Church's thesis & Sankara's argument re: Cause of liberation
hbdave
hbd at DDIT.ERNET.IN
Mon Apr 1 03:20:04 CST 2002
Jaldhar H. Vyas wrote:
> A forwarded message from Bhadraiah Mallampalli <vaidix at hotmail.com> which
> I think you might find interesting.
>
> ---------- Forwarded message ----------
>
> Alonzo Church's thesis & Sankara's argument re: cause of liberation
> -------------------------------------------------------------------
>
> While the Church keeps saying there is only one way for salvation, another
> Church was knowingly or unknowingly to himself proving something opposite!
>
> The computer scientist & mathematician Alonzo Church, in 1930s, had proposed
> what is called unsolvability of the halting problem. It is stated as:
>
> "There is no algorithm that, given a program of language L and an input to
> that program, can determine whether or not the given program will eventually
> halt on the given input."
>
> This thesis can be proven mathematically for a specific known computer
> language, but a generic statement like the one above is unprovable.
($)
> So
> Church's original thesis was never proved. In the words of Davis, Sigal,
> Weyuker' in their book "Computability, Complexity and Languages" this is
> explained : "But, since the word algorithm has no general definition
> separated from a particular language, Church's thesis cannot be proved as a
> mathematical theorem". One example of such a program not known if it halts
> is: "Every even number >= 4 is the sum of two primes" This is the 250 year
> old Goldbach's conjecture which is never known to halt for its search on
> its way to infinity.
The above statement ($) is not correct. In any standard book on Theory of
Automata
the above thesis is proved, without using any specific definition language.
The
word "algorithm" has a technical, definite, definition. Like a number, which is
an abstract thing, but has a representation, algorithm is an abstract thing,
but has
a representation. If we are talking about whether an algorithm works or not,
there is always an agency on which it is to be "executed" and that agency will
require a representation of the algorithm.
Of course, this does not distract us from the remaining part of the posting.
I generally agree with what you have said.
I had done some work on lines similar to these and come up with some
interesting
(i.e. for Advaitins) results. May I mention that as a part of my profession, I
have
been teaching this subject in Computer Science for quite a few years, so I
think
I know what I am talking about :-).
To show the results we have to go through a typical proof for unsolvability of
the "Halting Problem." This proof can be understood by anyone with a logical
and open mind, and a little bit (just a wee bit) of exposure to computers.
I shall require some time to prepare the note, may be a couple of days.
Will the List members be interested?
-- Himanshu
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