where is the harmonic oscillatorness?

From: Eric Cavalcanti <eric.domain.name.hidden>
Date: Wed, 11 May 2005 10:20:02 +1000

I think some of the discussions about COMP and simulating people
could be better understood if we can first understand a (much)
simpler problem: a harmonic oscillator.

The relevance of this is that ultimately there might be no meaning
in saying that a string in Platonia or wherever represents anything,
without the mapping that gives the semantics for it. If it means
something, then we should be able to explicit show how to objectively
find this meaning for a simple case of a harmonic oscillator.

Let's define a turing machine M with a set of internal states Q,
an initial state s, a binary alphabet G={0,1}. The transition
function is f: Q X G -> Q X G X {L,R} , i.e., the function
determines from the internal state and the symbol at the pointer
which symbol to write and which direction (left or right) to
move.

Write a program in M that calculates the evolution of a harmonic
oscillator (HO). The solutions are to be N pairs of position and
momentum of a HO, with time step T and d decimal digits. Let this
set of pairs be P.

The program will eventually halt and the tape will display a string
S.

The programmer knows (of course) how to read S and find P. The
programmer uses for that (unconsciously or not) a mapping A that
takes from strings to pairs of real numbers. This mapping depends
ultimately on the particular way the programmer chose to write the
program and is by no means trivial.
 
Suppose you didn't write this program. Can you look at the output
and know that it represents a harmonic oscillator, given that you
know all the details of M? This is a problem of reverse engineering
which could be feasible in principle for a simple enough program.
It would help particularly if M is reversible, since you could from
the output work out the program and with enough time and luck, work
out what the program is supposed to do. In this way you would be
finding the mapping A.

But is there anything objective about the string S and the machine
M that makes that program represent a harmonic oscillator, or is
that interpretation ultimately dependent on the mapping A?

Is there some "harmonic oscillatorness" in S?

Eric.
Received on Tue May 10 2005 - 17:20:02 PDT