Guarino Guarini

Born: 1624 in Modena, Italy
Died: 1683 in Milan, Italy

In the age-old connections between art and mathematics - however either is defined - no one is more worthy of attention than the Italian Baroque figure of Guarino Guarini. Trained as a theologian in the small but elite order of Counter-Reformation Clerics Regular, commonly known as the Theatines and the immediate model for the Jesuit Order, Guarini was also deeply interested in mathematics following in turn the Jesuit pursuit of all the arts and especially the new discoveries that surrounded the curious-minded of the Age of Discovery.

Guarini spent his novitiate in Rome where he learned at first hand what Bernini and Borromini, now recognised as great masters of Baroque architecture, were doing, and their example presumably caused him to practice architecture, then considered as a mathematical art but not strictly a member of the Quadrivium, the mathematical division of the Liberal Arts, still supreme in the world of learning. He then spent years teaching and building in Italy and Paris, all of his structures having now disappeared.

In 1666 he was called from Paris by the Duke of Savoy and Prince of Piedmont to his capital Turin, to take over the design of a great dynastic chapel to house the Holy Shroud, located within the Palace but opening into the choir of the adjoining Cathedral. This was to be his masterwork - la Capella dello Sindone, sadly badly damaged by fire in 1997. He remained in Turin for the rest of his life publishing mathematical works and tutoring the ducal family, while the Sindone Chapel was finally completed after his death.

Even from the beginning of the eighteenth century there was a turn against the triumphs of the Baroque, so that we now have great difficulty in understanding such a figure as Guarini and his work, which also includes his mathematical philosophy and figural meaning, or geometrical iconography. Many recent critics have muddied the waters by tending to see him as a precursor of the 'new philosophy' of the seventeenth century, including Sigfried Giedion, Rubolf Wittkower and Alberto Perez-Gomez. As can be seen from his Placita philosophica (Paris, 1665), the Modenese cleric was a reformer of Aristotelianism and a staunch supporter of the official Second Scholastic in common with both contemporary Catholic and Lutheran authorities, while at the same time open to well-considered innovations but within traditional limits. He was familiar with contemporary mathematics especially geometry, but did not adopt algebra - his encyclopedic Euclides adauctus et methodicus mathematicaeque universalis (Turin, 1671) was aimed at clerical students unable to command such a newfangled technique, or maybe he had his own reservations about it. Certainly for him, Universal Mathematics, proclaimed in the title of the Euclides adauctus, was to do with a purely contemplative usage of traditional canonics or harmonics based on Book V of Euclid. This concerned the determination of mean and extreme proportion expressed in perspectival constructions - the perspectival ladder of Brunelleschi, Alberti and Piero della Francesca, an alternate adaptation of the machine of Eratosthenes for finding two mean proportionals, also described as the mesolabium in Vitruvius, Book IX. In much of this work he is a follower of Gregory of Saint-Vincent, S. J., in the summation to infinity implicit in the perspectival ladder.

The line that Guarini refuses to cross is to pass from Universal Mathematics to mathesis, a term which for him seemed to represent the rising physico-mathematics of the Cartesian school. His reason for this is that ancient and medieval mathematics was not linked to causality, which was properly examined through discourse in the manner of Aristotelian physica or cosmology. He certainly believed in his Universal Mathematics, transcending all material concern to be analogous to a divina scientia, developed in the sixteenth century as a defence against scepticism, i. e. the alignment of mathematics with metaphysics or first philosophy. His notions were of course not singular, having been promulgated by Francesco Barozzi and Guiseppe Biancani, S. J. (Aristotelis loca mathematicis, Bolgna, 1615), and were espoused by John Wallis, the best English mathematician of the day, when he stated that beyond the equalities of quantity remained the similitude between qualities, i. e. proportion, which:-

... belongs more to quality than quantity.
Guarini referred to Wallis among the few authorities for his mathematics - both were involved in summation to infinity.

Guarini was adept at most applications of advanced curvature and projective techniques, if not indulging outright in the projective geometry of Desargues as his modern admirers have alleged, confusing 'projection' with 'projective geometry'. Guarini was therefore proficient in the French tradition of stone cutting using most difficult procedures, as well as gnomonics, or the study of sundials, devoting many published pages to each discipline. The key to such attitudes can be found in the Jesuit Bolognese belletrist and mathematical encyclopedist, Mario Bettini, who Guarini implicitly relied upon in much of his work. However while there are some indications of rationalising the elements of architecture more geometrico, found in his Architectura civile, Guarini accepted the traditions of Vitruvius and the High Renaissance with a bracing freedom in the decorative development of the orders, as well as a innovative appreciation of the daring of Gothic structure, exceptional at this date.

Guarini wrote a great summa of philosophy which carried a treatment of light, strictly discursive in manner, and he was reluctant to separate light from its traditional transcendental interpretation. Guarini was aware of the transformative implications of geometrical processes, especially through light, optics and projection so rhetorically advanced by Bettini. His great achievement must surely lie in the protracted if complex elaboration of mathematics and advanced architecture that was even in his own day little understood, elegant and elite answers to great challenges that have been either maligned or misinterpreted since.

Article by: James McQuillan, Famagusta, TRNC, July 2000.

July 2000
MacTutor History of Mathematics