M arx's M etaphors ... N ewton's I nfluence on the C apitalist E conomy ..........................1

Introduction................................................................................................................1

Twice Two is Four......................................................................................................4

Young's Science is Social Relations...........................................................................5Newton's Laws and Frames of Reference................................................................6

Engels' Dialectics of Nature.......................................................................................9

Marx's Imaginary Prices...........................................................................................11

Pareto's Mathematical Economics and Fisher's Economic Mechanisms.................13Economic ‘lines of force’: Fisher’s mechanical analogy......................................14

Marshall's Economic Equilibrium............................................................................17

Keynes’ “General Theory”: a “non-Euclidean geometry”.......................................20

Revelli's Economic, Social and Political Spaces......................................................22Fordist <<newtonian>> space...............................................................................22Spatio-temporal revolution....................................................................................24

Cillario's Sense of Cognitive Value..........................................................................27On Reflection, Cognitive Capital Makes Sense....................................................27"... there's someone in my head, but it's not me ..."...............................................28A bit of Nonsense..................................................................................................29

References................................................................................................................30

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M arx's M etaphors ... N ewton's I nfluence on the C apitalist E conomy

Introduction

Question: What was the ultimate aim of Marx's most famous work?

The answer is spelled out very clearly in his Preface to the first German edition of Das Kapital:

“... it is the ultimate aim of this work to lay bare the economic law of motion of modern society ..."

The ultimate aim of this essay is to encourage a closer look at this metaphor, and at other examples of metaphors drawn from the physical sciences and mathematics, in the context of a renewed interest – especially in the Italian literature – in "cognitive capital". I want to situate this critique in a space characterized by four contemporary authors: two Anglo-Saxons (Bob Young being Texan but long resident in England) and two Italians:

Philip Mirowski :

More Heat Than Light: Economics as Social Physics, (1989). New York: Cambridge University Press,. French translation: Paris: Economica, 1998.

Robert M. Young :

Science is Social Relations (1977) Radical Science Journal No. 5: 65-129 Darwin's Metaphor (1985)

Cambridge and New York: Cambridge University Press, 1985. Pp. xx+341

Lorenzo Cillario:

L'Economia degli Spettri (1996) (The Economy of Spectres ... or The Spectral Economy) Capitale e Conoscenza (1998) (Capital and Knowledge)

Marco Revelli:

Economia e Modello Sociale nel Passaggio tra Fordismo e Toyotismo (1995) (in Appuntamenti di Fine Secolo: End of Century Notes: Ingrao, Rossanda)

La Sinistra Sociale (1997) (The Social Left) Oltre il Novecento (2001) (Beyond the Twentieth Century)

Marx's metaphor encourages us – regardless of his subjective intentions – to view the capitalist economy as if it were a mechanical system, governed by Newtonian laws of motion. Philip Mirowski analyzed “Economics as Social Physics” – deliberately avoiding Newton’s name, but concentrating on the energy concept, especially in the history of classical mechanics. The bulk of this present essay, and others in the same spirit, were written in the 1980s, as a hobby, in ignorance of the fact that Mirowski was working with great enthusiasm along the same lines. The reader will find much more detailed and scholarly documentation of the central metaphor in the highly recommended “More Heat than Light”. This essay has more of a marxist bias and looks at some more recent tendencies in Italy, possibly not familiar to an anglosaxon audience. It also serves as a prelude to an essay looking at the metaphor of “economic circuits” – and beyond.

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Going back to the opening question, John Burkett (Dec. 1998) wrote a critical essay precisely on Marx’s Concept of an Economic Law of Motion. I hope it will become immediately clear that I do not consider Marx to have held a merely newtonian or mechanistic view of society, in the common sense of the term "mechanistic". My reading of Marx is that of gramscian historical materialism, and Ollman's "internal relations". Yet I feel, like Mirowski, that this metaphor is not merely rhetorical: it is significant, in the same way that Darwin's metaphor is significant.

Bob Young convincingly documents the importance of Darwin's metaphor: Nature selects variants of species for survival, as if she were a gardner, encouraging better strains of plants – or a farmer breeding improved pedigree animals. He also traced the analogy between commodities and scientific facts, in a most effective way: facts are produced, reproduced and exchanged in capitalist society according to capitalist relations – as commodities. His original intuition seems not to have been developed as far as it might now warrant. The integration of the worlds of academia (production of articles, books, theories, technologies, etc.) and of industry – in its common-sense, classical characterization (production of cars, computers, financial products and consumer services, etc.) – has come a long way. We may return to his formulation as "more than a metaphor". The production, reproduction and exchange of knowledge in general is increasingly integrated in the all-embracing capitalist matrix of social relations. There is a much less rigid distinction now between universities and laboratories on the one hand – and factories and economic markets on the other.

Cillario places great emphasis on the need, in the present context of globalization of the 'post-fordist' capitalist economy, for an analysis which develops Marx's formulation of the labour theory of value to account for the 'cognitive' component. He draws an explicit analogy, as follows:

goods value MoneyMessage sense Information

I do not (yet) find his description of the measure of sense/information convincing: marxist exchange-value is measured in terms of socially-necessary labour time; Cillario is looking for a measure of socially-necessary decisions, incorporated into complex commodities. In fact, we shall have to return to Cillario's assumption that it is essential to have a well-defined measure, as well as well-defined operations of real abstraction and accumulation of this form of capital. Yet the insistence on the importance of a second component, or dimension, in the composition of capital seems well worthy of further analysis.

Revelli, among others, analyzes the socio-political effects/co-relations involved in this phase of capitalism, considered as a total social system. I refer to Revelli, because of his exemplary observation – from close-up, as well as from a certain perspective, as it were, of the rise (and ... dematerialization?) of the FIAT empire. In particular, he makes considerable use of spatio-temporal metaphors. He contrasts the continuous space of fordist capitalism, for which there were no limits (infinite markets, infinite suplies of raw materials, infinite time to ammortize investments), with the discontinuous spaces of the 'network' economy (characterized by its limits). The continuous territories of nation-states, governed by a single sovereign authority, are destined to succumb to societies characterized by discontinuities and multiple authorities operating in overlapping spaces.

In all of these stories, I find a rich use – conscious and unconscious – of mathematical-physical metaphors. In the rest of this essay, I shall attempt to persuade the reader firstly that there is, indeed, something significant – or at the very least, of interest, in the use of these metaphors and analogies; and secondly that it is of considerable political importance to reread and rewrite these analogies such as to avoid the dangers of reinforcing the common sense perception that physics and maths

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describe a pre-existing, value-free real world – and that socio-economic theories are legitimized by their formulation in terms of this hegemonous worldview. In other words, we have to consider the very serious likelihood of a further naturalization of capitalist relations. This "essay", whose central theme was originally conceived by a young mathematical physics post-grad in the late seventies, at the same time as the economist and historian Mirowski was reflecting on the “sense” of a statement like “value must be conserved in the economic system” – will also include some humorous moments. Playing with words – in the spirit of Arthur Koestler's creative suggestion, albeit bourgeois, that there is a link between science, art and humour. The following diversion is just that: a knot of science, art and humour ...

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Twice Two is Four

Dostoyevsky was stone-walled, underground, back in 1846.

The impossible means the stone wall! What stone wall? Why, of course, the laws of nature, the deductions of natural science, mathematics. As soon as they prove to you, for instance, that you are descended from a monkey, then it is no use scowling, accept it for a fact. When they prove to you that in reality one drop of your own fat must be dearer to you than a hundred thousand of your fellow-creatures, and that this conclusion is the final solution of all so-called virtues and duties and all such prejudices and fancies, then you have just to accept it, there is no help for it, for twice two is a law of mathematics. Just try refuting it."Upon my word," they will shout at you, "it is no use protesting: it is a case of twice two makes four! Nature does not ask your permission, she has nothing to do with your wishes, and whether you like her laws or dislike them, you are bound to accept her as she is, and consequently all her conclusions. A wall, you see, is a wall ... and so on, and so on." Merciful Heavens! but what do I care for the laws of nature and arithmetic, when, for some reason I dislike those laws and the fact that twice two makes four? Of course I cannot break through the wall by battering my head against it if I really have not the strength to knock it down, but I am not going to be reconciled to it simply because it is a stone wall and I have not the strength.As though such a stone wall really were a consolation, and really did contain some word of conciliation, simply because it is as true as twice two makes four. Oh, absurdity of absurdities! How much better it is to understand it all, to recognise it all, all the impossibilities and the stone wall; not to be reconciled to one of those impossibilities and stone walls if it disgusts you to be reconciled to it; by the way of the most inevitable, logical combinations to reach the most revolting conclusions on the everlasting theme, that even for the stone wall you are yourself somehow to blame, though again it is as clear as day you are not to blame in the least, and therefore grinding your teeth in silent impotence to sink into luxurious inertia, brooding on the fact that there is no one even for you to feel vindictive against, that you have not, and perhaps never will have, an object for your spite, that it is a sleight of hand, a bit of juggling, a card- sharper's trick, that it is simply a mess, no knowing what and no knowing who, but in spite of all these uncertainties and jugglings, still there is an ache in you, and the more you do not know, the worse the ache.

We have been aching, disgusted with the mess, beating our heads against stone walls for a long time. I believe Dostyevsky himself understood perfectly well that the man of action would accept impossibility without breaking his head against "the way things are" - but that as far as the narrator is/was concerned, he would go rambling on, using his head, knowing very well that sooner or later he would get around the wall. If he found himself going round in circles, he would find some point where he could manage to get over it.

