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MATHEMATICS AND MODESTY IN THE SOCIETY OF JESUS
The Problems of
Christoph Grienberger (1564-1636)
from The New Science and Jesuit Science: Seventeenth Century Perspectives, ed. Mordechai Feingold, Dordrecht: Kluwer, 2003 (Archimedes vol. 6), pp. 1-120
CENODOXUS: Wakeful and
easeless are
my days and nights, consumed in careful studies
SELF-LOVE: But time cannot consume what all men's praises render immortal.
CENODOXUS: Yet how easily such honours can be
gained.
My life's whole purpose is therefore this: by
glorious deeds
to ensure that I and all my glory never perish. This
die I've cast.
Jakob Bidermann, Cenodoxus,
I. iii, transl. D. G. Dyer and C. Longrigg, Edinburgh, 1975, p. 47
In 1609 Jakob Bidermann's "Comico-Tragedy" Cenodoxus, or the Doctor of Paris was performed on the stage of the Jesuit college in Munich. The play, first produced seven years earlier in Augsburg, deals with the story of a Parisian scholar who, despite maintaining an ascetic public demeanour, privately prided himself on his unparalleled erudition. In Bidermann's graphic account, based loosely around the legend of St Bruno, the eleventh-century founder of the Carthusian order, Cenodoxus, recast as a Renaissance humanist, is finally condemned to eternal torment for the sin of kenodoxia or vaingloriousness[1]. The Munich production of the play provoked a memorable reaction, described in the preface to the first collected edition of Bidermann's dramatic works.[2] At first the audience laughed at the opening comic scenes, but as the play progressed the mood gradually changed to one of astonishment and horror as the spectators realised the enormity of the sins portrayed and became aware of the power of hell. By the end of the play, the terrified members of the audience were contemplating their own sins in stunned silence. The impact of the play was immediate. Fourteen members of the audience went into retreat to perform the Spiritual Exercises of St Ignatius, just as in the play Bruno retreated into the wilderness to found his monastery and lead a life of spiritual contemplation. The actor who played Cenodoxus himself then joined a Jesuit novitiate, and passed the rest of his life in the religious modesty of the Society of Jesus.[3]
It is difficult to find a more poignant example of the way the Jesuit order in general, and the Jesuit spiritual teachings embodied in the Spiritual Exercises in particular, were perceived amongst the ruling elites of early modern Europe as constituting a powerful antidote to pride, superbia, or vaingloriousness. Ignatius himself, following Gregory the Great and Thomas Aquinas, frequently emphasized the interdependence of modesty and obedience in his writings, arguing that disobedience, the ultimate enemy to the social fabric of the Jesuit order that he had founded, was an inevitable consequence of vaingloriousness.[4] The Rules of the Society of Jesus, first published in 1582 as a guide to the different functions and modes of social behaviour of Jesuits, contained a series of Rules on Modesty due to Ignatius. These rules, originally composed around 1555,[5] and well entrenched by the 1580s, really amounted to rules of bodily deportment. Members of the Society, in order to display modesty, humility and religious maturity, had to keep their heads pointing straight forward, with their necks inclined slightly downward. Eyes were to be kept down, especially when talking to others, wrinkling of the nose was to be avoided, walking more quickly than necessary was discouraged, and all gestures were to display humility and move the observer to devotion.[6] Speech too was to display modesty and edification.[7] Biographical writings about eminent Jesuits, taking their lead from Ribadeneyra's widely read biography of Ignatius[8], laid great emphasis on the qualities of modesty, humility and self-abnegation advocated by the Jesuit Constitutions and Rules.
Before the development of societies and institutions exclusively devoted to scientific pursuits in Europe from the 1660s onwards, and the subsequent emergence of codified and tacit forms of professional ethics specific to such institutions, natural philosophers and mathematicians attempting to make novel claims about the natural world were obliged to look outside science for models of acceptable conduct in the prosecution and presentation of their work. Rather than being obliged to acquiesce into a single model of personhood, scientific practitioners were free to make their own creative synthesis from a smorgasbord of religious and courtly models, to name just two of the more obvious options. Steven Shapin has emphasised the extent to which Robert Boyle drew on the social mores of the English gentleman in order to provide a social basis for credibility in the reporting of scientific observations. In a similar vein, Mario Biagioli has argued that Galileo fashioned himself as a natural philosopher by successfully deploying the vocabulary of Medicean dynastic emblematics.[9]
Whereas the court environment in which Galileo worked for at least part of his life promoted visibility and authorship -- the attachments of texts, inventions and observations to a proper-name[10] --, the cultural values promoted in the Jesuit order generally emphasised invisibility and self-abnegation, and denied 'authorship' to all but a relative few, sometimes denoted by the term scriptor in the catalogues of the Jesuit houses. Individual glory was, in general, to be shirked in favour of the collective glory of the order. In disciplining their adversaries in theological and philosophical disputes, Jesuit authors made frequent use of terms like jactantia and jactatores, using the inappropriate deportment of opponents to discredit their arguments. The playwright Jakob Bidermann himself, after the successes of his theatrical castigations of superbia, was brought to Rome to act as General Revisor for Jesuit literary works, where he had the opportunity to police the humility of a large number of learned Jesuit writers in person for almost twenty years.[11]
Admittedly many Jesuit mathematicians also worked in a courtly environment. Galileo's opponent in the dispute over sunspots, Christoph Scheiner, is one example.[12] Nonetheless, careers such as Scheiner's manifest the deep tensions between the type of deportment suitable to a court and the ready-made, modest "personality" provided by the Jesuit prescriptive literature and inculcated through the practice of the Spiritual Exercises.[13] Precisely for this reason I would like to look more closely in the present article at a Jesuit mathematician who worked almost exclusively within Jesuit-controlled institutions. I believe that the strategies of self-abnegation[14], deployed by the Jesuit mathematician Christoph Grienberger, who availed himself of every opportunity to remove his name from texts written with his pen and optical and astronomical instruments designed by him and built with his own hands, can reveal much about what it was to be both a Jesuit and a skilled mathematical practitioner in the early seventeenth century. At the outset, this may appear to be a task of some difficulty, as the 'person' that we would like to understand is a person who manifests himself by disappearing - erasing his tracks in the history of science with remarkable dexterity and even managing to avoid an entry in the Dictionary of Scientific Biography. However, through the indiscretions of some of his Jesuit colleagues, through his own epistolary confessions to his senior mathematical colleague, Christoph Clavius, and through the existence of a significant number of anonymous manuscripts that I attribute to Grienberger, some of which are published in the appendix, the public and private selves of this elusive individual begin to emerge. Where Galileo found a source of legitimation for certain types of mathematical practice in the colourful world of the Medici court in Florence, his exact contemporary Grienberger found his Archimedean point for the upward leverage of the status of mathematics deep within the complex bureaucratic structure of the Jesuit order.
Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger - the list of names used by his contemporaries to refer to Christoph Grienberger goes on and on.[15] Print has a tendency to fix the orthography of proper names, and Grienberger's name was one that, with the exception of a slim book of star-charts and a set of trigonometric tables[16], rarely appeared in print during his life. In approaching the question "Who was Christoph Grienberger?", I do not aim to provide anything like a biography of the sort that Charles Coulston Gillespie might have chosen to include in the DSB[17]. Instead, I would like to look at how people wrote about Grienberger and how Grienberger wrote about himself. I would like to examine Grienberger's own production in terms of texts and instruments, and his moderation of the productions of others, in his work as a revisor of mathematical works written by Jesuits and in his strategies of engagement in epistolary relationships with natural philosophers and mathematicians outside the Jesuit order.[18]
Christoph Grienberger died on 11 March 1636. Before his death he was in charge of the technical censorship of all mathematical works written by Jesuit authors. Often Grienberger would send detailed calculations and corrections to an author, demanding that they be incorporated before allowing the work to be published. In some cases, as in Gregorius a St. Vincent's attempt to square the circle, Grienberger advised the Jesuit General Muzio Vitelleschi to refuse publication altogether, on the grounds that the errors contained in the proofs would damage the reputation of the Society of Jesus.[19] When Grienberger died, he clearly lost control over the mathematical publications of his fellow Jesuit mathematicians. Perhaps more interestingly, he lost control over his own authorial presence, or rather, absence. A case in point is Mario Bettini's Apiaria, an encyclopedic collection of mathematical curiosities.[20] The censorship of the book took place in the mid-1630s, but publication was held up, possibly through a lack of a suitable patron.[21] The book finally appeared in 1645, and unlike other works, which merely incorporated Grienberger's corrections unacknowledged, Bettini takes great pains to highlight the contributions of the late Revisor, whom he hails at the outset of his book as having the stature of an "Archimedes of our time", combining "most ingenious practices and wonderful machinery" with "very acute theories".[22] Later in the work, Bettini confessed that "I have benefited, my Reader, from the mind and industry of the very learned and exceedingly modest man, Grienberger, who, while he would have discovered many marvellous things by himself, preferred to make himself serviceable to other people's inventions and other people's praises".[23] In his Aerarium, published three years later, Bettini included a Scholion Parergicon eulogising Grienberger, and continuing to compare him to Archimedes, adding that "Grienberger has no greater enemy than his own modesty, by which it has come to pass that his ingenious inventions have been neglected, and he will be consigned to oblivion".[24] Bettini added, echoing the Apiaria, that "It was a remarkable characteristic of [Grienberger] that, following the example of Archimedes, he combined most acute theories with extraordinary practices"[25], and his claims for Grienberger's achievements in designing instruments and machines are closely echoed by other contemporary mathematical authors.[26]
And yet Archimedes possessed such a lofty spirit, so profound a soul, and such a wealth of scientific theory, that although his inventions had won for him a name and fame for superhuman sagacity, he would not consent to leave behind him any treatise on this subject.
Plutarch, Life
of Marcellus, XVII.3-4
When Ernst von
Wittelsbach, Prince-Archbishop of Cologne, sought a telescope to replace the
instrument sent to him by Galileo with which Kepler had first observed the
Medicean stars, it was to Grienberger that he turned. The Galileian instrument,
Wittelsbach elaborated, showed stars to be triangular or four-pointed,
depending on how it was oriented, and also distorted terrestrial objects viewed
from a distance. Grienberger, Wittelsbach presumed, could provide him with a
more accurate instrument. As Mario Biagioli points out, shortly after the
publication of the Sidereus Nuncius
Grienberger possessed a more powerful telescope than anything Galileo had
constructed.[27]
In Bettini's Apiaria, we see Grienberger's instrumental proficiency forcibly exposed to the public gaze. In composing his corrections to the Apiaria, in his role as Revisor, Grienberger had noticed that a scenographic instrument described by Bettini could be improved in a way that would make it easier to use and more accurate. The instrument (fig. 1), rather similar to Christoph Scheiner's pantograph (fig. 3),[28] allowed the user to make accurate drawings from life with little effort and less skill. Grienberger wrote to Bettini in 1635 to describe his modifications:
On experimenting [tentando], I discovered that Your Reverence's instrument might be
made more easily. I removed the directing rod that moved transversely, until now
the part of the instrument that appeared to obstruct its operation. I added cursores in my own way, as you will see
below, and completed the job by means of four small beams, making a
parallelogram. I took care that the line of sight [radius visualis] and the line of writing [radius scriptorius] would both depart from one of its points, and
that both points would exist in a single straight line, namely the axis around
which the parallellogram will be rotated continuously.[29]
In addition to providing a lengthy description of the device, arguably at least as different from Bettini's own rude contraption as Scheiner's pantograph, Grienberger sent Bettini two copper-plate engravings[30] for inclusion in his book, one showing a schematised form of the instrument accompanied by Grienberger's trademark cursores, and the other showing the instrument manipulated by the eyes and hand of an invisible Grienberger (see figs. 1 and 2). Grienberger's pathological modesty is at work here again. Ever keen to divest himself of any vestige of authorship, he writes to Bettini of the modified scenographic instrument that
I could have sent this Bettinian Instrument to the
Emperor recently, but I did not wish to do this without the permission of Your
Reverence. I would rather receive that permission which Your Reverence would
bestow if [the instrument] were first published in the Apiaria.[31]
Another work in which Grienberger's instrumental manipulations in the Collegio Romano lie tantalisingly in the shadows is Christoph Scheiner's voluminous 1630 book on sunspots, the Rosa Ursina.[32] The dichotomy between court and Curia that characterised the work of Scheiner and of many other Jesuit astronomers is eloquently expressed by Daniel Widman's etching of the different techniques for observing sunspots (fig. 4). At the top we see Scheiner in the company of various members of the Orsini household, observing the sun on an ersatz viewing platform, complete with obelisks, on the banks of the Lago di Bracciano, close to the Orsini Castle, which can be seen in the left background. At the bottom we see Scheiner in duplicate, compasses still in hand, making observations from his room in the Jesuit Domus Professa in Rome.[33] The instrument used by Scheiner in the lower vignette is the telescope that he claimed to have used to discover sunspots before Galileo observed them in 1611, and suffered from the disadvantage of being difficult to move from a fixed position, thus making protracted observations over any length of time a very awkward business.
