Useful Equations

Equations that are relevant to the task of m21

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See shopping equation
See synergy equation

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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.

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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)

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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

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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

Number of interconnected agents	number of first order relations	number of second order relations	number of third order relations
1	0	0	0
2	1	0	0
3	3	3	3
4	6	15	105
5	10	45	990
6	15	105	5460
7	21	210	21945
8	28	378	71253
9	36	630	198135
10	45	990	489555
11	55	1485	1101870
12	66	2145	2299440
13	78	3003	4507503
14	91	4095	8382465
15	105	5460	14903070
16	120	7140	25486230
17	136	9180	42131610
18	153	11628	67599378
19	171	14535	105625845

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