learnt that he had been born in the same town and century as one of my favourite Renaissance painters, Piero della Francesca, who possibly taught Luca Pacioli mathematics. (Location 149)
Finally, and most significantly, bookkeeping now has the potential to make or break the planet. Because accounting reduces everything to its monetary value, it has allowed us to value least that apparently free source of life itself: the planet. Through its logic we have let the planet go to ruin—and through its logic we now have a chance to avert that ruin. (Location 167)
and the first technology invented for storing memory. (Location 195)
Note: debt is externalised contra lazzarato who claims it infests memory and becomes existential.
And so spheres became circles, cones became triangles, ovoids became ovals and writing was invented. (Location 212)
‘but because it encouraged people to see the world around them in terms of quantifiable outcomes’. (Location 218)
Note: fuf
Likewise, all Athenian citizens were required to keep regular accounts of their own financial affairs. If they failed to do so, they were severely punished by being forbidden to travel from the city, consecrate their property to a god, dedicate a sacred offering or make a will. (Location 228)
As historian A.C. Littleton put it: ‘That Jerusalem was won and lost and won again mattered less to civilization, as it proved, than did the incidental results which formed no part of the original intention.’ (Location 254)
position to free themselves from their feudal chains, (Location 258)
Note: l’uomo nuovo
In 1082, the Byzantine emperor’s Golden Bull guaranteed Venetian merchants tax-free travel (Location 260)
This simple Arabic arithmetic we all use today was mostly unknown in Europe at the time. (Location 273)
The most famous of his books, the 1202 Liber abaci (‘Book of Calculation’), begins: ‘These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.’ (Location 280)
One of these new counting men was Francesco Datini, a merchant from Prato, near Florence, a cloth manufacturer and dealer in armour, wool, wheat and slaves. On his death in 1410—without legitimate children—Datini bequeathed to Prato not only his fortune of 70,000 gold florins but also 500 account books, 300 deeds of partnership, 400 insurance policies, bills of exchange, cheques and some 150,000 letters. At (Location 329)
Two themes preoccupied Datini’s restless mind and infuse his many letters: religion and business. (Location 333)
‘In the name of God and of profit’. (Location 335)
plague. Towards the end of his long, healthy and prosperous life, Datini wrote to his wife: ‘Destiny has ordained that from the day of my birth I should never know a whole happy day.’ (Location 336)
Like many business practices new to medieval Europe, the cheque had long been used by Arab merchants, who gave us the English word ‘cheque’. (Location 341)
Note: see language log and chess
Their use was discouraged and often outlawed by the guilds and other power players such as the Church who believed that Roman numerals were superior and tamper-proof, and the scandalous new eastern numerals easy to alter and falsify. (Location 362)
Elsewhere in Europe the adoption of Hindu–Arabic numerals was even slower: in 1520 the German municipality of Freiburg refused to accept accounts as legal proof of debt unless they were made in Roman numerals or written out in words; and Roman numerals were still used in Scotland in the seventeenth century. (Location 365)
The same century also saw the merging of two streams of mathematics which had been split since the sixth century BC: the philosophical-speculative mathematics of Pythagoras and his successors, and the commercial arithmetic used by merchants. The mix would prove epoch-changing. It spurred the gradual rise of mathematics to its eventual usurpation of Latin as the lingua franca of Europe and ushered in a new era: the Age of Science. (Location 444)
‘The good Christian should beware of mathematics and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.’ (Location 452)
The Pythagoreans divided mathematics into four subjects—arithmetic (or numbers absolute), music (numbers applied), geometry (magnitudes at rest), and astronomy (magnitudes in motion)—with geometry as the cornerstone of all education. (Location 462)
‘God made the sun so that animals could learn arithmetic—without the succession of days and nights, one supposes, we should not have thought of numbers. The sight of day and night, months and years, has created knowledge of number and given us the conception of time, and hence came philosophy.’ (Location 470)
Following the fall of Rome, Greek mathematics survived in Europe in fragmented and reduced form in the cathedral and monastery schools set up by Charlemagne in the eighth century, which taught the Pythagorean mathematical quadrivium alongside the ‘trivium’ of grammar, logic and rhetoric. The mathematics taught, however, was basic: enough arithmetic to keep accounts, music for church services, geometry for land surveying, and astrology to calculate the dates of Christian feasts and fasts; it used Roman numerals, the abacus, and Latin translations of Greek mathematics (especially Euclid) by the Roman scholar Boethius (c. 480–524). (Location 480)
century. The first, of Euclid’s Elements, was by the intrepid English monk Adelard of Bath, who travelled to Spain in search of Arab learning and discovered their work on Euclid at a famous Moorish college in Cordova. (Location 497)
Note: kipling
René Descartes (1596–1650) would argue something similar four centuries later and revolutionise European philosophy. (Location 507)
Note: ofc RD did believe in magic. see also thom. harriot
But while scholarly Europe rejected and even outlawed Hindu–Arabic learning, the new mathematics found a ready audience among the merchants of Italy, where it became known as ‘abbaco’ mathematics. (Location 508)
the abbaco schools, intended for the sons of merchants, who were taught Hindu–Arabic mathematics and learnt to read and write in their native tongues, an innovation that would encourage both the codification and standardisation of the vernacular languages of Europe, and the demise of Latin as the language of scholarship. (Location 514)
rarefied atmosphere of the European universities—which began to emerge around 1100 in Paris, Bologna, Salerno, Oxford and Cambridge—mathematical techniques were regarded mostly as fictions. (Location 529)
Pacioli would have been taught the remnants of the old medieval scholasticism, based on the quadrivium and trivium of Boethius, as well as the new Florentine Humanism. (Location 547)
It was abbaco mathematics that made possible in the 1430s Brunelleschi’s celebrated dome of the Cathedral of Santa Maria del Fiore, which still dominates the skyline of Florence almost six hundred years later. (Location 557)
Note: How?
the notorious Girolamo Cardan (1501–76), a gambler and possible murderer obsessed with scandal, astrology and philosophy, whose Ars magna (1545) on algebra was the most advanced work of its day. (Location 917)
in these offices they often change their clerks, and as each one of these clerks likes to keep the books in his own way, he is always blaming the previous clerks, saying that they did not keep the books in good order, and they are always trying to make you believe that their way is better than all the others, so that at times they mix up the accounts in the books of these offices in such way that they do not correspond with anything. Woe to you if you have anything to do with these people … Maybe they mean well, nevertheless they may show ignorance. (Location 1266)
