Raul Miller writes: > Put differently, Iverson's approach (illustrated above) is to > traditional math something like what arabic numerals were to roman > numerals. It takes some time to get comfortable with reasons for > representing "nothing" (and different flavors of nothing) but once you > have grasped this kind of approach you are then faced with painful > tedium when trying to do what you now feel is simple, when using the > long winded arbitrarinesses of the older contrivances.
The introduction of the comparisons and further dyadic functions made notions such as reduction and inner and outer product much easier to assimilate, not by *simplifying* them, but by making them ubiquitous. - Ken Iverson, *Revisiting Rough Spots*<http://www.jsoftware.com/papers/rough.htm>, 1994 [Commenting on the empty vector:] I think we have the Arabs to thank for inventing zero, but I know that we have Dr. Iverson to thank for inventing nothing. — Donald McIntyre, APL Users Meeting<http://www.jsoftware.com/papers/APLQA.htm#nothing>, 1980-10 On Wed, Oct 2, 2013 at 7:33 AM, Raul Miller <[email protected]> wrote: > On Wed, Oct 2, 2013 at 9:45 AM, Pascal Jasmin <[email protected]> > wrote: > > I guess that I should completely understand why $2 is not 0 > > or 1, but I can let my pretty little head just consider that a list > > of 1 and a scalar must be different: > > Yes. > > In J, > > */$n must give the number of elements in ,n > > and > > */$$n must give the number of dimensions in n (which is also the > number of elements in $n). > > If $2 were 0 then 2 could not contain the value 2. > > If $2 were 1 then 2 would have one dimension and be a list containing > the value 2 instead of just being the value 2. > > Put differently, Iverson's approach (illustrated above) is to > traditional math something like what arabic numerals were to roman > numerals. It takes some time to get comfortable with reasons for > representing "nothing" (and different flavors of nothing) but once you > have grasped this kind of approach you are then faced with painful > tedium when trying to do what you now feel is simple, when using the > long winded arbitrarinesses of the older contrivances. > > Note also that J is not unique here. > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
