lamp post and turing machines

[chu@xxxxxxxx]

:Date: Tue, 25 Apr 1995 14:40:43 -0500 (EST)
:From: pdavidso@xxxxxxxxxxxxxxxxxx
:To: pknetwork <pkt@xxxxxxxxxxxxxxxx>
:Subject: Response to Gonzalo

<...>
:Finally, you apparently identify nonlinear models as providing a "logical
:precision" that neither linear models or general form models do.   But
:logical precision merely means that you have not made any mistakes in
:your syllogisms, etc. Can you explain why one loses "logical precision"
:if one uses  a general form of the equations
:model, if the latter is based on the same axiomatic foundation (except for
:the "Chu" axiom that ALL measured things must be nonlinear)?

Just to clarify: Gonzalo quoted me accurately.  My observation is that
among the numerical experiments that have been done to date, relationships
between observables have usually found to be nonlinear when a full range
is considered ( that's assuming any relationships were concluded ).
I hope that you don't dispute this observation.
For purely the physical universe, we have ample evidences to support this.

Regarding general forms of equations: a = f(b).
If that is the only type of information one has, one can only deduce networks
of 'relatedness' ( A relates to B which relates to C, etc.)  That is
obviously inadequate to explain or predict anything.  So I assume that
your general forms includes additional constraints like 'f is montonic
increasing' or 'f is bounded within this range,' etc.  If this is an
erroneous assumptions, please let me know.  The question then is how can
we tell which one is more genreal: general form with a list of constraints
or a family of nonlinear functions?

:Finally, you implicitly accept the Austrian view of uncertainty, namely
:that the future is deterministic but so complex that human computing
:power (the agent's estimate) is so limited, that the number of Christians
:in Damascus in 2400 AD is "unknown" except to God! (and to a Turing
:machine that the Austrians call the market!) If you truly believe this,
:then the system is ergodic (if not in the levels,i.e., with given
:parameters) but in the rates (or ways) that the parameters are "destined"
:to change according to God's grand ergodic (deterministic) scheme of things.
:And when you question why I insist on an ontological transmutable (by
:human action) reality as compared to your preprogrammed God-given
:parameters or rate of change in parameters, you have crossed the Rubicon.
:In your God-given preprogrammed complex reality, there is always a
:possible deus ex machina ("the market") that can transcend the
:individual's (or bureaucrat's) lack of computing power and display for
:the chosen people the God's software preprogrammed package for the future
:economy.

Turing machines are actually quite limited relative to Reality.  Even
within formal systems, there are noncomputable, undecidable problems
which CANNOT be solved by a Turing machine.  If the 'market' is construed
as a computing device, it cannot be more powerful than a Turing machine
and is similarly limited.  Thus it cannot possibly get a "God's eye view".

Regards,

A. Chu