Re: [OPE] Models and Marx

Dave wrote
When I wrote 'model' before I didn't mean a formalized model. Instead it
was a carefully chosen analogy, in that theories *model* underlying
causal mechanisms. As such all theories are models of reality.

----
I am not sure that this is correct on several counts.
1) Theories are not quite the same as models
2) Even if they were, not all theories succeed in modelling reality, some theories are just plain wrong - the theory that life is due to some spirit, breath, Ki, or pneumena for example.
Why do I say that theories are not models and theories do not model reality?
A scientific model is a machine for predicting how part of
reality will behave. We tend to think of models in an abstract
conceptual sense, I think we should look at them
in a very concrete material sense.
  We have the world and we have models of it. The model is, at one level
a ’black box’ which gives us answers about the world. Given
some initial observations we can feed them into the black box
and it comes out with predictions. The predictions are not
necessarily predictions in time, they may be predictions about
other things in the real world that we have not yet observed.
If we make the other observation we can then compare what
the model predicted with what has actually occurred. At a
global scale our model might be a general climate model
predicting the long term path of climate under CO2 emission
forcing. The initial observations could be the trends in CO2
emissions, and the predictions could be ones about future
average temperatures and rainfall.
When building such a model one could take past periods
say 1900 to 2000 as the initial observations and have it
make predictions about climate for the period 2001 to 2009.
Generally we work on the rule that the closer the predictions
to the other observations, the better is the model.
Are models ‘ideas’ or or theories or are they machines?
 The term model is used in two rather different senses. On the one hand
we speak of a model as something physical. A model boat
may server as an adult’s toy, but for a shipyard it also has
a serious predictive value. In a wave tank the model tells
us something about the performance of the finished boat.
Measurements from models were, in the past, used to guide
the construction of actual steel plates. So it is clear that models
in this everyday meaning of the word, have a real pragmatic
use. On the other hand a model is used to refer to something
conceptual. One talks of the Newtonian model of the solar
system as opposed to the Ptolemaic one. In this case we think
of the model as something abstract, an idea not a thing. And
this gives rise to all sorts of questions about how it is that a
conceptual or mathematical model can be so good at predicting
the real world. Wigner complained about the ’unreasonable
effectiveness’ of mathematics, Hamming asked how simple
maths could be so effective. If we think of things in this way,
as a correspondence between two quite different domains –
that of thought and that of reality – the whole process seems so
remarkable as to tempt one to ascribe some mystical properties
to mathematics.
But it is not the theory of Newton or of ptolemy that makes the
predictions. To make predictions you have to construct a model
guided by the theory -- the Antikythera device was a physical model
based on the theory of Hiparchus or perhaps fo Ptolemy and would
have had the ability to predict lunar eclipses and solar eclipses.
The difference between the theory and the model is that the theory
needs to be materialised and activated as a physical model before
any predictions emerge.
A theory is more abstract than a model, it tells you how to go about
constructing a model, but until you have built the model and activated
it you get no predictions out. This was harder to see in the past since
the computations required to model the mechanics of the solar system
according to Newtons laws were done by people using papers and pencils
so the model in the sense of the computing system that produced the
results, was distributed over the notebooks, the clerks who did the menial
calculations and the directors like Laplace who developed the high level
equations.
A model now can be physically localised in an appropriately configured
universal computer - and we at times abstract from the computer itself
and say that the software package, independent of the hardware, is
the model. But such a model is still something concrete, with a material
existence and more importantly, a specific parametrisation.
The general theory of celestial mechanics is not a model, but part of
the means of production of models. The theory can be used to produce
a multiplicity of models -- of different planetary systems, of galactic dynamics,
etc.
A model may be built in accordance with a theory, and if the theory allows a large
number of models to be built, all of which models turn out to have a good predictive
ability we say that the theory is a law.
If we turn to Ians model, I think one can say that the theory of prices of production
was a condition of the model's production, and it is quite a considerable achievement on his part to
produce codes that, when executed, behave well and reproduce the results that the
theory says should be produced.
But it seems to me that the relationship between Ian's model and Marx's theory is somewhat
different from that between Newtons theory and the mathematical models Laplace's celestial mechanics.
In the case of Ian, the condition of that the model aims at is being able to reproduce what Marx
says should happen. In the case of Laplace, the condition of validity was the ability to reproduce ex ante
the positions in which the planets would later be observed. Also, Newtons equations,
directly guided, after suitable elaboration and transformation, Laplace's own ones. In
he had to invent equations that would reproduce Marx's final result -- much more had to be filled
in as Marx did not provide precisely formulated 'laws to which Ian's micro dynamic equations
had to be subject. Beyond that, it can not count as a model of the capitalist economy as
it generates counter factual conclusions. It is a model for Marx's theory, not a model for
a capitalist economy. Its function is to reproduce in numerical terms what Marx's theory describes
in general qualitative terms.
If I understand it correctly, its utility lies in showing that given certain simplifying assumptions and
given certain mathematical form for various dynamical processes, then the general result described
by Marx's theory in vol 3 of capital can be reproduced.
The counter factual nature of the predictions though, shows that the model is not yet a good description
of real capitalist economies.
But this shortfall is not something that is limited to Ian's model, it is a shortfall of the less formal account
given by Marx as well.
The University of Glasgow, charity number SC004401
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