We are now ready to really move forward with the new paradigm. This diary in the series will show the way that opening science to all questions of causal entailment made way for the possibility to escape from the prison that reductionism and formalism unwittingly constructed. It also opens the way for the next in the series where the relationship between religion and reductionist science is seen in an entirely new light. The link to the last installment Reading Ramblings: Why do we try to make sense out of a complex world using simple models? will provide the chain of links that get you to the earlier contributions to the series. We have gone far enough now that it pays to review a bit. We have looked at the charge given us by Robert Hutchins and the failure of intellectuals to meet that charge. Rather than integrate knowledge and preserve the relationships between its various facets, we have built walls between them and destroyed large parts of that body of knowledge by severing links and connections. We have seen, through Rosen, that this has resulted in a very sterile picture of nature, for example, that has but one way of being seen through a myopic version of what has come to be called "science". The simple view of the world is easily gone beyond using the modeling relation which forces us to recognize that the complex real world needs a myriad of models and, as we will see, models that are necissarily context dependent and can not be used outside the context they were designed to deal with. As we go on this will become clearer. The first step in that clarification is to examine a simple idea. "Information" is a big word in science and technology and our world thrives on the transmission and consumption of information. Therefore there is a special irony in the way the reductionist science that has fueled the information age's arrival is also a block to some of the most important information we can learn about real world complex systems.Read on below to find out what this entails.
Looking back, it is easy to identify Plato with the dominant theme in today's reductionist science. His concept of ideals that we only see as shadows on the wall of the cave led to the formalist dream and the stripping away of the shadowy nature of our reality and its replacement by the clean model of recuctionist science. Further, the idea that we should consider anything outside the context of this largest model "unscientific" mixed some very important information about our world with superstition and the "supernatural". The irony in this will be the subject of the next installment. In this one I want to focus on what was missed and what tremendous value its content adds to our understanding.
Ironically, the study of causality is the legacy of Aristotle. The platonic world view sterilized the realm of investigation and Descartes completed the process by introducing the duality between mind and body and the machine metaphor that we have to this day. The largest model has been designed to treat everything in the world as a machine and when we turn it on the making of machines, our technology, it does its job very well.
The law of the Instrument: Give a small boy a hammer and he will soon learn that the whole world is a nailLet us get the direction for this from Rosen (AS)
But the concept of causality is itself a complicated one; this fact has been largely overlooked in modern scientific discourse, to its cost. That causality is complicated was already pointed out by Aristotle.to Aristotle, all science was animated by a specific interrogative: why? He said explicitly that the business of science was to concern itself with "the why of things". In our language these are just the questions of theoretical scienceI feel compelled to remind you of what I quoted from him in the second of this series. The duality between theoretical and experimenmal science in many ways mirrors the duality between the way reductionist science and the new paradigm view information and causality. It will be easy to establish that the machine metaphor and the largest model that characterize traditional science are antagonistic, to say the least, with the aspects of causal analysis that Rosen brought into the discourse. This is in spite of the fact that Rosen's use of category theory put his work on the most solid footing possible by the standards of reductionist science.
The basic issue and the basic division in the kinds of questions that reductionist science can handle using its machine metaphor and its largest model is the use of the question "how?" exclusively. The answer to "how? is a machine answer. We discover how it works. The rub here, and it is a vital shortcoming, is in the fact that once you know how a machine works you know all about it. You can reverse engineer it and build it. A quick consideration of any complex real world system will reveal that this is not so for them. In particular, living systems, and systems that involve living organisms, can be understood only in part by a study of their physiology, their genetic mechanisms, etc. From this knowledge we have no clue as to how we might go about making them. The words "fabrication of life" in the subtitle of Life Itself are there for a reason and this is a subject we will come back to later. For now we will go on building the case for the use of "why?" to learn important things missed by the reductionist approach.
Aristotle and Causality:
As noted above, the idea of asking “how?” fits the limited scope of the machine metaphor completely. We ask how machines work and our answer defines the machine. Had we included the asking of why the machine exists, we would have been led naturally to the issue of function. A later installment will be devoted to amplifying this central idea about the way that causal entailment and functional components of complex real systems are tightly linked.
Aristotle proposed that there are four distinct ways to answer the question “why?” For example, “why the house?” The house exists because:
1.Material Cause: The bricks, mortar, wood, nails, etc., of which the house is made.I want you to make special note that the whole idea of anticipation is tightly coupled to the fourth cause. The house was built with a purpose in mind. There is no way of reducing this event to a reactionary paradigm mode in order to conform to the "rules" of reductionist science without losing information. I taught physiology all my life and it is very difficult to even attemp to sterilize the content of lectures to avoid talking about the "purpose" of parts of the body, etc. In fact the entire discipline is organized around the function of systems in the body that are identified as such because of their purpose.
