Matrices and Contradictions

Chris Burford cburford at
Thu Mar 30 07:21:06 MST 1995

Hi Ron,

You wrote:

  I have recently begun to think of society in terms of a
  multi-dimensional matrix.


However as Scott's post illustrates, we face a problem of trying to sell a
highly complex language as a passport to understanding Marx. Our problems
are similar in this respect to those who promote the relevance of Althusser,
or Bhaskar. We are selling, but why should anyone buy? Isn't Marx difficult
enough already?

Although I gib at arrows of time, which seem to me in the realm of speculative
cosmology, I feel that non-linearity has become part of the fabric of modern
science. Children are growing up, so familiar with non-linear computer
modelling, (after all they see it everyday in computer graphical illustrations
on the television), that they will wonder that anyone could believe that reality
could be expressed scientifically in terms of straight line graphs.

The matrix is a fundamental concept that can be used in maths, in economics,
in sociology and in psychology.

Now just before your post, Steve Keen in reply to Jon produced a series of
formulations on the various contradictions in Marx's analysis in economics.

I buy that too, and I think it takes that debate a lot further.

So I think we can no longer duck the question, what is the possible link
between non-linearity and dialectics?

Briefly, [because I would never have dared to start this post, if I thought I
would have to give a comprehensive answer], a matrix in motion produces
loops and swirls that may set up self-reproducing patterns.

As Chris Sciabarra said once, to a Marxist a contradiction is a relationship not
a complete logical inconsistency. The polar forces that produce the swirls,
cycles and loops, may be conceptualised as interacting components of a
contradiction, which in turn interacts with other contradictions, sometimes
producing larger patterns.

"Libchaber believed that biological systems used their non-linearity as a
defense against noise. The transfer of energy by proteins, the wave motion
of the heart's electricity, the nervous system - all these kept their
versatility in a noisy world." (from Chaos by James Gleick, Cardinal p194)

The exasperatingly flexible and resilient capitalist system *benefits* from its
contradictions because they give it stability (!) and only occasionally
render it vulnerable to internal destruction. (That is why Marx is both
right and wrong in his predictions)

However as the speed of feedback increases in the world economy, there are
reasons for thinking the system is becoming inherently more unstable, or at
least may have a phase shift. We are perhaps entering a new ice age of
massive global unemployment.

Sorry this is diffuse. Can anyone sharpen it up without boring the other 95%
of the list's subscribers??


Chris Burford

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