[FRIAM] A question for tomorrow

[lrudolph at meganet.net]

Frank writes:
> I would hate to have to demonstrate that a modern computer is an instance
> of a Turing Machine.  Among other things they usually have multiple
> processors as well as memory hierarchies.  But I suppose it could be done,
> theoretically.

First a passage from a chapter I contributed to a book edited by a
graduate student Nick knows (Zack Beckstead); I have cut out a bit in the
middle which aims at a different point not under consideration here.
===begin===
If talk of “machines” in the context of the human sciences seems out of
place, note that Turing (1936) actually introduces his “automatic machine”
as a formalization (thoroughly mathematical, though described in
suggestive mechanistic terms like “tape” and “scanning”) of “an idealized
*human* calculating agent” (Soare, 1996, p. 291; italics in the original),
called by Turing a “computer”. [...] As Turing remarks, “It is always
possible for the computer to break off from his work, to go away and
forget all about it, and later to come back and go on with it” (1936, p.
253). It seems to me that then it must also be “always possible for the
computer to break off” and never “come back” (in fact, this often happens
in the lives, and invariably upon the deaths, of non-idealized human
calculating agents).
===end===
Of course Turing's idealization of "an idealized *human* calculating
agent" also idealizes away the fact that human computers sometimes make
errors. A Turing machine doesn't make errors.  But both the processors and
the memory of a modern computer can, and *must* make errors (however
rarely, and however good the error-detection).  To at least that extent,
then, they are not *perfect* instantiations of Turing machines.  On the
other hand, that very fact about them makes them (in some sense) *more*
like (actual) human calculating agents.

So, Nick, why are you asking what Turing machines think, instead of what
modern computers think?  (Be careful how you answer that...)