2.Efficient Cause: The materials were put into the form we recognize as the house by an agent, the builder.
3.Formal Cause: The form the house took came from some plan, a blueprint. The builder followed it when he constructed the house.
4.Final Cause: There was a reason or purpose for the house. Someone needed a dwelling place.
Rosen's use of causal reasoning to reframe the question "What is life"
Shortly after Rosen's death I was asked to fill in for him at the next International Society for the Systems Sciences (ISSS) annual meeting. My topic was: ROBERT ROSEN: THE WELL POSED QUESTION AND ITS ANSWER-WHY ARE ORGANISMS DIFFERENT FROM MACHINES? Here is the abstract of that paper:
AbstractThe paper was publishen in this volume:
The question "What is life?" has been around for some time. There is an impressive list of great minds that tackled the question. In spite of this, it never has been answered in any definitive way. Robert Rosen, a student of Nicholas Rashevsky and a product of the Mathematical Biology program at the University of Chicago started one line of research that grappled with the question in the late 1950's. It is worth examining the progression, which lead Bob Rosen to realize that he was dealing with a poorly posed question and that when rephrased, the question had an earthshaking answer.
The answer was earthshaking not so much due to its information content but more so due to the process by which it was answered. This process and its really revealing ramifications will be the subject of this review. It is no easy task to try to say these things in Bob Rosen's stead, and you will suffer from having to hear a surrogate. On the other hand, to see beyond where anyone has seen before has often necessitated standing on the shoulders of giants.
What we will examine here is the entire epistemological basis for modern science. We will examine it with a view that, in itself, is a product of that very examination. And, thus, from the onset, we will be forced to stop every step of the way in order to remind ourselves that what we are doing is only effective if it is changing even as we do it.
Why so bold a goal? Because anything short of that easily and deceptively lapses back into well worn tracks even if dressed to seem new and different. What Robert Rosen discovered had that effect on him, and, as he wrote and spoke over the years, it began to have an effect on some of us. The path we are about to traverse is very difficult. It was even more difficult for Bob, for as he saw, he had to communicate what he saw. This is difficult enough with new ideas even when they nicely extend the ideas upon which they are built. It is far more difficult when the new ideas radically change that perspective.
Now we will move on to the subject at hand. The role of the machine metaphor in science goes back to Descartes. Newton and those who followed built it into what has become modern science. The success of this world-view was so great that it became as strong as any of the other belief structures we might identify as religions. In this case, however, science was to liberate us from superstition and myth and to give us a basis for evaluating those things that were to be candidates for truth.
Hence physics dealt with the fundamental laws of nature and chemistry and biology were to use these laws to deal with specific applications of the general laws physics discovered. In other words, the relation of physics to biology, in particular, is that of the general to the special. Rosen was able to see that, in fact, this was a prison for our thought and an extreme handicap to our understanding. It was a legacy of the machine metaphor. How could this be? It is so because the world of the machine is a "simple" world. Its laws and inhabitants are simple machines or mechanisms. What if the objects in chemistry and biology are not that simple? Then we must reduce them to subunits that are. By this reductionist path we will learn all that there is to learn about the real world. Robert Rosen discovered that this approach was a dead end! He discovered that when the reduction is performed, something real and necessary is lost and in a way which made it unrecoverable. This profound realization turned the ontology of our world upside down! It isn't the atoms and molecules that are at the hard core of reality, it is the relations between them and the relations between them and things called processes which are at the core of the real world!
There is much to this discovery and we will only be able to have a taste of it. In that tasting we will examine the modeling relation that is the key to our own ongoing examination of what we are doing as we do it! We will examine the alternative to a mechanistic world, a world of processes and causes. A world ever changing and yet a world more rational than the sterile world of machines. Finally, we will utilize this new way of seeing to repose the question about life and answer it.
