[In the following essay, Borst highlights the relationship between calendar-making and advancements in computational mathematics in the sixteenth century.]

The age of perfection began with Canon Nicholas Copernicus. In 1543 he reminded Pope Paul III of the last Lateran Council and his questio de emendando kalendario ecclesiastico. In doing so, he justified his ‘more precise computation of times [supputatio temporum], required to work out the movements of the planets [in motibus caelestibus calculandis]’. However, Copernicus did not rely solely on arithmetical calculations. He also used astronomical measurements like Hermann the Lame, the only difference being that he worked with more modern instruments than the astrolabe. He used these to compare the chronologies of the ancient Egyptians and Greeks rather than the cycles of Christian historians, making no mention of the computus ecclesiasticus. The newly discovered regularity of the planetary movements in God's machina mundi surpassed all the medieval chronologists' conjectures, as well as the hypotheses of Oresme and Cusa. Science had progressed. Since people now had an overview of the long period of their development, they were at last able to see the whole truth. Mathematics supplied them with laws that uniformly obtained everywhere in the open universe, in heaven as well as on earth, promising to make them into masters of their world and their time.¹

From 1559, however, Protestant historians established a new form of great year: the century. In a multi-volume collective enterprise, the so-called Magdeburg Centuriators set out to show how the papal church had falsified the Gospel of Jesus Christ; its editors assigned regular, clear intervals to each author, a hundred years per volume. They were clearly not intending to emulate the custom of the Catholic jubilee year used by Boniface VIII to commemorate Christ's birth; and they scarcely had in mind the annorum centenarii of Alexander von Roes, the end of which was supposed to herald the world's demise at that very time, in the sixteenth century. The new chronology of centuries was initially no more than a technical stop-gap, but one that soon made historians more inclined to arrange events and documentary evidence in chronological order, even when, as in the majority of cases, no firm date was known. The Centuriators' concept of time was no closer to that of Copernicus than Herodotus's was to that of Plato.²

The Catholic Council of Trent was irritated by the advances made in mathematics. It once again impressed upon all priests the need to learn the computus ecclesiasticus. However, exactly what computus they had to learn, Durand's vulgar one or Copernicus's astronomical one, was something even the council Fathers themselves did not know. It was not until the arrival of reform-minded popes that the council was relieved of the decision. Even the popes hesitated, until the Copernican belief in the regular operation of the universal machine spread, almost to the end of the third Easter cycle formerly computed by Abbo of Fleury. In February 1582, Pope Gregory XIII set about the Gregorian reform of the calendar, suppressing ten days in 1582, fixing the beginning of spring on 21 March, re-regulating the omission of leap-days, and determining the structure of our calendar to the present day. The reform of the calendar introduced a greater level of precision, but at the price of reduced consistency. The pope combined the reform with a new version of the saints' catalogue and the missal now incorporating instructions on time-reckoning. Only a handful of Catholics consulted these charts and the list of saints' feasts in the Missale Romanum; most of them consulted their pocket diary like everyone else. Even European princes applied religio-political rather than scholarly criteria when deciding either for or against the new calendar. The Christian denominations now even quarrelled about the dates on which they should celebrate the birth and Resurrection of their common Saviour.³

In a satire of 1585, the Italian heretic Giordano Bruno, an admirer of Copernicus, celebrated the pagan god Mercury as the Oracle of Mathematics and compotista mirabile; but in the infinite worlds of the myth imagined by Bruno, more fantastic and irrational symbols prevailed than those of school mathematics that he held in contempt.⁴ On earth, the plain year-numbers were so remote from ordinary life that in about 1585 the French nobleman Michel de Montaigne protested against the reform. His rural neighbours divided up their days as before while he himself lived in ‘the years when we count differently’, when ‘no one has the time any longer to become someone else’. For him there was no other time-reckoning, compte du temps, than the solar year; it was as ancient as it was inaccurate. What, then, was the point in reckoning and improving? Modern French found no use for the word ‘computist’.⁵

