[ExI] Evolution "for the Good of the Group"
avantguardian2020 at yahoo.com
Sun Sep 21 23:59:42 UTC 2008
--- On Sat, 9/20/08, Lee Corbin <lcorbin at rawbw.com> wrote:
> >> > [The Avantguardian wrote]
> >> >
> >> > The good news is that the Ramsey Theorem
> makes it
> >> > nearly impossible in sufficiently large
> networks that at
> >> > least a few individuals don't cooperate,
> even if it is
> >> > entirely by accident.
> That is to say, if between *all* N parties, either the
> state COOPERATE or else
> the state NOT-COOPERATE exists, then the Ramsey Theorem
> that either a minimal number must COOPERATE or a minimum
> number must
> NOT-COOPERATE. If others don't understand then they
> should see the nice example
Quite right, Lee, that is exactly why I said "nearly impossible". If cooperation were *guaranteed* by Ramsey Theorem I would have said "strictly impossible" as only a mathematician can. And believe me, I would have liked to have been able to say that.
Furthermore you are neglecting my main point which is that mutual cooperators that police themselves well enough, have a large fitness advantage over mutual non-cooperators, so it only ever needed to happen once. But considering the enourmous number of replicators that would have existed in any hypothesized "primordial soup", I suspect it may have happened many many times. Indeed Hamiltonian kin-selection may have evolved as a mechanism of recognizing other cooperators instead of cooperation arising from kin-selection. After all biology has many examples of cooperation that have nothing to do with kin and it's not at all obvious which is cause and which is effect.
> Oh? I don't see any connection at all. Could you
> elaborate on the
> connection you see between Mike's puddles and the
> Ramsey Theorem?
Because the Ramsey theorem is derived from the pigeon hole principle. You could consider the space over which the droplets are dispersed to be pigeon holes and the droplets to be pigeons. As the number of droplets approaches the amount of space available, they are increasingly likely form puddles. And the moment that you have more droplets than you do space for them, they *must* form a puddle.
> Well, I don't understand why you would draw that
> or put it that way. It's easy to see that one may
> simply have
> *any* number of cooperators or non-cooperators in a group.
> There could be just one cooperator, or just two, or just N,
> all the way up to the size of the group. The Ramsey Theory
> only talks about the weird condition that GIVEN that among
> N entities there are Cooperators and Non-Cooperators,
> THEN it follows that there is some minimal number of
> cooperators or non-cooperators. This is not going to make
> non-mathematicians show any surprise at all, I think.
It is a subtle point, I know, but it has to do with the distinction between simple cooperators and a pair of *mutual* cooperators. I am not using Ramsey Theorem to model individuals but the relationships between individuals. Furthermore the *either* in your statement is erroneous because the results of the Ramsey Theorem are not mutually exclusive.
That is to say that given an ensemble of at least the Ramsey number N in question, you could have the minimal number of mutual cooperators *or* the minimal number of mutual non-cooperators *or* both.
Also keep in mind that there is probably no such thing as a universal "non-cooperator" that never cooperates with any other critter. After all even a monster that killed everything that crossed its path would be cooperating with the scavengers that followed in its wake.
Besides, I am only invoking the Ramsey theorem because it provides a mechanism for a "critical mass" of cooperation to form in the face of the strong Nash equilibrium of competition. Once that "critical mass" forms, the Pareto Dividend takes over. Also the Ramsey theorem is already couched in terms of graph theory, which makes it convenient for me.
That being said, I am sensitive to the fact that my theory is not yet bullet-proof. But I think it is a step in the right direction toward describing emergent complexity and order from mathematical first principles. I also appreciate your mention, in your other post, of Simpson's Paradox in regards to to the development of cooperation as that is an angle I hadn't yet considered.
> P.S. If you look at the table of known Ramsey numbers
> at the Wikipedia link above, then you can conclude that
> our civilization has discovered what I'll call
> "the fourth
> Ramsey number", i.e. we know that (4,4) is 18. One
> grade civilizations on how many Ramsey numbers they've
> figured out.
> For example, a higher civilization than ours (say a dozen
> ahead of us or so) may know the 5th Ramsey number, and
> yet a completely superior civilization may know the 6th or
> 7th Ramsey numbers! :-)
Yeah they are kind of cool like that, aren't they?
"See them clamber, these nimble apes! They clamber over one another, and thus scuffle into the mud and the abyss."- Friedrich Nietzsche
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