So go ahead J. R., add it <analog
computers> to the list.
No. Please wait. Let us ponder.
(Is J.R.'s mind digital or not?)
O-machines (Turing, 1938-1939) are Turing machines (1936)
augmented with one or more primitive operations each
of which returns the values of some function that is not
Each additional primitive operation is made available
by a black box: the "oracle".
One particular O-machine, the halting function machine,
can compute many functions that are not Turing-machine
Speculation as to whether there may actually be physical
processes that cannot be simulated by a (digital) machine
stretches back over at least four decades (Da Costa and
Doria 1991; Doyle 1982; Geroch and Hartle 1986; Komar 1964;
Kreisel 1967, 1974; Penrose 1989 and 1994; Pour-El 1974;
Pour-El and Richards 1979 and 1981; Scarpellini 1963;
Stannett 1990; Vergis et al 1986).
But if such processes do exist then perhaps future engineers
will use them to implement some O-machine.
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