Posted by
Marcus G. Daniels on
URL: http://friam.383.s1.nabble.com/Mathematics-and-Music-tp473042p475354.html
Prof David West wrote:
> A computer program, currently, is an attempt to mathematize; and the
> goal of traditional computer science is to refine the process of
> creating a computer program to the purely formal / mathematical. It is
> still an attempt, because a huge gulf remains between what I want and
> can say about what I want in a natural language and what the computer
> can 'hear' with its mathematical 'ears.'
>
I think the challenge is not to just facilitate use of natural
language. Natural language has the benefit of tolerating ambiguity and
thus making it possible to communicate half of an idea while continuing
a conversation. But I doubt that it is language issue per se. In
describing a problem to, say, a skilled computer programmer, the
programmer often models the intent in more operational and precise way
than the speaker delivers it. She has the benefit of sharing a lot of
common knowledge with the speaker, the challenge of acquiring domain
relevant knowledge which she does not share, and also having to keep
track of inconsistencies in the story, teasing apart things that are
clearly unspecified from those that come from her lack of knowledge of
the domain (things that are nailed down but not obviously so).
What we don't have now are programming systems that can take a vague set
of propositions and instantiate possible candidate computer programs for
evaluation. I think the answer is not magical automatic computer
programming that can cope with the most muddled of thoughts, but many
computer aided analysis and synthesis tools that help communicate back
to the user what is not resolved in their idea and the consequences of
that, i.e. I think humans have to change too.
I would further argue that computer programs are a good way to move from
coarse to refined science. A computer program is more expressive than
the mathematical toolbox can handle, but with it can also move in that
direction. It's a good staging ground for formalization.
Marcus
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