[From Bill Powers (920904.1100)]

Penni Sibun (920902.1400) --

What the net "is" depends on each user's conception of it, and that

conception isn't out there in the world. It's in a head.

well, i don't suppose solipsism is very useful.

That's too easy an answer. Control theory is not about solipsism. It

just recognizes that we don't all experience the same environment, so

whatever you say about the environment is probably not true for

everyone else. I don't doubt that there's an environment there. What I

do doubt is that our perceptual representations of it are isomorphic

to it.

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well, i probably confused you by saying ``machine''--let's stick to

``automaton.'' at any rate, neither is a program: an automaton is a

description, a theoretical abstraction. one can perfectly rigorously

say whether an automaton is deterministic or not; i gave the def.

above. determinism does not describe what the automaton does, it

describes how it is built.

OK, I think that's what I said. The automaton itself could behave in

unpredicted ways while still being deterministic. I suppose your

definition would hold even if the automaton is deterministic, but one

of its computing elements computes a random action when it's

operating.

Automata that are theoretical abstractions aren't very interesting,

are they? I prefer mine to be "concrete-situated."

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the natural numbers are the positive integers starting from 1, so a

function from natural numbers to world states implies discreet rather

than continuous time.

OK. The problem with discrete time is that it rules out real physical

phenomena unless it's handled in a way I haven't seen in any AI

models. Physical phenomena take place continuously, and their

properties determine how they behave through time. If you apply a

force to an object at time 1, how far will it have moved by time 2? If

there's no link between discrete time-points and the underlying

continuum, there's no way to tell. How far it moves will depend on the

clock speed of your computer. You have to define a dt in real seconds,

so you can derive distance moved from the double integral of

force/mass TIMES DT. If you make one computing cycle equal to dt

seconds, like 0.01 sec, you'll get one final position. If you make the

computing cycle equal to a longer dt, like 0.1 sec, the object will

move farther in the same number of computing cycles.

This problem is present any time that the computer has to deal with

processes that actually are continuous. When it's ignored, as it

usually is, the results of a simulation don't really mean anything.

Not if you're trying to model a real system, that is.

I've written a persuasive letter to Chapman, by the way. It's worth

another try.

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Best,

Bill P.