Now, I will admit that it is not very often that the term superposition is applied to a capitalistically-produced commodity by Marxists. In fact, I think I may be the only student of Marx who has ever used the two terms together in the same sentence, although I am prepared to be wrong about this.
The term is usually applied to physical systems that exhibit certain unique properties and some might even question that the term applies to the case of the capitalist mode of production for good reasons.
Well, according to the Wikipedia:
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
Note the term in the definition given by the Wikipedia: “linear systems.”
The sorts of systems characterized by superposition relations are typically highly mechanistic, linear systems. System of this type, according to the Wikipedia, exhibits certain other unique characteristic properties:
A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions (that is, for all inputs, all scaling constants and all time.) (my emphasis)
The additivity property states that if the same amount is added to both sides of an equation, then the equality is still true. And, according to Wikipedia, “In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities.”
Obviously, the capitalist mode of production is not, by any stretch of the imagination, a linear, mechanistic system; otherwise how could there be crises — periodic breathtaking cascades of disequilibrium that shake the entire system to its core? And since the mode of production evidently is not a linear system, it must be the other kind: a non-linear, apparently chaotic, system.
It would appear, then, that at first blush the term, ‘superposition’, probably could not be applied to the capitalistically-produced commodity, although the object appears to exhibit both the characteristics of a commodity and the characteristics of a capital — a commodity form of capital, with a price that appears to be determined by two — not one — laws of motion.
All is not lost, of course.
We could model the mode of production as a superposition through some sort of linearization, the way bourgeois simpletons try to do in microeconomics. It does seem to work for them at some level. But, seriously, how would it help us to understand what is, in reality, a crisis-prone system that is inevitably headed for collapse, by modeling it as a linear, mechanistic system?
So, instead, I want to try another tack.
As the saying goes among Marxists of a certain bent,
“Let me problematize the concept of linearity for you.”
While some might object that capitalistically-produced commodity qualifies as a linear, mechanistic system, most might accept the proposition that this characterization could apply to an ordinary commodity. As Marx defines the ordinary commodity, it is a superposition of two attributes: use-value and labor-value. The use-value of the commodity are its physical characteristics that satisfy a human want; while its labor-value is the socially necessary labor time required for its production.
As far as I can tell, these are linear relations.
For instance: If, in society, the need for a particular commodity increases, the labor time required for its production should increase. Likewise, if the need for a commodity decreases, the labor time required for its production likewise decrease. On the other hand, if the labor time required for production of a commodity should decrease, more of that commodity should be available to satisfy that particular social need — all else held equal. And vice versa.
(There may be objections and I would like to hear them.)
In any case, suppose we could reduce the Law of Value and the Law of the Average Rate of Profit to one and the same law: namely, the highly linear, mechanistic Law of Value. If we could do this, perhaps, we might be able to show how a linear, mechanistic, process like the Law of Value transitions at some point into a complex non-linear, apparently chaotic system characterized by two apparently contradictory laws that is hurtling toward its demise.
Now, is it possible to produce an apparently highly chaotic mode of production from a mode of production that is highly linear?
I think so.
At least this is the argument made by the physicist, Stephen Wolfram, last year in a popularization of his groundbreaking idea on the subject: Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful
Wolfram begin with a very counterintuitive idea for those not familiar with Marx’s theory:
Back when I used do theoretical physics for a living, I must admit I didn’t think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. And somehow I think I imagined that if there was a fundamental theory, it would inevitably be very complicated.
But in the early 1980s, when I started studying the computational universe of simple programs I made what was for me a very surprising and important discovery: that even when the underlying rules for a system are extremely simple, the behavior of the system as a whole can be essentially arbitrarily rich and complex.
And this got me thinking: Could the universe work this way? Could it in fact be that underneath all of this richness and complexity we see in physics there are just simple rules? I soon realized that if that was going to be the case, we’d in effect have to go underneath space and time and basically everything we know. Our rules would have to operate at some lower level, and all of physics would just have to emerge.
You can probably see where I am going with this, right?
Wolfram is talking about one or a few simple rules underlying the entire universe — a hugely chaotic system, composed of everything from tiny subatomic particles to massive black holes with the mass of a 100 billion stars at the center of galaxies.
You probably can see that his reasoning also applies to the rules underlying any complex, non-linear, apparently chaotic system, including the capitalist mode of production. Which means, if we dig a little, the appearance that prices of capitalistically-produced commodities are determined by two laws is probably just a little misleading.
So let’s see if we can reduce those two laws to just one law.