The immediate future belonged to a new science acquiring the name of chronologia, a humanist artificial term first coined in the sixteenth century. Its founder, an exile to Switzerland and the Netherlands, was the French Calvinist Joseph Justus Scaliger, the most famous scholar of his time. First, in 1583, he edited and annotated ten instruction books on calendrical computation for various nations and times: Hebrew, Ethiopian, Coptic, Syrian, Arabic, Greek, Armenian and Latin. He called them all computi annales, although he knew the word computus was attested late, and not before Firmicus Maternus. Scaliger also gave the name computus to his revised and condensed version, at least in its chapter headings, interpreting it as a doctrina annalis, a doctrine of years. Its medieval title once again held out the prospect that the summation of all computi would lead to one timeless truth concealed behind the many opinions voiced at different times.⁶

Scaliger himself relinquished this hope in 1606, in his final and most important work, Thesaurus temporum. First, he reconstructed and edited the oldest handbook on Christian time-reckoning, the chronicle of Eusebius and Jerome, complete with sequels. He then gave prominence to the most modern calendar, the Arabic; using mnemonic verses, he summarized its principal rules in a computus manualis so that travellers and merchants in Turkey would know how to use it. However, neither the moderns nor the ancients had full possession of the truth. The remaining objective was no longer to determine the divine or natural order of times, the beginning and end of time itself, but rather the historical specification of factual events; this was to be done with far more accuracy than had been attempted by the Magdeburg Centuriators with their vague enumeration of centuries. Since Scaliger conceived time as the ‘range of celestial motion’, modern chronologia must in his view be based on progress made by astronomers. Nevertheless, he regarded the Alfonsine tables as more accurate than the Copernican; newest was not necessarily best.

On its own, reckoning failed to attain the historical objective; even measuring was of no more than momentary help. As well as the natural sciences, those human sciences that preserved memories had to become involved. Using a critical, philological approach, Scaliger constructed a framework of fixed times from events recorded by the most ancient historiographers consisting of single days rather than sequences of years. These days fixed important points in time that helped posterity to date events: the destruction of Troy and the beginning of the Greek Olympiad calendar; the foundation of Rome and the start of the cycle of the Roman calendar; the biblical day of Creation and the day of Christ's birth; Mohammed's flight from Mecca and the era of the Seljuks. Instead of enumerating natural cycles, Scaliger's chronology noted high points of human endeavour that later became landmarks for historical thought. In short, it constituted historical time.

The earliest point in time was the least certain. When he tried to date the Creation, Scaliger arrived at the year 3949 bc, almost exactly the same figure as Bede. However, he did not share Bede's ambition to establish the true origin of world history; instead, his sole intention was to convert all foreseeable epochs into one another. To create some leeway for this, Scaliger assumed a period of 7,980 years for the entire tempus historicum, the product of the three most common yearly cycles in antiquity: 28 for the motion of the sun, 19 for the lunar orbit, and 15 for the indiction. He fixed the beginning of this period on 1 January 4713 bc, long before the advent of biblical time. When credible ancient Egyptian accounts forced him further back into no man's land, he added a tempus prolepticon, another arithmetical unit of 7,980 years, more mathematicorum.

By creating the space for a ‘prehistory’ in infinitum and for a future of at least equal duration, Scaliger separated chronology from the absoluteness and originality of all religious creeds, and bound it up with the relativity and progress of two technical procedures, the astronomical measurement of time and a critical-philological analysis of sources. As a Calvinist he criticized the Gregorian reform of the calendar because in his view it did not go far enough. He discovered no historical truths in the medieval computus ecclesiasticus, only ‘the dreams of the old computatores, unequalled in foolishness’.⁷ In order to save the Christian calendar, Scaliger's opponents resorted to operating with years ‘before the birth of Christ’, and this numbering, already used by Bede, became established not because it emphasized the first Christmas as the focal point in the history of salvation, but because it circumvented the uncertain date of the Creation.⁸

