The key concept is that of 'item'. An array (no, wait, a
non-atomic array) is a list of its items. Many of J's
primitives treat the items as unbreakable.
{. removes the first item. That leaves 0 items. The
shape of an item remains unchanged, but there are still
0 of them.
So 1 - 1 is indeed zero. In fact, the way J does it is
the only way to make that true. If the shape of
{. 1 1 $ 67
were not 0 1, you would be taking one item from one item
and being left with something other than 0 items.
Henry Rich
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On Behalf Of metaperl.j
> Sent: Saturday, October 13, 2007 11:12 AM
> To: [email protected]
> Subject: [Jgeneral] paradoxes - (2) Behead (1) arrays
>
>
> Paradox 1 - the very acceptance of the existence of an array.
>
> Atoms are without dimension. A series of atoms "forms" a
> list. But this is a
> paradox. How can something come from nothing? A list has a
> shape indicating
> how many nothings it has :wistle::confused:
>
> So a list is an idea. An intangible shaping of atoms. It does
> not exist.
> Just as lines and planes and cubes are made of points, we again create
> something from nothing.
>
> Paradox 2 - Behead: when 1 - 1 does not equal zero.
>
> Lets say we have this:
>
> ]trivial_tbl =: 1 1 $ 67
> 67
> $ trivial_tbl
> 1 1
> $ }. trivial_tbl
> 0 1
>
>
> So behead removes the leading item from a datum. The items of
> a rank-2 array
> will have rank 1. So the _items_ of trivial_tbl will be
> lists. In this case
> there is one list which has 67 in it.
>
> So when behead removes that one list, we dot get nothing.
> What we get is a
> table with 0 as the magnitude of its outer axis. %-|
>
> I guess the idea is to maintain a frame of reference. Beheading always
> returns a table even if that table is absent of data.
>
> I'm sorry for posting this, but it's what's on my mind.
>
> --
> View this message in context:
> http://www.nabble.com/paradoxes---%282%29-Behead-%281%29-array
s-tf4618581s24193.html#a13190550
> Sent from the J General mailing list archive at Nabble.com.
>
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