[Edu-sig] nouns and verbs

[kirby urner]

We have a spectrum of languages gluing equations and other special
notations into a larger patchwork of interconnecting disciplines.
It's not that there's the vernacular and then math.

OO is actually an approach to (mirror of) human grammar in taking the
object thing very seriously, maximizing its value as a generalizing
metaphor for building syntax ("dot notation" in many languages, Python
included), a really good idea I think, even if we continue with other
models as well, start new ones.

Is chess a language?  This kind of question gets discussed in
Wittgenstein's remarks on the foundations of mathematics, other
investigations.  Looking for a simple yes or no answer is missing the
point, of appreciating the varied landscape.

What makes machine executable math notations special is they must
follow a rule book very precisely, a feature one looks for in any
language game claiming to be logical.  Sheer runnability against an
interpreter is already a kind of proof (jumping a logical hurdle),
however trivial (like it runs, so what).

By the way, the LEX Institute, based in Japan, other places, takes
precisely this 'math is another human language' approach when needing
to learn about Fourier Transformations in order to tackle vowel sound
studies.

These language students tackled the job of teaching themselves using
their language-teaching philosophy, resulting in a book 'Who Is
Fourier?' and talked about early in the history of edu-sig, especially
by Jason Cunliffe, whom I had the good fortune to meet in New York
City that time.

http://mail.python.org/pipermail/edu-sig/2001-October/001788.html

Lots of dovetailing twixt the approach here, and what we find in say
O'Reilly's 'Dive Into...' series (also in 'Concrete Mathematics'
some...).

Kirby


On Tue, Aug 5, 2008 at 10:32 PM, Yoshiki Ohshima <yoshiki at vpri.org> wrote:
> At Sun, 3 Aug 2008 20:03:03 -0700,
> michel paul wrote:
>>
>> In secondary math classes we often say "Math is a language", but we really don't teach it that way.
>>
>> The closest we get to that is calling the comparison operators 'verbs' and the various kinds of values that can be
>> combined into expressions 'nouns'.
>
>  I enjoyed reading your lines of thought, and Edward has a good
> observation.  But I also have to point out that when people say "math
> is a language", it means that Math is a language to describe what it
> can describe well.  But trying to make an analogy to English doesn't
> get you go too far.  After all, why does it have to have anything to
> do with the English syntax?  It is not a great language to express
> what you would like to do over weekend either.
>
>  The "language-ness" is not in whether it has verbs and nouns, but
> the relationship between the target concept (Idea) and the description
> to mean it, and also something to "think in".
>
>  And, the language-ness is not in these mathematical symbols and
> syntax, either.  It would be possible to write equations in
> English-like syntax (like your "sum of 2 and 3" example).  But the
> aspiration of preciseness compactness tends to favor a simpler and
> less ambiguious notation.
>
>  So, it would be appropriate to say "math is a language for of
> physics" but saying "math is a language" doesn't sound like a complete
> sentence to me.  "Is math a language of math?" would be an interesting
> question^^;
>
>  Now, computer languages are like mathematics, but much more complex
> in many ways.  It is built on top of some axioms, but the set of
> axioms tends to be very big.  The notation is less ambiguous than
> typical mathematics one because one of the intended readers of the
> notation is the computer.
>
> -- Yoshiki
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