The context of this reply: Jeff gave a formulation of how to judge
the complexity of (modelling) systems in the Rosen style. The key
point was that those modelling relations whose codeing arms had "more
causal structure" were more 'complex'. I thus asked about the
meaning of this phrase. Don replied as immediately below.
Don Mikulecky, MCV/VCU, mikulecky@gems.vcu.edu:
> >> (causual structure is the number of) distinct ways with which we
> >> and the natural system are interacting. Note that "distinct" means
> >> needing encodings into distinct formal systems, i. e. ones which
> >> are not derivable from each other. I'll be sending some more on
> >> this out of Kampis' book.
(as a basis for comparing complexities this poses some problems
hence) me:
> > There a lot of problems here.
> >
> > 1. Usually the number of non-equivalent distinct formal systems is
> > infinite, in fact I am hard pressed to think of one that is not
> > (even when what is being modelled is purely formal!).
> >
> Why is this a problem? It merely insures that there ARE distinct
> formal systems to use on the right hand side of the modeling relation
> when we have distinct ways of interacting with the natural system.
> Seems like a gap in communication here somewhere?
Thus almost all modelling situations (having an infinite number of
distinct formal systems) are equally complex. Not very useful for
comparisons!
> > 2. It is an uncomputable problem in many cases to tell if formal
> > systems are thus distinct - thus the number of distinct formal
> > systems might not even be knowable.
>
> Right, but we don't need to know that in the discussion I was making!
> Again, so what???
This seems to indeicate that Don, was approaching this part of the
thread from another viewpoint from me (surpise!). From my point of
view if you can't tell if formal systems are distinct then you can't
know the number of such systems that are distinct. In some cases you
will not even be able to tell if there is exactly one such or more.
Thus ou can not use this definition PRACTICALLY in some
circumstances. Again this makes it difficult to use for comparing
complexities (Don, of course, is not concerned with this, for hime
its either complex or NOT).
> > 3. It is unclear how you can tell whether a model of a natural
> > systems commutes. You can easily tell when it does not, but how do
> > you ever know it does other than comparing the formal to natrual
> > model for an eternity. I will come back to this in another post.
>
> This too is true. Also tautological, no?
Aggreed. I added this point in here, but it is a bit out of context.
I was thinking about the utility of the crisp distinction: a model
or NOT. Rather, pragmatically this should ready "NOT a model or
maybe" same with "complex or NOT". It is my view that such
dicotomies are not so helpful (from my point of view) in analysing
the situation.
> > > > > stuff deleted ....
Me:
> > But a much 'simpler' formal model which interacts in two ways is
> > necessarily more complex, by your meaning. Doesn't this also mean
> > that a completely unsuccessful model that interacts in no (zero) ways
> > is even simpler. I find this all very counter-intuitive.
Don:
> Me too. But then your conclusions are what make that so. You seem to
> want to use the modeling relation as an object to pick apart rather than
> try to see what Rosen and others mean by it.
I think I understand enough of Rosen's meaning (though I will keep on
actively learning), but philosophically I find it unsatisfactory (not
in its aims, but in its modelling of modelling, etc.). Yes, I want
to pick it apart to see if underlying it there is any common
language, to find out exactly where we differ, whether this is a
formal difference or has practical implications etc. I do not
dispute its general utility and praise the fresh insights it gives
us. That don't mean I can't question it though.
> Most of the time, it is so
> useful in clarifying these issues that I tried to do the same here.
> Go back to the Benard cell as a standard example. One way of looking
> at the system and interacting with it is Newtonian mechanics. That
> does well BEFORE and AFTER the transition. It is useless for the transition.
> Thus, a simple system seems to exist if we don't know about the
> transition (one way of interacting, one formal system) Once we know about
> the transition, another, independent formal system, one which seems to
> not be computable, is necessary to describe the system, which we can
> now recognize as complex.
I agree with all this.
> Most of your concern seems to be with a classification of the formal systems
> according to various notions and degrees of complexity. That is a whole,
> different issue from trying to use those formal systems to learn about
> the natural system.
