[ExI] Evolution "for the Good of the Group"
Lee Corbin
lcorbin at rawbw.com
Sun Sep 21 06:58:15 UTC 2008
Stuart writes
> Mike 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 guarantees
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
http://en.wikipedia.org/wiki/Ramsey's_theorem#Example:_R.283.2C3.29.3D6
>> What you describe remind me of liquid gathering
>> into drops, and [then] drops into puddles. In a
>> sufficiently large field of evenly distributed small
>> drops, there is little required action to become part
>> of a puddle. This game may not be a perfect example,
>> but it has an interesting dynamic as levels increase:
>> http://www.1cup1coffee.com/fl/mercurydrops.swf
>>
>> Do you get a "feel" for what I'm saying?
>> Does this agree with your original point?
>
> My browser can't load the shockwave file but it sounds
> like you get it.
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?
> Although keep in mind that droplets and puddles can't
> differentially reproduce. The takehome message of Ramsey
> theory is that "complete disorder is impossible."
Well, I don't understand why you would draw that conclusion
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 *either*
cooperators or non-cooperators. This is not going to make
non-mathematicians show any surprise at all, I think.
Lee
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 could
grade civilizations on how many Ramsey numbers they've
figured out.
For example, a higher civilization than ours (say a dozen years
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! :-)
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