To cope with this problem, Grienberger developed a "telescopic heliotrope" or "heliotropic telescope", an instrument (fig. 5) which avoided the difficulties of the other device by being simultaneously mounted on two axes around which it could rotate freely to follow the trajectory of the sun, like the sunflower from which it took its name. Again, Grienberger seems to have been responsible for the engraving of this device published by Scheiner. Again, Grienberger as machine-operator is invisible, in marked contrast to the multiple representations of Scheiner in the previous figure. Scheiner, ever one to emphasise the collective nature of the scientific enterprise,[34] asked Grienberger to provide him with a description of his instrument, but he refused, to Scheiner's surprise:
And thus this machine is not entangled in as many
difficulties as the other one; and additionally [Grienberger's] machine is more
convenient, and carried out the work more quickly than that one. For this
reason, it will be worthwhile to write a short explanation of its nature, since the Architect of the Machine himself
seemed to be unwilling to furnish this: despite having later edified many
things with his demonstrations, and hastened and urged me to finish the work,
[as well as having] helped me most opportunely with similar services that were
virtually necessary to me in such a short space of time.[35]
Undoubtedly the polemic between Scheiner and Galileo was part of the reason for Grienberger's attempt to distance himself from the text of Scheiner's work. The rift between Galileo and the Jesuit mathematicians of the Collegio Romano that followed Galileo's attacks on Orazio Grassi's public disputation on the comets of 1618 was a source of much distress to Grienberger,[36] who could not see any reason for this turnaround.[37] In fact, Galileo's gesture seems to have been the result of a cynical, and rather unsuccessful attempt to cultivate the patronage of Archduke Leopold of Austria, also a patron of Scheiner.[38] Nonetheless, Grienberger's participation in the Rosa Ursina, performing observations (not with Scheiner in the Domus Professa, but in the Collegio Romano only a few hundred yards away – see fig. 7) and refining observational instruments is characteristic of the way he chose to present himself in other works. To understand the development of this pattern of effacement of claims to intellectual ownership, I would like to turn to Grienberger's earlier career in the Jesuit order.
On 15 September 1590, Grienberger, then mathematics teacher and student of theology at the Jesuit College in Vienna, wrote the earliest of his surviving letters to Christoph Clavius in Rome. Although Grienberger, who had spent the ten years since he first entered the Jesuit order in Prague and Olmütz,[39] had not yet met Clavius face to face, his letter betrays an unexpected degree of intimacy:
Why should I not love my teacher? And indeed so much mine that he seems almost to be mine alone. Are you not mine, who are so present to me always, that I began immediately to love you and now for almost the four years for which I have known you have hardly ever placed a foot outside my bedroom? [40]
Grienberger is, of course, cohabiting with Clavius's textual body - his
commentaries on Euclid's Elements and
the Sphere of Sacrobosco as well as
other works.[41]
Nonetheless, a short time after this letter was sent, along with the demonstratiunculae on spherical
trigonometry that Grienberger, like a good pupil, sent to his virtual master,[42]
Grienberger was summoned to Rome so that the two mathematicians could really
live under the same roof.[43]
The pattern was to become relatively common - Giuseppe Biancani and Odo van
Maelcote were also brought to Rome to assist Clavius (and to be fashioned as
mathematicians in his image) after sending unsolicited solutions to celebrated
problems or instruments to the famous professor in Rome,[44]
and many others sent demonstrations hopefully.
In 1595 Clavius went to Naples, leaving Grienberger in charge in Rome. Grienberger wrote to Clavius shortly after his departure:
Now the Mathematical Museum has put on new clothes,
nor does it cry out for anything other than the speedy return of its master. In
the meantime it will have me as a custodian. On Monday next I will give my old
[room] to two others[45].
The bedroom was a multifunctional space for the Jesuit mathematician. Generally, the rooms of Jesuits were not provided with keys, but, along with the rooms of the Superiors, the Procurator (responsible for the financial affairs of the College), the room of the senior mathematician of the College formed an exception.[46] The added security of a key meant that the mathematics professor could store valuable mathematical instruments in his domestic space, which was often referred to as a mathematical museum, or musaeum mathematicum.[47] Later, while in Lisbon, Grienberger would tell Clavius of a valuable clock that he had kept for several months in the privacy of his bedroom.[48] As well as constituting a space for the storage and construction of instruments, the mathematician's bedroom was the focus for the studies carried out by the private mathematical academy of the college.[49] Printed books currently being used by the academy, manuscripts of mathematical works and, perhaps most crucially, the letters sent to successive professors of mathematics in the Collegio Romano, were all stored in this space.[50] Whereas the private papers of a Jesuit were generally destroyed after his death unless deemed to be of particular importance,[51] the mathematicians of the college enjoyed the security of a place apart, allowing the correspondence and manuscripts accumulated by successive professors to constitute what Athanasius Kircher and his colleagues were later to use as a private mathematical archive.[52]
During Clavius's absence in Naples, Grienberger kept him informed with regular bulletins on the vicissitudes of college life. These allude to his own research, the work of the private mathematical academy under his guidance and the normal mathematics classes of the College. Grienberger's letters are punctuated by descriptions of humorous events, such as Fabricio Mordente's pompous display of his beautiful, but imprecise, geometrical compasses to the mathematicians of the college[53] and a rather excessive number of ponderous jokes about Clavius's penchant for Neapolitan pastries.[54]
On 12 January 1596 Grienberger told Clavius of a possible addition to his other duties:
I fear that perhaps I may have to teach privately to
a certain Count whose name escapes me. But I hear that he has studied little else,
and it appears to me that he is rather young, not to say a boy, so I hope for
little profit, even on my side, as I do
not know how to deal with that type of person correctly.[55]
Shortly afterwards, Grienberger's fears came true, making unfair demands on both his time and his character:
I do not have much free time, apart from in the
mornings. For after lunch all is taken up by the class and the academies, of
which there is the domestic one, as you know, and another at the Gate, to which
Count St. George, as he's known, comes, a boy with a reasonable mind, together
with a certain other [boy] of around the same age, called Orazio, from Perugia,
also of good family. Both of these asked the Fr. General if I could lecture
them privately. Your Rev. will wonder that I am suitable for this task, as it
should really require not a German but a Tuscan, who would be more affable than
me. But seeing that it has pleased them thus I hope that they will have
patience with me.[56]
Grienberger, unlike his more famous Tuscan contemporary Galileo,was clearly no courtier, and elsewhere diagnosed himself as having a particularly frigid nature, when speculating that Clavius might be prolonging his stay in Naples because Grienberger was occupying his bedroom:
But is [Clavius] perhaps excluded from his bedroom?
