In this installment we will build on the previous one Reading Ramblings: The danger of simplifying the notion of cause and move further to understanding what relational models are all about. Again we draw on Rosen's books Anticipatory Systems, Life Itself, Essays on Life Itself The use of functional components to make relational models allows us to focus on organization and relationships between the many activities going on in a complex system. If you are still in the Newtonian mindset maybe Rosen's suggestion that you think of these functional components as "particles of function" will help. He points out that the Newtonian paradigm dealing with actual material prticles is a synthetic theory that builds from the the behaviors of individual particles to families of particles. It is this synthetic theory combined with the atomic hypothesis that leads to the reductionist belief that every material system can be analyzed back to these families of particles. Thus partical mechanics became the largest model as we have discussed in earlier diaries. It is possible to do something more than this bottoms up modeling and that's where systems theory comes in. Later on we will look at rosen's concept of systems with more care. Read on below and we will now show how relational models use causality to look at the organization and function of a system without needing the particle physics at all.
Here's Rosen's idea:
It is clear that a corresponding synthetic relational theory of systems is incipient in the encoding of components into abstract mappings. For instance, we have at our disposal the formal concept of composition of mappings. In simplest terms, whenever the domain of one mapping intersects the range of another, the mappings may be composed to yield a composite mapping.He goes on to show how this is represented by diagrams that look like A ----->B and C---->D. If the sets B and C have members in common it is possible to compose these mappings into a simpler one A--->D. That is an important parallel to the particle analysis of a system.
Thus we can see that the analysis of relational systems is associated with the factorization of mappings, the synthesis of relational systems is associated with the composition of mappings...In these terms, then, we can now be a little clearer about the term "organization." Namely: organization is that attribute of a natural system which codes into the form of an abstract block diagram. To enlarge on our earlier image: if the component is an atom of organization, then a general abstract block diagram is a molecule of organisation.What is next is the way entailment enters the picture. here is where the causalities we have considered earier come into play. Further, it should be noted the distinction between the Newtonian (direct cause) form of entailment and this; namely in that the Newtonian version takes place in a state space while Rosen calls this entailment without states. The importance of this distinction can not be over emphasized.
Then for us, organization is itself a rather complicated concept; itinvolves a family of sets, a corresponding family of mappings defined on these sets, and above all, the abstract block diagram that interrelates them, that give us functions.
Let's do a part of the Metabolism repair model. This reference is to its beginnings is from the Rosen Bibliography on my web page: AN UPDATED ROSEN BIBLIOGRAPHY: Rosen, R. (1958) A relational theory of biological systems, Bull. Math. Biophys. 20:245-260. I still think his best explanation is in this magnificent work: Rosen, R. (1972) Some Relational Cell Models: The Metabolism-Repair System." Chapter 4 of Foundations of Mathematical Biology Vol. 2, 217-253. N.Y. & London, Academic Press.
We atrat with representing functional components as abstract block diagrams in terms of their causal roots. We start with the basis of all biological activity metabolism. Ithas this representation as anabstract block diagram reprsenting its material cause
A--->BWe are no where near finished with this one functional component and its material cause relationship. Yet is important to stop here and help you understand. If you were ever in a lab where they had one of those metabolic charts posted on the wall this should seem laughable! Well if it is then I will come back with the idea that you can create a model that takes in all of what is in one of those charts is far more laughable. What is included in this simple diagram? The whole of the material aspects of metabolism including the working of the genetic mechanism, etc. Many of the things at the level of biochemistry are things that do not have a unique mapping to this abstract block diagram. They, in fact, are often able to function in multiple ways depending on where they are in the organism and what is happening at the time. We lnow this to be tru of the DNA that is the "genetic code". The code is one of the most context dependent things we know.
Back to the relational model and causality. The next thing we need toask is "Why metabolism?" What entails metabolism. It has to have an efficient cause, call it f. Then the diagram can be extended showing the relationship of metabolism to its cause:
f >>>>>> A---->BThe next step comes from the fact that we have introduced f seemingly from nowhere (yet we know that metabolism has an efficient cause) so we can ask causal questions about f. This could lead to an infinite regression of causal questiions as it does in machines until an external efficient cause is supplied. In the organism, due to certain well known aspects of the3 genetic mechanism, the diagram closes on itself rather early in the game. This was Rosen's big discovery. Before you come up with the anticipated "so what" let us review what has been accomplished.
First of all we have a way of seeing complex systems that is independent from the traditional Newtonian decomposition and then replacement with a particle model that attempts to restore it as a whole system. Clearly this is a formidable (if even possible) task It is important to recognize the folly of statements about "wait until we know more" for we can not handle the details we have now. There has to be a way of avoiding that trap and going on and this is it!
Since this is Rosen's work I should not have to say this but experience tells me that I must! We have in no way negated the potential validity of models spawned from the Newtonian paradigm. They will stand or fall on their own merits. What has been clearly demonstrated here is that the Newtonian model has other models that can coexist with it and shed light on the nature of complex reality by asking and answering very different questions.
Whether or not you choose to preserve the exclusiveness of that paradigm you should be now ready to accept this one as being useful and able to stand side by side with the other.
There are many more questions to be answered regarding this new paradigm. I will be returning to that venture soon. Tomorrow (Thursday) I will take a break while preparing my annual rant for my birthday Friday. I am a very political person and my sense of urgency about the current political situation requires me to plunge in and rant!