The question in the title is especially meaningful if we learn over and over again that the simple models don't answer some of the most important questions we want to answer. In this fifth diary in the series I will construct a good bit of the answer to that question. The first four diaries (linked through the last one at the end of this one) laid the groundwork for this important statement of why our old methods were lacking and what we need to do to remedy that. We are working from two imortant books by the late Robert Rosen, Anticipatory systems: philosophical, mathematical, and methodological foundations (AS) and Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life (LI). In the last diary installment we looked at the way we make models of the world as Rosen analyzes the process in AS. Now we will make use of some of the material in LI to study complexity and the use of the Modeling Relation by reductionist science to substitute a surrogate, simplified world for the complex real world. This process began hundreds of years ago with Plato and then Descartes and has been our world model ever since. Clearly the model has evolved since then, yet it was never freed from some very limiting initial constraints. The Message we want to get from this diary is twofold: First there can be no one "largest model" for a complex system. And second that science has ignored this and replaced the real complex world with a surrogate world. This largest model has to have been defended in numerous ways over the years by declaring other valid ways of looking at the world to be "unscientific". This has been successful in the large and it is time to come to grips with its consequences for the state of the world today, and, in particular, the state of science in the world today, are a direct result of it. Read on below as we tell this story.
I'm going to supply some power point diagrams form my University Home Page. This particular batch was for a talk I gave at the University Of Alaska some years back. The title of the talk was IF THE WHOLE WORLD IS COMPLEX, WHY BOTHER? I am particularly interested in having you view the d=iagram of the Modeling Relation I apologize for not putting the diagram here but my attempts to follow the directions for doing that failed. I spent a lot of time trying. To describe the diagram in words we have a Natural System encoded into a Formal System which is then manipulated in some way to produce a change in the Formal System. The change is then decoded for comparison with the observed change in the Natural System. If we get a match, the modeling relation is said to "commute" and we have a model.
The reason this is so very important is, among other things, a way of seeing how we have operated for the past few hundred years in science (and elsewhere). The picture we have been led to accept from reductionist science is that there is only one model and that the encoding and decoding are not necessary. In place of the diagram of the modeling relation we get the well known direct cause explanation for everything:
AGENT ----Cause---> Effect.This is the picture of what Rosen called the reactive paradigm as I explained in the previous diary. Note also that George Lakoff has used this to explain the reactionary political mindset. The nature of the direct cause explanation as compared with the Modeling Relation leads us directly to the definition of complexity that rosen has used to make this distinction as clear as possible:
Complexity is the property of a real world system that is manifest in the inability of any one formalism being adequate to capture all its properties. It requires that we find distinctly different ways of interacting with systems. Distinctly different in the sense that when we make successful models, the formal systems needed to describe each distinct aspect are NOT derivable from each otherThat statement is loaded with meaning and we will be spending a lot of words to get to most of that meaning. In the context of the previous diaries, the reason we went back to Hutchins and then explored the conflict between hard and soft science was to get you ready for the clear necessity of the existence of many ways of interacting with systems in the real world and then creating appropriate models for each type of interaction.
Let us go directly to Rosen for more on this:(From AS)
It mut be recognized that we are speaking here entirely of complexity as an attribute of natural systems; the same word (complexity) may, and often is, used to describe some attribute of a formal system.The usual confusion here mixes the complicated nature of the formal system needed to model a natural system with the very different notion of complexity, which is a general attribute of all real systems even those that we are able to model with relatively simple formal systems. I will be very surprised if this does not happen as we discuss these matters here.
The plot thickens when we realize that what we take for granted to be formal systems are really natural systems that we have modeled with a formalism. To drive this point home Rosen goes back (in LI) to the Rutherford vs Hutchins pictures of science and says this:
I am now going to do do something that would bother both Rutherford and Hutchins, though in different ways. I am going to illuminate the duality they personify by looking at a cognate situation in an entirely different realm, the realm of mathematics....The mathematical world is emodied in percepts but exists independent of them. "Truth" in the mathematical world is likewise manifest in , but independent of, any material embodiment and is thus outside of conventional perceptual categories like space and time.In other words we learn about mathematics using our senses and our brains, yet we seem to also believe we create mathematics. Rosen is a very good mathematician and he sees beyond this.
To motivate our discussion, it is enough to observe that both science, the study of phenomena, and mathematics are in their different ways concerned with systems of entailment, causal entailment in the phenomenal world, inferential entailment in the mathematical.This identification is the key to where we are headed. We have the modeling relation which rests on the statement above. How this unfolds will be a revolutionary breakthrough in our thinking.
The use of mathematics as both a formal and natural system is an interesting ploy for it takes us quickly to the concept of complexity and what it is all about. It also quickly demonstrates the shaky nature of the paradigm we allowed to obscure the need for a modeling relation to understand the complex natural world. Rosen speaks of two great shocks in the world of mathematics in the past century or so.
the overthrow of Euclid and the discovery of inconsistencies in set theory.Some of you probably already see where this is going. For the idea that we can have a largest model and explain everything by direct cause will now be reduced to a belief and a shaky one at that. Let us see how:
The tewo great shocks of which I spoke above have coalesced, geginning in the early years of the present (20th) century, into a frantic concern with consistency, with a demand that a system of inferential entailment (e. g., a set of axioms or production rules, operating on a set of given propositions or postulates) be free of internal or logical contradictions.This scenareo sets the stage for the famous work of Goedel who effectively showed that any formal system can not simultaneously be consistent as required above and complete. Why discuss mathematics? It was Number Theory that was the battle ground where the attempts to show that there can be a largest system (complete) that was also consistent was impossible.
So we have laid the basis for the new paradigm. It must be built on the acknowledgement that the efforts of the Cartesian Reductionists with their duality and mechanism is built on a false premise. There can be no largest model and the world, even as it includes things like numbers, is complex. Hence we are now ready to look more closely at the inadequacies of the direct cause view of the world, which, unfortunately is the science we have come to know and love, has fallen short of the mark in spite of its many successes in helping us understand the mworld in part, and thereby transform it to what looks like our eventual peril.
If you have come this far your rewards will be forthcoming for we will be enjoying the efforts of Robert Rosen to deal with complex causality and a picture of how things happen in a world that has no largest model. The sixth installment will introduce complex causality and also refresh our memories about what George Lakoff has had to say about the central role of causal differences and models in understanding the major political differences in the way people view the same world today.
This diary will provide links to the others in the series:Reading Ramblings:Do we understand how we go about making decisions?We use models,consciously or not