Special Issue: "General Systems" Yearbook of the International Society for the Systems Sciences 1999Here are some of the passages that complete this installment for us:
Volume 17, Issue 5
Pages 415–484 (my paper pp 419-432)
Issue edited by: B. A. Banathy, J. P. van Gigch
Complex systems , as we have developed the concept, are merely real systems for which we want richer interactions than the limited kind dictated by the Newtonian paradigm. In such cases, we use the modeling relation to find models based on additional formal systems which are more than mere derivations of the Newtonian Paradigm. One of the first steps in developing such a formalism is the choice of question we pose about the real world. If we choose to replace "how?" questions which are only appropriate for the mechanistic approach with "why?" questions we see that there are four answers available to us. What is both interesting and consistent with the idea that Rosen's categories of simple vs. complex are useful, is the observation that in complex systems the causes behave in totally different ways. Besides the fact that complex systems always involve all four causes, they are generally mixed and can not be separated as they can in machines.
The use of a relational model to distinguish the organism from a machine.What follows is a development with diagrams of the argument using category theory. For many reasons, the main one being that this is already very long, I will ask the reader to go to link to see this. I will fast forward to the conclusion:
The trivial distinction in the context of the "what is life?" discussion is that between complex systems and simple mechanisms. Clearly, being real systems, organisms are complex and therefore differ from machines. But that is too easy and of little value. There is more which can be done in answering the question that will make the answer rest on the living nature of the organism. To deal with this issue, Rosen developed a class of objects he named Metabolism-Repair systems, or more simply (M,R) systems. What he was able to do with these systems was to explore the answer to the question when well posed in terms of a prototypical organism. The idea was a category theory application to the dynamics of biochemical and physiological systems. The mapping described above can be seen as a generalization of the more simple input/output diagrams used by engineers and others, such as pharmacologists doing compartmental analysis. They also substitute nicely for chemical reaction kinetics. He called them abstract block diagrams.
2.2.1 Abstract block diagrams formally model machines as well as complex systems
It is easy to model machines in terms of abstract block diagrams. The following is an example (Arbib and Manes, 1975). Let us look at a category theory formulation of a machine. It is surprisingly simple. It embodies everything a finiteTuring machine can do in an abstract way in terms of mappings. It also very nicely shows where dynamics comes into the entire picture. We next describe a sequential machine that can be in one of a finite number of states, receive one of a finite number of inputs, and emit one of a finite number of outputs.
DEFINITION: Sequential Machine: SM = ( X0, Q, d , q0,Y,b )
X0 is the set of inputs
Q is the set of states
d : Q x X0 à Q is the dynamics
q0 Î Q is the initial state
Y is the set of outputs
b is the output map
It has been said that this algorithmic character is restricted to sequential machines. I now will show that this is an illusion. A machine is a machine. Now can we describe a "parallel machine" as anything different?
DEFINITION: Parallel Machine: PM = (X0, Q, d , q0,Y,b )
X0 is the set of inputs
Q is the set of states
d : Q x X0 à Q is the dynamics
q0 Î Q is the initial state
Y is the set of outputs
b is the output map
Is there anything missing from this formulation? No, there is really none. The reason that they are the same in actuality is quite simple, it is always possible to simulate a parallel machine with a sequential machine. It is true that the symbols X and Q stand for different sets and that if Q is the set of states for the system it contains a subset, N which is the states of all the nodes in the parallel system. (In an ANN these would be the neurons). More importantly, the rules or algorithms behind the mapping , d , are very different in the two examples.
What is of particular interest is the mapping representing the dynamics of the machine. Even if we allow final cause into the picture, there is a paucity of entailment in the system. This will always be true in machines. In fact, if we try to answer "why?" for each aspect of the machine we can only finally answer by going outside the machine. This route leads to an infinite regression if continued. It is interesting that one way to end the process of nested entailments is to invoke some notion of deity.
The (M,R) system as a relational model of the organism
The History of relational models goes back to a seminal paper by Nicholas Rashevsky wherein he made a radical change in his approach to living systems (Rashevsky, 1954). After pioneering most of the mechanistic models we know about today, including reaction-diffusion systems and artificial neural networks as far back as the 1930s, he took stock of what he had learned and realized that he was not any closer to understanding what living systems were all about. He then decided to take an entirely new direction. His goal was to keep the organization of the living system while basically throwing out the physics. His tool for this was topology.
