At 11:27 25/05/00 -0400, you wrote:
> For those who are curious, I have a recently published
>paper on these issues.
>"Aspects of dialectics and non-linear dynamics," _Cambridge
>Journal of Economics_, May 2000, vol. 24, no. 3, pp. 311-324.
> It is also available on my website without the figures at
>http://cob.jmu.edu/rosserjb.
>Barkley Rosser
Congratulations on getting published in this journal.
This is an important area of left political economy. I will copy the
abstract and then comment on extracts.
> Abstract
>
> Three principles of dialectical analysis are examined in terms of
> nonlinear dynamics models. The three principles are the transformation
> of quantity into quality, the interpenetration of opposites, and the
> negation of the negation. The first two of these especially are
> interpreted within the frameworks of catastrophe, chaos, and emergent
> dynamics complexity theoretic models, with the concept of bifurcation
> playing a central role. Problems with this viewpoint are also discussed.
>I. Introduction
> Among the deepest problems in political economy is that of the
> qualitative transformation of economic systems from one mode to
> another. A long tradition, based on Marx, argues that this can be
> explained by a materialist interpretation of the dialectical method of
> analysis as developed by Hegel. Although Marx can be argued to have been
> the first clear and rigorous mathematical economist (Mirowski, 1986),
> this aspect of his analysis generally eschewed mathematics. Indeed some
> (Georgescu-Roegen, 1971) argue that the dialectical method is in deep
> conflict with arithmomorphism, or a precisely quantitative mathematical
> approach, that its very essence involves the unavoidable invocation of a
> penumbral fuzziness that defies and defeats using most forms of
> mathematics in political economy.
Do you know the book by Moshe Machover which was the first to analyse
Marx's economic theories with probalistic maths?
The Laws of Chaos, A Probabilistic Approach to Political Economy
by Emmanuel Farjoun and Moshe Machover
VVerso Editions London. ISBN 086091 768 1
Machover is a very reasonable marxist, and has an e-mail address. The only
qualification is that the publishers chose the title for him rather than
himself and he is not interested in chaos theory. The exercise stands on
its ground as a probabilistic working of a marxian political economy.
> However, this paper will argue that nonlinear dynamics offers a way
> in which a mathematical analogue to certain aspects of the dialectical
> approach can be modelled, in particular, that of the difficult problem of
> qualitative transformation alluded to above.
> In particular, we shall discuss certain elements of catastrophe
> theory, chaos theory, and complex emergent dynamics theory models that
> allow for a mathematical modelling of quantitative change leading to
> qualitative change, one of the widely claimed foundational concepts of
> the dialectical approach, and a key to its analysis of systemic political
> economic transformation.
> In most linear models, continuous changes in inputs do not lead to
> discontinuous changes in outputs, which will be our mathematical
> interpretation of the famous quantitative change leading to qualitative
> change formulation.
> Part II of this paper briefly reviews basic dialectical
> concepts. Part III discusses how catastrophe theory can imply
> dialectical results. Part IV considers chaos theory from a dialectical
> perspective. Part V examines some emergent complexity concepts along
> similar lines, culminating in a broader synthesis. Part VI will present
> conclusions.
>II. Basic Dialectical Concepts
> In a famous formulation, Engels (1940, p. 26) identifies the laws of
> dialectics as being reducible to three basic concepts: 1) the
> transformation of quantity into quality and vice versa, 2) the
> interpenetration of opposites, and 3) the negation of the negation,
> although Engels's approach differs from that of many others on many grounds
<>
> For both Marx and Engels (1848), the first of these was the central
> key to the change from one mode of production to another, their
> historical materialist approach seeing history unfolding in qualitatively
> distinct stages such as ancient slavery, feudalism, and
> capitalism. Engels (1954, p. 67) would later identify this with Hegel's
> (1842, p. 217) example of the boiling or freezing of water at specific
> temperatures, qualitative (discontinuous) leaps arising from quantitative
> (continuous) changes. In modern physics this is a phase transition and
> can be analyzed using spin glass or other complexity type models (Kac,
> 1968). In modern evolutionary theory this idea has shown up in the
> concept of punctuated equilibria (Eldredge and Gould, 1972), which Mokyr
> (1990) and Rosser (1991, Chap. 12) link with the Schumpeterian (1934)
> theory of discontinuous technological change. Such phenomena can arise
> from catastrophe theoretic, chaos theoretic, and complex emergent
> dynamics models.