On the contrary, it is so ready that it would invite him him there freely even
against his will. For I will easily find another one that is equally cold,
unless perhaps all rooms are cold that are occupied by exceedingly cold [frigidissimus] me.[57]
Despite pandering on occasions to a cardinal's desire for a sundial[58], or to the wishes of young aristocrats to have private tuition, Grienberger's concerns lay more with the well-being of his young disciples in the mathematical academy, bound to him by a common love of mathematics, than with courtly aspirations.
Unless the Superiors change their plans, I believe
that I will be freed from the ordinary domestic academy. [...] The other
private academy is creeping forward slowly [in the study] of Clocks. Out of the
three pupils, one (Janos Nagy, of course) as he was trying impetuosly to go up
two steps at a time four or five days ago, almost suffocated on his catharr.
However, Nature won, and made herself a way forcibly, but not without blood, as
together with the phlegm he vomited up no small quantity of blood.[59]
The impetuous mathematician clearly pays a price. Grienberger went to visit Nagy in the college infirmary, where he found two other indisposed mathematical practitioners:
As I was visiting Nagy today, I found Fr.
Villalpando and Fr. Mario (the one who saluted you in Naples when you were in
your sedan chair) in the same place [i.e. the infirmary]. Reading your letter
they rejoiced to hear of your good health, and indeed we sensed some unknown
fragrance from your letter, and some unknown pleasant odour, but without a
taste.[60]
Although the convalescent mathematicians might have detected the smell of the Neapolitan sweetmeats that Clavius hoarded in his bedroom in Naples, imbibed by his writing paper, Grienberger is suggesting with lumbering jocularity that the elderly mathematician had kept the taste of the pastries for himself.[61]
Public
mathematics in the Collegio Romano:
The Problemata
Shortly after Clavius left Rome for Naples, Grienberger castigated him for suggesting to the Rector that Grienberger might give a public oration to mark the commencement of studies in the Collegio:
I do not know what Your Reverence expected when you
promised our Rev. Fr. Rector that I would give an oration [Praefatio], for I happened to hear this from him at least twice, in
the presence of others. For you know
extremely well that, to me, that has always seemed an extremely difficult task.
Certainly, if they expected an oration they did not get one, but instead I
explained the dimension of the circle from Archimedes so slowly that it could
not be completed in half an hour.[62]
Grienberger did not enjoy speaking in public. No great surprise here, but what might appear initially to represent something of a paradox is a statement made in Mario Bettini's Aerarium, when concluding his eulogy of Grienberger and "correcting" Giuseppe Biancani's entry on Grienberger in his Chronology of Illustrious Mathematicians, appended to his 1615 Aristotelis loca mathematica.[63] Listing Grienberger's extant manuscript works, Bettini writes:
There are many optical and mechanical [machinaria] experiments present in our Roman
College that were once exhibited to the eyes and admiration of princely men
visiting that place.[64]
To understand how Grienberger's modesty and distaste for public speaking might be reconciled with his authorship of a large number of experimental problems presented publicly to the applause of princes visiting the Collegio Romano, I would like to consider the emergence of a highly specific genre - the Problemata.[65]
As discussed above, the 1586 first edition of the Jesuit Ratio Studiorum had proposed that Clavius should give private lessons in mathematics to eight or ten Jesuits, selected from all the different provinces of the order, in order to furnish the provinces with mathematics teachers.[66] The next published edition of the Ratio (1591) suggested that in addition to this private academia,
once or twice a month one of the students should
recount [enarret] an illustrious [illustre] mathematical problem in a
large gathering of philosophers and theologians, having first been instructed [edoctus], as is proper, by the master.[67]
Some of the surviving mathematical problems presented in the
Collegio Romano are published in the appendices
to the present article. Although these Problemata
are generally anonymous, a significant amount of evidence in addition to
Bettini's attribution, discussed in the notes accompanying each problem,
ranging from references in letters, literary style, internal evidence and
Grienberger's distinctive handwriting, points to Grienberger as the author of all
of these Problemata, which range in
date from 1591, the year of Grienberger's arrival in Rome, to 1614. As a
ceremonial form of culture, such presentations clearly had much in common with
the extravagant public defenses of philosophical theses made by aristocratic
students in the Collegio and so
disparaged by Federico Cesi. In the thesis defenses at the Collegio, studied in detail by Louise Rice,[68]
the script read by the student was generally written by one of the professors,
although if the theses (or the odes composed for the occasion) were printed,
they were accompanied by the student's name. The same practice seems to have
been adopted for the mathematical Problemata,
as suggested by the "instruction" by the master advocated by the Ratio Studiorum. Publication was a rarer
matter in the mathematical presentations, but when it happened, it followed the
same patterns. The Roman publishers Zannetti and Mascardi, favourites for such
philosophical "vanity publications", were also used for the mathematical
problems.[69]
Mixed
mathematical themes in the Problemata
It should perhaps be stressed that the individual modesty that I ascribe to the behavioural patterns of Christoph Grienberger was utterly different from the prescriptions of cognitive humility with regard to the mysteries of the natural world that characterised much theological discourse of the late sixteenth century discussed by Carlo Ginzburg.[70] Indeed, Grienberger's refusal to accept authorial dignities, and his confessions of bodily weakness[71] coexisted with the flow from his pen of a series of claims for the exalted powers and cognitive capacities of mathematicians with respect to the natural world. Such a combination of individual modesty with elevated claims for the power of a collectivity is a feature that can be found elsewhere in Jesuit culture, perhaps reaching its zenith the 1640 Image of the First Century of the Society of Jesus published to mark the centenary of the order.[72] As Marc Fumaroli has shown, the anonymous Jesuit compilers of this work excused its rather immodest claims for the achievements of the Society by attributing these achievements indirectly to Jesus, in whose hands the Society that took his name was merely a passive instrument. This relationship was captured emblematically by a device in which the Society of Jesus was the moon, reflecting the light of the Sun, representing Christ[73]. Another emblem in the same book reinforces the idea of the Society of Jesus as a passive, mechanical device, manipulated by Divine Love to raise the earth towards heaven by means of conversion (fig. 7). The device used is similar to one which forms the topic for one of Grienberger's most spectacular mathematical Problemata, dating from 1603 (fig. 8).[74] The problem in question, later plagiarized unashamedly by Gaspar Schott (fig. 9),[75] provides a graphic example of the enormous power over nature which Grienberger ascribed to the collectivity of mathematical practitioners.
