

Numbers and Pork Rinds

>Hey, all you out there: does anyone else care?  Has anyone's mind been
>changed as a result of our discussion?

Yes.  I have but a minor comment to make.  Alan, the inexactness you
attribute to floating point numbers is not a property of the
representation itself, but rather its interpretation (as a projection
of the space of real values).  I, knowing the algebra of a floating
point implementation, may certainly write down an "exact" computation
in terms of floating point values.  For example: (+ 2.0 3.0).  Knowing
that by 2.0 and 3.0 I mean exactly 2 and 3, and knowing
the floating point unit of my machine, I know that the 5.0 that
results will be an "exact" result.

By the same token, I may write down an "inexact" computation in
terms of integers.  For example, let H be a procedure that
heuristically evaluates a chess position and returns an integer
representing the goodness of the position.  I interpret H's return
value as an interval, a distribution, around the "real" goodness of
the board.  Now, when I write (max (H board-1) (H board-2)), I don't
expect max to understand that its arguments are grossly lacking in
precision.  Neither would I expect it to do so if H returned a
floating point value.  It is my job to determine the MEANING of the
representations I ask the computer to manipulate; I want only for the
computer to act predicatably upon the representations.  Predictably,
in the case of floating point values, has traditionally meant that the
computer behaves as though the values were exact.

-Luddy Harrison