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Friday, December 16, 2005


 The BCNGroup Beadgames



Challenge Problem  à



Communications on lattice of theories and

conceptual atomism


footnotes by BCNGroup


Communication from Judith Rosen


Hi Paul (and others!),


I'm honored that you've asked me to participate in this discussion, although coming in in the middle does tend to put me in a state of some confusion over what has been discussed so far. I'll keep my responses short until I get some feedback about whether I'm covering the ground you had hoped for, or if I'm missing the mark. [1]


One subject I can definitely clarify for you is that of "the largest model" as my father used that phrase. In his view, if a system has a finite "largest model"-- meaning it is possible to formalize/model the system, in its entirety-- then it's a simple (non-complex) system. One of the tests for complexity is precisely this one [2].


Another word for this is "computability". If a system can be rendered as syntax, or digitized, without loss of information, then it is a simple system. So, when studying complex systems, as Robert Rosen defined that word, there can be no "largest model" and there will always be too much semantic information for the system to be entirely computable. [3]


Regarding this quote:

Rosen talked about the largest model, and I always hated that, because I

never felt comfortable with the issue of relevance, and ordering . One

theory is Larger than another theory? How can one say that?


If the information in one theory can be entirely subsumed by another, then clearly the former is more limited than the latter. Looking at it from the other direction: If there are informational aspects of one theory which are not included in another, when everything else is the same or equivalent, then the former is "larger than" the latter. Theories are just bodies of ideas. They are human mental models of reality. If both sets of ideas are intended to describe the same aspects of reality, then of course it is entirely possible for one set to be more comprehensive than the other. This is the sense in which my father discussed science in terms of "general" and "special"


How does one know in the general case? Well I should say that my friend

Peter Kugler talked about Rosen talking about the largest model. Perhaps

Judith Rosen has time to help us a little on some issues.... This is not a

philosophical debate, but a search for a way forward for an ontology

community that is really stuck in a very real sense.


My father's contention was that complex systems are the general case in this universe, and simple systems are the special case. Therefore, a scientific theory (body of ideas) that relates entirely to simple systems cannot be a generally applicable theory. In his view, this is why physics cannot answer most of the fundamental questions in biology, for instance.


I think that perhaps a brief description of what "complexity" means, in Robert Rosen's parlance, is in order. Most of the other definitions of complexity that I've seen are quite different, some of them radically different. (see footnote 3)


I've never seen any other one that is as clearly defined, in terms of science.  Rosen’s definition of complexity is a critical definition, with many other ideas ramifying off of it.


In my father's view, complexity has to do with relational interaction.   In natural systems, the interaction between two entities can have effects that could not be predicted based on any amount of knowledge about those two entities, in an of themselves.   This is complexity.  (paragraph edited by Prueitt)


Furthermore, the way any interaction takes place is as important as the interaction, itself. This comes down to matters of relational context; to understand the effects of any given interaction, the relational context would have to be known as well as the interacting parties.


Some examples of contextual factors are proximity, temperature, volume, and multiple temporal aspects such as duration, rate, sequence, etc. Such contextual relations carry information, sometimes vitally important information, which becomes part of any effect, or "cause". In fact, my father's conclusion was that causality, itself, is relational. Nothing is "caused" until various entities interact, and the specific relations under whom any interaction takes place will determine the outcome/effects.


One of the consequences of this set of ideas is to recognize that the way a system is organized can be far more important than what the system is made up of.


In other words; if the system is organized in such a way that the relational information is critical for understanding the effects, then the list of ingredients can be meaningless without all the relational information. This kind of organization is complex. Ultimately, my father concluded that life, as a property or behavior pattern of organisms, is a relational effect-- it is a collective effect of extremely complex organization.


The fact that we can easily recognize life in systems as diverse as the myriad species of organism we can find here on Earth tends to support his conclusion that it (life) is a property not based on material components, alone.


As you can probably imagine, this set of ideas has rather grave consequences as far as contemporary science is concerned.


Science, currently, is built around certain assumptions, one of which is "the machine metaphor" (an assumption that "all systems are just like machines") and, therefore, science uses the machine as a general model for all natural systems. This is part of the foundations for the current paradigm of science:


It has led to a philosophy and approach, from which all our techniques and technologies are built, based around the idea that we can learn everything we need to know about big, complicated systems by taking them apart and studying the parts. In a machine, which is a simple system, that works:


This philosophy and approach insists that all the information we need will be found in the material components and the direct relations between material components (a definition of "structure"). However, in complex systems, not all relations are direct, structural ones. Indeed, I think most of us have probably experienced the realization that, sometimes, a small and indirect relation can have enormous impact on the outcome of any given interaction. That is what Chaos Theory tries to understand, in fact.


Well, I think this is probably enough for a first contribution. I hope that these ideas have shed some light on the various questions you have been discussing, which led you to contact me in the first place. If not, please let me know what other questions or concerns you have.



Judith (Rosen)


[1] Paul:  Judith, it is a honor for me.  Your father is admired by many people for having a deep and also original mind – and taking the time to communicate it clearly.  I am so pleased to find that after his passing that one in his family was able to take up a presentation of his work.  We thank you from the bottom of our hears.

[2] Paul: ie if we are talking about models that can be ordered into a lattice then we are not talking about complex models.  (Here the definition of “complex” is the one that Robert defined.)

[3] Paul:  One of the most important points to make here is the misuse of the term complexity by those who in mathematics and computer science talk about computational complexity.  It is ok that they use words the way they wish to.  But this phrase “computational complexity” is like the phrase “formal semantics”, that create an inability to address underlying problems that were exposed so well in Robert Rosen’s work.  If this is done, and that community ignores the fact that others find this incorrect, then we have a social issue.