In the past I've written about the importance of cuts within digitality. A cut indicates difference, difference of whatever kind. But a cut is not enough for a full-fledged digital system. Cuts will not spontaneously assemble into a regular series, and cuts will not calculate or compute, at least not if they remain in the larval stage of heterogenous difference. An additional operation is necessary to convert a cut into the basis monad for constructing a regular discrete framework. A number of names have been proposed for this second event: semioticians describe the emergence of a master signifier, Marxists refer to the selection of a general equivalent, in contemporary finance the name is tokenization. In each case, something valuable is converted into a new form where it may be expressed through, and measured in terms of, a specific representational basis monad.
Jean-Joseph Goux penned a useful summary of this operation in his important 1968 essay titled "Numismatics," first published as two parts in late 1968 and early 1969, where the refrain "Gold, Father, Phallus, Monarch, Language" announced the scope of his ambition.
By the mid 1960s Althusser had warned readers of Marx to avoid the opening sections of Capital, vol. 1 due to their purported philosophical excesses, a Hegelian admixture being the chief hazard. Yet Goux brazenly rejected Althusser's advice--and we shall follow his example--knowing that Marx's theory of value, which opens Capital, was absolutely crucial.
The apotheosis of the monad initiates, in fact, from rather humble beginnings. Goux began from the fact of exchange, be it commodity exchange, as it was for Marx, or the circulation of signifiers within language, as it was for Saussure, or the way in which the unconscious might substitute one thing for another, as charted in Freud's theories of displacement, condensation, and repression.
Indeed as Marx had argued already a century earlier, exchange generates an encounter between an exchange-value and a use-value, two radically different types of things that nevertheless act as proxies for each other. Or as Marx put it, "the physical body of commodity B becomes a mirror for the value of commodity A" (Capital, vol. 1 [1976], 144).
A mirror? Does the digital start with the optical analog? For Marx, the marketplace entailed the criss-cross of two desires, not unlike an object and its reflection in a mirror. One party, the seller, possesses a commodity but doesn't need it, and in gazing into the "mirror" of potential buyers sees a variety of proxy objects--things he needs but does not possess--all of which could potentially be swapped with his own unneeded item. Whereas, the opposing party, the buyer, sees everything in reverse reflection: what was first seen by the seller as a swappable abstraction is, in fact, the buyer's real possession, and from the buyer's perspective the other object now acts as the proxy.
In this way, the marketplace is a complex dance of needing but not possessing, and possessing but not needing.
Yet Marx's key insight was to venture beyond mere objective description, and to show that objects themselves are not, as it were, objective. The same object will necessarily take on different valences depending on what perch it occupies according to a specific participant's perspective. What a buyer may recognize as a use-value, a seller might recognize as an exchange-value; the same object will necessarily take on more than one form, which was precisely the kind of alchemical metaphysics that Althusser warned readers to avoid.
And yet abstraction itself is not immaterial or fictitious, nor is it an imaginary mental projection, much less a kind Platonic form. Abstraction is a real, material form directly evident within the real, material marketplace. To insist on this realness, Alfred Sohn-Rethel would later adopt the expression "real abstraction."
The replacement, the substitute, or the proxy--forms that emerge from exchange--these were the most important forms for Goux. They reside at the crux of value, value within economic exchange, but also within other spheres of circulation including sign systems and the libidinal economy of the unconscious.
Or, as Goux put it, "[m]etaphors, symptoms, signs, representations: it is always through replacement that values are created" (9). (I posted previously about how this opens up all sorts of quagmires around value and meaning; I'm still wrestling with the consequences of this, given that Goux seems to contradict Marx on whether value derives from circulation.)
Meanwhile, a marketplace is typically teaming with participants, where the many bivalent encounters between sellers and buyers proliferate into a multiplicity of exchanges. And the contingent marriage of resemblance tying a specific use-value here to a specific exchange-value there (for the purposes of swapping) evolves into an omni-market where any object could, in theory, be swapped with any other object.
At that very stage, a single object is plucked out of circulation in order to serve as the mirror for all other objects. And why not? If all is exchangeable with all, then any could be the sole reflection for all the rest.
The mirror becomes a measure. What was once an analog reflection of all others is now a quantitative yardstick with which a tally may be reckoned. This item is now "2 of x." That item is now "5 of x."
Or, as Hegel put it in The Science of Logic: "Whatever is, has a measure" (288).
Marx's name for this special object, the commodity plucked out of circulation, was the "general equivalent," because it was the thing nominated to serve as the equivalent (the value proxy) for any and all other objects within the general sphere of exchange.
In digital nomenclature, Marx's general equivalent is, of course, the basis monad itself, that is, the foundational element used to construct a regular discrete framework. It is labeled "discrete" simply due to the governing influence of the monad: values are not generic, continuous magnitudes, but rather values measured as multiples of a specific discrete one (the general equivalent), just as an integer (7) is, strictly speaking, the multiple of a one (7/1).
Goux's brilliance was to show how this same monadic logic exists across a variety of different symbolic economies. Hence within commodity circulation, the general equivalent takes the name money. But within the political sphere the general equivalent might be called the sovereign. In weights and measures, it could be a polished lump of platinum dubbed kilogram. In the libidinal economy of the family, it condenses into the father. In sexuality, the phallus. In racialization, whiteness.
To Goux's "Gold, Father, Phallus, Monarch, Language" we will affix another general equivalent, Digit.