BL=Bill Lam, RH=Roger Hui
BL> comparing dyad e. and i. I think that i. is abnormal, not e.
RH> What are some reasons for your assertion?
Let's take a poll: Who on this Forum, was not confused (or at least surprised)
by the order of arguments to i. when you first encountered it? (Or APL's
iota, if you came across that first?)
One of the most persistent of my early J frustrations was remembering the order
of arguments to i. . Long after I (finally!) memorized the meanings of and
differences between {. {: }. }: , I was still stumbling over the order of
arguments to i. . I even had a definition in my utilities i =: i.~ .
It wasn't that I learned e. first and that tinted my expectation of i. .
Nor had I encountered an i. analog in previous context, which might've
trained me to expect "the universe" to be on the right. There was no precedent.
It was just a "natural" expectation. I suspect that's why e. is what it is
today: decades (years? centuries? millennia?) of mathematical history has
shaped the epsilon notation, and the universe is on the right.
Even in casual conversation, we say things like we say "x is a member of y" ,
where x is the member and y is the universe. Similarly, we say "lookup x
in y " or "give me the indexes of x in y".
Now, I do agree that since J executes verbs from right to left, it is sensible
to design verbs such that their right arguments are the ones most likely to be
calculated (not known in advance). This avoids excessive parenthesization or
commutation.
But that doesn't invalidate the argument that people "naturally expect" the
right argument of i. to be the universe, or that that expectation is
unimportant. After all, J concedes to expectations for e. and % .
Perhaps, like the factorial function, the argument order of e. is a
historical accident, resulting in an ugly, inconsistent wart. OTOH, perhaps
there are psychological reasons underlying the choice of argument order, and
given human nature, universe-on-the-right was inevitable, and subverting always
causes cognitive dissonance.
Maybe the poll support one theory over the other.
-Dan
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