Per above Fisher is into the dynamics of development but seems to be using, like Commons, a static mathematical model to measure it. So why not a dynamic mathematical model based on living systems? Just such a mathematical model exists in dynamic systems theory applied to cognition, which uses differential equations instead of nested algebraic sets.
Lewis, Mark D. (2000-02-25). "The Promise of Dynamic Systems Approaches for an Integrated Accoun... (PDF). Child Development 71 (1): 36–43
Smith, Linda B.; Esther Thelen (2003-07-30). "Development as a dynamic system" (PDF). TRENDS in Cognitive Sciences 7 (8): 343–8.
In the article cited below it says something interesting about the kind of increasing complexity in dynamic systems:
"Complexity does not have to be constructed from preexisting forms nor follow a universal direction" (39). Emergence comes about through instability when old patterns break down. They are not included or enfolded in the set of a more complex level. Complexity yes, hierarchy not so much.
Lewis, M. (2000). "The promise of dynamic systems approaches for an integrated account of human development." Child Development, 71:1, 36-43.
From the essay "Piaget, DeLanda and Deleuze":
"It is a central concern for Deleuze...to do away with all ideas about structures...with ideas about ‘timeless forms’ or ‘essences’ that emanate from some Platonic heaven to give shape to the world of real things. Deleuze finds that such ‘essentialism’ pervades our normal perception and ways of thinking...things are thought of as belonging to categories and sub-categories which are defined in terms of invariant properties or, again, essences.
"This is all the more noticeable since Deleuze draws on almost all other branches of mathematics – number theory, the theory of sets; catastrophe theory, the theory of fractals and other branches of topology and in particular calculus and differential geometry.
"I would like to elaborate on this by jumping to one of the places where DeLanda discusses evolution. He says that the idea that evolutionary processes possess an inherent drive toward increased complexity reintroduces teleology – another kind of essentialism – into Darwinism. In this connection he mentions a mechanism in biological evolution called neoteny, which shows that novelty need not be the effect of terminal addition of new features; on the contrary it can be the result of a loss of certain old features.
"It is from the standpoint of this ontology...that Deleuze refutes evolutionism.... Returning to DeLanda’s example, in terms of genetic structuralism neoteny is a fine example of the way structure grows out of structure in a process that at bottom yields increased complexity by generating a new developmental level. The problem that makes discussions of evolution difficult is that Deleuze rejects the notion of epistemological and developmental ‘levels’, which is essential to Piaget. Instead, Deleuze introduces the concept of ‘strata’, which are intermingled or folded into one another and shot through by escape routes or ‘lines of flight’. At one point Deleuze says that among strata there is no fixed order, and one stratum can serve directly as a substratum for another without the intermediaries that one would expect from the standpoint of stages or degrees. Or the apparent order can be reversed.
"As mentioned earlier, Deleuze’s arguments draw heavily on calculus."
In my research I found an ebook called Continental Philosophy of Science and started a thread elsewhere in this forum. Therein I quoted from a chapter on Deleuze which is relevant here so it is copied below:
"Deleuze reads differential calculus not as a pragmatic matter of using differential equations to discover the slope of a particular function at a particular point. Rather, he sees in the differential an entire ontology of difference that can actualize itself into various functions and, consequently, specific curvilinear patterns" (247).
"In the later collaboration between Deleuze and Guttari, the writings of Ilya Prigogine become increasingly important. Prigogine, whose book La nouvelle alliance appeared in 1979, argues for a self-ordering of chemical components into patterns and relationships that cannot be read off from the previous state of chemical disarray.... It is not the introduction of some sort of ordering mechanism that makes the chemical clock appear. It is an inherent capability of the chemicals themselves for self-organization that gives rise to this phenomenon. It is as though there were virtual potentialities for communication or coordination contained in the chemicals themselves, or at least in their groupings, that are actualized under conditions that move away from equilibrium. As Manuel De Landa notes, in an echo of Deleuze’s treatment of Spinoza, ‘Matter, it turns out, can express itself in complex and creative ways, and our awareness of this must be incorporated into any future materialist philosophy'" (247).
Here's an excerpt from "Dynamical systems hypothesis in cognitive science":
"It should be acknowledged that the most widespread conceptualization of the mechanism of human cognition is that cognition resembles computational processes, like deductive reasoning or long division, by making use of symbolic representations of objects and events in the world that are manipulated by cognitive operations (typically serially ordered) which might reorder or replace symbols, and draw deductions from them. This approach has been called the computational approach and its best-known articulation is the physical symbol system hypothesis (Newell and Simon, 1972). The theoretical framework of modern linguistics (Chomsky, 1965) also falls within this tradition....the traditional approach hypothesizes that all processes of cognition are accomplished by computational operations that manipulate digital representations in discrete time. The mathematics of such systems is based on an abstract algebra dealing with the manipulation of strings and graphs of distinct symbol tokens. Indeed, Chomsky's work on the foundation of such abstract algebras (Chomsky, 1961) served as a theoretical foundation both for computer science and cognitive science, as well as modern linguistic theory."