Formal-ity and the Church-Turing thesis

[Ravi Sahni]

On Tue, Oct 8, 2013 at 1:20 PM, Steven D'Aprano <steve at pearwood.info> wrote:
> On Tue, 08 Oct 2013 10:46:50 +0530, Ravi Sahni wrote:
>
>> On Tue, Oct 8, 2013 at 8:47 AM, rusi <rustompmody at gmail.com> wrote:
>>> I can only say how ironic it sounds to someone who is familiar with the
>>> history of our field: Turing was not a computer scientist (the term did
>>> not exist then) but a mathematician.  And his major contribution was to
>>> create a form of argument so much more rigorous than what erstwhile
>>> mathematicians were used to that he was justified in calling that math
>>> as a machine.
>>>
>>> The irony is that today's generation assumes that 'some-machine'
>>> implies its something like 'Intel-machine'. To get out of this
>>> confusion ask yourself: Is it finite or infinite? If the TM were finite
>>> it would be a DFA If the Intel-machine (and like) were infinite they
>>> would need to exist in a different universe.
>>
>> With due respect Sir, you saying that Turing machine not a machine? Very
>> confusion Sir!!!
>
> The mathematical ideal Turing Machine has an infinitely long tape,
> equivalent to infinite memory, and may take an unbounded amount of time
> to complete the computation. Since no *actual* physical machine can be
> infinitely big, and in practice there are strict limits on how long we
> are willing to wait for a computation to complete, in the *literal*
> sense, Turing Machines are not *actual* machines. They are a mathematical
> abstraction.
>
> But in practice, we can wave our hands and ignore this fact, and consider
> only not-quite-Turing Machines with finite amounts of tape, and note that
> they are equivalent to physical machines with finite amounts of memory.
> One could even build such a finite Turing Machine, although of course it
> would be very slow. Or one can simulate it in software.
>
> So in that sense, computers are Turing Machines. Anything a physical
> computing device can compute, a Turing Machine could too. The converse is
> not true though: a Turing Machine with infinite tape can compute things
> where a real physical device would run out of memory, although it might
> take longer than anyone is willing to wait.

Thanks Sir the detailed explanation. You are offering me many thoughts
inside few words so I will need some time to meditate upon the same.

Presently Sir, I wish to ask single question: What you mean "wave our hands"??

Thanks
-- 
Ravi