During his enforced rambling, it is quite likely that he would ask himself who built the wall and why. If it was worth building, there is probably something worth seeing - or having - on the other side. Getting somewhat footsore, he might rail against the Enclosures laws, and given enough time and resolve, he might persuade others to act with him to do something about it all ...

But two and two make four. Worse, 2 + 2 = 4.

Patience, we shall get around mathematics, in good time. Possibly starting with the lower wall, curiously neglected by the "Twice two is four!" army: one and one are two.

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Young's Science is Social Relations

But Bob Young exhorted us to move on ... a very long time ago. Better late than never. Mysteries are reified mystifications ...

Nearly there. In the critique of commodity fetishism there are two key aspects: mystification and domination. In science, mystification prevents people from seeing that the scientific world-view and particular facts and theories are forged by their own labour from the unqualified raw materials of uninterpreted and unconstructed nature. ...... People are dominated by their own products, including their philosophies of nature, persons and society, of which the paradigm of explanation of modern science is a central expression and bulwark. Both the mystification and the domination lead people to be the deferential victims of historically - created systems of ideas and their material manifestations. We treat our social relations as if they were laws of nature in economic and social theory. These, in turn, rest on a more profound mystification: treating the laws of nature as though they were laws of nature.

The reader will possibly have had occasion to note how heatedly an opponent of this type of critique will react, when threatened by the affirmation that "laws" of nature are clearly metaphorical. The primary meaning of "law" is emminently social - and is a highly politically sensitive concept. Whose laws? Backed by what "legitimate authority"? It is better to back off, when your normally open-minded liberal friend-or-acquaintance insists that he-or-she is speaking perfectly literally, when referring to laws of nature; that the words mean just what common sense suggests; that they are not metaphors. "Twice two is four!"

Yet Marx's ultimate aim was to lay bare the economic law of motion of modern society. To give a little more context, the whole phrase (Preface to the first German Edition of Das Kapital) reads:

"One nation can and should learn from others. And even when a society has got upon the right track for the discovery of the natural laws of its movement - and it is the ultimate aim of this work, to lay bare the economic law of motion of modern society - it can neither clear by bold leaps, nor remove by legal enactments, the obstacles offered by the successive phases of its normal development. But it can shorten and lessen the birth-pangs."

The sympathetic-but-critical reader will already have objected that Marx had no intention of appealing to Newtonian laws of motion, even though he moved smoothly from the phrase "natural laws of movement" to "the economic law of motion". Hegels' influence, if nothing else, would have guaranteed that any reference to laws of motion – or movement – would evoke concepts of dialectical laws. John Burkett (Dec. 1998) makes the point clearly in his essay Marx’s Concept of an Economic Law of Motion:

Marx, who aspired “to lay bear the economic law of motion of modern society," derived his concept of law from Hegel rather than Newton. Hegel asserted that a law describes the “necessary" motion of a self-moving entity and expresses its internal “contradiction." However, he provided neither clear guidelines for distinguishing necessary from accidental motion nor clear requirements for supporting proposed laws with empirical evidence. His ambiguities provide his followers with great latitude in identifying contradictions, necessity, and laws. [Burkett, Abstract]

Engels spent a lot of effort, in the Dialectics of Nature, criticizing English physicists for not appreciating the universal nature of dialectical laws, which were to be discovered in nature:

“It goes without saying that my recapitulation of mathematics and the natural sciences was undertaken in order to convince myself also in detail of what in general I was not in doubt – that in nature, amid the welter of innumerable changes, the same dialectical laws of motion force their way through as those which in history govern the apparent fortuitousness of events … To me there could be no question of

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building the laws of dialectics into nature, but of discovering them in it and evolving them from it.”[Engels, pp. 17, 19]

Engels’ position is ‘corrected’ slightly by a preface to a collection of his works:

“In Dialectics of Nature, using ample evidence from the history of natural science, particularly from the Renaissance to the middle of the nineteenth century, Engels shows that the development of natural science is determined in the final analysis by practical needs, by production. For the first time in the history of Marxism, he dealt thoroughly with the problem of the relationship between philosophy and natural science, established their interdependence, proved that ‘the metaphysical outlook has become impossible in natural science owing to the very development of the latter’, that ‘the return to dialectics takes place unconsciously, hence contradictorily and slowly’ and that, divested of Hegelian mysticism, dialectics ‘becomes an absolute necessity for natural science … and called on scientists to learn to use the dialectic method consciously.”“Engels elaborated the fundamental postulates of dialectic materialism on matter and motion, on time and space. He gave a specific definition of dialectics and showed that ‘the dialectical laws are real laws of development of nature, and therefore are valid also for theoretical natural science.’”

[Preface to Engels, pp. 8,9]

We shall return to Engels' dialectics after a more careful look at Newton. The choice of language - the formulation of concepts - cannot be regarded as irrelevant. Yet just as Darwin could not - and would not - accept Wallace's advice to avoid the "selection" metaphor, Marx deliberately chooses a language which is guaranteed to evoke the common sense, newtonian, mechanistic paradigm - however much a philosophically-trained minority might want to deny it. Worse, these laws are not to be formulated, developed, or realized (dialectically): they are to be laid bare. Exposed. Uncovered. Revealed. Very undialectically.

The newtonian paradigm is - and already was - over-ripe with metaphors for abstract quantities. The laws of motion are immediately thought of in terms of Force, Mass and Acceleration; position, velocity and rates-of-change ... but the really powerful concept, in today's formulation, is that of ENERGY. The conservation and conversion (transformation) of a universal, abstract quantity "possessed" by a mechanical system: whether considered as a collection of bodies or in terms of fields.

This is the main argument of Philip Mirowski’s book, “More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics” . The concept of abstract exchange-value is analogous to that of energy. Money is a universal equivalent for economics, energy is a universal equivalent for physics. Potential energy is converted to kinetic energy is converted to heat energy is converted to (or from) chemical energy is converted to electrical energy ...

Newton's Laws and Frames of Reference

Any modern schoolchild is taught physics more or less in these terms. The following is taken from the secondary school text book with which I was introduced to the subject. It is appropriate here to use this summary presentation of the three laws, rather than to return immediately to the precise wording in the original. An impressionable young student can almost see a Mosaic figure “expounding” the tablets of the God-given Laws:

“In 1686, SIR ISAAC NEWTON published a work called Principia, in which he expounded the Laws of Mechanics. He formulated in the book three ‘laws of motion’:

Law 1. Every body continues in its state of rest or uniform motion in a straight line, unless impressed forces act on it.

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Law 2. The change of momentum per unit time is proportional to the impressed force, and takes place in the direction of the straight line along which the force acts.

Law 3. Action and reaction are always equal and opposite.” [Nelkon, Parker: pp 12, 13]

Thus, when we consider the “economic laws of motion” of society, we should keep firmly in mind the fact that we are essentially concerned with defining, or extending, a terminology with which we intend to make sense of economic phenomena. The relationships between the terms which we choose are not secondary. In fact, Newton is very aware of the importance of the definition of the fundamental terms he has chosen to use. It is well worth re-reading the opening paragraph of the much-cited "Scholium to the Definitions" of the Mathematical Principles of Natural Philosophy:

"Hitherto I have laid down the definitions of such words as are less well known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common."

We note his careful diction, "... the sense in which I would have them to be understood in the following discourse." The word sense, in Newton's day, as in ours, was used also in the sense of "the five senses": in fact, he refers to "sensible objects". We no longer use that particular expression, but we know what it means ... We also use the same word to describe vectors: mathematical quantities which have magnitude and sense, understood as a synonym for direction. The concept of sense is fundamental to the arguments of this essay, and the "coincidence" of its various meanings will be considered more fully in the consideration of Cillario's "cognitive capital". Here we are focusing on Newton's emphasis on the existence of absolute space and absolute time.

"Absolute space, in its own nature, without relation to anything external, remains always similar and immovable."

There can be no doubt that Newton believes in the real existence of this absolute space: it is not "merely" an ideal construct, it is not imaginary, it is not "even" a platonic form, of which "relative space" or "place" might be a "pale copy". Professional philosophers will bear with me if I use these words "loosely", and in inverted commas: the point here is the link between an essentially metaphysical concept, fundamental to Newton's worldview - and present day common sense. When we refer to something "really existing", we all know what we mean. Newton, in any case, qualifies the concept with the important phrase "in its own nature". Together with the metaphysics of absolute space, we have a strong sense of things which exist in themselves, or more precisely, things which have properties. The word "property" is suggestive, in the context of this essay - but to be fair to Newton and the language of his day, the word "accident" was also used. Nevertheless, we find references to "the properties of spaces", "that part of the ship which the body possesses", "a property of motion", etc.

When we come to his conception of force, we are impressed by the fact that forces are impressed upon bodies. They do not, as we tend to say nowadays, act.

Newton is very concerned with purity: the purity of truth.

"And if the meaning of words is to be determined by their use, then by the names time, space, place, and motion, their [sensible] measures are properly to be understood; and the expression will be unusual and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured

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quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities with their relations and sensible measures."

Hence we can understand why the names of Newton and Leibniz are easily taken as representing diametrically opposed worldviews: Leibniz states quite clearly that

"... As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistences, as time is an order of successions."I have many demonstrations, to confute the fancy of those who take space to be a substance, or at least an absolute being."

Leibniz has a strong belief in a rational God: his "demonstrations", as he immediately declares, rest on his "axiom" of "sufficient reason". God has created everything just so, and he had a reason for everything. In any case, he concludes that

"I find nothing in the Eighth Definition of the Mathematical Principles of Nature, nor in the Scholium belonging to it, that proves, or can prove, the reality of space in itself."

