> I use a slightly different language in describing complexity than
> Rosen et al. but agree on many (but not all) aspects of this view.
>
> Jeff writes:
>> Consider that there is some causal structure to the encoding and decoding arm
s
>> that are used in a modeling relationship between a natural system and a forma
l
>> system. Also consider, for sake of argument, that this causal structure
> cannot
>> be brought into the formalism (we can always try later on to bring it in, bu
t
>> that is a different issue).
>
> Often, I talk about relating the model (that roughly corresponds to the
> "formal model" above) to its language of representation (in which the
> encoding and deconding arms are implicitly or explicitly defined). I
> also include for consideration modeling of such "formal models", the
> modelling of the modelling of such etc. I also include "informal
> models" as a type of model on the opposite side to the natural
> system.
no problem there as I see it
>
>> Consider that for some particular modeling relationship (say between "natural
>> system A" and "formal system a") there is more causal structure in the
>> encoding and decoding arms than for another modeling relationship (say
>> between "natural system B" and "formal system b").
>
> I am unclear as to what exactly is meant by "causal structure" here,
> escpecially as it seems to be some sort of quantity ("more causal
> structure"). This is important to understanding this view, as
> judgements of complextity seem to rest upon it.
causal structure as I interpret it has to do with 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.
>
>> We could then classify the modeling relationship between "natural
>> system A" and "formal system a" as more complex than the modeling
>> relationship between "natural system B" and "formal system b".
>
> 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 olso has a very simple
causal structure.
>> At this point we can not really say anything about the relative complexities
> of
>> the natural systems themselves...only the modeling relationships.
>
> This is my view. I can not see it as useful to ascribe complexities
> to natural systems (in almost all circumstances).
good! we have another important convergence here
>
>> Now consider that "formal system b" is the same as "formal system a". Same
>> formal system; two different natural systems. Consider that the situation is
>> still true that there is more causal structure in the encoding and decoding
> arms
>> between ("natural system A" and "formal system a") than there is between
>> ("natural system B" and "formal system a"). It would then be tempting to say
>> that "natural system A" is more complex than "natural system B". But can we
>> really say this? I tend to agree with Don. We cant. Neither the formal
>> system nor the natural system entails what needs to go in the encoding and
>> decoding arms. We, the creator of the modeling relationship pragmatically
>> establish the encoding and decoding arms.
>
> Agreed, we create the modelling relations and model. The complexity
> is in the non-natural part.
This idea goes a long way, I think
>
>> The other situation can also be considered for completeness: Consider that
>> "natural system B" is the same as "natural system A" and the formal systems
>> (a and b) are different. Consider that the situation is again true that ther
e
>> is more causal structure in the encoding and decoding arms between ("natural
>> system A" and "formal system a") than there is between ("natural system A"
>> and "formal system b). I dont think that you could then say that either
> formal
>> system was more complex than the other.
>
> I find this much less obvious than the previous example!
>
>> To summarize: the complexity is not in either the natural system nor the
> formal
>> system. The complexity is in the modeling relation itself...think of it as
>> being (if you like) in the encoding and decoding arms.
>
> 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).
>
Here I'll have to side with Bruce. Chaitin certainly makes this a necessity!
> Let me see how far these are alternative descriptions, by trying to
> use each 'language' to represent the other.
>
>
> Using Jeff's 'language' to describe my language first:
>
> Given two 'formal' (i.e. non-natural) models, one bottom-up one
> starting from the causual interactions of the components and one
> top-down starting from some overall description of behaviour of the
> whole, we seek to 'model' the bottom-up model with the top down one
> with encoding and decoding arms. My definition of complexity is the
> difficulty of doing such top-down modelling w.r.t. to the
> representational language in which the coding arms are embedded.
> Thus this is similar to your 'complexity of modelling', but
> perpendicular to it. From your view the modelling situation is
> complex if there of more "structural causation" in the coding arms.
> From my view the modelling situation is more complex if it is
> difficult (winthin a language) to find good encoding arms.
>
Hmmm! I think there has been something lost here...both seem different
aspects of the same issue to me. have I missed something?
>
> Let us now try this exercise the other way around, using my language
> to describe your 'complexity of modelling'.
>
> From my viewpoint the natural system does not appear at all! The
> more natural side (the experimental data, recorded observations
> etc.) are already models (not necessarily formal in the wider sense
> but definitely non-natural). The modeller then comes up with a
> (usually more formal) model of this 'data-model'. My complexity of
> that modelling process is then the difficulty of coming up with
> this higher level model given a language of representation (which
> will constrain but not specify the encoding arms, which then become
> part of the higher-level model). Your complexity of the modelling
> situation is the amount of "causal structure" in the
> interpretation+language-of-representation given the data and the
> higher model.
Yes, that all is implicit in Rosen's approach...see "Fundamentals of measurement
"
>
>
> So what can we conclude?
>
> 1. There ARE links between the two approaches to complexity, but
> they are not exactly the same.
seems so
>
> 2. It depends a bit on what "causal structure" means (how is the
> stucture defined?).
here's where relational diagrams and category theory may be helpful representati
onally
>
> 3. We are considering different parts of the situation fixed and
> judging 'difficulty' as others vary (for me the bottom-up model and
> the language of representation are relatively fixed compared to the
> top-down model, for you the natural system is relatively fixed
> compared to the encoding arms (which constrain the formal model).
I think this is either a misinterpretation (did you mean that Jeff?)
or I'll have to diverge from Jeff's position here I think.
>
> 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.
> 5. For me natural systems never even get a look in (typical
> philosopher!), as there are distinct philosphical problems with this
> as a part of the model of modelling, for you (biologists?) it is of
> course the starting point, with the modelling part being the
> problematic end.
yes, we include empiracism, but not in the exclusive way our colleagues do.
see the statements about ways to interact above
>
> 6. I want to include informal models on the non-natural side.
>
and analog models, etc.
> 7. ??? what else ???
I'll try to send some stuff from Kampis next.
>
> ----------------------------------------------------------
> 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
Regards,
Don Mikulecky