Slide-rules and calculating machines were already being made in the seventeenth century, the age of manufacture. Clocks and machines had been combined from as early as the fourteenth century, when model cockerels, crowing and with flapping wings, were activated by planetary clocks. But was it not now possible for machines to compute time as well, along the lines of Copernicus and Scaliger? The first modern calculating machine, designed in 1623-4 by the Tübingen orientalist and mathematician Wilhelm Schickard, was actually meant to assist the chronological and astronomical work of Johannes Kepler. What his friend was undertaking logistice, he was attempting to do mechanice, Schickard wrote in a letter to him. His arithmeticum organum was poorly suited to the purpose, since it was unable to add up numbers of more than six figures automatically, datos numeros statim automatos computet. Computare, however, signified all four basic methods of arithmetic. Technology was made a function of theory.⁹

In 1642-5 the young Blaise Pascal, son of a tax collector, invented and built a machine d'arithmétique for practical use. He meant to relieve the calculateur, and the tax official in particular, of the soul-destroying task of setting out numerous counting beads (jetons) or writing out long series of numbers in order to settle funds. The counters on the adding machine also corresponded to the currency system of the time. Although Pascal compared it to a pocket watch (montre), with one clock-maker (horloger) later using it as a model, Pascal did not recommend its use to time-reckoners. Why not? Following his conversion in 1654, Pascal used Augustinian incisiveness to distinguish healthy common sense and mathematical method from natural spirit and religious contemplation. We know how to use time and numbers correctly in our daily lives; but their Aristotelian definition turns our heads. Human beings alternate between the infinitely small and the infinitely large, between the void and the universe. It is only in God's immensity that the extremes of times and numbers truly come together; all we glimpse in these abysses are probabilities. For four thousand years the Jews have affirmed that they are the most ancient nation of all, and who are we to disbelieve them; but the Creation and the history of salvation are articles of faith, not sums.

Pascal challenged the rationalist mentality of his century, a century in which man was conceived, under Descartes's influence, as a mechanism comprising body and soul, as something calculable. In his view, each human being, having been created in God's image, was an intellectual being consisting of reason, and was merely automate by virtue of habit. What distinguished human beings from other living things which behaved completely instinctively was the thinking soul. On whose side, then, did a calculating machine like Pascal's stand? ‘The machine d'arithmétique achieves effects that are closer to thought processes than anything done by animals.’ The calculating machine seemed to symbolize human ingenuity in the midst of absolutist constraints; but artificial intelligence lacked even the simplest animal will. Consequently, the gulf separating living things from instruments was maintained.¹⁰

The many Europeans inventing and experimenting with calculating machines in the seventeenth and eighteenth centuries followed Leibniz's example in laying the main emphasis on mathematical theory, and merely wanted to free the minds of prominent thinkers from routine mechanical work. For this reason they never called their technical products ‘thought-machines’, but instead gave them the Latin name machina arithmetica; the French name, machine d'arithmétique; the German name, Rechnungs-Maschine, later Rechenmaschine; and the English name, calculating machine. Some were intended for astronomical use, but none were made for the purposes of computation. About 1660, the German Jesuit Kaspar Schott incorporated slide-rules into his organum mathematicum for determining Easter, but unlike Schickard, he no longer enlisted the terminology of computus.¹¹

By the seventeenth century, those continuing to deal with time-reckoning in the old, computistical sense were almost exclusively creators of vernacular calendars. From then on, time-reckoners were called in German Kalendermacher (calendar-makers). We might single out the most famous, the catholic poet Jakob Christoffel von Grimmelshausen. In his Perpetual Calendar of 1670, the first of six columns assigned to each of the German-named days consisted of a martyrology listing the names of almost six thousand saints. The second column gave an account, using Latin dating, of all kinds of histories, the history of salvation and universal history for the common man. Under 18 March it read: ‘XV Calendas Aprilis: This is the first day of the world on which God created Heaven and Earth; that is, on a Sunday.’ Under the same day it read: ‘In the year 1502 the Bundschuh or peasants' war rose up around Speyer and Bruchsall.’ Sublime, primeval time and present privation converged. The third column was devoted to the moment, combining ‘farmers’ rules for the day's weather and stories as brief as enumerated time: Kalendergeschichten (calendar stories).

