RE: Terminology and Quantification

Aaron Lynch (
Tue, 20 Jul 1999 10:11:43 -0500

Message-Id: <>
Date: Tue, 20 Jul 1999 10:11:43 -0500
From: Aaron Lynch <>
Subject: RE: Terminology and Quantification
In-Reply-To: <002301bed280$ae37ec60$0d9e8cd4@paul>

At 09:22 AM 7/20/99 +0200, Paul Marsden wrote:
>David asked a simple, but critical question in Science that deserves a
>straight and clear answer.
>How do you define memetic fitness? Answers please.

David Sloan Wilson is not quite right when he says that "The ability to
define fitness independently of what evolves saves the concept of natural
selection from being a tautology." The parameters used to make a
non-tautological, specific statement of how much a meme spreads and on what
schedule need not be given the name "fitness" in order for the theory to
remain non-tautological. A serious mathematical model of memetic selection
should use multiple propagation parameters, no one scalar of which should
be considered "fitness" on its own. Hence, I do not use the term "fitness"
in my mathematical model. Moreover, when "fitness" is defined
mathematically, it is defined with respect to a specific mathematical model
based on particular premises that do not apply universally. Hence, there is
no one universal mathematical definition of "fitness" even when the term is

Though I did not find it particularly useful to define a mathematical
construct labeled "fitness" in my model, it is nevertheless possible to do
so. It would not be a scalar, but rather, a matrix composed of all the
propagation parameter functions listed as the rows with values for
different ages going down the columns. That is, it would be a formalized,
quantitative "propagative profile."

Blackmore's section on "Sociobiology and Culture on a Leash," (p. 32-36)
does, as Gatherer points out, mention Cavalli-Sforza and Feldman's use of
mathematics and the *concept* of 'cultural fitness.' However, she says that
their placement of culture on a leash distinguishes their model from a
truly memetic model. Hence, D. S. Wilson is justified in not taking this
section to have effectively pointed him to a quantitative definition of
specifically *memetic* fitness. Right after that, Blackmore even mentions
that Boyd and Richerson have "let go of the leash" (without using the word
"meme") but amazingly, she neglects to mention that they have developed a
mathematical analysis. Later in the book, she also mentions my 1991 paper
"Thought Contagion as Abstract Evolution," but again does not mention that
it contains a specifically memetic mathematical model. The problem is not
that Blackmore does not mention works that contain mathematical models of
culture or mathematical memetics, but that she does not explicitly *tell*
the reader that these works contain mathematical models that specifically
qualify as memetic rather that sociobiological. This problem could easily
have been averted by asking some who have worked with mathematical memetics
to check her manuscript. Hopefully, the situation will improve in revised
editions, although it is still too late to stop that round of "tautology"
charges in _Nature_ and _Science_.

--Aaron Lynch

This was distributed via the memetics list associated with the
Journal of Memetics - Evolutionary Models of Information Transmission
For information about the journal and the list (e.g. unsubscribing)