## Happiness Calculations

Where:

- C = Mass consumed by population (lb/year)
- H = Happiness (fraction)
- F = Ecological footprint (hectares/year)
- P = World population (people)
- S = Transport speed (miles/hr)
- Rmax = Initial resources in 1 AD (lb)
- Rearth = Resources produced by biosphere per year, "natural capacity" (lb)
- Hmax = Maximum happiness (1)
- Hearth = Happiness when C = Rearth
- Hmaxr = Happiness when C = Rmax
- Hcrash = Ideal happiness when population crashes (linear model)
- Hlight = Happiness at S = speed of light
- Cmax = Consumption at Hmax
- Cmin = Consumption in 1 AD
- Cpeak = Consumption at projected peak population
- Pmin = Population in 1 AD
- Ppeak = Population at projected peak population
- Pmax = Population at Hmax
- Slight =Speed of light
- Smax = Speed at Hmax

Relationships:C: k*F*P = k*n*EXP(2*(H-j)/g) lb/yr H: g*LN(F) +j P: n*F people S: m*C mi/hr F: EXP((H-j)/g) hectares/yr Constants (empirical):g: 0.124494544 j: 0.492513147 k: 1000 n: 2.51E+09 m: 2.78431E-11 Miscellaneous:Cmax: 8.71708E+15 lb/yr Cmin: 2.51409E+10 lb/yr Smax: 2.42710E+05 mi/hr Slight:

6.70615E+07 mi/hr Pmax: 1.47918E+11 people Ppeak: 8.16562E+09 people Rearth: 1.19E+13 lb Cmax/Pmax: 58931.6 Cmax/Rmax: 7.6 Cmax/Rearth: 732.5 Cmax/Cmin: 346728.7 Pmax/Pmin: 588.4 Cmax/Cpeak: 328.7 Pmax/Ppeak: 18.1 Cmax/day: 2.38824E+13 Smax/Slight: 3.61922E-04 lSlight/Smax: 2763.0 Cmax/Cpeak/12: 27.4 Lunar Periods: 1.0 n/Pmin: 10.0 Asteroid Diameter(Cmax): 18.0 km Hearth: 0.59 Hmax: 1 Hmaxr: 0.87 Hcrash:

0.65 Hlight: 1.49 Hearth/Hmaxr: 0.67 Hcrash/Hmax:

0.65 Hmax/Hlight: 0.67 Note: H(2/3 Hearth): 0.392923895 occurred in 1857, when max H was 0.581386935 (nearly Hearth, which was reached in 1861).

See also:

- "Peak Happiness" (blog post)
- "Two-Thirds Happiness" (blog post)
- Remaining Resources: A Simulated History
- Limits to Happiness
- Happiness and Population Growth
- Happiness and Resources
- Happiness and Acceleration

© Copyright 2011 Bradley Jarvis. All rights reserved.