Why is the j in i:2j8 more important than the i? -- Raul
On Tue, Jan 15, 2013 at 3:00 PM, Linda Alvord <[email protected]> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