Grienberger's speaker intends to demonstrate to his audience that "by means of no more than 24 wheels with toothed axes, the Earth's globe, even if it were made entirely of gold, could be driven away from the centre [of the universe], by the force of only one Talent".[76] The demonstration of this highly Archimedean claim is preceded by a long passage extolling the virtues of mathematics that is anything but modest.
"The boldness of Mathematicians," Grienberger begins, "has always been great, as has their power, Most Religious Fathers and other most honourable members of the audience; and they possess so much spirit in a small number of people, that there is nothing in the whole universe either cloaked in darkness or buried in difficulties that has been able to escape their ingenuity and that has not been investigated with their machines”.[77] Although nobody could doubt that the motions of the heavens had been translated into the laws of mathematics [leges Mathematicorum], someone might still query the dominion of mathematicians over the elementary world. However, "the elements themselves", Grienberger continues, "love to be governed by mathematics as much as they love their own dignities and powers, and prefer to be ornamented by mathematicians than to be reduced to almost nothing by natural philosophers".[78] The Naturales dress the elements poorly, in the different qualities of heat, cold, wetness and dryness, and imprison them in concentric spheres.
Why should [the elements] not be miserable, then,
being so poorly dressed, confined in prisons and constrained to serve people
that treat them so badly. They dig into the earth with ploughs, and utterly
disembowel it even to wrench out a handful of gold. They make water wash all
the filthiest people; condemn air to the mills and grindstones, and fire to the
furnaces. There is no service that is so vile that [the elements] are not
subjected to it [...] It should not seem strange, then, if the elements would
happily resort to the Mathematicians, who care for their dignity, and whose
works often free them from prison, and bring them into the gardens and palaces
of kings.[79]
The elements are happier under the dominion (imperia) of mathematicians than that of physicists, or natural philosophers. As the passage cited shows, in Grienberger's text, the social and cognitive status of the mathematical disciplines are inextricably entangled. Archimedes’ reputed military exploits at the siege of Syracuse with the aid of giant burning mirrors provide Grienberger with a vivid demonstration of the quasi-Promethean ability of mathematicians to steal Fire from heaven. Rather than invoking the astrological assistance of Jupiter, Archimedes wrought destruction on the Roman fleet by sheer mastery of the science of conics.[80] Moving on to the elements of Water and Air, Grienberger suggests that his audience need only read Heron’s De Spiritualibus to see their mathematical manipulation, or look at the device constructed by Giannello Torriano in Toledo to raise the water of the Tagus to the level of the city, the bird-fountains in the gardens of the Villa d’Este at Tivoli, or the hydraulic organ in the gardens of the papal Palazzo del Quirinale in Rome “in which merely by the flow of water, which provides the air and moves the wheels, the sound of an organ is reproduced without anybody playing”.[81] It is the remaining Aristotelian element -- namely Earth -- that Grienberger wishes to “exalt” on this particular occasion, however. As knowledge of the weight of the true terraqueous globe is the prerogative of God alone, Grienberger manufactures a false “geometrical” earth for his spectators, made entirely of gold, which he then attempts to raise by means of a system of 24 wheels at a mutual gearing of 1:10. Grienberger calculates that if the first wheel of this device (see fig. 8), which he borrows from Pappus’ Mathematical Collections, is rotated 40,000 times in one hour [i.e. around 11 times per second] the final wheel, attached to the rope lifting the earth will still take 100 million million years to complete a single revolution.[82] Grienberger suggests that the power for his earth-lifting device might be provided by a man in a treadmill, perhaps taking Archimedes’ reported claim over-literally, but cautions humourously that “I will not weave those ropes, or prescribe the material for the wheels or the place from which the machine shall be suspended: as these are other matters I leave them for others to find”.[83]
The high social status of the mathematical disciplines is a pervasive theme in Grienberger’s other Problemata. When Grienberger first arrived in the Collegio Romano in 1591, he delivered an oration on the mathematical disciplines, much of which was taken up with establishing the nobility of the family made up by the seven mathematical 'sisters': Arithmetic, Geometry, Music, Astronomy, Mechanics, Geodesy, Perspective and Practical Arithmetic (Supputatrix).[84] In the midst of a rather labyrinthine account of the resemblances and quasi-incestuous interrelations between the different 'sisters', he mentions an experiment to show that the study of perspective furnishes the causes of appearances that would otherwise remain a mystery, an experiment that is taken up and performed by the narrator of the following Problema.[85] Despite the iconic status of Archimedes’ performance at Syracuse, mathematical wonders were not limited to the military domain, and Grienberger also describes a trick-picture, possibly an anamorphosis, which he had heard of, in which a forest landscape seen from one position is transformed into a picture of the Emperor with his brother when one looks through a specially constructed hole.[86] As well as being an ancestral mathematical powermonger, Archimedes also provided a source for the credibility of the early-modern mathematical practitioner, and Grienberger makes much of the story (recounted by Proclus) that Hieron, King of Syracuse, ordered that everything Archimedes said should be believed.[87]
Describing the audience of his 1595 oration to mark the beginning of studies to Clavius, Grienberger wrote that
Our Reverend Father General was there, unexpectedly,
along with several other unexpected people, and he seemed to apprehend the
matter with some delight, as I understood afterwards from Father Pereira, who
complained to me because I didn't invite him.[88]
Pereira was unhappy not to be invited to hear Grienberger's discourse (one of the very few public speeches that he seems to have given in person), and indeed the statements about mathematics made at the beginning of the 1595 oration were little short of anathema to Pereira's perception of the cognitive impotence of the mathematical disciplines, discussed above:
You know that the whole of Philosophy is divided
