From: "Dan K McCoin" <lmccoin@elp.rr.com>
To: <DKM>
Subject: Temp File
Date: Tuesday, February 18, 2003 7:31 PM
Imagine observing a large number of random games of checkers that were played very quickly on a computer screen. We might not be able to capture enough detail in our observations to deduce
the actual rules of the game as the pieces zip around the board at blinding speed, yet we might be able to draw up some elegant mathematical descriptions of average piece density over time at various locations on the board.
We might even be able to come up with equations that made accurate predictions about future average piece densities. In short, we might create a mathematical theory of checkers that seemed, at the gross scale of our observations, to reflect some features of the game.
And yet the reality of the nature of the game is found in the simple procedural rules governing possible moves, and not in our elegant and somewhat useful mathematical theories.
The question naturally arises as to whether mathematics is even the correct tool to describe physical processes at the quantum level. Yes, we have elegant mathematics that has a great deal of practical usefullness, but do those mathematical models bear any resemblance to the underlying reality? Is nature inherently mathematical? Or might nature, at the deepest levels,
be inherently procedural? If it is procedural, then mathematical models can never capture any more than a blurred, highly abstracted approximation to the behavior of the system under
investigation. A mathematical model would never be able to describe the underlying reality if the underlying reality is not, itself, mathematical in nature.
In my own field of aerodynamics we have approximately 2.6 bazillion equations that describe the behavior of various bodies in a moving fluid, but which bear no resemblence to, or make no reference to the underlying processes which consist largely of molecules bouncing around and trading kinetic energy with each other.
Now suppose that instead of molecules trading kinetic energy, which can be modelled mathematically, there is, at the heart of quarks and gluons, processes which might more accurately be modelled with some system of symbolic logic, or as some simple cellular automaton or Turing machine as opposed to a system of differential equations. In that case mathematics can certainly say things about the behavior of the system, but it cannot explain the system as
well as some other approach that is not "mathematical".
I guess what I'm getting at is that the most accurate aerodynamic simulation program that could be written would be one that dealt with the vectors for kinetic energy from molecule to molecule for billions of air molecules and would have no need for one single differential equation. At it's root simple vector arithmetic "explains" aerodynamics better than systems of differential equations, which are merely abstractions and approximations of the average glob of results of a whole glob of vector arithmetic operations.
My hunch is that "mother nature" doesn't know calculus, and accomplishes what she accomplishes by some process that is probably very different from mathematics as we generally think of it, and probably very much simpler too. In that case, computing a Schroedinger wave function make as much sense (or non-sense) as dancing a chemical reaction, or painting a piano concerto.
