The region of Tuscany in Italy introduced banking and accounting to the Western world. But it would be wrong to hold that country totally responsible as they in turn took those concepts together with most of our mathematical terms and axioms from either Arabic or Hindu sources.
The word algebra is taken from the title of a ninth century book, Al-gebr we’l mukabala, by an Arab mathematician, Alkarismi, who gave his name to the algorithm. The Al-gebr is in turn based on the work of a Hindu mathematician and astronomer Brahmagupta, who consolidated India’s unwieldy arithmetical principles in the form of twenty basic processes. This hybrid system was introduced to Italian trading states by Arabic scholars where it was used as a system of notation to calculate and record results.
India had developed a written abacus, using its written numbers instead of beads, giving them the same signs regardless of the positions they assumed, and using 0 or a dot to indicate an empty column of the virtual abacus. Whereas in the West with the use of an abacus, they used different signs for numbers with different place values, such as 1 for one, and X for ten in Roman numerals, the Hindu system used the same digit, 1, to compose one, ten, a hundred and so on.
In Europe they were counting in bundles of Roman sticks I, II, III, etc., and these new alien Sanskrit figures were opposed by the Church as an infidel system which could pose a threat to the stability of the Western world. It wasn’t until the Italian Renaissance traders overcame the opposition of the Church that the numbers were introduced. By 1478 a manual printed in Italy, on one of the new Gutenberg presses, announced that “Numeration is the representation of numbers by figures, by means of ten letters or figures as shown, 1,2,3,4,5,6,7,8,9,0. Of these the first figure, 1, is not called a number, but the source of number. The tenth figure, 0, is called a cipher or ‘nulla’ (in Italian), i.e. the figure of nothing, since by itself it has no value, although when joined with others it increases their value.”
In addition to its numbers, the new arithmetic introduced negative numbers and irrational numbers, as well as zero and the decimal point. These features were crucial to the networks of banking and trade, which themselves were new concepts to the West. Once this new system was introduced it allowed for simple matters like the keeping of accounts, setting prices, doing deals and working with large numbers, which would have been impossible with Roman numerals.
In the West one was a problem where they had been used to its symbolic importance as an individuated and indivisible entity, the Sanskrit one functioned in relation to the other eight digits but as it closely resembled the old Roman line it was easily subsumed into the old paradigm.
Zero posed a very different threat. When it first appeared in the new string of infidel figures, the Church fathers did all they could to keep it out of the world which then revolved around one and its multiples; one God, one truth, one way and one one. However, they were concerned zero wasn’t really there at all and imagined it to be unimportant. If zero was nothing it should be as easy to absorb as the Sanskrit one had been. Sure enough, zero was appropriated as a sign of absence, nonbeing, and nothingness. The ancient unity of something and nothing was apparently undisturbed.
If zero is supposed to signify a hole, a space, or a missing piece, and one is the sign of positivity, digital machines turn these binaries around. In both the electronic systems and the punched cards of weaving machines, a hole is one, and a blank is zero and therefore there are two missing elements. It was no longer a world of one and not-ones, or something and nothing, thing and gap, but rather not-holes and holes, not-nothing and nothing, gap and not-gap.
Zero was always something very different from the sign which emerged from the West’s inability to deal with anything which is neither something in particular or not at all. And it is true that holes are never simply absences of positive things. Holes are not absences or spaces where there should be something else; a hole is a positive particle before it is the absence of a negatively charged electron, and the movement of electrons toward the positive terminal is also a flow of holes streaming back the other way. Holes are charged particles running in reverse. For quantum physicists, holes are not the absence of particles but particles travelling faster than the speed of light.
So it is a globalised universe we live in; we have Italy to thank for having such an open-minded trading nation-state; we have the British to thank for inventing the Difference Engine, the Analytic Engine (hence the computer) and the World Wide Web; we have the Arab and Indian sub-continent to thank for it’s system of numbers in general and it’s zeros and ones in particular for programming those computers; and the United States to thank for their vision and exploitative brilliance for putting it all together to make it a truly Digital World.