We may comment that far from being a "scientifically objective", materialist worldview, in opposition to that of a creative and active transcendental God, the common worldview of Newton and Leibniz is essentially monotheistic. Things exist, because of God's laws of nature. Nevertheless, the conceptual difference between absolute space and time, on the one hand, and relational space and time, on the other, has had important consequences for thought in general (if such a phrase is permissible) - and few would doubt that Newton's view dominated for a very long time. Summing up:

The newtonian worldview is that of infinite, uniform space and infinite, uniform time - in which systems of massive bodies interact. Space is an infinite container. The physical universe, considered as the totality of massive bodies existing in space, is a closed system. It has always been this way, and always will be: the infinite complexity of the universe, with all its unthinkable details and never-ending physical changes are nevertheless based on universal laws operating in a fundamentally simple and eternal absolute space, "from time immemorial", "from here to eternity". The newtonian worldview is extremely totalizing. It is essentially reductionist: the "competing" paradigms (Darwinian evolution and Freudian psychology) are "bought out" - taken over - subsumed, by the purchasing power of newtonian forces, energy, masses, space and time. Biological and psychic systems, that is, are reduced to manifestations, examples, of physical systems, based on matter and energy. That, at least, is the newtonian – or more precisely, the Laplacian, as Mirowski underlines – pretension. It brings the values of The Absolute and of Objective Reality to their extreme limits. The newtonian world is a "World without end ...". This worldview is radically different from its predecessor: the earthly, sub-lunar and celestial "spheres" were quite separate, quite limited by God's Creation, with their own "proper" laws of nature. And the einsteinian and quantum worldviews are radically different, again.

The question of the fundamental concepts of space and time is particularly relevant to our consideration of Marx's metaphor, and to current analyses of changes in the capitalist world. The argument of this essay is that the newtonian worldview has legitimized the capitalist worldview: they are fundamentally one and the same: there are eternal, transcendent laws operating in an absolute, eternal space. The changes – or transformations – in this worldview will be considered later.

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Engels' Dialectics of Nature

When Marx and Engels were writing, the terminology used to discuss mechanics was somewhat different from that taught in schools today. Engels and his contempories struggled with "two measures of motion" and their distinction:

“… the distinction which Leibniz had already made between dead and live forces: mv is valid for equilibrium, i.e., for statics; mv2 is valid for motion against resistance, i.e. for dynamics. Although on the whole correct, the distinction in this form … is accepted tacitly, it just exists. We cannot alter it, and if a contradiction lurks in this double measure, what can we do about it?”“Thus, for instance, Thomson and Tait say (A Treatise on Natural Philosophy, Oxford, 1867, p. 162):‘The quantity of motion, or the momentum of a rigid body moving without rotation is proportional to its mass and velocity conjointly. Thus a double mass, or a double velocity, would correspond to double quantity of motion.’And immediately below that they say:‘The vis viva or kinetic energy of a moving body is proportional to the mass and the square of the velocity, conjointly.’The two contradictory measures of motion are put side by side in this very glaring form. Not so much as the slightest attempt is made to explain the contradiction, or even to disguise it."

[Engels, p. 92]

Those who are inclined to mock Engels (and present-day post-modernists, perhaps, messing about with mathematics ... "Twice two is four!") - because they know the right answer - might take the time to read the whole passage: I have clearly quoted out of context. He continues:

“In any case, it becomes evident here that mv and mv2 /2 serve to determine two quite distinct processes, but we certainly knew that long ago …”

His contention, rather, is that

“What has to be done is to make it comprehensible why motion should have a twofold measure, a thing which is surely just as impermissible in science as in commerce.”

Which brings us back to the point of all this citation. In any case, physicists will be relieved to know that Engels’ conclusion is that

“… we find that mechanical motion has indeed a twofold measure, but also that each of these measures holds good for a very definitely demarcated series of phenomena. If already existing mechanical motion is transferred in such a way that it remains as mechanical motion, the transference takes place in proportion to the product of the mass and the velocity. If, however, it is transferred in such a way that it disappears as mechanical motion in order to reappear in the form of potential energy, heat, electricity, etc., in short, if it is converted into another form of motion, then the amount of this new form of motion is proportional to the product of the originally moving mass and the square of the velocity. In short, mv is mechanical motion measured by mechanical motion; mv2 is mechanical motion measured by its capacity to become converted into a definite amount of another form of motion. And as we have seen, these two measures, because different, do not contradict each other.“It becomes clear from this that Leibniz’s quarrel with the Cartesians was by no means a mere verbal dispute, and that d’Alembert’s “royal edict” in point of fact settled nothing at all. D’Alembert might have spared himself his tirades on the unclearness of his predecessors, for he was just as unclear as they were.” [Engels, p. 93]

Here we have the heart of the matter. How do we understand or define “unclearness”, and why do we accept the ‘common sense’ judgement against “mere” verbal dispute? Engels - and other great thinkers - were effectively seeking to make sense in a conceptual struggle centered on the following terminology: quantity of motion, vis viva, mechanical motion, measured by, capacity to

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become converted, a definite amount, form of motion, etc. When he slips in the word energy, we are near to grasping the conceptual key – as Mirowski has argued.

Today we use the term energy quite freely. There is a common sense understanding of its meaning, and that meaning has been extended considerably. We all agree that we have understood and explained physical systems when we analyze them, mathematically, using the tools of differential and integral calculus, in terms of the “conservation and transformation of energy”. In the present context, it will be useful to remember the historical development of this fundamental concept, and its analogical correspondence with “measures” of economic systems.

Engels’ fourth chapter ends with two notes, helping to remind us that the English word “work” acts as a kind of conceptual fulcrum in the economics/physics analogy …

1. We get no further by consulting Clerk Maxwell. The latter says (Theory of Heat, 4th edition, London, 1875, p. 87): "Work is done when resistance is overcome," and on p. 183, " The energy of a body is its capacity for doing work." That is all that we learn about it. [Note by F. Engels.]

2. The word "work" and the corresponding idea is derived from English engineers. But in English practical work is called "work," while work in the economic sense is called " labour." Hence, physical work also is termed "work," thereby excluding all confusion with work in the economic sense. This is not the case in German; therefore it has been possible in recent pseudo-scientific literature to make various peculiar applications of work in the physical sense to economic conditions of labour and vice versa. But we have also the word " Werk" which, like the English word "work," is excellently adapted for signifying physical work. Economics, however, being a sphere far too remote from our natural scientists, they will scarcely decide to introduce it to replace the word Arbeit, which has already obtained general currency - unless, perhaps, when it is too late. Only Clausius has made the attempt to retain the expression " Werk," at least alongside the expression " Arbeit." [Note by F. Engels.]

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Marx's Imaginary Prices

To jump again to Cillario's concern with measures of "cognitive capital", we might suggest the following analogy. Just as the Total Energy of a simple, closed mechanical system of particles moving in a conservative field is generally expressed as the sum of its Potential Energy (energy of position) and its Kinetic Energy (energy of motion), or E = P.E.+ K.E., so Total Value of a commodity could be expressed as the sum of a component formed by the incorporation of ordinary labour (value of socially necessary labour time in material production) and a component formed by the incorporation of reflexive or cognitive labour (value of socially necessary labour decisions). In other words, an extended labour theory of value would see ordinary labour creating a value component analogous to kinetic energy and cognitive labour creating a value component analogous to potential energy. The concept of “utility” is avoided, in favour of exchange-value, when thinking in terms of commodities produced by specific labour processes for capitalist exchange.

This could be considered as an alternative to the more immediate – but problematic – suggestion (Mirowski) that economic potential energy corresponds to the neo-classical concept of utility (see Fisher) and so economic kinetic energy should refer to consumer expenditure. In fact, Frank Ackerman (1999) makes the following criticism (anticipated by Mirowski):

In the economic analogy, if utility as a potential field induces predictable movements of individuals in commodity space, the "kinetic energy" of that movement should be consumer expenditure. The exact analogue of the law of energy conservation would thus be the conservation of the sum of utility plus expenditure, an economically meaningless concept. At this point the analogy breaks down.

On the other hand, we might want to go back to Marx, and develop his interesting consideration of imaginary prices when discussing the relation between value and price, in Money, or the Circulation of Commodities “The Measure of Values” (Capital, Vol. 1, ch. 3, section 1):

Magnitude of value expresses a relation of social production, it expresses the connexion that necessarily exists between a certain article and the portion of the total labour-time of society required to produce it. As soon as magnitude of value is converted into price, the above necessary relation takes the shape of a more or less accidental exchange-ratio between a single commodity and another, the money-commodity. But this exchange-ratio may express either the real magnitude of that commodity's value, or the quantity of gold deviating from that value, for which, according to circumstances, it may be parted with. The possibility, therefore, of quantitative incongruity between price and magnitude of value, or the deviation of the former from the latter, is inherent in the price-form itself. This is no defect, but, on the contrary, admirably adapts the price-form to a mode of production whose inherent laws impose themselves only as the mean of apparently lawless irregularities that compensate one another. The price-form, however, is not only compatible with the possibility of a quantitative incongruity between magnitude of value and price, i.e., between the former and its expression in money, but it may also conceal a qualitative inconsistency, so much so, that, although money is nothing but the value-form of commodities, price ceases altogether to express value. Objects that in themselves are no commodities, such as conscience, honour, &c., are capable of being offered for sale by their holders, and of thus acquiring, through their price, the form of commodities. Hence an object may have a price without having value. The price in that case is imaginary, like certain quantities in mathematics. On the other hand, the imaginary price-form may sometimes conceal either a direct or indirect real value-relation; for instance, the price of uncultivated land, which is without value, because no human labour has been incorporated in it.

