> 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.
You need to insert "(as yet)" between "there is" and "no J interpreter in the world than can answer that question". http://www.jsoftware.com/pipermail/general/2005-December/026024.html ----- Original Message ----- From: Dan Bron <[email protected]> Date: Tuesday, December 8, 2009 16:02 Subject: [Jchat] Number Machines (moved from jgeneral) To: [email protected] > (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 > unordereddata 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
