|
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
|