As soon as we try to be specific about writing a complete meme population dynamics equation that covers all memes in a society we encounter a counting problem.  What do we count?  Memes are arranged into various relation groups.  These are often referred to as meme complexes.  Is the meme complex a meme that we should count?  What if someone has not acquired all of the memes that are considered to be a part of the complex?  Does this form a different meme complex?  It seems best not to count complexes, but only the memes that make up the complex.  But what are those memes?  At what point do we stop subdividing a meme?  Is there such a thing as an atomic meme?  I know of no way to resolve this.  Therefore, I will simply assume that we have some arbitrary list of memes that will be called atomic. 

We cannot ignore all complex of these atomic memes because then we would ignore every variation of combinations of a given set of atomic memes.  The only way I know to resolve this is to use John Holland’s approach in his Genetic Algorithm.  This requires an encoding into some type of string (e.g. DNA).  I will apply this approach with mimemes which I introduce later.  But we are attempting to understand the concept of meme evolution without mimemes just yet.  So for the moment I will simply assume that there is another way to resolve this. 

I assume that there are a set of memes (including complexes) that we can number from 1 to N, where N is the number of different memes.  There are three fundamental processes within meme dynamics;

1. spread,
2. replacement,
3. changed meme value, and
4. creation.

Let’s consider each separately and then together.

Spread

We can capture logistics growth and competition by writing

Where  for i = j.  But we still need to account for three other obvious dynamics; prerequisite, cooperative, and antagonistic memes.  Cooperative and antagonistic memes can be accounted for as follows.

Where for i = j, for cooperation, andfor antagonism.  We still need to account for pre-requisite memes.  Let us write

,                                   (10.7)

where  if meme j is not a prerequisite for meme i and  if j is a prerequisite for i.

Replacement

From 10.6 we see we can add competitive replacement as follows.

,                 (10.8)

where  is the replacement rate of meme i with meme j.

Changed Meme Value

We need to account for the perceived value of a meme changing.  It can change in response to an environmental change, the acquisition of other memes, other person internal factors.  All of which points out that  and  are each driven by individual characteristics and that in assigning these parameters to a population we are assuming that it is possible to derive some useful average.  As it stands equation 10.8 assumes that  and  are constant.  There are likely periods of time of stability where this is reasonably true, but it is precisely those periods of instability that interest us the most.  Acknowledging that  and  are some function of the situation (S) we can write. 

,                     (10.9)

Creation

How shall we account for new memes?  It would be difficult to write a set of equations where N is increasing.  Therefore let us assume that N indexes all memes including those that have not been created (i.e. invented). 

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