A valued German merchant in the 14th century wanted to give his son useful instruction for the administration of his own company, but in his region, the teaching that was given in the quadrivium seems not to have gone beyond addition and subtraction. Only in Italy would he find something more, where the new system went as far as multiplication and division. These operations, which nowadays are quietly taught to children in the first elementary grades and which many would like to teach in advance in kindergarten, long ago required the services of a specialist. An operation that today takes only a few minutes, in the 15th century required many days of strenuous work.
The multiplication that was carried out with Roman numeration, to give an example consisted of a series of successive doublings until the desired multiplier was reached, while the division was limited to giving one half of a dividend, so that one could reach, without any hurry, a fourth, an eighth, and so on, but it was very problematic to obtain a fifth and other quotients of even divisors, not to mention decimals, which at that time were still inconceivable. With such a system of signs, each letter was used to express a fixed numerical value immediately recognizable in itself, regardless of its position: 1 was always 1, X was always 10, C was always 100, and so on.
To obtain intermediate serial values between X and its duplications, for example, to represent 34, the sign X was duplicated - as everyone knows - twice more, the V = 5 was added and a unit was subtracted, preceded by a 1. The XXXIV was in the end, in itself, impossible to multiply and divide, unless it was transformed into manipulable quantities, that is, into concrete symbols (pebbles, balls, cubes, etc.), as was done using the ancient abacuses that survived until the sixteenth century, and then represented again with Roman letters the result obtained. However, the reduced need for calculation in the early Middle Ages, given the scarcity of exchange and circulation of currency, did not suffer much from this rudimentary technique, which, however, threatened to become paralyzing a little later.
Although at the end of the 15th century the use of the Roman abacus, more or less modernized again, and the calculation with the fingers was still common in the workshops of craftsmen, merchants had already leaped almost centuries earlier: in fact, Arabic numeration was commonly used in various commercial charts already in the early years of the fourteenth century, practically since the notaries ceased to deal, as generic scribes, with the registers and charts of merchants and were replaced by specialized employees, who were trained in the new schools of arithmetical accounting techniques and who were, therefore, better equipped and educated in the new tasks.
Notaries, on the other hand, were trained for a more prestigious role, similar to that of the present, that is to say, to draw up official acts and as guarantors of contracts and wills. It is therefore understandable that they were concerned with preserving their style, even elevated to such a distinctive feature of their profession as writing; it was to be noted that notarial writing, conceived for acts in Latin, did not change even when drafting documents in the vulgar language. And how could it be demanded that in such a high and lasting form, signs such as Arabic numbering, reminiscent of the proof of issue or even the letters of the workshop managers, should be inserted?
Despite everything, the algorithm or arithmetic of Indo-Arabic origin did not have a triumphant reception, on the contrary. The struggle between the "Abaquists", who defended the Roman tradition, and the "Algorithmists" or new Abaquists, who advocated its reform, lasted from the eleventh to the fifteenth century and, as always, passed through all stages of obscurantism and reaction. In some countries Arabic numerals were excluded from official documents; in others, they were banned altogether.
Nevertheless, as is always the case, the prohibition did not lead to their abolition, but only to the spread of their secret use, of which ample evidence has been found in 13th-century Italian archives: from them it is known that Italian merchants used Arabic numerals as a kind of secret code. In other words, the relative clandestinity with which the algorithmists operated in the service of merchants, money changers and others, made their activity a little riskier, but it constituted and protected it exactly like a secret of the clerk's office.
Thus, in the delay of this slow and contrasting consolidation, the numbers were all the time to undergo successive graphic stylizations, until they reached their definitive form imposed by the reproduction of the printing press after the 15th century, thanks to which these numbers had a representation identical to the present one, except for a few nuances. In the seventeenth century all the rules that are currently taught in elementary schools, concerning operations with whole numbers, ordinary fractions, and decimals, were defined and were already being disseminated without any prohibition or resistance.
The Roman numbering system survived to the present day, but only on tombstones, on documents that were intended to guarantee a sign of authenticity, or as an alternative to the Arabic numerals, but as early as the thirteenth century it was radically abolished in the practice of accounting and technical-scientific techniques. The difficulties in calculating with the old system were so great that those who were able to make accounts were considered to possess almost supernatural powers, as can now be understood.
Hence it is understandable that whoever had more or less magically learned to handle this complicated practice, after a long and stormy apprenticeship, did not look too lovingly on those who demonstrated the possibility of introducing very simple, transparent, and rapid procedures.
It was, therefore, a real revolution, probably greater given the times, than the one represented today by the spread of electronic calculators. The introduction of the digit 0 will constitute the real great leap in the quality of calculation and will make it possible to dispense with the abacus, since it was sufficient by itself to indicate the position of the tens, hundreds, etc., making it possible to carry out calculations with written figures, instead of doing it with objects (pebbles, dice or balls) that represented quantities, as was the case with the old table.
With the new procedures, the vestiges wizardry of the abacquists disappeared as if by magic; with the new algorithm, even the most complicated calculations, essential above all in the merchants' activity, such as the simple and compound rule of three, the amortization of a loan, term loans, exchange rate fluctuations, discounts and so on, became enormously faster, more evident and more precise. It is safe to say that without the new accounting, the development of the merchants would not have lived its grandiose parable and history would have followed a different course.
By Antonio Santoni Rugiu