chiefly into three kinds of Sciences: Natural, Mathematical and that divine one
that is called Metaphysical. The first one verifies for itself things immersed
in matter, that is, abstracted neither from reality nor from reason. The last
one assumes as its objects things that are utterly alien to matter. Even if the
other two might seem to have all things distributed between them, the middle
one, however (which, even by virtue of being the middle one can be said to be
more excellent than the others), finds that in [treating] the same matters it
ascribes them to itself in such a way that in its object it nevertheless in no
way defrauds the other [sciences]. [89]
Although mathematics considered quantity abstracted from any specific material incarnation, such abstraction rendered mathematical truths universal in their application, rather than inapplicable to the natural world as Pereira and others wished to suggest[90]. The theme, later to be central to Giuseppe Biancani's De mathematicarum natura dissertatio (1615)[91] recurs frequently in the other Problemata, which Biancani may have had the opportunity to read during his time as one of the academicians in the Collegio Romano.[92] Mathematical conclusions made about quantity in general were applicable to any physical quantity, including motion; and Grienberger completes his oration with the suggestion that the possibility of incommensurable lengths implied the possibility of real incommensurable motions. The other Problemata put the application of mathematics to natural motions into action, and include one dealing with the motion of a weight attached to a rod, influenced by the medieval calculatores and Tartaglia, and another on the reality of the motions of the heavens described by astronomers.[93] In the latter, Grienberger, furthering an argument put forward in Clavius's Commentary on the Sphere of Sacrobosco, considers the motion of an ant on a moving table, to demonstrate, against the views of Pereira and the other "homocentrists",[94] that a single body, could possess two real motions simultaneously without involving a contradiction. This allowed Grienberger to argue for the reality of the convoluted motions ascribed to the planets by astronomers, although he avoids confronting the vexed question of the Aristotelian distinction between natural and violent motion. As geometry pervades Grienberger's depiction of the natural world, so it inhabits the artificial domain of buildings and other institutions necessary to civic life. In one Problema, Grienberger writes that
Without doubt that Bolognese structure [i.e. the
Torre degli Asinelli in Bologna] had an outstanding mathematician as its
architect [delineator] by whose
vigilance Geometry has come to inhabit that tower.[95]
Another problem was prompted by the disagreement between a group of Spanish sailors and a group of Portuguese sailors who arrived simultaneously in Lisbon, having circumnavigated the world in opposite directions, and unable to decide which day was Sunday,[96] and indeed the Gregorian Calendar, co-authored by Clavius, is an obvious example of an enormous mathematical artifice of a religious and civic nature.
On February 5th 1612, Christoph Grienberger interrupted a letter that he was writing to Galileo to report the news of Clavius's death in "real time":
While I pause from writing
for a moment, behold here is someone who rushes to announce that our Clavius is
about to be given his Travelling money, which he accepted this very evening at
the first hour of the night. So do not be surprised that I break off this
letter in a rather untimely fashion - such news does not allow me to linger any
longer on these matters. You will learn more from the bearer of the letter,
Father Odo van Maelcote, who, by returning to Flanders has shackled me once
more to the mathematics classes.[97]
Grienberger's relationship with Galileo had been strengthening steadily since 1611, as the physical powers of his senior colleague Clavius decreased. The Ad benevolum lectorem introducing Grienberger's 1612 star-charts eulogises Galileo's telescopic observations in highly charged language[98]. The decline of Clavius brought the Austrian and the Tuscan ever closer; and after Galileo's triumphal visit to the Collegio Romano Grienberger spoke eagerly to Galileo of future reunions of the aging Clavian telescope of the Collegio with Galileo's instrument.[99] Galileo's anger at the criticism of his opinions on the heights of lunar mountains by a Jesuit in Mantua led him to write a long letter to Grienberger to defend his position in detail[100]. Replying on the "anniversary of the death of our most beloved Clavius", Grienberger displayed a prudence that brings into relief the boundary of the corporate culture within which he carried out his work:
Do not be surprised that I am silent about your [letter]: I do not have the same liberty as you do.[101]
To have entered the dispute on Galileo's side would have constituted a breach of discipline for Grienberger, and would have been incompatible with his institutionalised modus procedendi. Instead, as ever, he breaks his silence through the words of others. A young former pupil of Galileo's studying in the Collegio Romano, Giovanni Bardi, wrote to him to describe a meeting with Grienberger:
I visited Father Grienberger on behalf of Your Lordship and saluted him in your name. He returns your salutations doubled. I asked him for his opinion on that book [i.e. Galileo's Sunspot letters] which he had already seen and he said that he thought very well of it, and that on this subject, as on the other matter of things that float on water, he was of [the opinion] of Your Lordship.[102]
Galileo had spent much of 1612 embroiled in a bitter dispute with a group of Florentine Aristotelians about the cause of flotation of flattened bodies having a “weight” greater than that of water. As the early part of the debate has been discussed at length elsewhere[103] I shall limit my discussion to a brief summary. Vincenzo di Grazia's claim that ice was condensed water was attacked by Galileo, who pointed out that in this case ice would sink, as is patently contrary to experience. Di Grazia replied that ice floated because of its flat shape, and a dispute quickly flared up about the true cause of the flotation of bodies. Ludovico delle Colombe then joined the debate, and began performing experiments in public with chips of ebony to demonstrate that, in this case, shape, not heaviness, was the cause of flotation. Galileo's Discorso intorno alle cose che stanno in sù l'acqua was published in 1612[104], and attempted to explain the flotation of the anomalous ebony chips in terms of a small dip in the surface of the water, leading the the combined weight of ebony and air to be less than that of water.