In the fourth column a scholarly dialogue ‘on calendar-making and related issues’ ran through almost the entire year; it was a proper computus, only Grimmelshausen no longer gave it this name. Like Aristotle (in truth more like Plato), the calendar-maker declared that time was ‘a number or expanse of the upper corporis [sic] of heaven’. He brought together the views of Jews and Christians who held that God created the world some time between 3707 and 6984 bc. He discussed at length the Christian computation of Easter, ‘when calendar-making is at its most important’. He even supplied a brief universal history of the calendar and its reforms. The final two columns dealt consecutively with astrology and soothsaying. The Carolingian triad of martyrology, chronology and computus was thus revived, albeit as fallen cultural assets, in the notorious society of weather-makers, star-gazers and soothsayers. It was to them that the saying ‘you're lying like a calendar-maker’ referred in the writings of Grimmelshausen himself.¹²

In England in 1646 the sceptical physician Sir Thomas Browne adopted Montaigne's style, demanding that people should not attempt to achieve the ‘exact compute of time’ but should instead be content with the ‘common and usual account’. Believing that they could illuminate the impenetrable darkness of time's origin as well as the calculation of ancients like Bede, and the chronology of moderns like Scaliger, self-opinionated scholars had a deterrent effect. Even more irksome were the popular assumptions, ‘the calendars of these Computers’, the weather-rules of calendar-makers who even failed to notice that the Gregorian calendar had only been introduced in Romance countries, while Great Britain and parts of Germany retained the Julian Calendar. These computists challenged the usual account by which the year numbered 365 days.¹³ It would take another century before the English could bring themselves to introduce the new calendar. In modern English the words computer and computist sounded like the Middle English compute and the Middle Latin computista. Browne, however, deprived the computists of what little remained of the reputation which Bede had gained for them nine hundred years earlier.

The word computer made another appearance in 1707, in a satire by Jonathan Swift. But instead of attacking medieval computation, he reached far ahead of his time to attack modern computer science, ridiculing the modern scholars who, in contrast to the ancients, would read and think nothing, but instead just collect everything. They study books from their back cover, merely leafing through abstracts and indices, using these to create many other books, even though all the really new ideas could quite easily be included in a single volume. Swift claimed that a ‘very skilful computer’ had told him so; he had proved it by arithmetical rules. In truth, this computer, a theologian and believer in progress, knew nothing of the science of number or time-reckoning, producing large numbers of books and profiting from the prevailing fashion.¹⁴

In 1726 Swift described a huge machine owned by an ‘advancer of speculative learning’, allegedly constructed using strict computation, and operated by forty people. With the help of this machine, ‘the most ignorant person at a reasonable charge, and with a little bodily labour, may write books on philosophy, poetry, politics, law, mathematics and theology, without the least assistance from genius or study.’ If the public were to build five hundred such machines, the world would soon possess ‘a complete body of all arts and sciences’. This device, storing all words in the language and reassembling them in ever new ways, would today be described as a computer used for processing non-numerical data. That this writing machine would be given the same name as the writer himself was something not even the waspish Swift could have suspected at the time.¹⁵ His satire nevertheless attacked the fundamental principle of the calculating machine, associating it with the term computer. The time used by the device and its operator was the ahistorical moment rather than the universal history, its number the amassed quantity rather than qualitative evaluation, its language a system of symbols lacking any deeper meaning.

