P8475423 at vmsuser.acsu.unsw.EDU.AU P8475423 at vmsuser.acsu.unsw.EDU.AU
Sun Sep 17 15:42:47 MDT 1995

The ten or so comments on chaos and marxism since I last posted
covered most issues that I would have raised since I downed
tools two days ago. However, Scott's comments on Chris Sciabarra's

|The above is built on a wrong and undialectical notion of Marxist theory of
|knowledge, but... If this is true then where does it leave us? Accepting the
|'way things are'? with the dubious 'knowledge' and 'humility' that we can't
|really solve anything or change anything. That all attempts to overthrow the
|system will just inevitably lead to disaster. This is a tired but very
|prevalent notion of those opposed to Marxism. How nice for those with a
|stake in the system.

, and a couple of issues others did not raise, prompt me to dip in again
after the weekend.

(1) With respect to Scott's comment above, no, chaos theory does not leave
us with accepting the 'way things are'; but it should makeus much more
careful about attempting large scale changes. Chris captured well the
issue that, in a chaotic system, unintended consequences can arise,
and these are all the more likely the larger the change attempted.

This is one reason that I see a traditional opposition in marxist thought
between 'revolution' and 'reform' is misplaced. The large, 'one-step'
change that revolution entails can easily lead to myriad 'unintended
consequences'; I don't think I need volunteer examples of that! The
'small step' change process that reform implies gives you more chance to
uncover unintended consequences as you proceed. Of course, this also
implies continued existence of the same old enemies for quite some time,
but it could be argued that such devils you know may be better than the
devils unintended consequences may create. Again, I doubt that examples
are needed.

(2) While Marx's philosophy was dialectical, all of his mathematics was
not. This, of course, was not his fault; on the one hand, no-one had
developed chaos theory in his lifetime (it began in 1899 with Poincare);
on the other, he had not been trained in mathematics, and made his own
attempt at self-education late in life (incidentally, I haven't taken
a look at his mathematical manuscripts, and would appreciate some
pointers to sources from those who have).

As a result, Marx's often attempted to express his dialectical thinking
in the guise of static equilibrium mathematics. While some insights
were so found--the relationship between sector I and II outputs and
demands, for example--many others were lost, because the maths was
not up to the task.

The modern development of the tools of chaos theory have at last
provided a form of mathematical reasoning which, while it may not
be able to capture all the nuances of philosophical reasoning, at
least allows its quantitative expression and some qualitative
assessment in that more rigorous language.

(3) As an example of (2), and as a counter to some on this list who
might think that my occasional defence of the Sraffian critique
of Marx makes me a Sraffian, I tender (briefly) a critique of
Sraffian economics based on chaos theory.

In 1992, the Sraffian who led the attack on marxian theories of
value (Steedman) launched a critique of Kaleckian pricing theory,
which argues that prices are set by a mark-up on costs. He
argued that a capitalist system has to solve the equation

p = (w*E + p*A)*(I+M)

(a matrix equation), which has the solution

p = w*E*(I+M)*(I-A-A*M)^-1

which puts strong constraints on the mark-ups that can be
applied in each industry, with the effect that mark-ups can't
be set by each industry, but must be set inter-dependently.

But Steedman's reasoning only works if capitalism is in long
run equilibrium--he is using a more sophisticated version of
the same kind of reasoning that Marx employed when designing the
reproduction tables. However, by the simple expedient of
recognising that capitalism is not in long run equilibrium,
and that therefore a truer equation is:

p(t) = (w(t-1)*E(t-1) + p(t-1)*A(t-1))*(I+M(t))

(which simply says that this time period's prices equal this
period's mark-up times last period's costs).

Since this is supposed to (very stylistically) capture the
behaviour of capitalism, it also has to capture the behaviour
of capitalists (and workers). Leaving out the worker side
of things (as Steedman did), this means the above equation
has to be supplemented for one for the setting of mark-ups.
Introducing one which presumes they try to iteratively
maximise profits:

M(t) = M(t-1) - a*(pf(t-1) - pf(t-2))

turns this into a system of coupled difference equations,
which, lo and behold, are nonlinear.

This time-based equation will *never* reach the
equilibrium value of Steedman's timeless one: the system
is inherently unstable, as can be shown by either
numerical simulation, or by working out the equilibrium
position and then calculating its stability.

In summary, I can't think of a less dialectical approach
to economics than that taken by Sraffians; and chaos theory
helps pull that type of thinking down. It can also be
used to enhance Marxist thought (as Alan Freeman has done
with his difference equation work on the transformation
problem), and indeed to express some marxian notions in
mathematical form, as Marx himself was unable to do.

Steve Keen
PS a paper on the Sraffian issue above will shortly be
available in my directory on the
ftp site.

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