Bardi complained to Galileo that, although Grienberger was very much in agreement with the Archimedean conclusions of the Discorso, students with only half a year of philosophy were pronouncing ridiculous judgements on the work, and the remaining professors were not yet discussing it.[105]
Grienberger’s backstage participation in the polemic surrounding Galileo’s Discorso illustrates both the possibilities and the limitations of the new public space for mathematical and experimental demonstrations provided by the Problemata in the Collegio Romano, a space that Grienberger had by now made his own. Previous problemata, particularly that concerning the nova of 1604[106] and the Nuntius Sidereus Collegii Romani recited by Odo van Maelcote in 1611[107] had demonstrated that the mathematicians of the Collegio Romano were prepared to risk conflict with the professors of Aristotelian natural philosophy by openly endorsing observations that challenged Aristotelian teachings concerning the incorruptibility of celestial matter. The dispute on galleggianti demonstrated that, under Grienberger’s guidance and instruction, they were willing to extend the domain of conflict to the most Archimedean domain of hydrostatics.
Bardi served as Grienberger’s public mouthpiece on this occasion. On 20th June 1614, Bardi wrote to Galileo sending him the text of the presentation in defence of Galileo's position that he was to make in the Collegio Romano.
As one of these Problems had to be done, and it was
allocated to me, Fr. Grienberger asked me what I would like to treat, proposing
some other things to me. I told him
that I would have liked to deal with some matter similar to this, so he took
this, which I think will please you no small amount, because it conforms
entirely with your opinion, or rather it is your opinion, with the addition of
those two experiments that cannot but support your view. And Fr. Grienberger
told me that if he hadn’t had to have respect for Aristotle, whom they are not
allowed to oppose in any way by order of the General, but must always save, he would have spoken more clearly than he
did, because in this [matter] he is entirely on your side; and he told me
that it is no wonder that Aristotle is in opposition, because he was most
clearly mistaken in that which Your Lordship told me once about those two
weights falling earlier or later[108]
The wording of Bardi’s letter is slightly ambiguous with regard to the authorship of the text he was to recite three days later. Nonetheless, Bardi’s claim that Grienberger “would have spoken more clearly than he did” clearly refers to the immediate context of the floating bodies debate, as shown by the remainder of the letter. Grienberger and Galileo had not met since the outbreak of the debate, and none of the previous surviving letters from Grienberger to Galileo mentions the dispute on floating bodies. I would like to suggest that Bardi is telling Galileo that Grienberger “would have spoken more clearly than he did” in the enclosed Problema, due to be recited by Bardi, but written by Grienberger on Bardi’s suggestion. This interpretation is consonant with a significant amount of additional evidence. The only surviving manuscript of Bardi’s presentation, entitled De ijs quae vehuntur in aquis, is preserved amongst Grienberger’s papers, where it is bound between rough trigonometric tables and a draft of his Problema on the basic principles of algebra. The differences between this text and the printed version suggest its priority – the manuscript contains corrections which are incorporated in the printed text. The handwriting of this Problema is identical to Grienberger’s other Problemata. Despite Bardi’s professed studies with Galileo and Grienberger no other evidence of his mathematical ability exists besides this single Problema and before its appearance Galileo dismissed his hydrostatic concerns as puerile.[109] The most recent discussion of Bardi’s text suggests that Bardi was subsequently unproductive, despite this prodigious beginning, due to eye-problems[110], but an attribution to Grienberger seems a more economic explanation. The sources cited in the Problema, including the works of Marino Ghetaldi and Juan Bautista Villalpando, are also cited elsewhere in Grienberger’s writings. Stylistically, the Problema De ijs quae vehuntur in aquis is also entirely in accordance with Grienberger’s other Problemata, as demonstrated by the excerpts published in the appendix.[111] From what we have seen of Grienberger’s behavioural patterns, it is unsurprising that Grienberger made no attempt to arrogate the work for himself, and indeed, as Bardi’s letter indicates, the Jesuit system of censorship made it more convenient for such a work to appear under the name of a lay-person.
Grienberger’s caution seems to have been grounded on fact. On 14 December 1613 the ageing Jesuit general Claudio Acquaviva had issued a lengthy Ordinance for the solidity and uniformity of doctrine to all of the Jesuit provinces. While strenuously criticising departures from Thomist theology, Aquaviva also condemned the introduction of new opinons in philosophy, and ordered the Provincials to ensure “that the opinions that are taught in philosophy are subservient to theology, and that our philosophers follow Aristotle alone, wherever his teachings are not at variance with catholic truth”.[112] An attempt by the Jesuit mathematician Giuseppe Biancani to publish a similar work supporting Galileo’s position in the floating-bodies debate fell foul of the Jesuit censors shortly after Bardi’s presentation because it was “an assault on, not an explanation of Aristotle […]. And the conclusion and arguments of the work are not those of the author, but of Galileo: it would have been enough to have read them in Galileo’s work. To transcribe in the books of Ours [i.e. Jesuits] the discoveries of Galileo, especially those by which he attacks Aristotle, seems neither decent nor expedient”[113]. These were accusations to which “Bardi”’s work would have clearly been equally prone, had they not avoided Jesuit censorship altogether.
