Tim,
The quote you posted of my father's is divorced from its context,
which I have warned time and again is not wise to do.
Here is a passage from "Anticipatory Systems" which touches on
the issue of what his main contextual base is and how it affects definitions
within that context:
From AS, page 177:
"In the present chapter, we turn to some specific
examples of encoding of Biological systems, with special reference to the way
in which characteristically biological qualities are related to the numerical
observables manifested by all natural systems. For this reason, we shall not
consider reductionistic approaches in detail, nor any of the encodings
belonging entirely to biophysics. The essence of such encodings is precisely
that they treat biological systems exclusively in terms of their numerical
observables. Thus, for example, we shall ignore the large literature on the
flow of blood as a hydrodynamic problem, pertaining to the flow of viscous
fluid in a family of elastic vessels. For our purposes, this literature is
part of hydrodynamics, and not of biology. It is of course true that such
studies are often of vital practical importance, but they raise no question of
principle beyond what we have already considered in chapter 3.2 above; the
biological origins of such studies and their application to cardiovascular
problems are essentially irrelevant to the encodings themselves, and the
manner in which inferences are drawn from them. We shall concentrate instead
on examples of encodings which exhibit a basic metaphorical aspect, and on
relational encodings. It is only in these cases that particular biological
qualities play a dominant role."
Another example of the impact of context on
definitions: From "Life, Itself," page 191, Robert Rosen wrote:
"Since the main thrust of the present work is to put
organisms on the left-hand side of [the modeling relation] diagram, the limits
of formalization are obviously important to us. But as we see, the issue
transcends even this and goes to the heart of scientific epistemology itself.
The assertion that formalizations suffice in the _expression_ of Natural Law,
and hence that causal entailment is to be reflected entirely in algorithms, is
a form of Church's Thesis, which I will discuss later... If it were true, the
consequences that follow from its truth would clearly have the most staggering
implications for all aspects of human thought. For good or ill, however, it is
not true, not even in mathematics itself.
Let us turn now to the question of what algorithms can
actually accomplish in a formal context... [which he begins to do,
mathematically]...
Conventional parlance has it that any mapping defined in
terms of an algorithm, as I have described, is "recursive". Note, however,
that this usage is different from my usage of the term in chapter 3. In our
parlance, a mapping (on the integers) was recursive if f(n) entailed f(n+1)
for every n. In that discussion, I have a necessary and sufficient condition
(see 4D.2 above) for such a mapping to be recursive. It is perfectly possible
to define mappings f in terms of algorithms, which do not satisfy this
condition. Conversely, there is no reason why a mapping recursive in our
sense, or rather, the transformation Tf(n)=f(n+1), which generates its values,
should be definable in terms of an algorithm. Hence the terms "definable by an
algorithm" and "recursive" are not coextensive. Indeed, it will be important
for us to carefully differentiate them. Henceforth, I shall call
algorithmically definable mappings "simulable," for reasons to become apparent
in a moment (they are also variously called computable and effective), and
reserve the term recursive for mappings (simulable or not) satisfying [4D.2]
above.
Thus, the word "simulable" becomes synonymous with
"evaluable by a Turing machine." In the picturesque language of Turing
machines this means the following: if f is simulable, then there is a Turing
machine T such that, for any word w in the domain of f, suitably inscribed on
an input tape to T, and for a suitably chosen initial state of T, the machine
will halt after a finite number of steps, with f(w) on its output
tape...."
He goes on to get into more and more detail in this vein, but the
point I'm making is that his definitions are contextually linked and he is
very careful to make the distinction. When he defines simulation in this way,
it is not the same as a model. (He even speaks, on p. 192, of
tricking the mapping and the algorithm that computes its
values, into evaluating a different map; "This trick is the essence of
simulation and of program.") However, he has defined the same words
differently in different discussions, in other parts of this same book, as
well as other places, and my point is that there is rarely
any generalization that can safely be made that ignores
context.
In this context, he is discussing how simulation pertains
to a machine and to programming. He says that the words "model" and
"simulation" are not synonyms (in this context) and goes on to explain
why. The fact that a simulation in another context can also be a model is what
leads to the interchangeability of the two words regardless of context and
that's where the problem lies. However, in the context of surrogacy and
modeling, there will be different definitions...
What I'm trying to get you to see is that in Rosennean Complexity
Theory, contextual constraints determine the effect. This is as true of my
father's way of writing as it is of natural systems in the universe, according
to his body of work (Theory). You've got to be more flexible in your
definitions because the definitions change as the context changes. The
relation between a good model and the natural system it models is what will
remain, and you have gotten that idea down pretty well. But I would caution
against getting too caught up in one definition of the difference between
simulation and model in a particular context and transpose that definition to
other contexts as if it were "a law".
Judith