Good.
> The interpenetration of opposites leads to some of the most
> controversial and difficult ideas associated with dialectical analysis.
> Another interpretation is that this unity of opposites implies a
> negation of the idea of the excluded middle in logic. Thus, both A and
> not A can simultaneously be true.
I would suggest something not contained in this essay: the dialectical
theory of contadiction is heavily influenced by the German language.
The problem for English readers is similar to that of reading Freud in
translations that put his more intelligible German concepts into Latin- or
Greek-based technical words.
The problem is that German is sloppy about time, and precise about place.
English is much more precise about time; eg the use of the future and the
continuous present, whereas the Germans may often use the present tense for
the future. German however has many words that are precise about place.
For example to say "He is in the toilet", is laughable if translated
literally into German. It means "he is swimming about inside the toilet" or
at least has his head stuck down the pan. In German it is dignified only to
be "on" the toilet.
In German words of direction of movement are important. Their words for
whither and whence remain current whereas ours are fussy and old fashioned.
Small indicative suffixes, hin and her, are added to many adverbs to denote
the direction of movement. Verbs of movement, like verbs of being, have an
ontological status with "sein" to be used to conjugate the perfect.
Although this does not extend to verbs of looking I would argue that for
looking as for movement German speakers have a much heightened sense of
place and perspective than those whose mother tongue is English.
Thus in literal translation of German we get expressions like "over and
against" which sound clumsy and meaningless in English (presumably
"gegenüber").
Now the word used in German philosophy for contradiction, does not imply a
total logical contradiction, with an excluded middle. It is "Gegensatz",
something that is "set" (setzen) "against" (gegen) something else. It
implies contrast and even comparison rather than total ontological
impossibility.
Thus I am arguing that the intricate tradition of German dialectics that
Marx and Engels inherited, examined entities in motion by analysing them
from contrasting perspectives, using words grounded in the colloquial
German with its fine distinctions of place and perspective. Whereas in
English there is a continuum of a subtle shades of time which blur
superficially "things change". It is a triumph for English speaking
scientists to accept that evolution is better understood as "punctuated
evolution". Marx would have read Darwin with the mind of someone whose
mother tongue was German, whereas Darwin would have thought as an Englishman.
Whether the German tradition of dialectics deals with contrasting
perspectives or really contrasting aspects of a complex process, is always
problematic. But the problem is less daunting if we make it explicit.
Certainly it is correct for English-speaking readers to emphasise that the
concept of contradiction in Marx absolutely does not exclude a middle, in
fact absolutely presupposes, in a philosphically realist fashion, the
existence of a complex entity. It will be easier to accept, this if we
assert along with our basic assumption that reality exists, that the real
entities or rather processes that constitute reality, are complex until
proved otherwise. Indeed in the endless flux of the universe only those
processes that maintain a complex interaction, remain long enough in
dynamic equilibrium to be a subject of observable science!
Occam's razor should be overthrown as a fundamental precept of science, and
as an early manifestation of operationalised, reductionist, essentially
bourgeois, thought. Reality is instead built up by layer upon layer of
complex self-organising dynamical entities.
> Rosser (1991, Chap. 1) argues that this is a matter of perspective or
> the level of analysis of the observer.
Sounds good, or shall we say convergent with what I have just been arguing.
> Engels (1940, pp. 18-19) confronted the contradiction between the
> apparently simultaneous acceptance of discontinuity arising from the idea
> of qualitative leaps and of continuity arising from the Afuzziness@
> implied by the interpenetration of opposites in the dialectical
> approach. He dealt with this by following Darwin (1859) in accepting a
> gradualistic view of organic evolution in which species continuously
> change from one into another, while arguing that in human history, the
> role of human consciousness and choice allow for the discontinuous
> transformation of quantity into quality as modes of production
> discontinuously evolve.
What is the evidence that Engels really accepted a smooth interpretation of
Darwinian evolution? After all the phase shifts of water were familiar to
any serious student of Hegel's dialectics.
