> Goodness me, I have got behind in replying to these! Must be I have
> had to do more mundane work (= stuff I'm paid for) this week.
>
> 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.
>
> 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?
> 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???
>
> 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?
>
> me:
>> > This I find odd (depending on what you mean by "causal structure").
>> > The complexity seems defined in terms of the 'success' of the
>> > modeling relation. Thus, by this definition, unsucessful models
>> > will always be less complex than successful ones, even if the
>> > unsucessful ones are far more intuitively 'complex' than the
>> > sucessful ones. This seems more like the 'difficulty' of modelling
>> > than its 'complexity'. I suspect that your idea of causal structure
>> > in the coding arms is more involved than it seems from the above.
>> >
>>
>> The simple system model which has only one way of interacting with the
>> natural system has been very successful. It also has a very simple
>> causal structure.
>
> 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.
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. 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.
Most of your concern seems to be with a classificationof 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.
>
>> > I find it very counter-intuitive that the 'complexity' of the formal
>> > models play no part in the complexity of the modelling. Maybe this
>> > is because we are approaching this from within different structures:
>> > I am talking about the complexity of models (relative to a language
>> > of representation, goals etc.) and you are talking about the
>> > complexity of modelling (natural systems).
>> >
I hope the above clarifies this difference.
>> Here I'll have to side with Bruce. Chaitin certainly makes this a necessity!
>
> Please explain, what you see as the ramifications of Chaitin's
> results for this discussion. There is a big gap between what I
> understand of his results and the consequences you state.
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.
>
>> > 4. For me the complexity of the formal model itself is relevant, for
>> > you essentially not (but its input-output is constrained by the
>> > coding arms). For you the 'content' of the formal part does not
>> > matter, it is a black-box given the constraints of the coding.
>> >
>> au contaire...it is indeed important if it can be linked to the number of
>> distinct ways we interact with the natural system. Here is, as I see
>> it, a reason why the natural system must retain its place in the modeling
>> relation.
>
> What if it can't, so formal models of different 'complexity' have
> identical coding arms, does the formal model matter then?
>
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.
Best regards,
Don Mikulecky