J is not fully there yet I like the fact that On Tue, Dec 8, 2009 at 10:03 PM, Roger Hui <[email protected]> wrote: >> 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".
J is not fully there yet but I like the fact that ^: works well in many situations: a=:0 (3 : 'y+2^(1+a=:a-1)') ^: _ ] 0 2 Can this be written cleanly and tacitly with no assignment and no nesting ^: ? > > 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
