Reductive abstractions in explanatory systems serve very well to ground those systems in self-validating (if demonstrably incomplete) logic, and possess considerable power and compelling reasons to believe them. Observe the thread of Turing‘s abstraction arrive in the (perhaps inevitable) artefacts, entities and exceptional utility of cloud computing – the simulated computing machines of various kinds: […]
Alan Turing’s proof of the undecidability of non-trivially sophisticated algorithms is sufficient reason for:• the autonomously adaptive, complex information strategies of life; and,• the intractably problematic and recursively non-terminating information transcription of cancer.
Some truths are only known by inversion, by negation and through a proof by contradiction. Alan Turing’s proof of the undecidability of non-trivially complex algorithms, that is – the impossibility of analysis to arrive at certainty concerning whether a given computer program will terminate or continue forever, was just such a proof. Kurt Gödel’s proof […]
A philosophical perspective: I accept that conscious machines are plausible, but I have trouble believing that the diverse algorithmic and networked approaches under development are anything beyond sophisticated, limited, mechanical or incomplete axiomatic models. It provides reflexive psychological comfort to assert (and believe) that the hard problem of consciousness is explicable via a reductive algebra […]
If a non-trivially complex organisational system of any kind or scale is to be considered (even notionally) as complete or entirely self-consistent, it can not also be adaptive, flexible and resilient.