Harry Erwin wrote:
> You're missing my point. Symbols are signs. They belong to a countable
> set. Wind-tunnel models can vary continuously (or discontinuously). That
> matters--there are some applications (for example in hydraulic analysis)
> where symbolic modeling encounters an intractable problem, but analog
> modeling works fine.
Intractability is a an issue relating to computational efficiency --
i.e. the time or space required to perform the calculation. It has no
bearing on Church's thesis. A Turing machine can be written to solve the
hydraulic problem to any desired degree of accuracy because the TM has
an infinite supply of time and space. It may take a while, but that's
okay, because Church's thesis concerns computability in principle, not
in practice.
> Why do I care? Disambiguating an acoustic scene
> based on multisensor data is very difficult because of all the ghosts
> that have to be eliminated _sequentially_. Bats do it in real time. How?
Real time has no bearing on Church's thesis. The issue is whether a bat
can perform a calculation which a TM cannot, not whether a bat can
calculate faster than a TM. (After all, TM's are the most inefficient
machines ever conceived!)
Kevin K.
