Friday, December 16, 2005
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.
Slainte,
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.