This passage is extremely suggestive. Today, the "certain quantities in mathematics" to which he refers are indispensable for any consideration of current formulations of "laws of motion". Real numbers have not been made redundant, but complex values are much more useful ... in the real world. This is one of the passages to which Cillario refers, possibly, at the end of his sketch for a program of development of his "cognitive capital" theory:

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"... to elaborate a new formulation of the relation values/prices which is capable of polverizing the discussion which - taking as absolute certain imprecisions in Marx's approach, which were only historically unavoidable - has claimed to demolish the labour theory of value ..."

So another analogy to consider, in the context of Cillario's analysis, is that of complex values. Value could be considered a complex quantity, with a real component (ordinary labour, measured on a social time axis) and an imaginary component (reflexive labour, measured on an orthogonal social axis labelled “social decisions”). Price is the real scalar quantity, expressed in terms of the (abstract) universal money-commodity, and equal to the "modulus" of complex value. We may return to these considerations, in a more "mathematical" context. Here we are emphasizing the analogy between exchange value (or prices) and energy.

The question of the price of uncultivated land will be considered by analogy with energies associated with "rest masses" or constant "field energies": the latter being more than a play on words (what is the definition of a farmer? A man who is outstanding in his field!).

We shall return to Marx, to consider other pointers to scientific metaphors. In particular, the concept of "circuits" and circulation requires a closer look. First, however, we will follow up Newton's Influence, by looking at some non-marxist economists who have had a significant place in the history of economic theory: Pareto, Fisher, Marshall and Keynes.

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Pareto's Mathematical Economics and Fisher's Economic Mechanisms

Irving Fisher, together with the Italian Pareto, may be considered to be two of the more influential pioneers of the application of mathematical analysis to economics. In fact, Fisher’s Mathematical Investigations in the Theory of Value and Price can be taken as an anglo-saxon frame of reference for the development of economic thought along mathematical–physical lines.

Perhaps he is today most immediately remembered for a simple algebraic equation:

“… Fisher’s equation of exchange MV = PT, where M stands for quantity of money, V for velocity, P price level, and T turnover …” [Hansen, p. 28]

Anyone who has had even a school-level exposure to physics may note a certain coincidence, in his choice of symbols. Newton’s famous second law of motion defines the FORCE acting on a body as identical to the rate of change of its MOMENTUM, expressed as exactly this product of its mass M and velocity V. When he goes on to express MV as the sum (from i = 1 to n) of piqi we cannot help thinking (rightly or wrongly) of classical mechanics’ generalized momenta, pi , and coordinates, qi .

The coincidence becomes more significant when we read the second paragraph of the Preface to his major work:

“How few scholars of the literary and historical type retain from their study of mechanics an adequate notion of force! Muscular experience supplies a concrete and practical conception but gives no inkling of the complicated dependence on space, time, and mass. Only patient mathematical analysis can do that. This natural aversion to elaborate and intricate analysis exists in Economics and especially in the theory of value.” [Fisher, p. 3]

Angelo Guerraggio, in "Forms and Contents in the Modern Development of Mathematics”, points out the importance of the Italian school of mathematical economics, represented by Vilfredo Pareto (1848-1923).

"In Pareto (and in this phase of development of marginalism) the analogy between mechanics, which, in the positivistic culture becomes the reference point for every science, performs a clarifying and legitimizing action. Just as mechanics begins its discourse with <<the abstract entity called material point, and then another which has the name of rigid system or solid body>>, so mathematical economics starts out from the abstraction of homo oeconomicus. This latter constitutes the principle element which positivist philosophy defines as natural, neither socially nor historically determined. His behaviour can be described a priori, obeying precise laws similar to those of a material point or an element of the celestial system."

After the death of Pareto,

"The main figure in Italian mathematical economics is now represented by Luigi Amoroso, who characterizes his research project as a dynamization of the pareto schema: <<just as for rational Mechanics, mathematical Economics contains two parts: a static part and a dynamic part. The mathematical formulation of the fundamental principles of static economics is established exhaustively in the work of Vifredo Pareto. Economic dynamics is much less developed>>. In this short quotation the two characteristics appear - the analogies between mechanical and economic phenomena and the translation of Pareto in a dynamic key - which constitute the calling card for a research in which one notes increasingly frequent signs of repetitivity and which, in any case, fails to recover the previous freshness."

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To make the point even more strongly, returning to Fisher's turn-of-the-century work, we have only to read the first paragraph of Chapter 2, entitled in bold print:

“MECHANISM.”

“Scarcely a writer on economics omits to make some comparison between economics and mechanics. One speaks of a ‘rough correspondence’ between the play of ‘economic forces’ and mechanical equilibrium. Another compares uniformity of price to the level-seeking of water. Another (Jevons) compares his law of exchange to that of the lever. Another (Edgeworth) figures his economic ‘system’ as that of connected lakes of various levels. Another compares society to a plastic mass such that a ‘pressure’ in one region is dissipated in all ‘directions’. In fact the economist borrows much of his vocabulary from mechanics. Instances are : Equilibrium, stability, elasticity, expansion, inflation, contraction, flow, efflux, force, pressure, resistance, reaction, distribution, (price) levels, movement, friction.”“The student of economics thinks in terms of mechanics far more than geometry, and a mechanical illustration corresponds more fully to his antecedent notions than a graphical one. Yet so far as I know, no one has undertaken a systematic representation in terms of mechanical interaction of that beautiful and intricate equilibrium which manifests itself in the ‘exchanges’ of a great city but of which the causes and effects lie far outside.” [Fisher, p. 24]

And again, in the paragraph numbered 10, he leaves little doubt as to his passionate vision of the role of the economist and of his new calling:

“The effort of the economist is to see, to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.” [Fisher, p. 119]

We may comment that this visionary and evangelical style, combined with firmly grounded and durable content, seems to be an increasingly devalued commodity among Fisher’s many descendants.

Economic ‘lines of force’: Fisher’s mechanical analogy

One of the interesting aspects of Fisher’s use of this particular analogy, centered on the concept of ‘force’, is that he seems ready to anticipate the development of Newtonian concepts towards the more modern formulation in terms of field theory; although the details of this imposition are easily criticized. His mathematical background becomes evident when we find reference not only to the concept of lines of force but to the differential operator (“grad”), familiar to present day students of fluid dynamics and vector fields:

“… the ‘lines of force’ are drawn perpendicular to the indifference loci. The direction of these lines of force are alone used in the formulae … which determine equilibrium … Thus we may dispense with the total utility density and conceive the ‘economic world’ to be filled merely with lines of force or ‘maximum dierections’ …”“… Even if we should give exact meanings to the length of these arrows (so that the equation U = F(I) should signify not only that for each position in the economic world a definite ‘maximum direction’ exists but also that the rate of increase of utility or the length of the vector along this line is given) – even then there would not be a complete primitive U = (I) unless certain conditions were fulfilled.” [Fisher, p. 88]

Fisher refers explicitly, here, to Osborne Differential Equations (p.12). He concludes that

“… If U is not distributed in the above manner integration is impossible and there is no such quantity as total utility or gain.”

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His underlining of this possibility must be considered significant. The reasoning behind it and his all but explicit formulation of the problem in field theoretic terms, by which the question becomes that of characterising the ‘economic field’ as being conservative or otherwise, cannot be dismissed as mere rhetoric, or empty analogy.

We must leave speculation as to the possible ramifications of this conception of ‘economic field theory’ to a later phase of our general consideration of analogies between physics and economics. The terms of this analogy are traced very clearly in Fisher’s work, however. The correspondence between utility – historically a crucial concept of classical economics – and energy – the central concept of modern physics – is spelled out explicitly, term for term, leaving no room for doubt about the author’s intentions. The following excerpts are taken from the first two paragraphs of chapter 3, entitled:

“MECHANICAL ANALOGIES”

“For each individual situated in the ‘economic world’, suppose a vector drawn along each axis to indicate the marginal utility in that ‘direction’ …”“… This corresponds to the mechanical equilibrium of a particle the condition of which is that the component forces along all perpendicular axes should be equal and opposite …”“… If marginal utilities and disutilities are thus in equilibrium ‘gain’ must be a maximum. This is the mere application of the calculus and corresponds exactly to the physical application of the calculus which shows that at equilibrium the balancing of forces implies that energy is a maximum. Now energy is force times space, just as gain is marginal utility times commodity.”

[Fisher, p. 85]

Fisher goes on to tabulate the terms of his mechanical analogy: “In Mechanics

A particle corresponds toSpace “ “Force “ “Work “ “Energy “ “

“… The ‘total energy’ ( the work done upon theparticle) may be defined as the like integral with respect to impelling forces.

In Economics

An individual.Commodity.Marg.ut. or disutilityDisutilityUtility.”

The total utility enjoyed by the individual is the like integral with respect to marg. Utilities.”

[Fisher, pp. 85, 86]

Again, one can certainly question the rigour of his definitions on the mechanical side – apprentice mathematical-physicists might amuse themselves by checking appropriate modern definitions. Fisher may be criticized for forcing (excuse the metaphor) certain aspects, but there can be no doubt about his being serious in making this analogy. His prime concern, as an economist, is indeed to “see, to picture the interplay of economic elements”.

