fe_proj + 2 FeMin_proj ) ]	FeMin_adj = adjusted FeMin P_proj = Pprogpref * ( Plimit_year-1 - P_year-1) F_proj = Fprogpref * ( Flimit_year-1 - F_year-1) FeMin_proj = projected Femin = P_proj * Fmin Fe_proj = P_proj * F_proj
F_adj = Fmin * ( FeTotal_year - 2 * FeMin_adj ) / Femin_adj	P_adj = adjusted P = FeMin_adj / Fmin
P_year = P_year-1+ Pdelta	Pdelta = Pweight * (P_adj - P_year-1) Pweight = P overshoot weight = 1
F_year = F_year-1+ Fdelta	Fdelta = Fweight * (F_adj - F_year-1) Fweight = F overshoot weight = 1
Economy = 3.57763284972246E-18 * ( P * h )²	Economy = Gross World Product ($T 2009) h = happiness = F / ( 1.22 * F + Fmin ) Fmin = 7.23E-11
L = 1.74359E-06 * Fe⁴ + -0.000292725 * Fe³ + 0.01679366 * Fe² - 0.314351519	L = life expectancy in years Fe = global footprint in Earth/year

The allocation of resources is shown in the following graph, where:

Creations and People together use Fe resources
Supporters use Femin resources
Producers use Femin resources

The following graph plots casualties over time, using two ways of estimating them. Drop From Peak is the difference between the peak (maximum) population and the population calculated for a given year. Cumulative adds up all negative changes in population. These represent low and high estimates, respectively.

This case is summarized in the following report, which is used in other related cases:

For a discussion, see the blog post "Two Stories."