On Jul 16, 2015, at 9:30 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote: (01)
> On 7/16/2015 9:36 PM, Pat Hayes wrote:
>> I presume you are referring to Turing machines. But actual computers
>> attached to the internet are not Turing machines. For example, they
>> are able to respond in real time to a telephone connect tone, which
>> is beyond the capacity of a Turing machine.
>
> Robert Soare wrote a good survey of Turing's Oracle machines,
> Emil Post's further developments of Turing's rather brief
> comments, and the implications of connecting a Turing machine
> (or any digital computer) to the Internet:
>
> http://www.people.cs.uchicago.edu/~soare/History/turing.pdf
> Turing Oracle Machines, Online Computing, and
> Three Displacements in Computability Theory
>
> His concluding paragraph:
>> For pedagogical reasons with beginning students it is reasonable
>> to first present Turing a-machines and ordinary computability.
>> However, any introductory computability book should then present
>> as soon as possible Turing oracle machines (o-machines) and relative
>> computability. Parallels should be drawn with offline and online
>> computing in the real world. (02)
Oracle machines deal with some issues of computability in the real world, but I
was thinking more of the fact that actual computer behavior often depends on
real time of responses, which is a crticial aspect of computer science and
computer engineering which is completely invisible from the perspective of the
theory of Turing computability. (03)
As a general intellectual rule, any identification of the living/computer
contrast with any xxx/Turing-computable contrast, for pretty much any xxx, is
probably nonsense. For a thorough debunking of one famous attempt, see
http://www.ihmc.us/users/phayes/Pub/LaforteHayesFord.pdf (04)
Pat (05)
>
> John
>
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> (06)
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