From: BMSDGATH <BMSDGATH@livjm.ac.uk>
To: memetics@mmu.ac.uk
Subject: Old memetics/new memetics
Date: Thu, 11 Jun 1998 11:29:41 -0400 (EDT)
A couple of weeks ago, I promised to put out a list of
mathematical models of memetics. I haven't quite finished
collecting all the relevant stuff, but here are a few things that
I hope list members might be interested in.
Firstly, there is a paper just out in a Net-journal called
Sociological Research Online, which treats memes as solitons in
terms of chaos theory. It's not just about memetics, and the
brief summary of memetics given in the paper might not be
agreeable to all of us, but it is interesting to see memetics
starting to make an impression in other areas.
http://www.socresonline.org.uk/socresonline/3/1/11.html
So, from the very new to the very old. I think that the earliest
attempt to put forward a mathematization of what we might
recognise as memetics is in:
Rashevsky, Nicolas (1951) Mathematical Biology of Social Behavior.
University of Chicago Press.
especially part III - Imitative Behavior, and part V - Learned
Behavior.
I don't know much about Rashevsky. A brief search of the ISI
showed that he published about 65 first-author publications
between 1933 and 1973. He is still extensively cited today in
information theory, telecommunications and ecology, but not in any
area which looks vaguely like memetics.
His basic model, in Chapter XI - "Behavior of a social group, in
which individuals imitate one another", consists of a
predisposition (to perform a certain behaviour), epsilon, he calls
it a 'spontaneous central excitation'. The probability that the
behaviour will be performed is then:
P(1) = 0.5*e factorial [-k {epsilon(1)-epsilon(2)} ]
where the 2 epsilons are the spontaneous central excitations
tending to the two 'allelic' behaviours.
when one individual imitates another it brings in another
variable, phi - the 'proclivity to imitate', which is added to
epsilon, so that the factorialised part becomes {epsilon1 + phi -
epsilon2}
He then rapidly develops his set of equations, adding variables
such as tau (the time delay in imitation), kappa (the frequency of
contacts and therefore potential imitations, between individuals)
It rapidly proceeds beyond my mathematical abilities, so I'll have
to leave it to others to say how it relates to memetic maths as we
understands it currently.
The chapter titles will give a flavour of the problems Rashevsky
contrues his system as analysing:
XIV: Altruistic and egoistic societies
XVII: Possible relation between imitative and motivational
behavior
XX: The learning curve of a social group
XXII: Interaction of imitation and learning
and best of all:
XXII: Acceptance of faith versus rational thinking
which would seem to be essential reading for all you mind
virologists out there.
In this Chapter, Rashevsky considers 'cross-inhibitory' beliefs.
The examples he gives are science and theosophy, R(F) and R(R)
(presumably referring to 'faith' versus 'rationality')
Rashevsky then posits a threshold h which controls the likelihood
that a certain stimulus S(F) or S(R) will result in the expression
of R(F) versus R(R). It gets a bit Pavlovian at this point with
religious and rational beliefs being turned out in reponse to
environmental cues.
Once again, I can't claim to follow Rashevsky's argument fully,
but he concludes by claiming that he has shown why people who are
agnostic or atheist in middle age often become religious as they
get older.
More recent, and more easily recognisable, mathematical treatments
of memetics appear in:
Laland KN (1992) A theoretical investigation of the role of social
transmission in evolution. Ethology and Scoiobiology 13, 87-113
This is a typical meme-host epidemiology-oriented treatment. In a
similar vein is:
Takahasi, K (1998) Evolution of transmission bias in cultural
inheritance. Journal of Theoretical Biology 190, 147-159.
This is online at the www.idealibrary.com site for those whose
institutions have a subscription.
There is also a frankly anti-memetics article in:
Harms W (1996) Cultural evolution and the variable phenotype.
Biology and Philosophy 11, 357-375.
This takes the 'sociobiology II' line, as Durham (1991) calls it,
which basically runs along the lines that culture is a product of
evolution (ie. genetic evolution) but does not itself evolve (ie.
does not exhibit the variation-selection heuristic necessary to
'take off' as a replicator in its own right. I don't agree, of
course, but just mention it so that you can see what the
opposition are up to.
Derek
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