A fine example of this ‘prime concern’ is to be found in an important decription of the process by which economically interacting individuals, and coalitions or couplings of individuals, arrive at what is now termed the core of an economy. As Edgeworth himself wrote (1925), when considering “the differential calculus applied to economics”:

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The particles of an economic system neither cohere as a solid, nor collide with the independence of a gas. Their liquid movements are comparable to a dance in which youths and maidens move in unison; harmoniously, but subject to a change of partner.” [Edgeworth, p. 369]

We may comment, at the risk of spoiling the poetry of this vision, that a physicist would resolve this mixed metaphor by substituting the dancing youths and maidens with dancing electrons and protons. The well-known particles of atomic physics ‘neither cohere as a solid, nor collide with the independence of a gas’, but form and break bonds, are excited to levels from which they return to their ground state, radiating energy – and they combine their states of spin according to rules which rival the formality and ingenuity of any human choreographer.

Alternatively, one should seriously consider the concept of “liquid movements”, and examine the implications of a conscious and coherent development of fluid dynamic analogies. The notion of fluid pressure (alluded to by Fisher, earlier), compressibility ( . U “div U“) and fluid rotation ( x U “curl U”) should be considered in the context of Fisher’s appeal to the operator “grad”, scalar potentials and vector fields…

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Marshall's Economic Equilibrium

As confirmation of Fisher’s claim that “the economist borrows much of his vocabulary from mechanics”, let us take a quick first look at another very influential author, again following in Pareto's footsteps, to whom we shall return when we examine “the mutual debts of biology and economics”. In fact,

“Alfred Marshall, on whose Principles of Economics all contemporary English economists have been brought up …” [Keynes, p. xxv]

in his introductory chapter “On Markets” in the crucial Book 5 (‘General Relations of Demand, Supply and Value’), opens with some

“Biological and mechanical notions of the balancing of opposed forces”.

After making the analogy between the growth of a firm and that of a man, he notes that

“… to prepare the way for this advanced study we want first to look at a simpler balancing of forces which corresponds to the mechanical equilibrium of a stone hanging by an elastic string, or of a number of balls resting against one another in a basin.”“We have now to examine the general relations of demand and supply; especially those which are connected with that adjustment of price, by which they are maintained in ‘equilibrium’. This term is in common use and may be used for the present without special explanation. But there are many difficulties connected with it, which can only be handled gradually: and indeed they will occupy our attention during a great part of this Book.” [Marshall, p. 323]

We may comment that the difficulties connected with the concept of equilibrium have occupied the attention not only of Marshall and Fisher. Keynes himself, having opened his Preface (to the German and Japanese editions) of the General Theory of Employment, Interest and Money with the name of Alfred Marshall – as the most authorative representative of that “classical” economics which he intended to revolutionise – is far from criticizing the concept of equilibrium as requiring “special explanation”. Bent Hansen, in A Survey of General Equilibrium Systems (1971), for example, opens with a consideration of …

“The Concept of Equilbrium”“General equilibrium theory is, in this book, conceived of in a very broad sense, including those dynamic models to which the concept of equilibrium is applied. For this reason, and also because to some the word ‘equilibrium’ may connote political harmony and ring of apologetics, it may be helpful to begin by explaining exactly what is meant by equilibrium, and how it is used in economic analysis …”

“Equilibrium and economic theory”“Equilibrium plays an important role in economic theory, and although many economic problems cannot reasonably be dealt with in terms of equilibrium theory, it remains an indispensable tool. It has often been criticized as being a purely static concept with no relation to the evolutionary world in which we live. This criticism is entirely beside the point, however …”“First it should be understood that equilibrium is essentially a dynamic concept, and sometimes problems in static equilibrium theory can be answered only if the dynamic nature of the equilibrium is considered … The concept of economic equilibrium has been taken from classical mechanics, where it belongs to the theory of dynamics. It is loosely defined as a state wherein the forces that operate on a point (or body) ‘cancel each other out’. A more precise definition states: ‘Any configuration of a rigid body, or of a system of bodies, is said to be one of equilibrium if the body or the system can remain idefinitely in this configuration under the forces acting upon it’ (Rutherford, 1957, p. 119). The concept of economic equilibrium also requires specification of the forces working in or upon the economic system.”

[Hansen, p. 1: my emphasis]

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The following, similar passage, from a 1965 essay by Chipman on The Nature and Meaning of Equilibrium in Economic Theory, explicitly recognizes the existence in mathematical physics of at least three distinguishable types of ‘stability’: a concept closely linked to that of ‘equilibrium’:

“Equilibrium – meaning a balance of opposing forces – is a concept as fundamental in economics as it is in physics. The reason it is so fundamental is that the concept is much more complex than might at first be supposed.”“In its most narrow meaning, equilibrium is a state of affairs in which things are at rest. It is obvious, however, that things which never change would not warrant much study. The real content of the equilibrium concept is to be found not so much in the state itself as in the laws of change which it implies; that is, in the tendencies to move towards it, away from it, or around it. I say ‘it’ guardedly; it would be more accurate to say ‘them’, for we cannot rule out in advance the possibility of multiple equilibria. That is not all: we cannot be sure that equilibrium always exists; thus it happens, paradoxically, the importance of the concept derives precisely from the negative statement that no equilibrium is possible.”“Fruitful analysis of equilibrium therefore requires analysis of stability conditions. The word ‘stability’ has a variety of senses. Sometimes, as in the phrase ‘stable price level’, it signifies a state of relative constancy, that is, a state in which prices remain within certain prescribed limits. In this sense it is a kind of approximate equilibrium; it finds a close counterpart in what is known in mathematical literature as ‘Lyapunov stability’. More usually, in technical economic discussions, it signifies asymptotic stability, a tendency to move towards equilibrium when the latter has been subjected to small disturbances; there is also ‘global stability’ which signifies a tendency to return to a particular point of equilibrium even after large disturbances. All these concepts are related, but distinct. For the most part, it should be clear, from the context of what follows, which concept is intended; in technical discussions it will usually be asymptotic stability.”“The above remarks are of a formal nature. Our interest in this essay is on the substantive issue of the extent to which the equilibrium concept applies to the study of the balance of economic conflict …”

[Chipman, pp. 435, 436]

The author goes on to relate the concept of equilibrium to the roots of economic history. We note in passing the introduction here of the concept of

“a general equilibrium that results from the interaction of individuals.”

This is an image common to the classical physics of ‘billiard ball’ dynamics and, more significantly, to large areas of modern fundamental particle physics. We shall return to this aspect of analogies between economics and physics, in subsequent discussions of field theory and quantum mechanics.

“The basic idea expressed here is that of a general working out of economic forces, a general equilibrium that results from the interaction of individuals each of whom strives for his own advantage. In the famous words of Adam Smith (1776, p. 400), ‘each individual intends only his own gain, and he is in this … led by an invisible hand to promote an end which was no part of his intention’. This notion of a natural harmony and order goes back at least to the laissez-faire doctrines of François Quesnay and his Physiocrats, and can be traced back still further to the medieval concepts of natural law (cf. Schumpeter, 1954 …)” [Chipman, p. 437]

As a neat epitaph to these historical words of wisdom, Chipman comments, in his section on ‘The equilibrium of expectations’:

“If people truly accept their fate as inevitable, then the chances for a social order – equilibrium – are undeniably good. But as Mrs. Robinson (1951, p. 189) has remarked: ‘The hidden hand will always do its work, but it may work by strangulation.’” [Chipman, p. 462]

To return to Marshall, we may assume from the following passage and its footnote, in an appendix on the “limitations of the use of statical assumptions”, that his understanding of the mathematics of equilibrium, though perhaps not arriving at the rigours of today’s theory of systems of differential equations, was nevertheless not completely superficial:

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“For indeed, though in the account of the oscillations of demand and supply about a position of stable equilibrium, which was given in the third chapter, it was tacitly implied, as is commonly done, that there could be only one position of stable equilibrium in a market: yet in fact under certain conceivable, though rare, conditions there can be two or more positions of real equilibrium of demand and supply, any one of which is equally consistent with the general circumstances of the market, and any one of which if once reached would be stable, until some great disturbance occurred.” [Marshall, p. 806]

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Keynes’ “General Theory”: a “non-Euclidean geometry”

At this point, it is legitimate to ask whether the foregoing observations are of any real interest, other than that of mere academic, historical curiosity. An affirmative answer clearly depends on a conviction that theory influences practice, and that economic theory has in fact been shaped to a significant extent by formulation in mechanical – mathematical terms. To support the former condition, we may refer to J.M. Keynes, noting the centrality yet again of the concept of “equilibrium”, and making no excuse for quoting the entire first chapter, entitled:

“THE GENERAL THEORY”

“I have called this book the General Theory of Employment, Interest and Money, placing the emphasis on the prefix general. The object of such a title is to contrast the character of my arguments and conclusions with those of the classical [1] theory of the subject, upon which I was brought up and which dominates the economic thought, both practical and theoretical, of the governing and economic classes of this generation, as it has for a hundred years past. I shall argue that the postulates of the classical theory are applicable to a special case only and not to the general case, the situation which it assumes being A LIMITING POINT OF THE POSSIBLE POSITIONS OF EQUILIBRIUM. Moreover, the characteristics of the special case assumed by the classical theory happen not to be those of the economic society in which we actually live, with the result that ITS TEACHING IS MISLEADING AND DISASTROUS IF WE ATTEMPT TO APPLY IT TO THE FACTS OF EXPERIENCE.”“[1] ‘The classical economists’ was a name invented by Marx to cover Ricardo and James Mill and their predecessors, that is to say for the founders of the theory which culminated in the Ricardian economics. I have become accustomed, perhaps perpetrating a solecism, to include in ‘the classical school’ the followers of Ricardo, those, that is to say, who adopted and perfected the theory of the Ricardian economics, including (for example) J.S. Mill, Marshall, Edgeworth and Prof, Pigou.”