Bardi, I am suggesting, did little more than provide the occasion for Grienberger to give public legitimation to Galileo’s explicitly anti-Aristotelian conclusions in the Collegio Romano in the courtly and collegiate context of a Problema. Without delaying more on the question of attribution, I would like to move on to the content of Bardi’s theatrical hydrostatic performance. Bardi described the planned event in some detail in his letter to Galileo
There will be, in addition to the paintings [dipinte] and printed sheets [stampate], all of these experiments on a
table, so that they can be seen by everybody, in such a way that they cannot
deny what they see with their eyes[114]
The reference to dipinte suggests either a large panel bearing the picture (fig. 10) appended to the end of the manuscript, or possibly small copies distributed to each member of the audience which could be taken away as souvenirs. Bardi's reference to stampate is not so clear, but may refer to a printed list of his Archimedean conclusions, handed out to the members of the audience, possibly accompanied by schematic diagrams bearing the letters that he cites in his talk. Shortly after the event Stelluti wrote to Galileo giving a full report of Bardi's performance. He described his delight in seeing Galileo's opinion defended to rapturous applause, and admired the "experiments made in the presence of everybody by Father Christoph Grienberger, after he had brought all of the instruments which you can see in the enclosed picture into the room where the Problem was recited”. Stelluti observed that "although there was the odd Peripatetic who shook his head... everything was made quite clear by the end". Stelluti also provides crucial information on the audience, which included, as well as Stelluti himself and Federico Cesi, the brother of the latter, Bartolommeo Cesi, the mathematicians Luca Valerio[115] and Johannes Faber and other Prelates and "signori letterati". All of these spectators were, Stelluti continues, "extremely satisfied to see such a "good Jesuitical demonstration" towards Galileo, to the annoyance of his imitators.[116]
The opening of Bardi’s talk recounts Galileo’s recent metamorphosis from sidereal messenger into Neptune. Announcing his aim to “uncover the cause by which things that should sink in water […] are discovered to float in water” in accordance with Galileo’s explanation, Bardi frames the polemic in distinctly violent terms:
[F]rom this dissertation of ours it is to be hoped
that every victory and every trophy of truth will be in your possession. The
material will be abundantly supplied by Experience which, as it fights for the
cause of this serious dispute, as in a battle, gathers soldiers, provides them
with weapons, and urges them to war, and, like anyone who wishes to encourage
people to fight vigorously, must take up a position on the front line itself.[117]
The wonderful drawing appended to Bardi’s presentation (fig. 10) illustrates the extent to which Grienberger’s mathematical problemata drew on Jesuit traditions in emblematics. The use of putti to perform experiments, later to become widespread, was a convention first adopted a year previously by Rubens in his illustrations for the Jesuit Francois Aguilon’s collosal work on optics, the Opticorum libri sex.[118] Rubens appears to have drawn some of his inspiration from the iconographic conventions of the profusion of Jesuit emblem books representing divine and profane love that flourished in the late sixteenth century.[119] In our case, as we are informed that the experiments described by Bardi were actually carried out by Grienberger, the performing putti might be said to represent his ultimate act of iconographic self-effacement - Grienberger's only surviving self-portrait, one might say.
Pictures, as well as words, formed essential tools for persuasion in the Jesuit rhetorical tradition.[120] Works such as Jeronimo Nadal’s Evangelicae Historiae Imagines used carefully crafted engravings to reinforce the gospel message, and played a crucial role in Jesuit missionary work.[121] Grienberger’s lavish illustration, far more elaborate than the few schematic diagrams present in Galileo’s own Discorso, also formed an integral part of the persuasive artillery of Bardi. Central to the illustration is the phenomenon that formed the focus of Galileo’s dispute with the Florentine Aristotelians: a flat metal disc floating in a circular dish full of water, accompanied by two putti locked in discussion. The Galileian conclusion – namely that the plate floats because of a small dip in the water’s surface – a “well” (puteus) in the language of Bardi/Grienberger, is assumed in the diagram, which gives the water’s surface a conspicuous hollow. Such a minuscule experimental phenomenon is unlikely to have been easily visible to the grouped aristocratic and ecclesiastic spectators, unless their gaze was carefully shepherded. While Galileo’s Discorso legitimated its own existence by arguing that writing was more efficacious than speech as a means of distinguishing truth from falsehood,[122] Bardi’s oration endorsed direct, shared ocular experience, assisted by instruments.
Some things
are heavier than others, others are lighter, and some are of the same weight
[as each other]. It is by means of balances [bilances], scales [trutinae]
and steelyards [staterae]that weights
are conferred on heavy bodies. Although these are common [devices] neither
Philosophy nor Mathematics abhorrs them.[123]
Grienberger’s rough manuscript notes and calculations (see fig. 16) reveal that he was no stranger to the balance, and conducted a series of measurements of the specific gravities of different metals in the wake of Marino Ghetaldi’s Archimedes Promotus. A representative excerpt, in coarser style than the public Problemata, reads as follows:
The weight of the cylinder in air according to one of my observations is 1 pound and 11.1/4.1/8.1/128 ounces. In water, however, it is 1 pound and 8 1/8.1/16.1/64 ounces, or, in 128th parts of an ounce, 2993 parts in air and 2586 parts in water, and since the difference is 407 parts a cylinder of water equal to the cylinder of tin will thus be of 407 parts, and the proportion of the weight of tin to the weight of water will thus be 2993 to 407.[124]
Returning to the public stage of Bardi’s Problema, it might be opportune to consider the remaining experiments illustrated in his diagram (fig. 10). On the left we have a floating brass ‘boat’ (scapha), which the weight of the putto is insufficient to submerge. On the right is a further “miracle of nature”: a cylindrical tube, beneath which a lead plate remains suspended when plunged into water. Grienberger suggests that this additional experiment, taken from Simon Stevin, provides additional evidence that a cylindrical “well” of air can lead bodies heavier than water not to sink. The device in the upper-middle is another experiment derived from Stevin – a scales in which 10 pounds of lead are balanced by only 1 pound of water, through the insertion of a cylinder fixed to the wall which occupies the space of 9 pounds of water. Grienberger/Bardi suggests that since the shape of the immersed body is arbitrary, this provides further evidence in favour of Galileo, and in direct opposition to the Florentine Aristotelians, that “in similar experiments no account whatsoever should be taken of shapes or resistances of the medium”.[125]
Bardi hoped that the publication of “his” text would provide a non-Italian public with a Latin compendium of the central teachings of Galileo’s Discorso.[126] Federico Cesi, to whom Bardi wished to dedicate the work was unhappy with the dedicatory letter, complaining obliquely to Galileo that “when one is dealing with men who are truly great, I would like them to be treated in a fitting manner”.[127] Stelluti elaborated to Galileo that Cesi objected to the dedication “both because he did not state that it was recited in the said College [i.e. the Collegio Romano] and because he does not give your Lordship the mention that your valour deserves, passing over it with most languid expressions”.