RE: memetic fitness

Gatherer, D. (
Thu, 22 Jul 1999 09:18:54 +0200

Date: Thu, 22 Jul 1999 09:18:54 +0200
From: "Gatherer, D. (Derek)" <>
Subject: RE: memetic fitness
To: "''" <>


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).


Shifting the goalposts now, Aaron? I don't recall any mention of
mathematical group selection theory up till now. What you said was:

>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

Sue says p75:

"This [imitation] is only worthwhile if the environment does not change too
fast, a factor that can be modelled mathematically. Richerson and Boyd
(1992) have shown the conditions under which natural selection might favour
more reliance on social learning (including imitation) rather than
individual learning. Economists have devised models... [a passage which
draws attention to the mathematical work of Bikhchandani et al and Conlisk]"

I think that it is amazingly obvious that Sue has drawn attention to the
mathematical work of B&R.

Sue says: p198

"Indeed Boyd and Richerson have used mathematical models to show that group
selection is particularly likely to occur when behavioural variation is
culturally acquired"

That is a reference to a memetic simulation of group selection, not a
genetic one. It is mathematical memetics. Sue has mentioned it.


however, that Dennett recently found the paper's {Lynch 1998] mathematics
distinct to mention in his forthcoming paper, "The Evolution of Evaluators"
in a volume of the Siena workshop on evolutionary economics.


Really? Let's see what Dennett actually said [In fact you don't get a mention
in the body of his text, just in footnote 5]

"5. Aaron Lynch (1991) has attempted a mathematical formulation of some
aspects of memetics, focusing on the simplest stripped down cases--which
still swiftly spawn complications. Like Cavalli-Sforza and Feldman, he
postpones treatment of the awareness side of the awareness/adoption
distinction, though his model permits the distinction to be expressed.
Whether these tactical simplifications permit the resulting model to tell us
anything surprising (and confirmed) about real phenomena remains to be

If your model really was a major new contribution, why didn't Dennett
mention it in the main body of the text?:

"Dawkins' theory of memes, as briefly sketched in a single chapter of The
Selfish Gene (1976, but see also Dawkins, 1993), is hardly a theory at all,
especially compared to the models of cultural evolution developed by other
biologists, such as Cavalli-Sforza and Feldman (1981), Lumsden and Wilson
(1981), and Boyd and Richerson (1985). Unlike these others, Dawkins offers
no formal development, no mathematical models, no quantitative predictions,
no systematic survey of relevant empirical findings."

I think this demonstrates that Dennett recognises that your model is of the
Cavalli horizontal transmission variety. You may call it:

"non-linear,partial differentio-integral difference equations"

but what you have is an epidemiological model with a few bells and whistles
attached. I may not have a degree in maths like you, but I've done enough
of the stuff and spent enough time pouring over mathematical memetic models
to recognise that.

You know what it is that get's me going, Aaron? The reason that you can
reduce me to mouthfoaming anger at the drop of a casual phrase? It's your
contempt for the whole corpus of work that has gone before. Your insistence
on tearing everything up and starting again from scratch, and on your terms.
For instance:

You say:

"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

Now there are several things in there that illustrate this process of
contempt. You cannot just throw 60 years of Fisherian theory out of the
window and redefine fitness unless you have a very, very, very, good reason.
If you are right, that fitness is not best defined as w = 1-s, then the
whole edifice of population genetics becomes a ruin. You can't just
casually dismiss a theory that has worked extremely well for several
generations. Fitness is a scalar, it is normalised. End of story. Imagine
if I said something similar about quantum mechanics. Imagine if I, with no
training in physics, were to casually speculate that there are inherent
weaknesses in de Broglie or Dirac's work. I dare say you, as a physicist,
would be livid and rightly so. You previously decided that Hardy-Weinberg
equilibrium (a theory even older and more solid than Fisher's) can just be
flamed because it doesn't suit your 'new' theory of homosexuality, and now
you're casually dismissing the founder of modern population genetics too.
Also your statements on tautology indicate that you want to throw out the
Russell-Wittgenstein work on the inherent tautology of all mathematics - one
of the solidest philosophical conclusions of the 20th century. "properly
done mathematics in either genetics or memetics is sufficient to avert real
or apparent tautology" - no, no ,no a correct mathematical theorem is
necessarily true, ie. all correct mathematical equations are tautologies.

Aargh! I think I need to go and lie down!!!! Anybody got any valium?

and finally... what was I going to say? I don't know I've lost it
completely now, I'm just a gibbering wreck maybe you're right we shouldn't
debate any more

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