> Finally there is the idea of wholes consisting of related parts
> implied by this formulation. For Levins and Lewontin (1985) this is the
> most important aspect of dialectics and they use it to argue against the
> mindless reductionism they see in much of ecological and evolutionary
> theory, Levins (1968) in particular identifying holistic dialectics with
> his "community matrix" idea. This can be seen as working down from a
> whole to its interrelated parts, but also working up from the parts to a
> higher order whole. This latter concept can be identified with more
> recent complex emergent dynamics ideas of self-organization (Turing,
> 1952; Wiener, 1961), autopoesis (Maturana and Varela, 1975), emergent
> order (Nicolis and Prigogine, 1977, Kauffman, 1993), anagenesis
> (Boulding, 1978; Jantsch, 1979), and emergent hierarchy (Rosser, Folke,
> Günther, Isomäki, Perrings, and Puu, 1994; Rosser, 1995). It is also
> consistent with the general social systems approach of the dialectically
> oriented post-Frankfurt School (Luhmann, 1982, 1996; Habermas, 1979,
> 1987; Offe, 1997).
Bravo. These appear to be the pertinent links, especially the emergent
orders as described in complexity theory. The system approach is also an
important bridge.
> Lavoie (1989) argues that markets self-organize out of chaos.
"Chaos" is used in two different senses in chaos theory. Chaos theory
proper explains why dynamical systems of this type are a) *relatively*
stable within defined bands of probability most of the time
b) may undergo sudden phase change to a different *relative* steady state.
Only one possible phase is total chaos in the sense of without any
identifiable pattern at all.
The behaviour of markets, emerging out of the exchange of commodities, is
exactly compatible with this broad description.
> Finally, the negation of the negation has also been a very
> controversial and ideologically charged concept.
It was explicitly left out of Stalin's summation of dialectical and
historical materialism, presumably taken as the last word on the subject by
millions of communists, and it was specifically criticised by Mao.
>It represents the combining of the previous two concepts into a dynamic
>formulation: the dialectical conflict of the contradictory opposites
>driving the dynamic to experience qualitative transformations.
This seems a helpful suggestion about how to think of it. It does not occur
often however, since by definition qualitative changes does not occur often.
>III. Catastrophe Theory and Dialectics
> The key idea for analyzing discontinuities in nonlinear dynamical
> systems is bifurcation, and was discovered by Poincaré (1880-1890) who
> developed the qualitative theory of differential equations to explain
> more-than-two-body celestial mechanics.
Bravo. The serious and highly respected maths behind this is over 100 years
old.
Only the advent of computers has made it easier to model the implications.
I assume catastrophe theory is a somewhat earlier representation of aspects
of the dialectical process. As materialists we need to look at what is the
fundamental nature of the universe such that it repeatedly throws up ideas
like this, as reflected, with partial accuracy only, in the human mind.
There is a bridge here with the anthropic perspective in cosmology.
> Ironically, in mainstream economics most of the criticism of
> catastrophe theory has come from the opposite direction, claims that it
> is too imprecise, too poorly specified, unable to generate forecasting
> models with solid theoretical foundations, too ad hoc, and so
> forth. Much of this criticism has probably been overdone as discussions
> in Rosser (1991, Chap. 2) and Guastello (1995) suggest.
> Yet another issue that cuts across all nonlinear dynamical
> interpretations of dialectics is that catastrophe theory analyzes
> equilibrium states and their destabilization. There is an old view among
> dialecticians that equilibrium is not a dialectical concept, indeed that
> dialectics is necessarily an anti-equilibrium concept. However, drawing
> on the work of Bogdanov (1912-1922), Bukharin (1925) argued that an
> equilibrium reflects a balance of conflicting dialectical forces and that
> the destabilization of such an equilibrium and the emergence of a new one
> is the qualitative shift. This view was sharply criticized by Lenin
> (1967) and was viewed by Stalin as constituting part of Bukharin's
> unacceptable ideology of allowing market elements to persist as an
> equilibrating force in socialist society. Stokes (1995) argues that
> Bogdanov's views provided the foundation for general systems theory as it
> developed through cybernetics (Wiener, 1961). These approaches would
> eventually lead to nonlinear complexity theories, some of them
> emphasizing disequilibrium or out-of-equilibrium phase transitions as in
> the Brussels School approach (Nicolis and Prigogine, 1977).
VVery interesting suggestion that Lenin took a wrong philosophical turn on
this point. The reference you give is to Lenin's Materialism and
Empirio-Criticism. This was a materialist work but one not strong on
dialectics. It was only after he read Hegel's philosophical notebooks in
1914, struggling with the shock of the destruction of the second
international by the First World War, that his thinking became more
dialectical.
