Useful Equations

Equations that are relevant to the task of m21

See shopping equation
See synergy equation

Synergetics

• Fuller (Synergetics) that, in triangulated systems, the number of faces = the number of vertices X2 - 2
• The number of edges = (no. of vertices) X3 - 2
• Hence:
• F = 2(V - 2)

and

• E = 3(V - 2)
  Simplifying,
• F = 2V - 4, E = 3V - 6
• F + 4 = 2V
• E + 6 = 3V
• Combining the two equations by subtraction, we have E + 6 = 3V
• - (F + 4 = 2V)
• ___
• E - F + 2 = V
• or
• E + 2 = V + F.

Ehrlich and Holdren's original (1971) equation for environmental damage states that:

I = P x C x T

where:
I = environmental Impact
P = Population
C = Consumption per head
T = 'environmental intensity', or environmental impact per unit of consumption

A revised (2002) version states that:

TEI = P x UC/hp x EE -1

where:
TEI = Total Environmental Impact
P = Population
UC/hp = (average) Units of Consumption of products and services per Head of Population
EE = the environmental efficiency of the production, use and disposal of those units.
(N.B. - Rebound effects may be caused by improvements in EE because they tend to stimulate consumption)

Arne Naess (Naess, 1989) devised an equation for Well-being

W = G squared / Pb + Pm

where:
W = Well-being
G = Glow
Pb = bodily Pain
Pm = mental Pain

Maximum number of relations within a set of agents

This can be calculated thus:

R = {(n-1) x n} / 2

Where:
R = maximum number of relations among agents
n = number of agents

A Table of Results