Re: Category Theory and Rosen - some clarifications (i hope 8-))

[Barry McMullin]

glen e. p. ropella wrote:
> This is an important criterion.  But, having fluctuating constituents
> does not mean that it's not iterative.  And it doesn't even mean that
> it's not a "bag of stuff".  I don't really want to degenerate too far
> into this; but, "stuff" doesn't have to be "particles".  Stuff can
> consist of just about anything.  So, even if the stuff globs up into
> particles for a little while, it can de-glob anytime it wants.
> 
> You seem to be talking mainly of "dissipative" or "open" systems.
> These are *still* iterative systems.

The systems I am talking about might be open and/or dissipative -
though that's a little prejudicial because it implies that the universe
in one in which something like normal thermodynamics holds, which
isn't essential.

Regardless of that, I will claim that they are not "just" 
dissipative, or open...
 
> Again, you're concentrating too much on the idea that the "stuff" in a
> "bag of stuff" is matter or atomic.  Think of a bag of stuff as more
> like the "ambience" around us where the stuff can be divided and
> parsed in an infinite number of ways.  That's the way I used the
> phrase.

That's precisely why I equated your "bag of stuff" to a *universe*,
to distinguish from the *embedded* systems I wanted to point it - the
latter *not* being bags of stuff. And this is not saying anything
about the nature of this stuff - material, particulate, whatever.
Rather, I'm taking the informal notion of universe as "bag of stuff"
as implying *some* decomposition of the universe into "component"
"pieces", such that that decomposition holds for all time.  Under the
dynamics of the universe these pieces may "aggregate" and "separate"
or otherwise change their individual realationships, but the pieces
all still exist, and the "universe" is always identical with the collection
of all the pieces (however arranged).  I admit that the easiest way of
visualising this is by thinking of the decomposition as, in some sense,
"spatial", so that the pieces are "particles", but I don't insist
on that.  All I insist on is that the decomposition is invariant.
If you want a formal notion for it, I'm envisaging the "universe"
as a dynamical system - something with varying state within an
invariant state space.

Now, having clarified (for myself, if nobody else (;-) what the
heck I was reading into "bag of stuff", it may be that this is not
at all what *you* meant to imply by the phrase.  In which case,
I'll withdraw with as much dignity as I can muster, since it would
probably indicate just that I should have read all the previous 
messages before jumping in with the old size 13's...

> Is there anything you can say that will give an understanding of
> the difference between a "sub-" system and an "embedded" system?

My paradigmatic example for this case is that of a glider in
Conway's game of life.  In the game of life system, a "sub" system
would mean (to me) some specific subset of the cells making up
the whole universe.  A glider does *not* map onto any such subset.
Therefore it is embedded in, is "of", the whole system, but is not
a "sub-system".  Now again, I don't want to argue about what words to
use: I'm just pointing out that there are at least two different kinds
of things that *can* be embedded in that kind of system, and it's
worth distinguishing between them (I think?).


- Barry.


                  ==================================
   Swarm-Modelling is for discussion of Simulation and Modelling techniques
   esp. using Swarm.  For list administration needs (esp. [un]subscribing),
   please send a message to <address@hidden> with "help" in the
   body of the message.
                  ==================================