Somewhat, but not entirely. I don't talk about "formal systems" so
much, this is your description of one side of the modelling relation
(opposite the natural). Thus for me we don't EVER really interact
with "natural systems" directly, but only through models, even if
this is at the level of the model our sensory equipment makes of
reality. The data we get by measuring is already a model (a data
model), which we extract using our senory models and informal models
of the system of study. We then try and model this data model with
an analytic or synthetic model. This is not always easy (ne
possible). This is the complexity we face each day - the difficulty
of modelling these bottom-up (data or otherwise) models.
Thus my view is from a more philsophical perspective, becuase (like
Rosen) I want to uncover the sources of things like 'complexity',
'life' etc (or at least find new langauges and perspective that throw
some light on them). I am not assuming that we can interact with
natural systems, (at least not practically) and hence my concern with
modelling other modells (what are called formal models in your
terminology - but I include informal ones also (but definitely
non-natural)).
You are starting more (it seems) from a less abstract viewpoint where
you are assuming that the sensory stage of modell building of natural
systems will cause no essential new difficulties to the situation. I
disagree and thinks that some of these assumptions DO cause
confusions.
.....................................
On an entirely different matter (upon which I do not disagree with
Don).
> As I interpret you, you are interested in the complexity of formal systems.
> Chaitin has made large contibutions to "algorithmic complexity" and therefore
> provides criteria for what I thought was your goal.
Yes, but I think this attempt is flawed as a non-trivial model of
complexity. It is a good measure of information though. If you are
interested I can fgo into the arguments on this.
..............................
Don:
> As I've been trying to establish, you are focusing on the complexity of formal
> systems. We are focusing on the way we "see" the nature of natural systems.
> These overlap to a great extent, but the focus ids different. We see Rosen's
> distinction between simple and complex systems resting in the way we
> interact with those systems and the way we use formal systems to get to
> a description of that interaction. We use the modeling relation to try
> to capture this process conceptually. It IS a process, however, and not
> the usual kind of object you are used to dealing with. There is a lot of
> baggage involved in this characterization which we need to consistantly
> deal with in these conversations unless you wish to destroy a straw man.
> Rosen's development is very involved and not easily dealt with in this
> manner. We have been trying to devlop parts of the whole, knowing that
> there is a difficulty in that. Please help us discuss these issues as
> part of a whole, rather than trying to deal with them point by point
> out of context.
1. Yes the focus is different, but this does not effect my
question: "why doesn't the *content* (i.e. that which is independent
of the coding arms) of the 'formal system' (i.e. non-natural part)
not effect the complexity of modelling (as a process)?". You seem
to want to seperate out the content of this as if it were a black box
with no essential meaning of its own. This is especially important
when we have (as usual) a whole stack of modelling relations,
modelling the model of the model etc..
2. You seen to constantly assume that any difficulty I have (or more
generally dialogue) is due to me not understanding Rosen's point of
view enough. This is not the case, I want to question this view - it
does not seem to me entorely satisfactory. You do not seem to
accept the possibliity of improving/modifying this view (i.e. Rosen
is perfect). Please discuss the questions at hand based on YOUR view
(however based), That fact that some view or other is not easily delt
with is not helpful to me. Newton was not only important in his
results but also in his new and important method - we should be
grateful to him for this. What we should not be grateful for is the
ossification of later thinkers around this view who did not build
upon/modify/correct this where necessary - let us not do the same
thing with Rosen. Just becasue he had some important insights does
not mean we should not question it/ change it/ improve it/correct
it/realise its assumptions. In fact the reverse, the importance of
his views cries out for such a process - other wise we would not
bother! Thus, more re-capitulation of Rosen is not enough, I need a
dialogue about it if this exchange is to be productive. I value
YOUR views, I wnat to engage in a dialogue with YOUR views. If I
want to know what Rosen said I'll read him.
----------------------------------------------------------
Bruce Edmonds
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Building,
Aytoun Street, Manchester, M1 3GH. UK.
Tel: +44 161 247 6479 Fax: +44 161 247 6802
http://bruce.edmonds.name/bme_home.html