From the examples mentioned above it is inescapable that Rashevsky's desire to capture the contribution of organization was key to understanding living systems. There are many ways of expressing this , none of which are totally adequate due to the totality with which the Newtonian Paradigm made mechanism everything and clouded the real structure of the modeling relation. The essence is in the idea that organization can not be preserved during reductionist analysis. The concept of analytic models that do not reduce to synthetic models captures this formally. The task then is to formulate an analytic model of the organism that captures the organization even if it must sacrifice the physics. For this task, category theory is the method Rosen saw as capable of doing exactly what he wanted. He applied category theory to the (M,R) system to answer the question of why an organism was different from a machine. The presentation that follows will not be concerned with the fine points of category theory, but will focus on the representation of the mappings as they develop as answers to the question "why?'. The fundamental idea is that each mapping represents the input/output relations in an abstract block diagram. The first step is a single input/output diagram to represent "metabolism" as a mapping f taking inputs in A to outputs in B, f:A ® B. This is about as abstract a way there is to represent metabolism. In fact the symbols here can represent an infinite number of different schemes all of which have in common the mere taking inputs to outputs. Thus the symbolism has more to say about the organization of the organism rather than its mechanisms. Also, the symbolism as mere syntax, without the rich semantics attached to it, is rather meaningless. Notice also that the symbolism could represent any input/output relation. That is why it must carry with it certain semantics to fit the situation we are addressing here. A, the set of inputs, is being replaced from the environment as well as having certain members leave to the environment, but that need not be made explicit. What is missing is information about causality. A is clearly the material cause of B and f the efficient cause of B. In the sense of these causes, f is unentailed. We know the organism is repairing itself continuously, so that in the organism f is entailed by something. Again semantics is the key to making the syntax meaningful. Let us therefore represent that by use of a second mapping, F : Bà f. Now we have F as the efficient cause of f and B as its material cause. Call this second mapping the representation of repair in the system. This implies that among the products of metabolism are the materials necessary to keep the system maintained due to turn over of its components. What this simple symbolism connotes is truly profound. The system is in a constant turnover. Part of the turnover is the causal basis for the system's self repair.
The closure of the relational diagram has a parallel significance with Newton's achievement of closure in his dynamics. It establishes a category of objects called organisms that are clearly distinguishable from machines. This distinction arose from a procedure, which did not reduce the system to its material parts, nor did it explicitly invoke dynamics. In fact, the procedure, by necessity, treated processes and organization (mappings) as if they had the same ontological reality as the material parts. Specifically, to recognize mappings in which the mappings f play the role of material cause is to acknowledge a broader meaning for the notion of "material". Also, the concept of "replication" here is new and broadens the meaning of that term as well. What is replicated is a functional component, not a material part as such. It is necessary to recognize that the system of interest was complex, but that complexity alone was not enough. Thus organisms are complex, but all complex things are not organisms. The nature of the organism is that it possesses the kind of unity Maturana and Varela invoke for their autopoietic systems ( Maturana and Varela, 1980). It would seem appropriate for this result to be incorporated in the discussion of autopoiesis.I am going to leave you to stew on this. Hopefully some discussion and questions will follow. Meanwhile, I plan to go back over these ideas with more attention to making them understandable and to pointing out their significance in great detail. The next installment will begin to take care of that task but will alsio show how much of the controversy about "life" and the relationship between science and religion takes on a whole new meaning once you realize that this distinction between organisms and machines, in fact, why the science behind the machine metaphor logically requires that a supenatural cause (diety) be introduced to achieve closure in an otherwise infinite regression of incomplete causal entailment. Stay tuned.
It should be clear from this result that not only is it useful to recognize functional components as making up separate tangible aspects of the system, but that it is necessary to do so. Once this idea becomes clear, it becomes possible to look at complex systems in a new and meaningful way. Up until now, these ideas have been poorly understood and the suggestion that there are non-material aspects to the system as important , if not more important, as the material parts has often been looked upon as a form of mysticism. On the contrary, in order for science to be less mystical, these aspects need to be given more consideration.
An application: Is the Gaia hypothesis sound?
The Gaia hypothesis asserts that earth and its surrounding atmosphere constitute a living organism (Lovelock, 1979). Now that we have a clear-cut criterion for distinguishing organisms from simple machines as well as from other complex systems, we should be able to classify the system. Let us assume that the metabolism, m, of the earth consists of certain ongoing cycles including ecosystems, the water cycle, and others, C, that are made from resources, R, which include sunlight, the atmosphere, and the planet. As a relational diagram, this is, m: R à C. Next, in order that m is entailed, we recognize a set of natural processes that renew these metabolic processes from existing cycles when they are disrupted, n: C à m. At this point, n is unentailed. If another process, g, replicated the natural processes then a favorable analogy with the example above by Rosen is obtained. In fact, the diagrams are the same with the correspondences (A, R), (B, C), (f, m), (F , n), and (ß, G). Thus, by this criterion, the earth system, or Gaia, is indeed an organism.