Hi Lawrence,
Congratulations on a fine essay! But I wonder whether the arguments you advance are against a straw man... pertinent to an abstract and continuous theory of reality, rather than what may actually be a discrete and non-continuous material cosmos. You wrote:
> Physical systems in some funny sense have a premonition about how to evolve.... There is no information transfer in this process, but in a nonlocal manner a quantum particle "knows" how to evolve by sampling all possible paths
To apply the Principle of Least Action you need to specify the end state as well as the starting state. It is therefore, more a view "looking back" than "looking forward". In fact, you can take the viewpoint of essayist Don Limuti, and say that particles do not have to have a continuous trajectory, and only have to appear intermittently. With this sort of interpretation, computation remains feasible.
> Godel's second theorem indicates that any consistent theory is unable to prove its consistency.
The precondition to Godel's theorem was that the theory be able to formulate *all* of arithmetic, not just finite models of arithmetic. Actual computers have finite word size and memory size, and might be better modeled by Primitive recursive arithmetic, which is provably consistent in Peano arithmetic. So the application of Godel's theorem is valid only for abstract models of computation, not actual discrete computational models of the cosmos.
> Taylor's argument may be seen as follows...
As you note, Taylor's argument depends on the Law of the Excluded Middle. Joseph Brenner (who is also an essayist here) has previously written a paper entitled "The philosophical logic of Stéphane Lupasco (1900-1988)" that describes Lupasco's alternate "Logic of the Included Middle" and argues that it better applies to reality. With a different logic I think you could reach a different conclusion about computability.
> Quantum gravity is then a quaternion theory, or a system of quaternions in the octonions. There is then a hierarchy R -> C -> H -> O, where classical mechanics is real valued, quantum mechanics complex valued, and underneath are quaternion and octonion valued fields and vacuum structures.
Nice idea. You might appreciate my advocacy of Geometric Algebra for the formulation of a computable cosmos in Software Cosmos, where I take up the simulation paradigm and construct a digital model.
> The digital model of the universe or "It From Bit" is not decidable. A model of the physical universe encoded by algorithmic means will not compute reality.
I am most curious whether you think this limitation applies to my picture of a discrete computational model for the cosmos.
Hugh
