Re: A cake recipe is a computer program
From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 06/02/04
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Date: 2 Jun 2004 10:53:50 -0700
"Matt Timmermans" <mt0000@sympatico.nospam-remove.ca> wrote in message news:<rpavc.95429$tb4.3786216@news20.bellglobal.com>...
> "Eray Ozkural exa" <erayo@bilkent.edu.tr> wrote in message
> news:fa69ae35.0406010900.7349ecc@posting.google.com...
> > Many years ago, there was a debate about whether a recipe was a
> > computer program or not. Now I have seen Neil refer to a recipe so I
> > must state: I think affirmative. What do you think?
>
> Over here in comp.theory, that depends entirely on whether or not the
> language you write it in is Turing complete.
In philosophy of computation, we do not necessarily limit ourselves to
discrete computation, but nevertheless, we can do such for the sake of
present discussion.
The language I write the recipe in is English. It is most certainly
Turing complete. [Whether it is something else *in addition* is a
useless concern, philosophically]
I can instruct you to perform any algorithm in English. I can do it,
because I understand that human language is just another programming
language. In fact, any philosopher who took advanced algorithms
courses would see it.
Try me. I can have you compute quicksort([5;2;7;1;10]) by a program
written in ordinary English, given your charity.
> One may argue about whether or not any particular language is Turing
> complete as defined, because such definitions are often vague, but in every
> specific instance of communication the expressiveness of the language being
> used is clearly determined by the interpretive capabilities of the receiver.
I think you know I know these easy facts about languages and
computation.
English is a Turing complete programming language, for instance. The
syntactical ambiguity is irrelevant, that its interpretation does
result in desired computation in reliable manner is. [As a matter of
fact, ambiguity is an affordance, not a disadvantage. Humans use
shared context to resolve ambiguity.] [+]
> I think, therefore, that we can call a cake recipe a computer program if and
> only if humans are computers, or more specifically, universal Turing
> machines, when they read recipes.
I maintain that humans are *at least* UTMs for we can teach them to
understand a programming language, and compute its outcome, either in
memory, or using pen and paper. I thought you could see just *why*
Turing devised the Turing Machine: it models the operation of a
mathematician using pen and paper.
> I doubt that humans are universal under any circumstances.
You will have to substantiate this suspicion. The above argument is a
trivial, but strong argument for the universality and does so
empirically, ie. without resorting to silly metaphysical explanations.
In fact, that is what philosophy of computation is all about...
> They certainly
> are not when reading recipes. I doubt, for example, that there is anything
> I could write in that recipe that would cause a rational human reader to
> compute and output the SHA-1 hash of the recipe text, even though I can
> write computer programs to do that easily.
You can certainly tell that to somebody who knows logical and
arithmetic operations in plain English and minimal mathematical
terminology [which is natural language]. Your doubts are ungrounded.
[But it would be a twisted recipe, mind you. :->]
> Even if we could find strange
> people who could be convinced to do such a thing, there would certainly be
> computations those people would be unwilling or unable to perform just
> because a recipe told them to.
Are you familiar with analytical philosophy? Let's translate your
statement to a statement about computers and demonstrate its
absurdity.
"Even if we could find strange computers which could be programmed to
do such a thing, there would certainly be computations those computers
would be unwilling or unable to perform just because a program told
them to."
The substitutions are obvious. So is the absurdity.
> Since no recipe reader will emulate a universal Turing machine, then, we
> must conclude that recipes are not computer programs.
Both the premise and the conclusion are wrong.
> On to the next banality, please....
It is somewhat amusing that somebody who takes pleasure in theory of
computation finds legitimate questions in philosophy of computation
banal.
Regards,
-- Eray Ozkural [+] This can be also formally proved.
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