Monday, June 28, 2004
On the nature of logic and computing, is there a difference?
(new beads are edited for a few days until the grammar is correct)
From a living system's point of view the environment is as it is. Heinz von Foerster called the environment 'an invention of the living system' and I tend to agree.
But this invention is not arbitrary: it is a reductionist process of establishing causalities (as axioms, hypotheses or theories) and using causal deduction (or logic, if we have language) to make inferences form these causalities. Establishing a causality is, I suspect, a process of analogical inferences, (or abduction).
Adapting to the environment could be described as an oscillating combination of synthetic and analytic reasoning. We can also call it thinking or biological computing.
Technical computing today is restricted to only the analytic part of the process.
The problem is that all we really have in order to build, program and operate machines is logic. The key to adaptive computing seems not to be another logic, but, as Gotthard Guenther was probably the first to emphasize, another architecture of logic.
By this I mean that we need a way to integrate as well as trace arbitrary logic domains (logic systems). This capability will allow us to stick to logic (and thus to use computing machinery we can build and control), but still break the Cartesian closure that restricts logic operations to one domain at a time.
Analogic reasoning is -in my understanding- a way to move in arbitrary hierarchies and still be connected to all intersecting trees at every step, so you could switch trees at any step. This requires an interconnected combinatorial space.
My intuition is that such a structure and system actually goes beyond the Turing machine, the Lambda calculus and Godel's recursive functions.
We, the community, need a couple of very good mathematicians to look deeply into this matter.
The fascinating thing is that one can build machines using logic, by building mechanisms like CPUs.
Mon-linearity is an emergent phenomenon of the architecture of logic.
But possible complexity, properly understood, is the secret of biological computing.