Posted by
glen e. p. ropella-2 on
Nov 03, 2009; 1:26am
URL: http://friam.383.s1.nabble.com/Crutchfield-s-Is-anything-ever-new-tp3917261p3935990.html
I think I explained all this in the past 2 e-mails; but let me repeat
just to waste everyone's bandwidth before net neutrality fails. [grin]
And I changed the subject since we're not talking about Crutchfield's
model classes anymore.
Thus spake Nicholas Thompson circa 09-11-01 07:27 PM:
> What kind of levels are we talking about, here.
>
> I guess I think that levels are logical. So A black bird is one level, a
> bunch of black birds is another level, and warehouse full of bunches of
> black birds another level. Ditto, a black bird, a flock of black birds,
> and a sky full of flocks of blackbirds. What makes the individual-to-flock
> level shift interesting is the manner in which the flock takes form
> because the behavior of the birds varies with their positions within the
> aggregate. Ditto the form of a pile of sand, for that matter.
I don't have a problem with using the word "level" in general. I only
have a problem trying to define (or construct) emergence while using it.
It's not the circularity that bothers me so much as the sloppiness.
For example when you say "a black bird is one level, a bunch is another
level", that sort of thing drives me batty. The only sense I can make
of it is in the mathematical induction sense where we construct a set
using the successor function. And, in that sense, there's no difference
between 2 black birds and a bazillion black birds. And "level" just
fails to capture whatever intuition you're after between 1 black bird
and 2 black birds.
The same is true for a warehouse full of bunches of black birds. All
you've done is redefine the unit. There's no fundamental difference
between a warehouse of bunches and a bunch of birds. No level has been
crossed. All you're doing is drawing lines around things in different
ways and claiming that's important in some mysterious way.
Now, if you took the route of Rosen and said that drawing lines that way
is one thing but drawing lines with non-well-founded sets is quite
another thing, then I'd understand because sets that cannot be members
of themselves are very different from sets that can be members of
themselves. Imagine a warehouse full of bunches of black birds, each of
which contains a warehouse containing bunches of black birds, ... Now
_that's_ interesting and different.
> Reading Glen concerning SCALE, I am thinking that scale and variance are
> necessarily interrelated -- unless scale is just how big something is in
> relation to the distance between the pole and the equator of the earth or
> the length of the King's stride.
Yes, indistinguishability is the dual of scale. If you fix the scale,
any variance in the thing being observed will either be observable or
not. Scale, as I'm using it, isn't about how big something is. It's
about the measuring stick you hold up against that something.
--
glen e. p. ropella, 971-222-9095,
http://agent-based-modeling.com============================================================
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