d=:%&2
d
%&2
d 13
6.5
d d 13
3.25
d d d 13
1.625
3 d 13
1.625
,.(i.25) d 13
13
6.5
3.25
1.625
0.8125
0.40625
0.203125
0.101563
0.0507813
0.0253906
0.0126953
0.00634766
0.00317383
0.00158691
0.000793457
0.000396729
0.000198364
9.91821e_5
4.95911e_5
2.47955e_5
1.23978e_5
6.19888e_6
3.09944e_6
1.54972e_6
7.7486e_7
d
%&2
NB. x u&n y ↔ u&n^:x y
That part is good.
How can you get from there to the power rule?
NB. x u^:n y ↔ x&u^:n y
Linda
-----Original Message-----
From: programming-boun...@forums.jsoftware.com [mailto:programming-
boun...@forums.jsoftware.com] On Behalf Of Dan Bron
Sent: Saturday, May 04, 2013 10:14 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Transcomputational numbers
TL;DR: Simply deleting words will never work. Removing an offending word
without compensating for its function will break code. To remove an
offending word, one must compensate by using other words which express the
same meaning.
Linda wrote:
> I feel quite confident about removing @: carefully.
> Viewmat had 5 uses of @:
> I simplifies the sentence to a simpler version.
> viewmat @: ([ load @:('viewmat'"_)) @: ((Josephus2 % <:@])"0/~) @: >:
@:i. 32
> viewmat ([ [: load 'viewmat'"_) ((Josephus2 % [:<: ])"0/~) >:
i. 32
Let us put aside stylistic questions, and allow that disliking conjunctions
is as valid as any other preference. In pursuit of that preference, what I
want to focus on is what it means to remove @: (or anything else)
/carefully/.
In particular, I want to highlight that _all words have a meaning_. And
that when people put a word in a sentence, they do it for a reason. Use of
conjunctions is not random, nor arbitrary, nor are conjunctions used just
for decoration. Everywhere they're used, they have a function and a purpose.
And if you want to remove them, that's ok, but you must do so with
consideration for that purpose. In particular, /simply deleting words will
not work/. If you remove a conjunction, you must make some alteration,
some substitution, which reproduces its function.
Let's take some examples from your reformulation of the viewmat verb. You
took <:@], deleted the @, and _reproduced its function_ using [: . That's
fine. And again, you took load @:('viewmat'"_), removed the @:, and
_reproduced its function_ using [: . Great!
But then you took >:@:i., deleted the @:, and ... did nothing. And again
with ((Josephus2 ...)"0/~)@>: you deleted the @ but did not compensate for
the deletion. And again with viewmat@:... you deleted the @: but did
nothing to reproduce its function.
Where does that leave us? Well, similar to the earlier comparison between
^.&1e93 and ^.1e93, you've taken a re-usable verb and created a one-time
noun. Check out what happens if we try to re-use your version:
original =: viewmat @: ([ load @:('viewmat'"_)) @: ((Josephus2 %
<:@])"0/~) @: >: @:i.
linda =: viewmat ([ [: load 'viewmat'"_) ((Josephus2 % [:<:
])"0/~) >: i.
original 32 NB. Colorful chart
original 16 NB. Colorful chart
linda 32 NB. Blank
linda 16 NB. Blank
So, in deleting the conjunctions, without compensating for their intended
purpose, you haven't "simplified" the code - you've broken it.
Let's approach this from a different angle. In deleting the three @s where
you didn't reproduce their functionality with a [:, you were saying those
three @s were simply unnecessary. You were asserting that these words
served no purpose, and should be deleted as superfluous. In effect, you
were saying that when Pepe put them there, he didn't know what he was doing!
Do you really feel confident in that kind of assertion? Or how about this:
when you deleted those @s, you replaced them with a space. Which means you
thought space (juxtaposition) could perform the same function as @ . And
when you deleted & earlier in this thread, you though space could carry its
function, too. And similarly for &. and @: and ` etc. In effect, you were
saying these words are unnecessary, that space (juxtaposition) can do for
them all, and when Ken introduced them into the language, /he/ didn't know
what he was doing.
Now, I don't believe that you're thinking "Pepe was wrong, Ken was wrong"
when you're making these transformations. I'm just highlighting that that
kind of arrogance is an implication of deleting words without compensating
alterations, as a kind of reductio ad absurdium. What I'm trying to
instill in you is the tenet that /simply deleting words will never work/.
And worse than "not work", deleting words will /break code/.
The words we use, we use for a reason. We're trying to convey meaning.
Removing words from expressions - whether English or J - changes the
meaning! If you don't like certain types of words, that's fine - everyone
has his own style. But when you come across a word you don't like, rather
than simply "let's get rid of that!", I want you your first reaction to be
"ok, I want to remove that word; how can I express it differently?". Or
"how can I /replace/ this word I don't like with /other words that mean the
same thing/?", or, in a more formal, J sense: "if I delete a conjunction,
how can I reproduce its functionality?".
The hitch with that is, the only way to make such changes with confidence
is to learn what the words @ @: & &: &. &.: ` etc _really mean_. You can't
express them a different way if you're not sure what they mean in the first
place.
-Dan
PS: A good exercise for you might be to make another attempt at creating a
verb equivalent to Pepe's original viewmat function, but without using @ .
The operative word there is /equivalent/. It must produce the same results
under all conditions, not just a test case or two. You're actually pretty
close already, and if you just consistently follow your original pattern of
removing @s and compensating with [:s, you'll get there.
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