> Don Mikulecky replies:
> Help me I'm confused? I am sorry if I left off the word "finite" from the
> definition. Clearly I am working with Arbib's definition of a finite Automata.
> It
> doesn't work for the case you asked about. That has to be dealt with in
another
> way. The issue we seem to be dancing around is realizability, not anything
like
> complexity. Maybe I'm missing something?
> Don
No, Don, I am not trying to reduce the things to Universal Turing Machines
(UTM),
.... , I think my point can be better explained by the following statements:
1-) Rosen showed that there is more than UTMs.
2-) So, taking UTM as a starting point, why not try to make "things" (to not say
"machines") that are more than UTMs ?
3-) Let's get something like an "Analogical machine", i.e., a machine (or
whatever
you like to name it) that does not keep only with the finite state automata, but
is
also able to deal with the continuous (my previous suggestion of derivation).
Suppose that this artifact goes beyond an UTM (i.e. it can not be fully
described by
an UTM). The question is ... are we allowed to call this "artifact" a machine ?
If
it is not a machine, then what it is ? Are we dealing with complex systems or
something between "machines" and "complex systems".
I have another point related to formalization. I have found two different
understandings for what a formalization is. The first one is the one given by
Rosen,
when he says that a system is formalized when you set up a finite set of
propositions that fully describe a system, and then you are able to abstract the
semantics of such propositions and treat them only by its syntactic (symbolic)
properties. In other words, ... , formalize is to "put it on a machine", i.e.,
use a
machine to model it. I have also heard people using the term "formalization" as
meaning "put into mathematics", i.e., people say that a system is properly
formalized when we have a mathematical description for such system.
In your opinion, mathematical systems are still "machines" or there is room for
having something "beyond machine" systems that can be modeled mathematically ?
In
other words, is it mathematics an adequate "language" in order to model things
like
"organisms" ?
Ricardo
--
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