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

[glen e. p. ropella]

Barry McMullin writes:
 > 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...

OK.  I typically think of "open" systems as those systems having
the property you're referring to, namely, they have at least a
semi-permeable membrane.  So, the systems you're talking about
will certainly be open.

But, again, just because a system has this property (of dynamic
formation and change of constituents) doesn't mean that it's
not iterative.  In fact, most Alife systems implemented on
computers will be iterated through time.  The Game of Life is
a perfect example of an iterated system.  (Of course, iteration
through time is almost always a proxy for the successive application
of some other operator, like CA rules.  So, it's not *really*
the iteration through time that is important; rather, it's the
application of the rules on the output of the last iteration.)

 > 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.

OK.  Now, I think I understand.  By using the term Universe, you
intend to imply systems with a certain "boundedness," where that
boundary is not permeable... or, at least, the organization of
the goo inside is not dependent on the goo outside the boundary.

I usually refer to systems like that as "closed."

 > 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...

Well, I really didn't intend to isolate the stuff inside the
bag from the stuff outside.  And I purposefully refrained from
saying "bag of things" to avoid the inference you made, namely
that the *goo* inside the bag had a fixed organization.  So, I
would rephrase it now from "bag of stuff" to "bag of goo".
[grin -- just shoot me]

 > 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?).

pragma GROUNDED (Status => Off);
I'm glad you brought this up.  It took me awhile to place these
pieces properly in my head.  I agree that a glider in GoL is
*not* a sub-system, but not because it's not "sub".  I don't think
the glider is a "system" at all.  It's certainly an object (and is
subject to decay).
pragma GROUNDED (Status => On);

But, as you say, there's no real sense in arguing what to call
that type of thing.  Maybe it would be useful to apply Rosen's
ideas to the GoL.  Anybody interested?

I'm going to try.  The first question is, what about the GoL is
underdetermined by formal systems?  My first guess would be that
the actual CA (the state and the rules by which it iterates) *is*
completely well-defined by a formal system.  I really have no idea
if that statement would be accepted by CA theory; but, it is defensible
in that the definition of a CA *is* the state and the rules by which
the state changes.  No problem there.

The problems arise when we try to make statements about the *apparent*
structure we see as we watch the CA iterate.  For instance, we want to
classify the types of "objects" we see form and decay and we want to
be able to talk about the the shapes and pictures we see.  That is
where the formal system that specifies the behaviour of the CA is not
adequate.  For instance, before we began experimentally taking data on
the GoL, we couldn't predict that gliders of type p would form and
persist for x amount of time.  Now, we can, of course, because people
have gathered data on the system.

Since we can't make those kinds of statements, it seems ridiculous
to ask questions like, "Why did glider g1 emerge at time t1 and
move to the bottom right of the screen?"  There is no causal relationship
between the emergence or behavior of glider g1.  This is because there
is no such thing as glider g1 in the system.

Now, don't get me wrong, gliders *do* exist.  They just don't exist
*inside* the GoL.  They are a part of the larger system that consists
of the CA, the visualization mechanism, the computer, and the person
who identifies ... or "objectifies" the glider.  So, in order to ask
causality questions about the behavior of the glider, we have to,
basically, provide more complete entailment of the CA by "wrapping"
it in a larger system.  When we do that, we can say things about the
meta-system.  For example, "The glider is there because the CA has
these rules, this initial state, this mechanism for affecting the
computer screen, and because I tried several different combinations
until I got something that I could identify."

This "wrapping" is exactly an iteration (or an "upward recursion") of
causal entailment.  It is exactly what Rosen is referring to when he
talks of *approaching* finality.  Of course, to achieve what he calls
"maximal organization," we would have to try a little harder to build
a system that has more self-entailment in it.

Here's an attempt at a simplified "block diagram" for this system:

             +------------------------+
             v                        |
         +--------+                 +-----+
         |Computer|----+ +----------|Human|<-------+ ?
         +--------+    | |          +-----+
             |         | |            |
             | +-------|-|------------+
             | |       | |
             v v       v v
          +------+   +----+
          |VisMec|   | CA |
          +------+   +----+
              |        |
              |    +---+
              |    |
              v    v
            +--------+
            | Glider |
            +--------+

(I was tempted to put in an arrow from the human directly to the
glider... but, it's not necessary.  I don't want to argue about 
whether or not God is in the Quad.)

With this, it makes sense to ask questions like "Why did the glider
emerge?"  The *cause* of the glider is not just the VM and the CA.
It's also because the human was looking for something interesting...
This is it's final cause.  (Of course, the cause of the human isn't in
this diagram.)

Now, obviously, this analysis of this system is of very little use to
anyone.  But, one can imagine finding somewhat defendable analyses of
more relevant systems.  The important thing is the idea.

glen
-- 
{glen e. p. ropella <address@hidden> |             Hail Eris!             }
{http://www.trail.com/~gepr/home.html|                =><=                }


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