Henry, this will be a long reply so please bear with me.
It is comforting to a mathematician that @: is "associative". For example,
|:@:(+:@:|.) i. 3 3
12 6 0
14 8 2
16 10 4
(|:@:+:)@:|. i. 3 3
12 6 0
14 8 2
16 10 4
"Associative" means moving the parentheses cannot change the answer. (I have
not proved @: is associative -- this is an example to illustrate the meaning of
"associative".)
But @ is NOT associative:
|:@(+:@|.) i. 3 3
12 6 0
14 8 2
16 10 4
(|:@+:)@|. i. 3 3
12 14 16
6 8 10
0 2 4
"Not associative" means moving the parentheses can change the answer. (This
example proves @ is not associative.)
The fact that @ is not associative makes me pay more attention when I am using
it, as compared to using @: .
Kip
Sent from my iPad
On Feb 4, 2013, at 7:28 AM, Henry Rich <[email protected]> wrote:
> Perhaps @ should not count as a 'thing' here. The language could have been
> defined so that u v meant the composition of u and v; is the space a
> thing then? How many 'things' is f g h ?
>
> For my mental load, parentheses are things; @ and @: nothing; fork something;
> hook something more.
>
> Henry Rich
>
> On 2/4/2013 12:21 AM, km wrote:
>> And we can notice that with v c v c v c v (four verbs and three
>> conjunctions) we reach your count of seven!
>>
>> Incidentally, replacing |. with ] improves my examples:
>>
>> -@]/ 1 2 3
>> 3
>> -@(]/) 1 2 3
>> _3
>>
>>
>> Sent from my iPad
>>
>>
>> On Feb 3, 2013, at 9:28 PM, Tracy Harms <[email protected]> wrote:
>>
>>> My experience has been that my openness to long chains of modifiers has
>>> increased as I get better at reading J. Also, I find value in the
>>> widespread idea that seven, plus or minus two, is a count of things that
>>> people can keep in mind simultaneously. I don't think it's worth proposing
>>> specific standards for what counts as "a thing" for such tallying, but do
>>> think it's worth noticing as a rough guide.
>>> ----------------------------------------------------------------------
>>> 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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