Re: [OPE-L] is algebra dialectical and vice versa?

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Thu Sep 15 2005 - 11:35:36 EDT

One has to consider what is involved in modeling.
When one constructs a model you isolate off one part
of the world/universe and use it to represent another
part. You make assumptions about the form of representation
and then see if the behaviour of the model is
similar to the behaviour of the system you are
interested in.

To take a very obvious example, shipbuilders construct
small model ships which they pull through test tanks
to see how a ship that they intend to build will respond
to the waves.

Here the two models are of the same sort and differ
only in size.

If I have a railway timetable, I have a model of another
sort, by reading accross the lines corresponding to
a particular station - say Birmingham New Street,
I can use it to predict when trains will arrive at
the station. The model is of a very different sort
from a ship tank, but it is still a sub part of the
world that is used to predict the behaviour of
another part.

Suppose I now have a ballistic model, it is a set
of equations which tell me how far a projectile will
travel as a function of the elevation of a gun, the
weight of the cannonball and the charge of powder used.

These equations by them selves are not yet a working model.
They only become a model when combined with an appropriate
method of calculation. This could be a person who knows
how to do algebra and has appropriate paper and pencils,
it could be a set of brass wheels and dials which when
rotated to record elevation, charge and ball, read
off a range.

Now consider a set of equation like those used by Sraffa
to model prices. These are a model template. To make them
function as a real model, you need to parameterise the equations
with the number of industries, readings from input-output
tables, and then apply a computor - either a person or
a machine that understands algebra. The end result is a
set of predicted prices and profit rates that you can
compare with empirical observation.

The computational step has been a key part of all exact
sciences whether that computation is carried out by humans
using equations, by instruments like astrolabes or the
old curve integrators that shipwrights used, or by
a modern digital computer.

The advantage of the digital computer is its universality.
Just as human labour is potentially universal and abstract,
a computer is and abstract logical worker. It can perform
any sequence of logical or mathematical operations.
Thus if our theory of a given domain is specified in logical
or mathematical form, the computer gives us the opportunity
to test out the implications of that logical structure.
It can pursue the logic to a degree which we may be unable
to do, and in the process bring out the implications of our
logical models.

One of the things that I find interesting about Ian's work
is just how sparse the logical assumptions he has to make
about capitalism in order to generate results that
have the correct general form for a capitalist economy.

Gerald_A_Levy@MSN.COM wrote:
> Ian and Paul C:
> The analogies that both of you are making suggest that you believe that
> the if computer simulations can be used to model physical/natural
> processes then they can also be used to model capitalism.   This
> presumes that the 'mechanics' of capitalism are analogous to
> classical and statistical mechanics and extensions thereof.
> Are you thereby making some claim about the "dialectics of nature"
> and the (natural?) "nature" of capitalism?
> In solidarity, Jerry
>     (Ian wrote) Replace "social processes" with "physical processes" and
>     "intelligent behaviour of the actors involved" with "quantum
>     mechanics", and re-read the paragraph. It would then be an argument
>     for denying classical mechanics.
>     Yet we know that classical mechanics is a very successful predictive
>     theory (upto very small and very large scales) and talks about real
>     entities, such as forces, momentum etc. Computer simulations of
>     physical processes (e.g., for industrial design, computer games
>     etc.) employ classical mechanics. There's no need to simulate the
>     quantum level upon which the classical ontology is ultimately
>     implemented because this is an unnecessary level of detail for most
>     purposes.
>     (Paul C wrote) I think one can also attack his thesis from the other
>     side – that of statistical mechanics. One does
>     not need to simulate gases down to the particle level to make useful
>     bulk predictions in the way
>     that thermodynamics does. That obtains the Gibb’s Boltzman energy
>     distribution without one
>     having to simulate every particular configuration of a gas.
>     Similarly you obtain the same sort
>     of distributions for cash holdings making some very simple
>     assumptions about the social structure
>     of capitalist relations.

Paul Cockshott
Dept Computing Science
University of Glasgow

0141 330 3125

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