(Thread moved from General to Chat; all follow-ups here)
Don,
First, let me show you a parlor trick. Here is a puzzle for
mathematically-minded Jers. What is the result of the following sentence?
+/ 2 ^ - i. _
Don, note: there is no J interpreter in the world that can answer that
question. So the only way for a Forum member to answer me is to read the J
as a notation, and manipulate it, symbolically, in his head. If you want to
ask the same question via email, using your preferred 2D notation, how do
you do it?
Now, on to my thoughts on your message to Chris:
* Why do you think math should be taught using standard math
notation (SMN)?
* Many members of the J community are mathematically-minded
and take interest in teaching math. Several have used J
with success in that endeavor. How?
* SMN is not some holy, god-given language for the expression
of mathematical thoughts. In fact, as John Randall is fond
of pointing out, it is an inconsistent agglutination of
notation from recent centuries.
* If teaching math is a way of promoting rigorous, consistent
thought, should we not use a rigorous, consistent notation?
* KEI, whom you admire, invented APL (and its later dialect J)
as a rationalized, simplified revamping of (some parts of)
SMN.
* Can you really tell me that
2
3x + 9x + 27 = 0
is superior to (3 9 27 * x ^ 2 1 0) or even (27 9 3 p. x)?
And that {big sigma, iterator declaration, bounds, indicies}
And {big pi, iterator declaration, bounds, indicies} are
preferable to +/ and */ respectively? If so, what do
you prefer to ^/ ?
* Originally, APL was only a notation, but because it was
rationalized, it was amenable to computerized execution;
and so an interpreter was built for it. The effect was
that as the notation developed, much attention was
paid to maintaining and increasing that amenability, with
the results you see today.
* In addition to being an executable mathematical notation,
APL is a programming language, which IMO, is a
generalization.
* What advantages does SMN have over APL? Obviously, it
is incumbent and widespread, which is large hurdle to
overcome (viz QWERTY). But if no one tries to overcome it,
it will rule forever, warts and all. Vive la revolucion!
* Since you propose to teach math to children who don't
know math yet, we have a good opportunity to change
the notation.
Now, the above is a bit tongue-in-cheek. I do not see APL/J as a
replacement for SMN. Because it's not as general as SMN; for example, J is
a numerical platform, not a symbolic platform, so SMN is much more advanced
for symbolic manipulation. Similarly, J is well defined on ordered data;
lists and vectors and matrixes and such, and much less used for unordered
data like sets. Finally, J is a well-defined, architected notation. It is
not easily extensible for exploring new notation for still-fuzzy concepts (a
whiteboard is infinitely more powerful here).
So why don't we use J for what it's good for? I can see it being practical
and useful to teach arithmetic, algebra, trig, statistics, some calculus,
etc, but progressively less useful for higher maths, particularly as they
become more abstract.
-Dan
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