Twas the night before election and all through the house (and senate) creatures were shaking in their boots. So what better time to get one's mind on other things?
Last night I had the strangest dream like I never had before. Here I am past my 78th birthday and for the first time I dreamed about what my next book will be about.
Some of my colleagues in science and I have broken away from the mechanist/reductionist science that has led us to many potential tipping points, none of them very good. We are practicing a new paradigm, which for lack of a better name we have called complexity theory. I also toy with the name "relational systems theory" since complexity has been almost completely co opted by the reductionists.
This is where we must start for language is a prison. Words do not exist for new ideas and the old words have been framed in a context that is counter productive. The best we can do is to use metaphors to try to break the old framing and introduce new ideas in the place of the old meanings. Complexity is a good example. We will come back to this shortly.
If you are interested in seeing where this goes, read on below.
Language itself is a problem for it is inherently linear. At least this is true of the English language as we have learned to use it. This is intimately related to our logic which forbids impredicativity.
In mathematics and logic, a self-referencing definition is called impredicative. More precisely, a definition is said to be impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set which contains the thing being defined.
The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over. A prototypical example is intuitionistic type theory, which retains ramification but discards impredicativity.
Russell's paradox is a famous example of an impredicative construction, namely the set of all sets which do not contain themselves. The paradox is whether such a set contains itself or not — if it does then by definition it should not, and if it does not then by definition it should.
The obvious way to break out of an old paradigm is to confront its weakness directly. Our approach does exactly that for the inability to deal with self reference excludes most of what is interesting about the real world, especially where living systems are involved.
Robert Rosen was a theoretical biologist who
proposed a methodology that he called Relational Biology which needs to be developed in addition to the current reductionistic approaches to science by molecular biologists. Relational is a term he correctly attributes to Nicolas Rashevsky who published several papers on the importance of set-theoretical relations in biology prior to Rosen's first reports on this subject. Rosen's relational approach to Biology is an extension and amplification of Nicolas Rashevsky's treatment of n-ary relations in, and among, organismic sets that he developed over two decades as a representation of both biological and social "organisms".
Rosen’s relational biology maintains that organisms, and indeed all systems, have a distinct quality called organization which is not part of the language of reductionism, as for example in molecular biology, although it is increasingly employed in systems biology. It has to do with more than purely structural or material aspects. For example, organization includes all relations between material parts, relations between the effects of interactions of the material parts, and relations with time and environment, to name a few. Many people sum up this aspect of complex systems by saying that the whole is more than the sum of the parts. Relations between parts and between the effects of interactions must be considered as additional 'relational' parts, in some sense.
In particular, Rosen recognized the central role of impredicativity in the complex real world and developed his own version of category theory to deal with it.
In mathematical biology he is known as the originator of a class of relational models of living organisms, called (M{,}R)-systems that he devised to capture the minimal capabilities that a material system would need in order to be one of the simplest functional organisms that are commonly said to be "alive". In this kind of system, M stands for the metabolic and R stands for the 'repair' subsystems of a simple organism, for example active 'repair' RNA molecules. Thus, his mode for determining or "defining" life in any given system is a functional, not material, mode; although he did consider in his 1970s published reports specific dynamic realizations of the simplest (M{,}R)-systems in terms of enzymes (M), RNA (R), and functional, duplicating DNA (his beta-mapping).
He went, however, even farther in this direction by claiming that when studying a complex system, one "can throw away the matter and study the organization order" to learn those things that are essential to defining in general an entire class of systems. This has been, however, taken too literally by a few of his former students who have not completely assimilated Robert Rosen's injunction of the need for a theory of dynamic realizations of such abstract components in specific molecular form in order to close the modeling loop for the simplest functional organisms (such as, for example, single-cell algae or microorganisms). He supported this claim (that he actually attributed to Nicolas Rashevsky) based on the fact that living organisms are a class of systems with an extremely wide range of material "ingredients", different structures, different habitats, different modes of living and reproduction, and yet we are somehow able to recognize them all as living, or functional organisms, without being however vitalists.
The above quotations are replete with examples of the language problem I started with above. Therefore if you accept the words with their usual meaning you will miss the point. This is hard and it takes work to realize that Rosen has moved us into a new paradigm where the words now have new meaning.
Before going on with this thought I need to make sure you are aware of just how sound all this reasoning is. A. Louie, a student of Rosen, has done a magnificent job of solidifying the theory using category and lattice theory. His book, More Than Life Itself: A Synthetic Continuation in Relational Biology (Categories)
is an exploratory journey in relational biology, a study of life in terms of the organization of entailment relations in living systems. This book represents a synergy of the mathematical theories of categories, lattices, and modelling, and the result is a synthetic biology that provides a characterization of life. Biology extends physics. Life is not a specialization of mechanism, but an expansive generalization of it. Organisms and machines share some common features, but organisms are not machines. Life is defined by a relational closure that places it beyond the reach of physicochemical and mechanistic dogma, outside the reductionistic universe, and into the realm of impredicativity. Function dictates structure. Complexity brings forth living beings.
It is the relational closure that is so revolutionary. It involves loops of causality that are closed and which defy classical modeling methods.
That brings us to the second part of the diary title. Just like category theory is a new er form of mathematics which was developed to study the structure of mathematics, the new relational approach is a form of natural philosophy designed to study the structure of natural philosophy. What could be more circular than that?
One of my favorite symbols is the yin and yang
Yin and yang can be thought of as complementary (rather than opposing) forces that interact to form a dynamic system in which the whole is greater than the assembled parts. Everything has both yin and yang aspects, (for instance shadow cannot exist without light). Either of the two major aspects may manifest more strongly in a particular object, depending on the criterion of the observation.
. The new paradigm has much of the flavor of these ideas but goes much further in establishing a formal methodology to model the things of interest. In this way we are able to "step out of the box" and watch ourselves as we examine what we are doing.
I have written many diaries here based on these ideas and now am ready to make the leap into another book. Wish me more good dreams. If you have come this far I managed to get your mind off the election for a bit. Now GOTV!