>IV. Chaos Theory and Dialectics
>. Truly chaotic systems exhibit highly erratic, apparently random, yet
>deterministic and bounded dynamics.
I would not restrict the idea of "truly" chaotic systems to those that
exhibit "highly" erratic dynamics. Remember we are dealing with the
proclivities of hard nosed mathematicians, who sometimes produce a quirky
name for a phenomenon, just as sub-atomic physicists raid the Hunting of
the Snark for names for their ephemeral particles. "Chaos Theory" is an
unfortunate name, because it suggests that most of the time naturally
occurring processes are in chaos. I suggest they, or at least the ones
stable enough for long enough for us to observe, are not in a state of
chaos. The scientific, emotionally neutral term for all of this is
"non-linear dynamical systems". If we could get over the hegemony of
straight lines being kosher linear ,and non-straight lines not really being
linear, much of this would be easier for future generations to absorb with
their mothers milk and their first exposure to dynamical graphics on
television.
Sensitive dependence on initial conditions (SDIC): the conditions are only
"initial" in a closed model. The real universe has no closed models, so at
any time a small variation in one variable, may be just the trigger to
precipitate a phase shift if the other stages in the dynamical process are
sensitive to this trigger at that moment in time.
> Although there are systems that are everywhere chaotic, many are chaotic
> for certain parameter values and are not for others.
I would rephrase this: Although many systems follow non-linear dynamics
they transform themselves when subjected to a small stimulus, into a
chaotic phase only if their parameters have certain values.
> May (1976) studied this equation in the context of an ecological
> population dynamics model, in which k has the interpretation of a
> carrying capacity constraint, but he also first suggested the
> applicability of chaos theory to economic analysis in this paper.
Yes this ecological population dynamic model has inherent similarities with
economics. In economics market activity reaches saturation when economic
activity rises to hit a certain ceiling, whether that ceiling is a matter
of the availability of land, of cheap labour, of consumer spending power,
or the boundaries of a lake which can contain no more subtrate for the
multiplication of a species of fish. Inherently this a picture of a limit
cycle. As economics is about the expenditure of human energy labour power,
according to Marxist theory, there are fundamental similarities with the
eneregy economics of life forms occupying a niche in their environment.
> The second such interpretation involves the concept of the
> interpenetration of opposites. This interpretation can be derived from
> considering the dual role of the x variable in (4). It operates both in
> a positive way and in a negative way, both tending to push up and to push
> down. Now, this may seem fairly trivial, as many such equations
> exist. But indeed, at the heart of most chaotic dynamics is a conflict
> between factors pushing in opposite directions. In effect, as a
> increases, the strength of this conflict can be thought of as intensifying.
I think this is an interesting comment. We are indeed looking for
approaches which in themselves may appear trivial but help us to get a
handle on the dynamical nature of the system.
> In the population ecology model of May (1976), a represents the
> intrinsic growth rate of the population, and the negative aspect
> represents the effect of the population crashing into the ecological
> carrying capacity, k. One can view this system dialectically and
> holistically as a population with its environment. Conflicting forces
> operate through the same variable, the population, hence the
> interpenetration of the opposites whose interaction drives the
> dynamics. As this conflict heightens, bifurcations occur and
> quantitative changes lead to qualitative changes in dynamics as the
> system transits to chaos.
>V. Emergent Dynamics Complexity and Dialectics
> In contrast to the theories of catastrophe and chaos, there is no
> single criterion or model of complex dynamics, but rather a steadily
> increasing plethora which we shall not attempt explicate in any detail here
Agreed. It is even more a mental product of the availability of the new
technology of computers, than Mandelbrot's computerised reworkings of Julia
sets from the beginning of this century.
>Many of these models involve large-scale equations systems and simulations
>with self-organization phenomena emerging from the dynamics of conflicting
>forces. Such self-organization has long been identified by many observers
>as constituting exactly the kind of qualitative change that the
>dialecticians seek, and may represent overcoming the problem of the lack
>of new variables or functions emerging associated with the catastrophe and
>chaos models. All of these models can be united under the label emergent
>dynamics complexity.
> Europeans in general are more willing to admit the dialectical
> interpretations of emergent order and self-organization in complex
> dynamical systems as we have presented them above than are their American
> counterparts.