In his polemic, Karl Marx and the Close of His System, Bohm-Bawerk’s levels the charge against Marx is that Marx initially begins with the Law of Value in Volume 1, where the exchange value (or price) of the commodity is a direct expression of its value. Marx then withdraws this Law in Volume 3 to describe how the mode of production operates in its full scope, when he equally forcefully argues that the prices of commodities are determined by their costs of production plus an average rate of profit:
I do not think that any one who examines the matter impartially and soberly can remain long in doubt. In the first volume it was maintained, with the greatest emphasis, that all value is based on labour and labour alone, and that values of commodities were in proportion to the working time necessary for their production. These propositions were deduced and distilled directly and exclusively from the exchange relations of commodities in which they were “immanent.” We were directed “to start from the exchange value, and exchange relation of commodities, in order to come upon the track of the value concealed in them” (i. 23). The value was declared to be “the common factor which appears in the exchange relation of commodities” (i. 13). We were told, in the form and with the emphasis of a stringent syllogistic conclusion, allowing of no exception, that to set down two commodities as equivalents in exchange implied that “a common factor of the same magnitude” existed in both, to which each of the two “must be reducible” (i. 11). Apart, therefore, from temporary and occasional variations which “appear to be a breach of the law of the exchange of commodities” (i. 142), commodities which embody the same amount of labour must on principle, in the long run, exchange for each other. And now in the third volume we are told briefly and drily that what, according to the teaching of the first volume must be, is not and never can be; that individual commodities do and must exchange with each other in a proportion different from that of the labour incorporated in them, and this not accidentally and temporarily, but of necessity and permanently.
I cannot help myself; I see here no explanation and reconciliation of a contradiction, but the bare contradiction itself. Marx’s third volume contradicts the first. The theory of the average rate of profit and of the prices of production cannot be reconciled with the theory of value. This is the impression which must, I believe, be received by every logical thinker. And it seems to have been very generally accepted. Loria, in his lively and picturesque style, states that he feels himself forced to the “harsh but just judgment” that Marx “instead of a solution has presented a mystification.” He sees in the publication of the third volume ” the Russian campaign” of the Marxian system, its “complete theoretic bankruptcy,” a “scientific suicide,” the “most explicit surrender of his own teaching” (I’abdicazione piu esplicita alla dottrina stessa), and the “full and complete adherence to the most orthodox doctrine of the hated economists.”
I have said in the previous posts that there are two laws that appear to determine the price of a capitalistically produced commodity — the Law of Value and the Law of the Average Rate of Profit. Bohm-Bawerk seems to agree with me in the above passage.
But what, in reality, is the Law of the Average Rate of Profit?
If you are just a teeny bit sharper on the uptake than Eugen von Bohm-Bawerk — who clearly was a couple of bottles short of a six-pack when it came to figuring out the really simple stuff — you have probably guessed that in reality, this is only an illusion.
Marx himself said so; he always insisted there was only one law: the Law of Value.
And for good reason: The Law of the Average Rate of Profit is just the Law of Value applied to the one commodity that is unique to the capitalist mode of production: labor power.
What makes the capitalist mode of production distinct from simple commodity production in general is that, with the advent of the capitalist mode of production, labor power, the source of value, has itself become a commodity.
All the rules governed by the Law of Value as described in chapter one of Volume 1 still apply, but these rules are now applied to this unique capitalist commodity with historically unprecedented implications for commodity production and exchange itself.
Well let me mention a couple of reasons.
One I can think of off-hand is that labor power is not really an individual commodity; it is a directly social commodity. Among other things, this means that although labor power consists of many separate individual labor power, its true power is that it can cooperate socially. In fact, it acquires power through cooperation, power that is greater then mere additive properties of typical linear processes. Ten labor powers are not simply ten times more productive than one labor power, but 20, 50 or one hundred times more productive. And with greater numbers comes increasing heterogeneity and sophistication of organization, a division of labor — an attribute not typically found in linear homogeneous processes.
These last two attributes tend to undermine the linearity of the mode of production and lend it a chaotic character. I could probably go on, but I just wanted to show that it is possible to derive a non-linear, highly chaotic process, from a linear, highly mechanistic one.
In Bohm-Bawerk’s polemic, there is no way the Law of Value as Marx described it in chapter one of Volume 1, could give rise to the Law of the Average Rate of Profit as he describes it in chapter ten of Volume 3 because it never occurred to B-B that the Law of Value could be applied to the source of value itself as it is in Marx’s Labor Theory of Value. In fact, B-B didn’t believe there was something called value or labor power.
But once we apply the Law of Value to what is, in Marx’s theory, the source of value — the exact same rules, mind you, and no more — what is up until then a linear, highly mechanistic mode of production is converted into a highly chaotic system, with the potential for periodic, breathtaking cascades of disequilibrium that shake the entire system to its core and ultimately dooms it.
So, let’s touch on why in my next post.