Ben:but even so they [TM's] seem to be capable of simulating any kind of 
intuitive computation, at
least attempts to show otherwise seem to have failed so far.

Would you argue they can handle the most intuitive thought / problemsolving - 
creative?  A TM by definition has a set of instructions/rules for 
problemsolving.But there are no definite rules for handling a creative problem -

"Ben, I want a new kind of program - that will make money - for a function that 
no one has ever thought of before.."

- are there?

Some kind of computer can handle such problems but not, I would have thought, a 
rulebound TM.

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