To recurse

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Life and the work of recursion

To recurse
To perform the same sequence of operations on successive results. To repeat a process whose output at each stage is applied as input in the succeeding stage.

Actions that verbs indicate recurse, they work recurrently, repeatedly, continuously for a time through successive instances of themselves, shaping their outcome in the light of prior results. Hence "it ain't over 'till it's over." Verbs denote a process, a sequence that unfolds or recurs in time, comprising the recursive reiteration of its constituent operations. People often examine recursion in a rather abstract ways by studying how recursion works in special domains like language, mathematics, computer science, as well as art and music.

I think recursion operates fundamentally as a biological phenomenon, a key to embodying cognition, something close to the essential process of life through the cycles of death and reproduction. The world of matter and energy has numerous repetitive phenomena, but they are not recursive. In the physical world some processes maintain themselves for a time. Under the right conditions, they form, then sustain themselves as long as the conditions last, and then they expire. Perhaps life began when some natural cycle of repetition became recursive. Life, living processes, seem to have been self-sustaining physico-chemical process that acquired recursive capability, the power to call forth a new instance of itself before expiring. However the living origins of life came about, life has continued, life continues, and life will continue despite the mortality of its constituent members, and even more, by virtue of it. It has continued to maintain itself through cellular division and eventually through sexual reproduction. Despite the mortality of every instance of life, life itself defies mortality.

An interesting literature on recursion has developed, although I think work on various forms of recursion such as computer-based artificial life generally proceed by relying on recursion but saying little about what must take place in the recursive cycles to properly say that the process lives. How should observers distinguish between actions that maintain a process and those indicate the self-maintenance of the process? Douglas Hofstadter's large but impressionistic work, Gödel, Escher, and Bach: An Eternal Golden Braid (20 Anniversary edition, 1999) did a great deal to bring thinking about recursion beyond the confines of computer science, mathematics, and linguistics. The Recursive Mind: The Origins of Human Language, Thought, and Civilization by Michael C. Corballis (Updated ed., 2014) provides an excellent recent survey emphasizing the development and importance of the recursive power of language.

In a highly speculative mood, I wonder whether time itself constitutes an encompassing recursive function by which the universe, natural and vital, continually calls up a new instance of itself? But only time will tell.