[Keynes, p.3: my emphasis]

The first capitalised passage is indicative of Keynes’ acceptance of the mathematical-physical terminology; the second leaves no doubt about his awareness of the PRACTICAL implications of changes in the dominant economic world view. The thesis that Keynes’ own contributions to economics have indeed influenced real, historical, economic and political behaviour needs no elaboration.

It may be of interest to note, in this context, Keynes’ concern to explain the title of his most famous and influential work. He could not have been unaware of the relatively recent, much-publicized and far-reaching theoretical revolution in fundamental physical theory. Einstein, in the first years of the twentieth century, overthrew the classical Newtonian mechanics, based on a Euclidean geometry – where space, time, mass and energy were essentially mutually independent concepts – with the publication of his General Theory of Relativity. This ‘general theory’, as is well known, includes not only his own, recently-formulated ‘Special Theory’, but also Newtonian mechanics itself as “special cases”. We may remember, in passing, the previous reference to Fisher’s first tentative use of field-theoretic concepts, noting that the Einsteinian formulation depends on this view of a gravitational field, as being associated fundamentally with a non-Euclidean space-time continuum.

“(Hence) Euclidean geometry does not apply (to K’). The notion of co-ordinates defined above, which presupposes the validity of Euclidean geometry, therefore breaks down (in relation to the system K’) … So there is nothing for it but to regard all imaginable systems of co-ordinates, on principle, as equally suitable for the description of nature …”[Einstein, p. 116]

And thus it comes as rather less than a total surprise to find, from an author who is in general somewhat less given to poetic and fanciful passages than was the case with Marshall and Fisher, the following suggestive rhetoric:

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“The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight – as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required today in economics. We need to throw over the second postulate of the classical doctrine and to work out the behaviour of a system in which involuntary unemployment in the strict sense is possible.”[Keynes, pp. 16, 17]

Keynes must have seen himself as a revolutionary – at least in the sense of rejecting the orthodox economics of his day. The famous “Popper – Kuhn” debate of the 1970’s centered on the difference of views concerning the nature of scientific development. Popper’s concept of “progressive tinkering” as an essentially reformist activity – using the idea of falsibility to progress towards increasingly "less false" theories – was contrasted with Kuhn’s insistence on the separation of periods of “normal science” from the shorter, traumatic periods of “revolution”. It is a matter of political and historical interpretation as to whether Keynes’ General Theory should be considered revolutionary, in this sense. A marxist would probably emphasise the practical effects of Keynes’ work, as merely reinforcing (reforming) the capitalist world’s capacity to govern, in the strictest sense of the word, and to manage the inherent contradictions of such a system by open, centralized intervention in the so-called “free markets”.

The revolution in scientific thought represented by Einstein’s general theory of relativity, on the other hand, is by now widely accepted as such – in that the very formulation of the problem requires a different language with respect to that of classical mechanics. Even a superficial glance, by a non-specialist mathematician, at the mathematical tools involved – tensors and generalized differential operators, instead of the familiar algebra of quantities like m, x, v and F – gives an immediate impression of moving in a different world.

And this is perhaps a key to understanding the question of “progressive tinkering” versus “revolutionary change”. Just as in a material productive process, the invention of a new tool or technology can often be linked to a revolutionary period of change in economic relations, the development and acceptance of new theoretical tools characterises a period of ‘revolutionary science’. In this sense, mathematical economics was revolutionary, as was the introduction of dialectic, class analysis – as instruments in the process of understanding economic relations. Keynes, while explicitly modifying an “axiom” of classical economics, and redefining the domain of its application, introduces little or nothing in terms of language, or methodology. His famous multiplier, for example, is essentially an ad hoc addition to the economist’s toolbox – as its generic name suggests.

We will leave Keynes here, returning to him – via Von Hayek and Tustin – in the essay on Prices Re-valued as Information: Circuit Elements.

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Revelli's Economic, Social and Political Spaces

At this point, we finally come to Revelli's relatively recent writings – which move us on from a narrowly economic point of view to a more general consideration of socio-economic evolution. He uses several 'scientific' metaphors, essentially as rhetorical device, for 'picturing' the changes he wants to describe. In “La Sinistra Sociale”, (1997) he particularly likes the French choice of "crystal and smoke", for example. I apologize for my rather literal translation of all that follows – obviously the reader is encouraged to read Revelli in the original Italian version if possible.

"The third point where the <<fordist paradigm>> is broken concerns, in fact, the principle of rationality incarnated in it: the passage from a rigidly structured system ... to a fluid and mobile system ..."The French, in order to express the depth and scope of this discontinuity, have invented the antithetical image of crystal and smoke. This is a metaphor drawn from the biological sciences, but it serves perfectly to represent the new industrial divide ..."A crystal, with its closed structure, which is petrified in its linear geometries, expresses the fordist philosophy well, where the business, starting precisely from the diamantine hardness of its own productive nucleus, from the metallic linearity of its own factory geometries - in a word, from the perfect and absolute rationality of its own productive <<order>>, unmodifiable because technically <<perfect>> in itself -, could aspire to <<ordering>> the surrounding social universe. To project its own <<internal statute>> onto it, simplifying its structure, selecting components from it, decomposing vital worlds along rectilinear vectors, exactly as a crystal decomposes and projects light. Smoke, on the contrary, fully evokes the protoform, changeable, ungraspable, in some ways <<opportunist>> character of the new business logic, in which the structures disolve into thin air, expanding into it and occupying every angle, adhering to the currents which cross the environment, allowing itself to be infinitely diffused, without opposing any resistance but seconding and <<putting to value>> every new configuration. Destructuring where the crystal structured. The one dissipating where the other aligned. Complicating and confounding where, instead, the old industrialism simplified and spread. Gramsci, as early as the beginning of the thirties, was able to ascribe to fordism just such a <<poietic>> power in the social field ..." [p.68]

A rigid, structured, fordist mode of production structured social space and ordered it in its own image: like a crystal structure splitting white light and projecting a spectrum ... Post-fordist production is nebulous, ever-changing, smokey. It adapts its forms to its environment ... no longer structures social space, but is structured by it ...

Revelli speaks loosely of a biological metaphor, but the power of this description is essentially physical. The fordist - newtonian - image is of massive, rigid bodies (factories like stars or planets - and later, Revelli will describe FIAT as a "supernova"!) moving in space (social space, like newtonian or euclidean space pre-existing). This is the point. The analogy then suggests the move to post-newtonian, or einsteinian and quantum worldviews: before we go on to references to the more popular "theories of chaos" (evoked by Revelli immediately prior to the above-quoted section).

Fordist <<newtonian>> space

So let us look more carefully at Revelli's use of spatio-temporal metaphors: used with much greater explanatory force, and consistency, than is the case with the more "literary" metaphors. In the second part of his book - entitled Dal Fordismo al Postfordismo - he emphasizes the factors which spell the end of the fordist dream ...

" ... of an unlimited development: with unlimited availability of the workforce, unlimited availability of raw materials, unlimited willingness to consume. ... The idea of the <<absence of limits>> had in fact been constitutive of the fordist model."

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We note that there is a profound, qualitative difference between "motion in the absence of limits" (boundary conditions only "at infinity") - and limited, or bounded motion (systems "in a box", or moving in a "potential well", etc.). The first lead to continuous solutions - the concept of continuous space, if you like; the second - important in the quantum worldview - lead to discontinuous or discrete solutions. And sure enough, Revelli, cautiously, touches on this metaphor - when he moves on to the section entitled From Centralization to the Network Enterprise, to describe the old fordist factory "space":

"In some ways, one could say, a perfect <<newtonian>> space, open in the urban territory as an area of gravitation and of monopolization of <<producing>>; as a place of concentration - and rationalization - of the entire productive network which was previously dispersed in a myriad of small workshops, which anticipates, on the crucial terrain of the fordist <<spatial revolution>>, another typical corollary of its organizational model: industrial giganticism."

In fordist society, especially in Company Towns, to be more concrete - in the fordist phase of capitalism - we picture systems of relatively small but well-defined and limited economic masses (small businesses, enterprises) gravitating around the massive productive nucleus (River Rouge, Mirafiori). We even have the "satellite" structure typical of central forces (like the gravitational and electromagnetic forces) - familiar from text books on the solar system, as well as the popular picture of the "atomic" model:

"[companies of various dimensions] ... spatially arranged in concentric circles ... from the closest, grouped around the mother-factory like the medieval servants of the glebe were gathered together at the foot of the lord's castle, to the most distant and delocalized ones, projected into the far reaches of the world."

We might comment, in passing, that this poetic reference to feudal structures is by no means out of place. We are always concerned with the dominant mode of production and hegemony, but old forms never completely disappear. Gramsci's reference to 'layers' of society, and fossilized forms is exemplary in this context. Anyone living through this particular change of phase in the capitalist mode of production cannot fail to note strong aspects of neo-feudalism. The lords of the manor may dress in different ways and have more modern castles - and feuds - but they are quite clearly recognizable. This is particularly familiar in Italy: we are all well aware of Il Gattopardo: "cambiare tutto per lasciare tutto come prima".

We should also comment, referring back to the image of a central force, on the emphasis Revelli places on technology - in my opinion running the risk of an excessive technological determinism in an otherwise convincing historical materialist analysis.

