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

[Barry McMullin]

glen e. p. ropella wrote:
[...]
> Hmmmm.  Now I'm lost again.

Me too - we may need a break from this...

> Invariant composition necessarily implies an invariant (or at least
> finite possibilities of) organization at *some* level.  
[...]
> For example, we can put together a system of particles in several
> different ways without varying the particles themselves, which gives
> us variant organization and invariant composition.  But, the
> organization(s) used to plug those particles together is not infinite. 

As I say - lost.  I don't know what force you want to apply to 
"infinite" here, but we could easily have an invariant composition
of an *infinity* of elements, which would presumably (?) yield an
infinity of organisations; even if the number of elements are finite,
any continuous valued "relationship" would yield (another kind of)
infinity of potential organisations.  We're surely taking across
each other in some way here, but I'm not sure there is any
substantial point at issue...

> But, you are arguing for *variable* composition where I'm arguing for
> *arbitrary* composition.... I.e. my case includes your case because
> not only can the type and amount of the composite pieces of my goo
> change, but the fact that they are pieces at all can change (e.g. a
> pi-meson can decay into a muon and another pion at any time).

In my mind that is certainly an interesting further wrinkle.  But my
point (there is one buried there somewhere) is that even with
"variable" composition, we can already point
at this funny class of "systems" ("objects", whatever) like gliders
that are not "dynamical systems", and that I (for one) have no idea of 
"appropriate" formalisations for.

[...]
>  > Yup, that's where I'm at (albeit wary of a creeping inductivism)...
> 
> I don't think there's really anything "creeping" about this.  It is at
> least analogous to induction, if not synonymous with it.  But, if we
> don't allow induction, then we're in trouble.  What we need to avoid
> is inappropriate generalization.

OK, coming swiftly out of the closet, I point out that I side
strongly with Karl Popper on the issue of induction (briefly, 
"logical" induction simply doesn't exist; "psychological" induction 
does, is a fascinating subject, but is outside the scope of the 
current conversation). I don't mention this in order to start an
induction thread (though I sometimes enjoy philosophy too), but
only to explain my unconsciously cryptic allusion to "creeping 
inductivism".  Unbelievable as it sounds, I sometimes forget 
that, in rejecting induction, I'm currently in a very very tiny 
minority  <shrug>.  For what it's worth, I agree that not allowing
induction means "we're in trouble" - I just don't think that 
particular trouble is avoidable, so we have to deal with it.  But that
is going way off topic (though I'll happily continue - out of band -
if anyone wants).

[...]
>  > 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?
> 
> No.  What I mean to say is that gliders do not exist in the context of
> the CA.  They only exist in the context of the system of which the CA
> is a part.  Gliders are meta-CA objects.

Hmmm.

> And if the human didn't exist, then the computer wouldn't exist and
> the visualization mechanism wouldn't exist and, therefore, the glider
> wouldn't exist.  However, if the human exists at time t0, the computer
> at time t1, the visualization mechanism at time t2, and the CA at time
> t3, then the glider would certainly exist at time t4.  This is an
> imprecise way of stating that the system is not really time-dependent.
> But it is causally dependent.

So you grant that the gliders *will* still exist at t4, even if, 
by then, the humans and the visualization mechanism have been 
trashed?  Am I understanding correctly?

[Incidentally: the "would certainly exist" seems too strong: many
GoL configurations do *not* yield any gliders...]

> This is fundamentally different from the "God is in the Quad" problem
> because the glider is artificial/synthetic/man-made.

Ya got me: what is the "God is in the Quad" problem?

> I'm *extrememly* glad to hear that we're getting closer. [grin] The
> relationship between this recent stuff and "modeling" may seem
> tenuous; but, in my oh-so-humble opinion, could end up being critical.
> But, then again, I *like* philosophy.

Cheers to that: but if others on this list are getting tired of it,
please feel free to tell us (preferably by private email, not via 
the list).

Thanks for sticking with it Glen,

- Barry.


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