[Edu-sig] nouns and verbs

[Edward Cherlin]

On Sun, Aug 3, 2008 at 8:24 PM, kirby urner <kirby.urner at gmail.com> wrote:

> 2008/8/3 michel paul <mpaul213 at gmail.com>:
>> In secondary math classes we often say "Math is a language", but we really
>> don't teach it that way.
>
> << SNIP >>
>
>> This semester, at a high school level, I do intend to teach math as a
>> 'language', and I'd like to get really clear about these kinds of things.
>>
>> Thanks very much for any feedback,
>>
>> Michel Paul
>
> Hi Michel,
>
> If you haven't already, I seriously recommend you check out the J language
> from Jsoftware.com, a direct descendant of APL's that is (a) self-consciously
> an "executable math notation" (this was Iverson's shoptalk) and (b) is very
> deliberately taught in terms of parts of speech, milks that analogy very
> creatively and intelligently.  Verbs, nouns, adverbs... check it out!

Yes, that's what I was talking about.

> http://www.jsoftware.com/jwiki/Phrases
>
> Also, I did a few web pages on J myself at
> http://www.4dsolutions.net/ocn/cp4e.html
> -- Kenneth Iverson himself helped me with typos in 'Jiving in J', though I still
> think there's one or two left (my responsibility).
>
> I see nothing oxymoronic nor even perverse about recommending J on a
> Python list, as my position all along has been you need at minimum two
> widely differently languages, preferably more though, to get a sense of the
> freedoms one has, when being inventive in this lineage.

I have always said that you need more than two. In Computer Science, I
recommend learning not just the surface languages, but how LISP,
FORTH, and APL work internally, in comparison with the more
conventional languages. Each of these three languages is based on a
single unified concept of data objects, with a minimalist syntax. LISP
uses prefix syntax with parentheses (+ 2 3), APL uses infix, 2+3, and
FORTH uses postfix, 2 3 +. I suggest

The Little LISPer or The Little Schemer
The Anatomy of LISP

Starting FORTH
Thinking FORTH

Any math book written in APL, such as Iverson's Arithmetic.

There is no good introduction to APL internals, but the source code
for J has been published, is quite short, and is a miracle of style.

> Python and J would be a dynamite combo I've long considered teaching.
> Someone should try it, report back.
>
> As an intro math course, we're not expecting miracle levels of proficiency
> with either out the other end, however we already know both communities
> support a rich and relevant mathematics-related literature, complete with
> lots free / open source code.  See Roger Hui's stuff especially, and our
> own Tim Peters.
>
> Kirby
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