Zero-Centric History¶
Reaction – even Neoreaction – tends to be hard on Modernity. God knows (so to speak) there are innumerable reasons for that.
If the criterion of judgment is set by the Occident, whether determined through its once dominant faith or its once dominant people, the case against Modernity is perhaps unanswerable. The Western civilization in which Modernity ignited was ultimately combusted by it. From an Occidental Traditionalist perspective, Modernity is a complex and prolonged suicide.
An Ultra-Modernist, who affirms the creative destruction of anything in modernization’s path, assumes an alternative criterion, inherent to Modernity itself. It asks: What had to happen to the West for it to become modern? What was the essential event? The answer (and our basic postulate): Zero arrived.
We know that arithmetical zero does not make capitalism on its own, because it pre-existed the catalysis of Modernity by several centuries (although less than a millennium). Europe was needed, as a matrix, for its explosive historical activation. Outside in is persuaded that the critical conditions encountered by zero-based numeracy in the pre-Renaissance northern Mediterranean world decisively included extreme socio-political fragmentation, accompanied by cultural susceptibility to dynamic spontaneous order. (This is a topic for another occasion.)
In Europe, zero was an alien, and from the perspective of parochial tradition, an infection. Cultural resistance was explicit, on theological grounds, among others. Implicit in the Ontological Argument for the existence of God was the definition of non-being as an ultimate imperfection, and ‘cipher’ – whose name was Legion – evoked it. The cryptic Eastern ‘algorism’ was an unwelcome stranger.
Zero latched, because the emergence of capitalism was inseparable from it. The calculations it facilitated, through the gateway of double-entry book-keeping, proved indispensable to sophisticated commercial and scientific undertakings, locking the incentives of profit and power on the side of its adoption. The practical advantage of its notational technique overrode all theoretical objections, and no authority in Europe’s shattered jig-saw was positioned to suppress it. The world had found its dead center, or been found by it.
Robert Kaplan’s The Nothing That Is: A Natural History of Zero is an excellent guide to these developments. He notes that, at the dawn of the Renaissance:
Just as pictorial space, which had been ordered hierarchically (size of figure corresponded to importance), was soon to be put in perspective through the device of a vanishing-point, a visual zero; so the zero of positional notation was the harbinger of a reordering of social and political space.
Capitalism – or techno-commercial explosion – massively promoted calculation, which normalized zero as a number. Kaplan explains:
[The growth of] a language for arithmetic and algebra … was to have far-reaching consequences. The uncomfortable gap between numbers, which stood for things, and zero, which didn’t, would narrow as the focus shifted from what they were to how they behaved. Such behavior took place in equations – and the solution of an equation, the number which made it balance, was as likely to be zero as anything else. Since the values x concealed were all of a kind, this meant the gap between zero and other numbers narrowed even more.
That is how zero, as a number rather than a mere syntactic marker, crept in. In three of the elementary arithmetical operations the behavior of zero is regular, and soon accepted as ordinary. It is of course an extreme number, perfectly elusive in the operations of addition and subtraction, whilst demonstrating an annihilating sovereignty in multiplication, but in none of these cases does it perturb calculation. Division by zero is different.
Zero denotes dynamization from the Outside. It is a boundary sign, marking the edge, where the calculable crosses the insoluble. Consolidated within Modernity as an indispensable quantity, it retains a liminal quality, which would eventually be exploited (although not resolved) by the calculus.
The pure conception of zero suggests strict reciprocity with infinity, so compellingly that the greatest mathematicians of ancient India were altogether seduced by it. Bhaskara II (1114–1185) confidently asserted that n/0 = infinity, and in the West Leonhard Euler concurred. (The seduction persists, with John D. Barrow writing in 2001: “Divide any number by zero and we get infinity.”)
Yet this equation, appearing as the most profound conclusion accessible to rigorous intelligence, is not obtainable without contradiction. “Why?” [Kaplan again]
Our Indian mathematicians help us here: any number times zero is zero — so that 6×0 and 17×0 = 0. Hence 6×0 = 17×0. If you could divide by zero, you’d get (6×0)/0 = (17×0)/0, the zeroes would cancel out and 6 would equal 17. … This sort of proof by contradiction was known since ancient Greece. Why hadn’t anyone in India hit on it at this moment, when it was needed?
Kaplan’s proof demonstrates that for zero, peculiarly, multiplication and division are not reciprocal operations. They occupy an axis that transects an absolute limit, neatly soluble on one side, problematical on the other. Zero is revealed as an obscure door, a junction connecting arithmetical precision with philosophical (or religious) predicaments, intractable to established procedures. When attempting to reverse normally out of a mundane arithmetical operation, a liminal signal is triggered: access denied.