[EMAIL PROTECTED]: > Nobody will ever be able to fully describe anything that is not > computable in the limit by a general Turing Machine.
It hasn't been proven that Turing computability is ultimate in computability, only its equivalence to other proposed models of computability with finite descriptions. It seems unlikely today, but tomorrow someone could come up with an organization that can't be simulated on a Turing machine. Somewhat unsatisfactory possibilities have been around, that can do uncomputable things: Turing machines with various oracles (with a Chaitin's Omega oracle, a machine can solve the halting problem and compute many uncomputable numbers). Machines with true real-valued registers. The registers would be initialized in a finite way, say to 0, but operations could produce register contents corresponding to infinite expansions. I think there are "algorithms", like the sieve of Erastothenes, on such infinite binary expansions, able to do work in single steps that would take Turing machines forever. Halting-type problems can be solved by computing all possible cases along the expansion, then doing a zero/nonzero test on the final answer, to check for the presence or absence of a single bit anywhere.
