A partial index of discussion notes is in http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html
On Tuesday 12th June I gave a short talk at this workshop
http://www.mathcomp.leeds.ac.uk/turing2012/inc/
Overview of workshop themes:
http://www.mathcomp.leeds.ac.uk/turing2012/inc/give-page.php?2
THE INCOMPUTABLE is one of a series of special events, running throughout the
Alan Turing Year, celebrating Turing's unique impact on mathematics, computing,
computer science, informatics, morphogenesis, philosophy and the wider scientific
world.
After the workshop, while reorganising my (still messy) slides http://www.cs.bham.ac.uk/research/projects/cogaff/talks/#talk102 and thinking about the issues raised at the workshop about the relationships between physics (including chemistry), evolution, life, mind and computability, I reached the conclusion that the following rather startling (and somewhat complex) thesis is implicitly widely believed to be true, because it is either a consequence of, or presupposed by, many many things that are now taken to be true, including some variant of Darwin's theory of natural selection. Its implications are profound and seem to require a long term, multidisciplinary, research programme linking a wide variety of disciplines, including the variant of Computer Science that includes the study of naturally occurring forms computation.
How? Can a Turing machine do all that?Starting merely with a rich enough physical/chemical machine, without any external input apart from solar energy, stellar radiation (especially light), and occasional disruptive physical perturbations (e.g. asteroid impacts), it is possible to produce every feature of both natural and artificial intelligence that has ever been manifested on earth -- and presumably many more, since the processes are continuing; and there are many branches that could have been taken but were not taken, e.g. what might have happened if there had not been highly disruptive asteroid impacts, or if there had been different impacts at different times. So, a sufficiently large and complex, multi-component, knowledge-free physicochemical machine is capable of producing every sort of intelligence, and every sort of product of intelligence, that has so far turned up on earth, without needing an external teacher or programmer, though it may take a very long time and require a huge amount of parallelism to allow effects of competition and cooperation to play a major role, and also to allow high level requirements to feed back into very low-level designs (e.g. adding neural computation to chemical computation, and also extending chemical computation by selecting more complex forms that serve higher level needs). Results include Euclid's elements, the idea of a Universal Turing Machine, proofs of incomputability and undecidability, sonnets, plays, paintings, symphonies, skyscrapers, airliners, bombs, democracies, dictatorships, wars, pandemics, and these notes.
I suspect those claims are true, but it may turn out to be impossible ever to find
conclusive proof, or a conclusive refutation.
Could it be refuted? At least the evidence could be challenged, e.g. by providing
evidence that some life form from another part of the universe interfered with
biological evolution on earth, including feeding in philosophical, mathematical,
scientific, and artistic goals and ideas. But that would merely shift the claim to
refer to a larger subset of the physical universe.
But as far as I know there was no such influence, though something not very different
was the influence of optical radiation from planets and stars, presenting changing
patterns in the sky that prompted ancient thinkers to try to impose a structure on
the observed motions. It is not obvious that Newton would have come up with his
mechanical theories and his new mathematics if he and his predecessors had not been
faced with the tutorial problem of explaining observed "heavenly" movements.
NOTE 1
I first encountered the idea that stars and planets visible at night played a
crucial role in the development of human minds, in a presentation Oliver Selfridge
gave at the University of Sussex in 1981.
He suggested that gazing at, talking about, and trying to record and understand,
the night sky and the ways in which it changed over time, was one of the few
activities available to ancient humans in the absence of sunlight.
If that was as important as Selfridge suggested, then we could say that the solar
system and visible stars did function as a sort of tutor for early humans. If there
had been no night sky would there ever have been a Newton or an Einstein?
However, for the sky to play that role, the biosphere must already have produced
highly sophisticated natural information-processing systems (computers).
NOTE 2
The ideas summarised above are closely related to one of the UKCRC Computing Research
Grand challenges: GC7
http://www.cs.york.ac.uk/nature/gc7/
Grand Challenge 7: Journeys in Non-Classical Computation
The Challenge: to produce a fully mature science of all forms of
computation, that unifies the classical and non-classical paradigms
A few small steps towards understanding the evolutionary progress summarised above are proposed in the "Meta-morphogenesis" project. See
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham