WHAT’S GOING ON WITH THE TOPOLOGY OF RECURSION?
Donald H. McNeil
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The notion of “recursion”
— by various definitions — goes around and about in scholarly
circles, but too often without the appreciation which it deserves. Meanwhile,
the quest for invariants lies at the core of human pursuits generally. This
article offers a reminder about how invariance mutually entails recursion and
how the topology of recursion helps to make sense of it all. Examples are drawn
from mathematics, physical sciences, cybernetics, biology, and finally from the
realms of the psyche and society in order to cast recursion into various
perspectives. The topology of the torus is found to be ubiquitous where
recursions and invariants are concerned. What counts as a “self”
and what makes for “self-reference” are reconsidered, and some
semiotic implications of topology are suggested.
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