Hegel's Science of Logic involves a trinary process: understanding -> dialectical reasoning -> speculative reasoning -> understanding at a higher level. This is analogous to a period 3 orbit, a return to self mediated by the other A -> B -> C -> A.
A direct consequence of a really strange theorem in dynamical systems due to Sharkovskii is that for any continuous function on the reals f: R -> R, if f has an orbit of minimal period 3 then it has orbits of any minimal period (because 3 is the first number in the Sharkovskii ordering). This happens in particular for certain values of lambda for the logistic map, exhibiting the phenomenon of 'chaos'.
The graph of successive higher iterations of the logistic map exhibit self-similarity, a fractal-like nature. This again mirrors the structure of the logic in which each part is similar in its trinary structure to that of the whole, i.e. Being -> Essence -> Notion, but in Being we have Quantity -> Quality -> Measure. In Concept we have Subjective Notion -> Objective Notion -> Absolute Notion. At a further finer level inside Quantity we have for instance Pure Being -> Nothing -> Becoming, etc.
In Hegel's "Science of Logic," the trinary process involves understanding -> dialectical reasoning -> speculative reasoning -> understanding at a higher level. This is analogous to a period 3 orbit, a return to self mediated by the other A -> B -> C -> A.
A direct consequence of a peculiar theorem in dynamical systems by Sharkovskii is that for any continuous function on the reals f: R -> R, if f has an orbit of minimal period 3, then it has orbits of any minimal period (because 3 is the first number in the Sharkovskii ordering). This occurs particularly for certain values of lambda for the logistic map, exhibiting the phenomenon of 'chaos.'
The graph of successive higher iterations of the logistic map exhibits self-similarity, a fractal-like nature. This again mirrors the structure of logic where each part is similar in its trinary structure to that of the whole, i.e., Being -> Essence -> Notion. In Being, we have Quantity -> Quality -> Measure. In Concept, we have Subjective Notion -> Objective Notion -> Absolute Notion. At a finer level inside Quantity, we have, for instance, Pure Being -> Nothing -> Becoming, etc.
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Hegel might have something to offer to researchers working in mathematical general systems theory, object specification logic, concurrency, systems biology, etc. Hegel is fascinating and infuriating. There seems to be a rich formal structure in Hegel which anticipates abstract conceptual schemes of modern logic, mathematics and computer science. Yet Hegel himself was opposed to formalism. And it is difficult to find the right approach though several people have tried...
It must not be forgotten that Hegel possessed an almost encyclopedic knowledge of the philosophy and history of his own time. In particular of historical philosophy. This knowledge was then condensed and re-interpreted in a novel and perhaps somewhat opaque terminology. From a systems theory perspective much of what lies behind Hegelianism, such as the concepts of aufhebung, return-to-self and reflection-in-self, can be found in pre-Hegelian philosophy (for instance in Aristotle, Plotinus, Leibniz and Kant himself) as well as independently in post-Hegelian logic, mathematics and science (see for instance Hofstadter's Gödel, Escher, Bach). What is novel in Hegel is the sociological interpretation - or rather the application to sociology and history - of abstract and complex philosophical concepts. The same goes, it seems, for psychology and psychoanalysis.
I can't help remembering that according to Arthur C. Clarke 'the Ramans do everything in threes'.
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