Notes

1. Nicholas Copernicus, De revolutionibus, ‘Praefatio’, ed. Heribert M. Nobis and Bernhard Sticker (1984), pp. 4ff: calendar reform and universal machine; III, 11, pp. 213ff: computation of times and history. See Hans Blumenberg, Die Genesis der kopernikanischen Welt, 2 (1981), pp. 503-606, on the concept of time (the calendar question is mentioned on p. 533, but receives insufficient attention). On the devaluing of the astrolabe, see Borst (as n. 20), Computus, med särskild hänsyn till runstaven och den borgerliga kalendern (1953), pp. 104-210, 244-82; Ludwig Rohner, Kalender geschichten und Kalender (1978), pp. 33-5. In Austria and Switzerland such farmers' calendars even today continue to appear in print.

2. Paul Lehmann, ‘Einteilung und Datierung nach Jahrhunderten’, in: Lehmann (as n. 42), vol. 1 (1959), pp. 114-29; a more accurate account is given in Johannes Burkhardt, Die Entstehung der modernen Jahrhundertrechnung. Ursprung und Ausbildung einer historiographischen Technik von Flacius bis Ranke (1971), pp. 11-28.

3. Friedrich K. Ginzel, Handbuch der mathematischen und technischen Chronologie, 3 (1914), pp. 257-66: the details. The most recent full account is given in: Gregorian Reform of the Calendar, ed. George V. Coyne (1983). The latest mathematical and chronological critique is provided by Zemanek (as n. 8), Kalender und Chronologie Bekanntes und Unbekanntes aus der Kalenderwissenschaft (1987), pp. 29-34. The most recent historical survey is provided by Gerhard Römer, ‘Kalenderreform und Kalenderstreit im 16. und 17. Jahrhundert’, in: Kalender im Wandel der Zeiten, ed. Landesbibliothek Baden (1982), pp. 70-84. An original account of the Missale Romanum is given in Joachim Mayr, ‘Der Computus ecclesiasticus’, Zeitschrift für katholische Theologie, 77 (1955), pp. 301-30.

4. Giordano Bruno, ‘L'asino cillenico del Nolano’, in: Dialoghi italiani, ed. Giovanni Aquilecchia (1958), p. 922. See Frances A. Yates, Collected Essays, 1 (1982); Gerhart von Graevenitz, Mythos, Zur Geschichte einer Denkgewohnheit (1987), pp. 1-33.

5. Montaigne, Essais, III, 10, ed. Maurice Rat, 2 (1962), pp. 455ff: another person; III, 11, pp. 472ff: time-reckoning. See Hans Blumenberg, Lebenszeit und Weltzeit (1986), pp. 148-52. …

6. Joseph Justus Scaliger, Opus novum de emendatione temporum (1583), pp. 294-379: ten computi; pp. 380-431: his own account, here p. 405, doctrina annalis. See Walter E. van Wijk, Het eerste leerboek der technische tijdrekenkunde (1954), pp. 1-6.

7. Joseph Justus Scaliger, Thesaurus temporum, facsimile edn, ed. Hellmut Rosenfeld and Otto Zeller, 1 (1968), part 1, pp. 1-197: Eusebius and Jerome; vol. 2 (1968), part 3, p. 240: computus manualis; p. 117: time; p. 276: chronologi; p. 308: Alfonso and Copernicus; pp. 276-309: tempus historicum; pp. 273ff, 309ff: tempus prolepticon; pp. 274ff: computus ecclesiasticus; p. 277: computatores. See Anthony T. Grafton, Joseph Scaliger (1540-1609) and the Humanism of the Later Renaissance, Diss. phil., Chicago (1975), pp. 173-220 on the historical context; Zemanek (as n. 8), pp. 61-74, 122-9 on the mathematical and chronological consequences up to the present day. Scaliger would number our exemplary date—2 March 1988, 6 p.m.—as 2447223.75.

