Are car engines complex?

["Tim Gwinn" <***>]

This is a post I have been intending to write for some time, but I have been
too busy to do so. The title of this post refers to a discussion that took
place some time ago on the VCU list regarding Rosennean complexity and
natural systems. The example system in question was a car engine. Whether
such a material system is complex or not was in question. I find it
interesting because I think the question goes to the heart of several
fundamental notions of the Rosennean view.The following is my opinion on the
topic.

"Natural system" is the term used by Rosen to describe a collection of
observables and the apparent relations between those observables. Which
observables make up the basis of a given natural system is entirely a
subjective choice: they simply "seem to us to belong together".

Obviously, the idea is that natural systems, and the observables of which
they are composed, are taken in some basic sense to be representative of the
material world which we posit to exist external to ourselves. This posited
material world is something that we know only via these observables, these
perceptible qualities. We do not directly know the material world in-itself.
Rosen uses the Kantian notion of "noumena" - things-in-themselves - which
are unknowable directly. Instead, all we have to go on are the "phenomena":
what we can observe. It is we who impute these phenomena back to the
material world that we (or most of us, anyway) presume to exist
independently and objectively.

The main point is that natural systems, while composed of these perceptible
qualities in the external world, are still abstracted from the material
world in (at least) three ways: 1) natural systems are *phenomena* of the
material world, not the material world in-itself; 2) natural systems are
*subjectively selected* sets of observables; and 3) the relations between
observables are not directly sensed - instead we construct the relations
mentally and then *impute* those back to the natural system (and to the
material world that is behind the natural system).

Once we have defined our natural system, we can then place that natural
system in a Modeling Relation with some other system, such as a formal
system (mathematical, graphical, linguistic, etc.).

An unavoidable aspect of this Relation is that in order to measure
observables (either qualitatively or quantitatively) we must *interact* with
the natural system. Interaction is simply the fundamental basis of
measurement; without interaction no senses or constructed measuring device,
or meter, could detect anything. So it is that in science, there is
generally a concerted effort to minimize the impact of interactions of
meters on the system under study. Further, measurements mean there is a
mapping of a physical interaction to some set (typically numeric) of values.
This mapping in itself is another kind of abstraction.

Another aspect of the Modeling Relation is that the *choice* of which
aspects of the natural system we are attempting to establish a congruence
relationship with are subjectively selected. So it is that constructing a
Modeling Relation is an act of art, not a rote mechanical process.

In this way, natural systems are, in a sense, once more abstracted in the
MR: in addition to the 3 points noted above, we have now additionally the
subjective selection of those certain desired aspects of the natural system
with which we expect to establish congruence in the MR.

Rosen defines one certain class of natural systems as "mechanisms".
Mechanisms are those *natural systems* whose models are all entirely
simulable (Turing-computable). Systems (formal or natural) meeting that
criteria (all its models simulable) can also be labeled "simple systems".

Suppose now, that we ask about a car engine: is it simple or complex? Well,
first of all, we need to be more precise: by "car engine" - to what are we
exactly referring? This question essentially asks: what comprises the
natural system we are inquiring about?

This then forces us to make our subjective selections of 1) certain
observables; and 2) certain apparent relations that we impute to the system,
and 3) certain choices of interactions with that defined system.

Once we have chosen the specifics of our natural system, we then have to
further choose which aspects of that natural system with which we wish to
establish a congruence relationship when constructing the MR.

The point is this: with the appropriate selection of observables, relations,
and points of congruence we can, I believe, certainly construct a MR that
will meet the requirements of Rosen's definition of "mechanism". Therefore,
the natural system *that meets these conditions* will be a "simple system".
So, in this case, the 'car engine' will be "simple".

But, in doing so, aren't we just fooling ourselves? Surely there are more
intricate things going on in a car engine, particularly as we look at more
detailed aspects, such as at the atomic level? Particularly examining it in
ways that would make that system complex (not all models simulable)?

But what is required to examine these more intricate things? We must
interact with the system in different ways, and likely in more ways. This
means a different (or more likely, a richer) set of observables which to
measure and to discern relations between. As well, it means increasing the
extent of our interactions with the system (to perform the additional
measurements), and it also means that the number of aspects of the system
with which we intend to establish congruence are also increased.

In so doing, we have, in my opinion, done several things: 1) we have, in
effect, defined a *new* natural system by making these different choices of
observables and relations and interactions; and 2) we have necessarily
constructed an *entirely different* Modeling Relation than the one in the
car-engine-as-mechanism natural system MR.

In short, we are now discussing an entirely different situation than the
first one I posed. The words "car engine" mean two entirely different things
in the two cases. The commonality is that we reasonably assume that the same
material world underlies both defined natural systems. If we recall that
constructing an MR is "art", then it may be more clear that these are two
distinct and separate situations, not unlike two artists painting images of
the same scene using different styles and paying attention to different
aspects of that scene. To me, this is just a consequence of the subjective
nature of our choices of observables, relations, extent of interactions, and
points of congruence.

Rosennean complexity is, after all, as much dependent upon the manner of the
observers participation as it is of the manner of the system under study.
That is, "complexity" is not an intrinsic property of a natural system, nor
of the material world. The material world just "is". On the occasions when
we interact with the material world via defined natural systems and Modeling
Relations such that at least one model in *that* MR is nonsimulable, then we
say that natural system is "complex".

But what of the underlying material world? Surely if a certain natural
system is complex, then the presumed underlying material system is complex
too? I do not think Rosen would agree. As noted above, complexity is defined
as a certain result of a given MR. Since we do not directly establish an MR
with the material world, but rather indirectly through observables in
defined natural systems, there is no set of models to qualify the material
system as simple or complex.

At the least, though, we can reasonably impute back to the material world
the relations - the entailment structures - that we apprehended and imputed
to the natural system. In this way, we can make reasonable study of the
nature of those causal entailment structures we presume to occur in the
underlying material world.

This finally brings me back to "mechanisms" (and, by extension, Rosennean
"machines"). By being defined as a certain class of natural systems with
predefined criteria, mechanisms have built-in limitations. The class of
mechanisms can only describe those natural systems whose entailment
structures meet the constraints of the definition of mechanism;  for
example, such a natural system cannot possess an entailment structure that
necessitates a nonsimulable model. The definition of mechanism is thus
*intrinsic* - it is a definition that rests on its own internal criteria,
not on external observation. Once again, it is not that we cannot "discover"
mechanisms in the world; but, rather, because the definition of mechanism is
intrinsic, it is incorrect to say that finding a mechanism is any kind of
evidence for an underlying mechanistic material world with only mechanistic
entailment structures.

Regards,
Tim