I am considering the structure of mathematics education. A domain of numbers from _2 to 2 in steps of one half could be understood and developed in elementary school even in J. It is not really sensible until square root is mastered. After that an imaginary numbers might show up. So %:_1 becomes 0j1 in J. It will take a while to master numbers like 2j8 and other imaginaries. The leap to an idiom which uses 2j8 in a totally different way is counterproductive until much later.
How can you explain the connection to imaginary numbers in this expression: i:2j8 _2 _1.5 _1 _0.5 0 0.5 1 1.5 2 Linda -----Original Message----- Froch: [email protected] [mailto:[email protected]] On Behalf Of Raul Miller Sent: Tuesday, January 15, 2013 11:35 AM Tr o: [email protected] Subject: Re: [Jprogramming] atop continues to puzzle me I am uncomfortable with this reasoning, because: *) i:9j3 is related to complex arithmetic only by notation. *) class becomes boring when its pace is set for someine else (when it does not match the student's needs). *) simplicity is good, but so are different perspectives. Waiting to introduce imaginary numbers before introducing this notation seems analogous to waiting to introduce polynomials before introducing decimal numbers. Anyways, I this notation can be optional, but if I were stuck teaching a class using J (rather than providing guidance, pacing and structure to a group of students who had been taught how to learn and who were being responsible for their own education) I think I'd introduce this as an optional notation about the same time I introduced i: -- Raul On Tuesday, January 15, 2013, Linda Alvord <[email protected]> wrote: > Devon, Since I think of everything going forward from kindergarten > (maybe someday we'll do more with prenatal education) I would use Y=: > _2 + 0.5 * i.9" until the middle of the second year of algebra. > > I really like your solution! It would be a great next step when > teaching imaginary numbers. > > Linda > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Devon > McCormick > Sent: Monday, January 14, 2013 2:58 PM > To: J-programming forum > Subject: Re: [Jprogramming] atop continues to puzzle me > > Linda - > > a nice short cut for your expression "Y=: _2 + 0.5 * i.9" is "Y=: i:2j8". > In general, providing the complex argument PjN to i: gives you N+1 > points from -P to P. > > Regards, > > Devon > > > On Mon, Jan 14, 2013 at 12:24 PM, Jose Mario Quintana < > [email protected]> wrote: > >> To Henry: >> >> My apologies, the worst part is that I noticed the misspelling but I >> neglected to correct it; I guess watching the playoffs and writing to >> the forum do not mix very well. >> >> To Linda: >> >> That is a nice feature; thanks for sharing it. One refreshing thing >> about J is that one never seems to stop learning it. Moreover, if one >> follows the forums and this one in particular one is shown (or >> reminded) how capable the J system really is. >> >> On Mon, Jan 14, 2013 at 3:10 AM, Linda Alvord >> <[email protected]> >> wrote: >> > Jose, Here's a simper version. Using the aspect ratio helps make >> > the derivative more obvious. I use Chrome and I don't know how >> > this will >> look >> > elsewhere. >> > >> > Load 'plot' >> > u=: -: >> > v=: *: >> > Y=:_2 + 0.5 * i.9 >> > f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' >> > f >> > plot f Y >> > 'aspect 1'plot f Y >> > >> > Linda >> > >> > -----Original Message----- >> > From: [email protected] >> > [mailto:[email protected]] On Behalf Of >> > Linda >> Alvord >> > Sent: Sunday, January 13, 2013 9:21 PM >> > To: [email protected] >> > Subject: Re: [Jprogramming] atop continues to puzzle me >> > >> > load'plot' >> > >> > u=: -: >> > v=: *: >> > Y=: _2 + 0.01 * i.401 >> > f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' >> > f >> > ] ; [: |: u@v d._2 _1 0 1 2 >> > plot f Y >> > >> > If this is in a jijs and then run, it will shw the graph you >> > expect bu >> t >> > it will provide a long J error message in a separate window. I >> > don't >> know >> > how to prevent it. >> > >> > Also, maybe when u@v can be replaced by ([:u v)"v that will >> > work >> also. >> > >> > Linda >> > >> > >> > -----Original Message----- >> > From: [email protected] >> > [mailto:[email protected]] On Behalf Of Jose >> Mario >> > Quintana >> > Sent: Sunday, January 13, 2013 5:17 PM >> > To: [email protected] >> > Subject: Re: [Jprogramming] atop continues to puzzle me >> > >> > To Raul: >> > >> >> I have no idea what "works reasonably well" means. >> > >> > That is a very subjective statement, apparently one can make use of >> > (@) and (@:) within the scope of (d.) but, of course, that depends >> > on >> one's >> > point of view. >> > >> >> But consider also: >> >> >> >> AT=: 2 :0 >> >> u@v"v >> >> ) >> >> >> >> +:AT*: d. 1 >> >> 0 4x&p."0 0 0 >> >> +:@*: d. 1 >> >> 0 4x&p. >> > >> > Th> >> --- For information about J forums see >> >> http://www.jsoftware.com/forums.htm >> > ------------------------------------------------------------------- >> > - >> > -- For information about J forums see >> > http://www.jsoftware.com/forums.htm >> > ------------------------------------------------------------------- >> > - >> > -- For information about J forums see >> > http://www.jsoftware.com/forums.htm >> > >> > ------------------------------------------------------------------- >> > - >> > -- For information about J forums see >> > http://www.jsoftware.com/forums.htm >> --------------------------------------------------------------------- >> - For information about J forums see >> http://www.jsoftware.com/forums.htm >> > > > > -- > Devon McCormick, CFA > ^me^ at acm. > org is my > preferred e-mail > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