8. Adalbert Klempt, Die Säkularisierung der universalhistorischen Auffassung. Zum Wandel des Geschichtsdenkens im 16. und 17. Jahrhundert (1960), pp. 81-9, in which the search for predecessors overlooks the most important, Bede. … Kaletsch (as n. 97), p. 80, ignores all predecessors.

9. Bruno von Freytag Löringhoff, ‘Wilhelm Schickard und seine Rechenmaschine von 1623’, in Dreihundertfünfzig Jahre Rechenmaschinen, ed. Martin Graef (1973), pp. 11-20, here pp. 11ff: the quotations. See Michael R. Williams, A History of Computing Technology (1985), pp. 123-8.

10. Pascal, ‘La Machine arithmétique’, in Oeuvres complètes, ed. Louis Lafuma (1963), pp. 187-91: the description; ‘De l'esprit géométrique’, pp. 349-51: time and numbers; Pensées, no. 199-72, pp. 526ff: God and man; no. 456-618, p. 561: Jews; no. 821-252, p. 604: automate; no. 741-340, p. 596: thinking machine. See also Williams (as n. 183), pp. 128-34; Herbert Heckmann, Die andere Schöpfung. Geschichte der frühen Automaten in Wirklichkeit und Dichtung (1982), pp. 90ff. For a diverse, yet informative, collection of details on the mechanization of the seventeenth-century world-view, see ibid., pp. 165-209.

11. Ludolf von Mackensen, ‘Von Pascal zu Hahn. Die Entwicklung von Rechenmaschinen im 17. und 18. Jahrhundert’, in: Dreihundertfünfzig Jahre (as n. 183), pp. 21-33; Williams (as n. 183), pp. 134-50: generally; pp. 92-7: Schott.

12. Des Abenteurlichen Simplicissimi Ewig-währender Calender, facsimile, ed. Klaus Habermann (1967), pp. 4ff: content of the six columns; p. 60 (II)b, 18 March; p. 45a: calendar-makers; p. 11a: definition of time; pp. 29a-31a: date of Creation; p. 39a: Easter; pp. 47a-49a: history of the calendar; p. 91a: lies by the calendar-makers. For a study of the term, see Grimm (as n. 62), Deutesches Wortebuch, vol. 11 (1873), col. 63. On the work, see Habermann, Beiheft (supplement to the facsimile edition, 1967), pp. 15-46; Rohner (as n. 175), pp. 119-58. In Johann Peter Hebel, Der Rheinländische Hausfreund 1808-1819, facsimile, ed. Ludwig Rohner (1981), p. 146, the phrase Wir Sternseher und Calendermacher (‘we stargazers and calendar-makers’) was intended to be at once more ironical and more scholarly.

13. ‘Pseudodoxia epidemica’, VI, 1, in: The Works of Sir Thomas Browne, ed. Geoffrey Keynes, 2 (1964), p. 409: exact compute; p. 403: Bede and Scaliger; VI, 4, p. 419: computers; VI, 8, pp. 454ff: computists. See Arno Borst, Der Turmbau von Babel. Geschichte der Meinungen über Ursprung und Vielfalt der Sprachen und Völker, 3/1 (1960), pp. 1317ff.

14. Swift, ‘A Tale of a Tub’, ch. 7, in: Prose Works, ed. Herbert Davis, 1 (1965), pp. 91-3. More recent references to computer are given in: The Oxford English Dictionary, ed. James A. Murray et al., 2 (1933), p. 750.

15. Swift, Gulliver's Travels, III, 5, ed. Davis (as n. 188), vol. 11 (1965), pp. 182-5, with a comical drawing. See Klaus Arnold, Geschichtswissenschaft und elektronische Datenverarbeitung, Historische Zeitschrift, supplement NF 3 (1974), pp. 98-148, here 101ff; as to the context of the enthusiasm for, and criticism of, machines in the eighteenth century, see Heckmann (as n. 184), pp. 235-80.