Some aguments for this:
1. The ",true complexity", of almost all real objects (if
it existed) would be beyond us.
By increasing the level of detail considered a lower bound for any ",true
complexity", of almost all natural systems can be arbitrarily increased
until it is well beyond our means of representation, understanding and
modelling ability. There is no apparent upper bound to how complex things
appear. It seems that most things are arbitrarily complex, just dependent
on the number of aspects and the level of detail on is willing (or able)
to consider. This would not be the case if there was a practically accessible
real level of complexity.
For example, a brick is a fairly simple object if you consider only
its macroscopic properties but is much more complex at the level of its
component particles. This particulate complexity is averaged out at the
macroscopic level at which we usually relate to them, so we can usually
abstract from the details, but if you are insisting on an entirely objective
basis then you must include this particulate complexity. The complexity
further increases beyond our comprehension when we consider such a macroscopic
object, such as a brick, at the sub-atomic level of detail.
Even the complete modelling of sub-atomic particles stretches our abilities
to the limit, and here it may be argued, we are by necessity dealing with
high level abstractions from the reality of our experimental results and
thus we can not tell whether this apparent simplicity is well-founded or
merely due to our ignorance.
2. The complexity of things seems to vary depending on the framework
within which you are considering them.
Changes of goal, language of representation, aspect, and scale can all
greatly effect the practical complexity of natural systems. In the ant
colony example (Section 2.1.5) whether your goal was merely predictive
of behaviour at a purely macroscopic level or was seeking to explain this
macroscopic behaviour explicitly in terms of the behaviour of individual
ants, effects the practical complexity of the modelling task. People can
have very different views of the complexity of systems, sometimes differing
far more by changes accross framework than accross changes of subject matter
3. Any ",true complexity", is irrelevant, as we never interact
with the total systems, only certain limited aspects of them at any one
time.
This argument is effective in conjunction with the one above (2). Compare
this with ",mass",: the ",true mass", of objects is not
irrelevant despite the fact that we only interact with different aspects
of mass at one time, because the mass does not change depending on the
aspect from which it is considered. The complexity of a natural system,
on the other hand, can vary sharply on the aspect chosen.
4. The complexity of an object is only realised though interaction
with another system.
When this other system seems more critical in determining the resultant
complexity, then it is hard to see this complexity as primarily a property
of the object system.
5. There would be little relation between this ",real",
complexity and the complexity of that object as represented in communications
about it.
In practice we are often concerned with modelling and comparing such
models, so these then become the primary object of study.
6. Ascribing complexity to natural systems makes an account of simplification
difficult
The ascription of complexity to natural systems also make an account
of simplification difficult. One would be forced to judge all strictly
equivalent models of a natral system as equally complex.
7. Without natural systems there would still be complexity, without
models there may not
If there were no natural systems there would still be complexity as
different artificial and formal systems are not equally complex. If there
were no models it is quite plausible there would no possibility of complexity
judgements. Of course this is very difficult to imagine as these are extreme
counter-factuals. Would there be any complexity for an omniscient god (as
opposed to understanding how complex things may appear to us), who presumably
has direct cognisance of reality?
8. By analogy with other properties such as beauty or primality
There are analogies with other properties which certainly make it plausible
that certain things lie in the modeller rather than the modelled. Beauty
is one, it is very plausible that ",beauty is in the eye of the beholder",.
Similarly primality is properly considered a property of numbers not objects
(even if these objects are enumerated).
All of the above difficulties come down to the same nub: if real things
do have complexities, then they are unmanageablely large. Thus at the moment,
and quite possibly anyway, it is not useful to try to do this. If we choose
only one aspect and one scale, we are no longer dealing with the complete
object, only an abstraction of it.
It comes down to why we ever consider properties to be of things rather
than our models of them in the first place - because they have the ",same",
properties independant of the observer or the models (e.g. mercury or thermocouple
models of temperature) - this is patently not true of complexity judgements.There
are several arguments against this view. I consider these below.
Countering some arguments against:
1. Some real complexity comparisons are objective.
An example is ",An amoeba is objectively simpler than a human",.
There are two ways of interpreting this argument, firstly as a variant
of the cell example (Section 2.1.7), i.e. that an amoeba is simpler than
a human however you look at it, and secondly as an implicit call on upon
a privileged (and hence common) framework, i.e. there is one objective
framework to use and within this the amoeba is simpler.
The first argument assumes that the comparison is valid, regardless
of the framework. This is an immensely strong assumption, one that seems
to draw its strength from an identification of the amoeba with a human
cell and invoking the sub-system property that we noticed in the cell example.
Otherwise it would seem possible to choose a framework where the amoeba
differed substantially from the cell (its method of encapsulation and subsequent
digestion of food?), where the judgement of relative complexity was not
so clear. If one then argues that this is an inferior or more specific
judgemental framework, this would bring us to the second interpretation.The
problem with arguing for a uniquely (or even relatively) privileged framework
is that of its justification, given that it does not allocate impractically
large complexities to almost everything (or that a framework revealing
more complexity is always better). Also that in practice there are always
pragmatic choices of factors like scale, so that a privileged framework
is no use for actual complexity judgements. Finally the very identity of
many things seems inextricably linked to which aspects you are considering
(e.g. 'society').
2. Claiming that complexity is not a property of natural systems
is just a category mistake.
It could be argued that even if it is admitted that complexity comparisons
can only be meaningfully made on the models of reality, the complexity
refers to the things themselves, and that it is only due to our limitations
(in particular our understanding) that we see different complexities from
different viewpoints.This is a possible standpoint, but it is hard to see
how this could be then applied in practice without in effect attaching
the property of complexity to the models rather than the original systems,
as otherwise in practice the complexity of such systems would change arbitrarily
depending on the model chosen.
3. This would make objective complexity judgements impossible.
If a framework is agreed upon then the complexity of something can be
objectively determined by different observers w.r.t. this framework. For
example in the physical and mathematical study of chaotic systems a framework
which implicitly disregards some level of detail as ",random",
is so familiar that it has become a background assumption. Thus the researchers
in the field seem to uniformly agree that a perfectly disordered system
(like a gas ) is as simple as a perfectly ordered one.
4. There are real causes of complexity
This is true but not a compelling argument for complexity pertaining
to natural systems. It derives from a confusion between accounts of what
complexity is and what can cause it. To take an analogy heat can be caused
by a variety of forms of energy which are not heat. In the end it is a
pragmatic consideration, it is useful to attribute properties to natural
systems when this is largely independent of models but more useful to consider
it a property of the models if it is not (but is of models of models) (e.g.
beauty is attributed to the beholder, because is known to be culturally
dependent - 60's tower blocks - Miss World competition). If beauty had
no inter-personal validity then it would not be attributed much objective
reality (like the detail of people's dreams or their favourite numbers).
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