Re: Language design values (Re: message primitive)

[Lynn Winebarger <owinebar at free-expression dot org>]

   Completely tangential, but...

On Sun, 2 Jan 2000, Gregg Reynolds wrote:

> Lynn Winebarger wrote:
> >     Are you sure a nand operation wouldn't be sufficient (once you build
> > Peano arithmetic with it, you've got all you need, right?)
> > 
> 
> Uh, yeah, you know, that's just what my grampa used to say.  Me, I've
> heard of this Peano fella, but I never really trusted him.  :)

   Well, let's see, I know you can build all the proprositional logic with
just nand.  Then I believe you can build the arithmetic circuits (adders
at least) from those.  Once you have addition/subtraction, multiplication,
and exponentiation, you can encode arbitrary recursive functions in them
(that is, you translate your program over to numbers and arithmetic
according to some simple rules, then compute the resulting expression,
then translate back and you have the result of computing the program).
   I could be wrong - I never memorized this kind of stuff, and it
generally makes my brain hurt.
   Nonetheless, the point should be that "irreducible" is not exactly what
you want - you want some notion of "irreducible with respect to programs
in a given domain and whose resulting construction is simple" where
"simple" remains to be defined.

> Actually, for an olde Humanities grad, this is the interesting stuff -
> how to put these indescribibably cool mathematico-structural ideas into
> language non-dweebs can understand.  I suspect that's one of the reasons
    I'd say it's a good reason for studying math.  They don't make it hard
to keep it a mystery - it's just hard (or at least abstract).  5 1/2 years
of graduate study and I still need whacking by the cluestick on more
occasions than I'd care to admit.

Lynn