JR=John Randall, CL=Christopher Lett
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" :)
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?".
JR> All of the disputes about argument order to me center around which way to
JR> bond a dyad:
Not for me. Even if we didn't have bond, the dispute would still exist, and
the choice still be relevant. (Wasn't iota invented before jot?)
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.
CL> for iota, I came up with, "In x, where do I find y?". It seemed
CL> "natural" (to me at least),
And you didn't find that mouthful a bit convoluted? Even the English sounds
backwards to me. Plus, it's begs the question somewhat: you memorized a
phrase that described what iota did do, not what you would've expected a
"lookup function" to do.
CL> But what is "natural" is probably in the eye (ear? brain?) of
CL> the beholder.
Ah, that's what we're debating. Is there a 50/50 chance than a given beholder
would expect x&i. over i.&y , or do "most beholders" expect one over the
other?
-Dan
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