In "Life Itself" Rosen gives the following definition of a machine:
"A natural system N is a machine if and only if it is a mechanism, such
that at least one of its models is already a mathematical machine"
Further: "A natural system N is a mechanism if and only if all of its
models are simulable."
He goes on to say: "my characteristic of mechanism will be seen to be
nothing but Church's thesis"
There are a set of conclusions which follow from this.
1. mechanisms have "largest models" from which all others may be
derived.
There is a finite set of minimal models. The largest model is a direct
sum of these. It is therefore a synthetic model (reductionism works).
I would simply note, that accepting this definition places all the
reductionist findings in the category of machines.
The reason I posted Arbib's formulation of finite machines was to show
that as a definition, it was not enough. Some people were hung up on
the finite character of Arbib's definition, but it was never intencded
to be all encompassing.
Here we divide the world into two categories, simple mechanisms and
things which are complex. Clearly, this definition of complexity places
all of computer modelling and artificial life in the realm of the simple
mechanism, NOT the complex. Please realize that there is far more to it
than what is briefly outlined here. I merely am trying to introduce the
definitions here.
Don Mikulecky