"Fordism, by now there are no doubts about it, rooted its own <<organizational paradigm>> in what had been the hard core of the technological leap of the beginning of the century: electrification". Its organizational model was, so to say, <<centered on electricity>>: because electrification - guaranteeing a diffusion of energy which was homogeneous and free from problems of <<distance>> ..."But also, and above all, because electricity offered production its own <<organizational model>>; its own <<systems vision>>, which can be summed up in the idea of a motive force emanating from a single center and such as to ennervate a complex system, distributed over a definite space, producing synchronous effects in every point of it, connected to the center.. A model, therefore, by its own <<nature>> - by virtue of the character itself of the technology of production and distribution, based on a "powerhouse" in which power is generated and accumulated, and on a network of cables leading out from it ..."

The author immediately goes on to contrast this "centralized" model with the newer "network" model, based on ("rooted in"?) electronics and information technology, by contrast with the electrification model. The problem here is to explain what is meant by "rooted in": hence the importance of insisting on the role of metaphor and analogy.

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But let us concentrate here on the newtonian worldview. Individuals (social individuals) perceive social space as the space in which these massive bodies (fordist factories) are situated. There is one, infinite, homogeneous, isotropic space in which individuals (like particles) interact: and the social field (like the gravitational field) is determined (structured) by these massive bodies.

The concept of isotropy - and space as being homogeneous - is important: we were taught in secondary school physics that "space looks the same, whichever way you look, and wherever you go", or less vaguely - it does not make any difference to the laws of physics where you carry out an experiment - provided, of course, that you are clear about your frame of reference. As Mirowski admirably explains, this isotropy - or symmetry - is correlated with important laws of conservation. In particular, Newton's first law (of inertia) is considered as an expression of the principle (or axiom) of the conservation of (linear) momentum - which is itself based on the "common sense" axiom of the conservation of inertial mass: mass can neither be created nor destroyed, in a closed system.

Time is considered in the same way, although in the newtonian worldview, space and time are absolutely independent concepts. And we postulate that time is also "isotropic": it does not make any difference to the laws of physics when you carry out an experiment. And this is correlated with the priciple (or axiom) of the conservation of energy: the total energy of a closed system can neither be created nor destroyed.

Spatio-temporal revolution

In the third part of his 1997 work, in particular (La Fine del Territorio - The End of Territory), we find extended reference to "spatial revolution", "spatial isomorphism", "the radical transformation of space and of its social perception". The second section of this third part is entitled Spazio economico contro spazio politico (Economic space against political space). The analysis is material, concrete, and of great importance for the understanding of epocal changes in the nation-state. Our interest here, however, is with the conceptual framework, or metaphorical tools. We note first, then,

"... the modern conception of political space ( a <<homogeneous>> space, defined by certain confines, qualified by <<isomorphic>> operation of the norm)."

Although the term isomorphic (the same form) should probably read isotropic (the same in all directions), Revelli's formulation is clearly newtonian (political space is isomorphic to newtonian space). There is an epocal change in this conception of space:

"... in the new globalized economy, <<flows>> (transterritorial by definition) instead of <<places>> are the privileged seat of efficacious decisions (flows of money, flows of information, flows of organizational resources ...)"

and this reminds us of vectors, vector spaces and vector fields - as opposed to scalar points. It also encourages us to think towards the next physical paradigm - that of electronic circuits, based on electromagnetic fields, but let us concentrate, still, on the newtonian worldview and gravitational fields.

"... territory regresses from <<constituent>> factor for social action to <<constituted>> factor."This is, in many ways, a revolution. If territory, up to now, could be considered for good reasons as a prius with respect to the human activities carried out in it (in particular with respect to the economic activities) - if, that is, it could constitute itself socially as an environment which was tendentially unmodifiable or anyway not easily modifiable in its strong viscosity -, from now on it will tend with

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increasing frequency to appear as a mere <<object>> of them. As a variable whose extension, density and geometry can be from time to time decided according to criteria which are different from those which had consolidated its scansions (substantially nature and history), and implicated directly with the real powers of the time: technical factors [la tecnica] and the economy."

If we translate the poetic Italian style into a more anglosaxon prose, it is clear that we are thinking in terms of a revolution in the newtonian conception of space. As we sketched earlier, newtonian space and time exist independently of the existence or otherwise of material bodies, fields or physical activity in space and time. Newtonian space is a container: as J.J.C. Smart commented, "a container in the sense that the sea contains fish, rather than a cigar box which contains sweets". Not so with post-newtonian, einsteinian space-time. We can simplify, at the risk of upsetting serious mathematical-physicists, by saying that matter shapes or forms the fabric of space-time. Space-time is inconceivable, has no meaning "outside" of the distribution of real masses. Vice versa, mass can be imagined as the condensation (clearly a metaphor, but why not) of the space-time continuum. The popular picture of einsteinian gravitation is that of mass warping the fabric of space-time, and singular points of the gravitational field corresponding to point masses: gravitational force is linked inextricably with (non-euclidean) geometry. It is extremely useful, at this point, to turn to Einstein's own autobiographical notes, remembering our previous considerations of Newton's absolute space and time:

The equations of mechanics ... claim validity only when referred to ... the 'inertial systems'. In this the co-ordinate system as bodily object is without any significance. It is necessary, therefore, in order to justify the necessity of the specific choice, to look for something which lies outside of the objects (masses, distances) with which the theory is concerned. For this reason 'absolute space' as originally determinative was quite explicitly introduced by Newton as the omnipresent active participant in all mechanical events; by 'absolute' he obviously meant uninfluenced by the masses and by their motion."

Uninfluenced by the masses ... uninfluenced by the masses … rings a bell …

Further on, returning to Revelli, we find territory (and let us keep in mind our picture of newtonian space) described as a "direct factor of production", or

"... generator of social energies destined to be <<consumed>> in the production process ...""... territory constitutes, thus, the place where the local resources of sociality are mobilitated and <<consumed>>; that is, metabolized and transfered to the inside of the abstract circuits of the global economy."

The generation of social energy recalls the idea of field energy and, again, points forward to the electromagnetic metaphor. Einstein again:

"The factor which finally succeeded, after long hesitation, to bring the physicists slowly around to give up the faith in the possibility that all of physics could be founded upon Newton's mechanics, was the electrodynamics of Faraday and Maxwell. For this theory ... showed that there are electromagnetic phenomena which by their very nature are detached from every ponderable matter - namely the waves in empty space which consist of electromagnetic 'fields'. ..."One got used to operating with these fields as independent substances without finding it necessary to give one's self an account of their mechanical nature; thus mechanics as the basis of physics was being abandoned, almost unnoticeably ..."Since then there exist two types of conceptual elements, on the one hand, material points with forces at a distance between them, and, on the other hand, the continuous field. It presents an intermediate state in physics without a uniform basis for the entirety, which - although unsatisfactory - is far from having been superseded ..."

Revelli's metaphor becomes mixed: one pictures a Leviathan devouring social resources, and at the same time we are referred to abstract circuits. Later again, we find a contrast between the biological

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- or organic - metaphor, and the physical - or atomic - metaphor of individuals (much referred to in Revelli's previous writings) :

"The reference anthropology is not so much that of the organic community, of Blut und Boden , but rather that of the market. Of competitive individualism. Of the unrelated singularities which Aldo Bonomi conceptualizes in the image of the <<multitude>> (mass now devoid of sociality). It is this - mercantile, atomistic, competitive - the <<natural>> substrate ..."

The author concludes this important section with a reference to Silvio Trentin's "liberare e federare" (Liberate end federate). Revelli sums up the need

"To emancipate growing areas of human inter-relations ...""... Because if the prevailing logic, today, is the economization of the world as a direct product of the parallel mondialization of the economy - if, that is, what we are facing is in the first place the colonization of our vital worlds by the generalized economy -, then the answer cannot but proceed by way of a first, radical process of liberation of the collective imagination ...""... Only in this way, through the reconstruction of a close-knit network of communication between self-organized realities, capable of posing themselves as territorial counter-powers and to produce, in this way, new relations and new <<sense>> (prefiguring and anticipating a radical <<social elsewhere>>), will we be able to counter the disaggregating tendency implicit in the multiplication of <<horizontal conflicts>>."

We will leave Revelli's work here, recommending the reader to "metabolize" his main message (whether or not one regards the role of these metaphors as significant and useful), because this is an excellent point to link these considerations up with Cillario's analysis of 'cognitive capitalism'.

This essay was written before the publication of Revelli’s controversial – and more well-known – work entitled “Beyond the Twentieth Century – the decline of the labour civilization”. Italian marxists debated his theses hotly, in the daily newspapers (liberazione, il manifesto). Over-simplifying, a major bone of contention was Revelli’s affirmation that Lenin (and those who followed) swallowed whole the mathematical-physical model of production identified with the name of Taylor, as universally valid and necessary for a socialist or communist economy, without understanding its far-reaching implications. Revelli also seems to portray the ‘revolutionary’ change to an information-technology economy in overly optimistic terms. The viewpoint of this essay is that of noting how the continued use of mathematical-physical metaphors in all of these stories – histories or analyses – cannot be passed over as mere rhetorical device.

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Cillario's Sense of Cognitive Value

On Reflection, Cognitive Capital Makes Sense

Revelli spoke of "producing sense" - and this is a key concept for Cillario. The English expression, whereby sense is made - as in "I'm not sure that what you're saying makes sense ..." - is not available to an Italian writer. Translated word for word, that English phrase means something quite different to an Italian: “fa senso” means “it makes you feel squeamish” … more or less! Gramsci contrasted good sense with common sense, as is well known - but the idea was to discover it (good sense), rather than to make it. In Italian, things have - or do not have – sense: “Non ha senso!”.

