I'm not sure who you are asking this question. My answer would be that I
read from right to left and you come to 2j8 first. This is a complex
number to my way of thinking. Thus I get i: applied to a single number. In
this case you get something like:
i:4
_4 _3 _2 _1 0 1 2 3 4
The sit of complex numbers are unordered so this is meaningless.
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Raul Miller
Sent: Tuesday, January 15, 2013 3:17 PM
To: [email protected]
Subject: Re: [Jprograming] atop continues to puzzle me
Why is the j in i:2j8 more important than the i? wa
--
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
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For information about J forums see http://www.jsoftware.com/forums.htm
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