Useful numerical synergies

(return to synergies page or see other key terms)




These notes describe synergies as relationships that are auspicious because they deliver abundance.

• This is implied in the popular shorthand for synergy as: 1+1=3
• i.e. each '1's' represents a thing that we combine to obtain the surplus (i.e. a '3' instead of a '2').

1. Harry Beck adapted his famous (1933) London Underground map notation from Leonhard Euler.
2. In mapping teamwork we represent the nodes as 'things' (agents/actors) and the interconnecting lines as relationships.

1. The above diagram represents 1+1=3 if we can accept that the relationship (line) exists as 'Thing 3'
2. If we start with 3 'things' we will get an equal number of relationships (i.e. potential synergies).

1. We can represent this as 1+1+1=6 if we only count each 'things' as a 1, then add in the relations.
2. If we increase the number of interconnected things we transition from a 2D to a 3D figure.
3. As we increase the number of nodes (i.e. ingredients/players) the number of interrelations increases exponentially.

1. In 1751, Euler noticed a pattern in polygons that can be usefully applied to the organisation of creative teams.

• Euler's Law states that V + F = E + 2 where -
  • V represents the number of vertices
  • F represents the number of faces
  • E represents the number of edges

1. Each relationship has the potential to be regarded or applied as a useful synergy. 
2. Therefore, by focusing on relationships, rather than agents we may notice important synergies.
3. Leonhard Euler's formula for polygons (1751) demonstrates that quartets have 6 x more relations than duets. 
4. This can be charted as an ingredient:relations ratio.

NUMBER OF AGENTS		NUMBER OF POSSIBLE RELATIONS	RATIO OF PLAYERS TO RELATIONS
1	0	infinite
2	1	1:0.5
3	3	1:1
4	6	1:1.5
5	10	1:2
6	15	1:2.5
7	21	1:3
8	28	1:3.5
9	36	1:4
10	45	1:4.5

1. At the low number end of the scale the biggest increase (300%) is from 2 ingredients to 3. 
2. but 3 is not ideal because there is no additional benefit from combining the relations to create 'relations-of-relations' (3 creates 3 ad infinitum)
3. After 3, the rise to 4 agents means that the relations double from 3 to 6
4. Going from 3 to 4 players therefore doubles the advantage of clustering 

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

1. A more quantified analogy of the different granularities of thought can be expressed as the difference between noughts and crosses, chess, and 'Go'.
2. Noughts & Crosses = board with 3 x 3 squares = 765 essentially different moves
3. Chess = board with 8 x 8 squares = Ten to the power of 120 possible moves
4. GO board = 19 x 19 squares = Ten to the power of 761 possible moves