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

[Barry McMullin]

glen e. p. ropella wrote:
[...]
> 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]

Bang! (;-)

I didn't say the stuff/goo/whatever had to have a "fixed
organisation"; I said it had to have a fixed "composition": that
is, *which* goo belonged to or composed the "system" was fixed
(howsoever "goo" might be defined in context).  The "organisation"
(state) of the goo could still be changing all the time...

> 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);

OK, I was (semi-deliberately) using "system" in a loose sense.  This
was intended to resonate with the fact that, colloquially, people -
even scientists - do use the s-word for things (like gliders) that
are not "systems" in certain technical senses (e.g. dynamical "systems").

We can call them "objects" if you like. Of course, we'd better admit that
this is the informal, loose, sense of "object", not, for example, the technical,
computer science sense, as in "Object Oriented Programming" ... the latter
"objects" would be perfectly good "systems" in the previous sense.  

Don't ya just love natural language...

> 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 interested ... not yet optimistic, but certainly 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.

Yeah - I didn't even think there could be any question 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.

Yup, that's where I'm at (albeit wary of a creeping inductivism)...

[...]

> 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."

Yikes!

Do I hear the muffled sound of a glider crashing into a tree
in the forest, with nobody around to see?

Do you really mean to say that the gliders are not there unless the
state of the Life world is being projected on a monitor (in the
"usual" projection) *and* some person ("sentient observer"?) is
watching?

[...]
> 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.

Absolutely.  But as you can see, I don't (yet) buy the idea as you
seem to be suggesting it.  But we are definitely getting closer!

Cheers,

- Barry.


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