> I basically agree with this point. On these grounds, ! is the wrong > way round: you are more likely to calculate x ! y for fixed y than > fixed x.
What are some examples of fixing an argument of ! ? The only non-trivial one I am aware of is 2&! = +/@i. ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Tuesday, April 17, 2007 1:01 pm Subject: Re: [Jgeneral] "J for C Programmers" - asymmetry / control /datadiscussed without definition? > Dan Bron wrote: > > John, > > > > I wanted you to know that it was just for you that I wrote: > > > > JR> decades (years? centuries? millennia?) > > > > instead my original "centuries". We've had more than one talk > about the > > modernity of mathematical notation. And now I'm feeling pretty > smug tha I > > hit it on the money with "decades" :) > > > > Well thanks, Dan: I rose to the bait. Cajori's book is the reference > on such questions. > > > Seriously though, I bet, even before Peano, people would be > inclined to > > say "is x is a member of y?" more often than "does y have member > x?".> > > I don't think people really thought about sets the way we do now. You > could not make up your own: they were more God-given. Bear in mind > the latter half of the 19th century was the time mathematicians were > formalizing the notions of real numbers and integers that we use now. > It was not until the early 20th century that people realized all of > mathematics could be built on sets. > > My point with bonding is that x&P should be more common than P&y. I > agree that x e. y with fixed y is more common than with fixed x. In > particular you are more likely to ask "which elements are in this > set?" than "in which sets is this element?" Mathematicians do > use a > backwards epsilon, corresponding to e.~ . > > > Because J is right-to-left, a primitive P should be designed > to make: > > > > x P y =. thing I'm likely to calculate > > > > more likely than > > > > y P ~ x =. thing I'm likely to calculate > > > > or > > (x =. thing I'm likely to calculate) P y > > > > Dyadic i. follows this design principle. But that doesn't > mean it > > wasn't a tradeoff. > > I basically agree with this point. On these grounds, ! is the wrong > way round: you are more likely to calculate x ! y for fixed y than > fixed x. On the other hand, | is the correct way round. > > I still think it is a matter of convenience and convention. > Naturality arguments and self-evident truths often don't last. > > Best wishes, > > John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
