Been away from the internet for several days due to snow. Back to the
original question to figure out the sentence "+/2 ^ - i. _". J may not
handle it, but J can still be used to help understand the expression.
Simply replace the _ with something like 10x and remove the sum:
2 ^ - i. 10x
1 1r2 1r4 1r8 1r16 1r32 1r64 1r128 1r256 1r512
Makes it easy to see what is happening.
J is an excellent tool to explore mathematical expressions.
On Tue, Dec 8, 2009 at 5:01 PM, Dan Bron <[email protected]> wrote:
> (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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>
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