Agreed. This is an important discussion to help English speakers escape
from being stuck as dialecticians in a Marxist ghetto. Note though how the
concept of "non-equilbrium economics" has provided a bridge between
progressive economists. (I am thinking of the sort of articles published in
"Capital and Class"
> As a final frisson to this discussion, let us consider somewhat more
> closely the Stuttgart School synergetics approach of Haken (1983) that is
> very closely related to Prigogine=s Brussels School approach.
On a small point, have you attended enough conferences to know how
Prigogine's name is pronounced? Could you spell it phonetically, as I am
not sure of its cultural roots.
> Unsurprisingly, Krugman completely ignores any dialectical
> interpretation of the self-organization phenomenon, reflecting the
> Anglo-American bias.
This is indeed not surprising. Cultural prejudices will not disappear
overnight, but you paint a wide-ranging picture of how many different
theoretical models are converging on a complementary perspective.
>VI. Conclusions
> We have reviewed the three main Alaws of dialectics@ as presented by
> Engels in The Dialectics of Nature (1940, p. 26). These are the
> transformation of quantity into quality and vice versa, the
> interpenetration of opposites, and the negation of the negation. We have
> seen how such nonlinear dynamical models, such as those capable of
> generating catastrophic discontinuities, chaotic dynamics, and a variety
> of other complex dynamics such as self-organization can be interpreted as
> manifesting these laws, especially the first two. In particular the role
> of bifurcation is seen as central to implying the first of these
> concepts, although we note that we have presented at best a very
> superficial overview of these various nonlinear dynamical models.
> However, we must conclude with a caveat that has floated throughout
> this paper. Dialecticians who oppose the use of mathematical modelling
> at all, who identify such modelling with Aarithmomorphism@ and a denial
> of essential dialectical fuzziness, will remain unconvinced by all of the
> above. They will see the kinds of discontinuous changes implied by the
> various bifurcations in these models as simply sudden changes in the
> values or behaviors of already existing variables, rather than the true
> qualitative emergence that cannot be captured mathematically. They might
> have a harder time maintaining such a position with regard to complexity
> models with self-organizing or emergent hierarchy dynamics, but even with
> these they can make similar arguments that one is simply seeing different
> behavior of already existing variables, however new and different that
> behavior might appear.
> Of course, this hard core position is exactly that which is derided
> by the analytic Anglo-American tradition that sees dialecticians as
> hopelessly fuzzy and unscientific. The debate between these strongly
> held positions can itself be viewed as a dialectic that remains
> unresolved.
Many congratulations. Bravo!
Without being in economics myself, I would have thought this deserves to be
read and cited frequently. It conforms to the conventions of scientific
discourse and is open to debate. I think it is particularly shrewd and well
judged to nudge any marxists reading it, to consider the importance of
getting their hands dirty with maths.
I think you are wise to survey the literature and the movements in the
direction you describe. At a certain level it is a manifestation of the
technology with which we now work, and one can afford to take a relaxed
overview of the diversity of approaches.
I specifically applaud your inclusion of references to Hayak. The best way
to deal with him is to finesse him. Indeed few humans are capable of
talking total nonsense, and he is not one of them.
In making this particular bridge you may be interested in an admirable
short pamphlet published by the right wing British "Institute for Economic
Affairs" IEA 2 Lord North Street London SW1P 3LB. Fax (if the 1994 numbers
can be safely updated) 0044-20-7799-2137.
It is a 112pp Hobart Paper, entitled "Chaos, Management and Economics: The
Implications of Non-Linear Thinking". By David Parker (University of
Birmingham and Ralph Stacey, University of Hertfordshire.) It is concise
and well-written, and sure-footed in its description of chaos theory.
Interestingly it says the ideas are most compatible with those of Hayek and
the other "Austrian" economists. Even more interestingly it suggests the
best way for a country to survive in these inherently turbulent economic
conditions, is to be highly flexible (a clear right-wing agenda) but to
invest in the skills and health of the work force (less right-win). They do
not emphasise this latter point, but it is a clear implication of their
line of thinking. I suggest it would be useful for elegantly finessing
their contribution and indeed that of all those influenced by Hayek.
Hope these comments are helpful.
How was the Denmark conference BTW?
Chris Burford
London
