Re: memetic fitness

Aaron Lynch (
Wed, 21 Jul 1999 08:58:39 -0500

Message-Id: <>
Date: Wed, 21 Jul 1999 08:58:39 -0500
From: Aaron Lynch <>
Subject: Re: memetic fitness
In-Reply-To: <2CDFE2C8F598D21197C800C04F911B203492AD@DELTA.newhouse.akzo

At 09:06 AM 7/21/99 +0200, Gatherer, D. (Derek) wrote:
> 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
>There is however, a universal evolutionary definition, and that's the one we
>should stick to. There's no reason to throw out Cavalli-Sforza's
>definition, provided the assumptions his theory requires are acknowledged.
>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
>Amazingly she does mention it p75 and p198
>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.
>But your model is an epidemiological one, so mentioning Cavalli-Sforza and
>Feldman covers it. A model is only worth mentioning when it's sufficiently
>unlike previous models to merit discussion in its own right.
>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.
>I don't see the point. Fitness is fitness, whether you're dealing with a
>strict gene-determinist sociobiological model or a Cavallian one.
>This problem could easily
>have been averted by asking some who have worked with mathematical memetics
>to check her manuscript.
>As I've said before Aaron, I have several publications in mathematical
>genetics. Your persistent attempts to imply that we Meme Labbers are a
>bunch of mathematical illiterates would be insulting if it weren't so
>ludicrous. There is nothing in MM that constitutes a mathematical error, or
>even a mathematical misrepresentation, of any kind.

I disagree on all of these points, but have also learned that attempting
discourse with you is futile. It seems that I can discuss disagreements
with Mario about "replication" and with most other memeticists about a
variety of topics and come away with a sense that efficient, productive
discourse took place even if basic disagreements remain. I do not yet find
that with you, Derek.

I also do not expect you to budge one millimeter from arguing against
calling attention to certain works of specifically memetic mathematics. I
will, however, say that if less attention were given to finding reasons for
not discussion such work more clearly, then the reviews in NATURE and
SCIENCE might have gone better. One should not get caught up in questions
of why Blackmore should be so "nice" to Moritz, Lynch, Heylighen, etc., as
to tell people about their mathematical memetics. Rather, it is a question
of accepting that others have already been "nice" enough to make such work
available to her, thus fortifying her book against certain criticisms
raised in NATURE and SCIENCE.

I recommend that readers check to see what Blackmore actually said on p. 75
and 198 to see if it really announces the existence of mathematical
memetics (as distinct from mathematical group selection theory). I also
recommend that readers read my mathematical model directly to form their
own opinion about whether it is sufficiently distinct from previous works
to warrant mention--again, I see no point my arguing this with Derek. Note,
however, that Dennett recently found the paper's mathematics sufficiently
distinct to mention in his forthcoming paper, "The Evolution of Evaluators"
in a volume of the Siena workshop on evolutionary economics. And I would be
fascinated to hear from anyone who can point to any system of non-linear,
partial differentio-integral difference equations previously used in any
field whatsoever. (Please be prepared to fax or mail a "personal use" copy
to me, as the source article may be obscure).

I also stand by my assertion that there are inherent weaknesses to treating
"fitness" as scalar, whether normalized or not. However, my model does not
even require labeling any mathematical construct as "fitness," so I again
refrain from extended argument. Contrary to D. S. Wilson, I maintain that
properly done mathematics in either genetics or memetics is sufficient to
avert real or apparent tautology whether a quantity is labeled "fitness" or

--Aaron Lynch

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