To begin in the middle of Cillario's exposition, and to underline the fact that he is at pains to find the right "weight" to ascribe to what he clearly considers to be of value (excuse the term) to current analysis of capitalist society, we note his appeal to a sense of cautionary confidence in the basic concept of "cognitive capital" (again apologizing for my literal translations):

"As with the other forms, to cognitive capital one should ascribe a character which is historical and determined within capitalist social relations. No millenary and totalizing pretension should be associated with the idea - in itself correct - that the "cognitive" paradigm is a strong paradigm of the current mode of production."To the new concept should be given all that - and only that - which is due to it. Overloading it with responsibility, with improper generalizations, one would obtain the effect of impoverishing it."

This sober passage comes immediately before the "fulcrum" of his reasoning - and immediately after a phrase which reminds us of previous considerations about value being analogous to energy:

"Industrial capital is one thing, financial capital is another, ... and yet another is capital, which contains [racchiude = encloses?] in itself, unitarily, the different forms of its manifestation and the different modes of labour structuring which pre-side [over/under] it. [vi presiedono]"

Indeed, for physics: gravitational potential energy is one thing, electromagnetic energy is another, and yet another is energy, which expresses unitarily in itself the different forms of its manifestation and the different fields which pre-side it ...

Cillario, an engineer, writes in a very clear, structured way. An apprenticeship in the traditional, logical, scientific method makes itself felt strongly. When he writes the crucial final subtitle in his central chapter (1.5 Cognitive Capitalism) - Value and sense - he instinctively lists the fundamental tennets of his approach, much as Keynes did when "overthrowing" the "euclidean" geometry of the classical economists - though Cillario resists the temptation to number them ...

"The labour theory of value, together with the analysis of capitalist labour processes, constitutes the fulcrum around which the marxian theory of capital revolves."The changes in production and circulation which have come about since the middle of the last century make it necessary to reckon again both with the analysis of labour processes and with the concept of value."Problems are raised of the same nature with respect to the questions which have already been examined in the previous points. With the labour theory of value, too, i.e. taking into consideration the historical changes and the scientific difficulties, one glimpses that it is ripe for a reformulation; it should be configured as a <<theory of sense-value>>.""As is well known, the labour theory of value in Marx starts from the definition of the double nature of goods [commodities] - use value and (exchange) value; having placed the magnitude of value as the basis of the measure of value, this magnitude in its turn being quantifiable through the length of labour time

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contained in it, Marx arrives at the analysis of the <<value form>>, from which springs the explanation of the nature of money - as <<general form of equivalent>> - in mercantile and capitalist society."

He then enumerates 3 fundamental axioms on which the production of capital is based, before introducing his new concepts:

"In order to define the capitalist dynamics of valorization of the new conditions of labour processes (in which the <<reflexivity of labour>> and the <<pysychic dissociation>> act, as interiorization of social dynamics) it is necessary to make use of the concepts of <<sense>> and <<cognitive value>>."

After a kind of "schema" of a "micro-process" - by way of example of the mechanism - he focuses on the duality of the two concepts:

"<<Sense>> is necessary for defining the form assumed by <<value>> in the worker's mental process. <<Cognitive surplus value>> quantifies the expropriation of wealth giving the measure of cognitive productivity of capital."Summing up: between the cognitive component of value and sense there is continuity in the metamorphosis. Value transforms into sense - and sense, expanded, transforms into cognitive value, which increases the invested value ..."Potentials and problems open up, starting from the definition of the chain of homologies:

goods [commodities] value moneymessage sense information

"In particular:1. Information figures as <<communicative money>>. Not <<commodity>> but <<money>, in that it is

considered from the point of view of the form, not the content of knowledge. Analogously to the functions of money, it assumes the functions of <<measure of sense>> and of <<means of circulation of messages>>.

2. There opens up the problem of the measure of value, marked by a dialectical contradiction inherent in cognitive labour ..."

And here we will leave Cillario's "L'Economia Degli Spettri" - because I feel that he himself recognized that the "problem" was far from being dealt with in a satisfactory way, at this stage. The potential was clear. The problem of "measure" remained … a problem.

It is more than a metaphor - or pun - to say here that it is all a question of making sense of our world.

"... there's someone in my head, but it's not me ..."

Revelli will recognize that Cillario's analysis of psychic dissociation makes sense. He describes the "division of labour" extending to the division of a worker's psyche - leading to "the splitting of the atom", or rather of the individual - and the subsequent release of productive energy.

Those of us working in one of the key roles in this labour process, as systems analysts, surely recognize the truth - and the potential - in what Cillario is trying to describe - and capitalize - through his own reflexive labour. I doubt that I could do my job without a strong sense of "making sense" of the productive processes I am paid to analyse - and transform ... My psychic dissociation is strongly developed. I, like many of my "conscientious" colleagues, know very well what it is like to skip coffee breaks (despite legislation requiring us to interrupt continuous work at terminals!) and to wake up at night with the (unpaid) "solution" to yesterday's (paid) intellectual labour. I feel good about making sense of production systems - exactly the way I feel good about making sense of Marx's Metaphors, Revelli's writings and Cillario's challenge to "make sense". It does not make much difference, at this point, psychically, to realize that I am selling myself to work for the king of Prussia, while "creating" social capital intended to serve as munition against his sovereignty.

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We formulate solutions, taking informed action, on information collected formally and informally from workers invited to inform us about their reflections on their productive processes - using technical formalisms, like structured analysis and design techniques. SADT, for example the IDEF formalism we used to use, is the result of other workers reflecting on OUR systems analysis experience - as a production process. Our activity has been analyzed, abstracted, accumulated, reproduced, valorized. No doubt about it, cognitive labour is a very real, important concept.

We are surely concerned here with a revaluation of Aristotle's formal cause. Material and efficient causes were valorized in previous phases of Capitalism; final causes remain problematic (the final aim of capital is to reproduce and expand capital, if we are prepared to resort to the biological metaphor). But we have only to return to Guerraggio's essay on "Forms and Contents ..." to understand the pressure on and by mathematics for a preponderantly formal explanation of the world: physical, economical and social.

A bit of Nonsense

Cillario's concern with the measure of sense and/or information leads him into a position that risks turning the analysis into a farce. He wants to arrive at a convincing definition of "Information as money", and ends up with a fetishism for the bit.

"... the bit poses itself as the form of general equivalent of communicative exchange and interchange within the world of signs and messages ..."... the bit, this <<conoscitive atom>>...""... From the historical and social point of view, the bit has descended like manna from heaven to strengthen and coordinate capitalist control over labour and communication processes ..."

Unfortunately, other writers who take up Cillario's analysis do not seem to regard this "misplaced concreteness" as a problem, criticizing instead a presumed misunderstanding of the marxist concept of "real abstraction". Yet if one could imagine someone seriously measuring the labour time incorporated in a commodity (despite the evident redundance of such an operation) - critics of postmodernism in particular and of social scientists in general will have a field day imagining our capitalist friends counting the bits of a new automobile or package holiday. On the other hand, it is quite amusing to think that Bill Gates' wealth is composed not only of Mega-dollars but also of Gigabytes. Databank managers calculating interest rates on loans of Euro-kilobytes.

What is interesting in the analysis of cognitive capital is best understood in terms of metaphor and analogy - not in terms of bits. The operations of abstraction and accumulation described by Cillario are useful and make sense. The question of valorization of reflexive labour - of its incorporation in commodities (goods and services, produced according to the more-or-less invariant capitalist mode of production, to be exchanged in markets mediated by money) - can be analyzed without counting bits.

At this point, we will leave our marxist struggle to make sense, for the time being, and take a closer look at one of the most influential conservative economists, Von Hayek. Ironically, we find some extremely useful bits in his formulation of the price system as a system for communicating economic information.

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References

Burkett J., (1998). Marx’s Concept of an Economic Law of Motion:

Chipman J.S., (1965). The nature and meaning of equilibrium in economic theory (in Price Theory (2nd ed.), edited Harry Townsend (1980) Penguin Books)

Cillario L.: per una Teoria del Capitalismo cognitivo (Towards a Theory of Cognitive Capitalism)(1996) L'Economia degli Spettri (The Economy of Spectres ... or The Spectral Economy) (1998) Capitale e Conoscenza (Capital and Knowledge)

Edgeworth F., (1925). Papers Relating to Political Economy, MacMillan, vol. II

Fisher I., (1892). Mathematical Investigations in the Theory of Value and Price, Yale University Press,

Hansen B., (1971). A Survey of General Equilibrium Theory (in Price Theory (2nd ed.), edited Harry Townsend (1980) Penguin Books)

Keynes J.M., (1936). The General Theory of Employment, Interest and MoneyIn Collected Writings of John Maynard Keynes, Vol. 7 - The General Theory, edited by Donald Moggridge, London: Macmillan for the Royal Economic Society

Marx, K., (1867). Capital (Vol.1)

Mirowski P., (1989) More Heat Than Light: Economics as Social Physics, New York: Cambridge University Press. French translation: Paris: Economica, 1998.

Revelli M. : (1995) Economia e Modello Sociale nel Passaggio tra Fordismo e Toyotismo (in Appuntamenti di Fine Secolo: End of Century Notes: Ingrao, Rossanda)(1997) La Sinistra Sociale (The Social Left): Bollati Boringhieri(2001) Oltre il Novecento (Beyond the Twentieth Century):Einaudi

Young R.M.: (1977) Science is Social Relations Radical Science Journal No. 5: 65-129(1985) Darwin’s Metaphor Cambridge and New York: Cambridge University Press, Pp. xx+341

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