were then lacking in Europe. This provided huge motivation for transmis- sion to Europe of precise Indian trigonometric values, and through them the infinite series and the calculus. Coincidentally, the first Roman Catholic mission in India was founded in Cochin, in 1500, and later turned into a col- lege for the indigenous Syrian Christians, in the neighbourhood, who spoke Malayalam. The Raja of Cochin simultaneously patronized both Portuguese and the authors of key texts documenting expositions of the Indian infinite series used to derive accurate trigonometric values. This provided a splendid opportunity for the Jesuits, who systematically gathered knowledge by ap- plying the Toledo model of mass translation to Cochin, soon after they took over the Cochin college in 1550 CE. Apart from the local languages, the Je- suits were soon trained also in practical mathematics and astronomy. Also, sailors and travellers returning from India routinely brought back books, as souvenirs or to be sold to collectors in Europe. From the mid-16th c. CE onwards, circumstantial evidence of the knowledge of Indian mathematical and astronomical works begins to appear in the works of Mercator, Clavius, Julius Scaliger, Tycho Brahe, de Nobili, Kepler, Cavalieri, Fermat, Pascal, etc. Indian sources were rarely directly acknowledged by these Europeans due to the terror of acknowledging "pagan" sources during the Inquisition, and the church doctrine of Christian Discovery, which preceded racism. (This is in striking contrast to the Arabs in the 9th c. CE who had enough religious freedom to acknowledge Indian sources.) The prolonged difficulties that Eu- ropeans had in understanding the epistemological basis of the calculus fur- ther characterizes the calculus as knowledge imported into Europe like the algorismus.
8 Number Representations in Calculus, Algorismus, and Computers
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Śūnyavāda vs formalism
Berkeley's objections reflect the doubts about the nature of fluxions, infin-
itesimals etc., which neither Newton, nor Leibniz, nor their supporters could coherently explain to sceptical contemporaries. These doubts led eventu- ally to the formalisation of "real" numbers using Dedekind cuts and set the- ory (itself formalised only in the 1930's), which finally gave a formulation of the calculus acceptable in the West. These prolonged European diffi- culties with the calculus arose because the Indian derivation of the infinite series used a philosophy of non-representables similar to
śūnyavāda, and in-
compatible with Platonic idealism or formalism--thoughtlessly taken as the "universal" basis of mathematics in Europe. The central problem of rep- resentation was left unresolved by the formalisation of real numbers, which achieved nothing of any practical value. A similar problem had arisen ear- lier in Europe, in the dispute between abacus and algorismus, which involved zeroing of non-representables in a calculation. The
śūnyavāda philosophy re-
gards idealistic conceptualizations (as in Platonism or formalism) as empty and erroneous (e.g., in direct opposition to Platonism it regards an ideal geometrical point as an erroneous representation of a real dot). It is also better suited than Platonic idealism or formalism to numbers on a computer