Tutorial 2. Mathematics and the mechanical arts

In the preface to the Instauratio magna (120: SEH, iv. 14; cf. OFB, xi. 13), Francis Bacon famously contrasted the stasis of theoretical philosophy with the liveliness of the mechanical arts: 

‘For many ages’, he observed, the speculative sciences derived from the Greeks have stood

almost at a stay, without receiving any augmentations worthy of the human race; insomuch that many times not only what was asserted once is asserted still, but what was a question once is a question still, and instead of being resolved by discussion is only fixed and fed; and all the tradition and succession of schools is still a succession of masters and scholars, not of inventors and those who bring to further perfection the things invented.

In the mechanical arts we do not find it so: they, on the contrary, as having in them some breath of life, are continually growing and becoming more perfect. As originally invented they are commonly rude, clumsy, and shapeless; afterwards they acquire new powers and more commodious arrangements and constructions; in so far that men shall sooner leave the study and pursuit of them and turn to something else, than they arrive at the ultimate perfection of which they are capable.

Philosophy and the intellectual sciences, on the contrary, stand like statues, worshiped and celebrated, but not moved or advanced.

This sense of the liveliness and progress of the mechanical arts is nowere better captured graphically than in the series of engravings entitled Nova reperta or New Discoveries, created by Jan van der Straet or Johannes Stradanus a few decades earlier (source no. 1 below). As Stradanus's engravings and other passages from Bacon's Instauratio magna both suggest, the natural home for the mechanical arts in this period was in the civic marketplace as well as the armouries of the great powers. The primary purpose of this second tutorial is to investigate the strengths and limitations of the practically and economically motivated approach to the mastery of nature evident in practical mathematics and the mechanical arts.

A complementary focus of attention is the place of mathematics in the university. To a degree which may seem paradoxical in our utilitarian age, the association of mathematics with mechanical practitioners deflated the prestige of mathematics in most European universities in the sixteenth and early seventeenth centuries. According to the University's most celebrated mathematician of the subsequent generation, John Wallis, Oxford was no exception (source 2); and it was in order to repair this neglect that Henry Saville founded Oxford's first chairs of geometry and astronomy in 1619 (sources 3-4). The same period saw all four disciplines of the mathematical quadrivium -- arithmetic, geometry, music and astronomy -- given parity of esteem with the other liberal arts in the Schools Quadrangle, constructed between 1613 and 1624 (source 5). The same building programme culminated the first introduction of classical architecture into Oxford with the Tower of the Five Orders (source 6). The link between mathematics and the classical orders is nowhere better illlustrated than in the 'Mathematical pillar' (source 7) given to the University in 1620 and originally displayed in the Bodleian Library along with the armillary sphere given by the founder's brother (source 8).  The prescribed selections from The Booke of Five Columns of Architecture by Hans Blum (source 9) are designed to illustrate the fundamentally mathematical basis of the classical orders, while the readings from Plato's Timeus relate to the five Platonic solids displayed on the 'Mathematical pillar' (source 10) and fundamental to Kepler's Mysterium cosmographicum of 1596. Finally, amongst the obligations imposed on the professor of astronoy by Savile's statutes obliged his professors of astronomy to teach 'the whole science ... of gnomonics', and the proliferation of sundials in seventeenth-century Oxford illustrates another aspect of mathematical theory and practice which came to be avidly cultivated in the University in these same years.  

  1. Johannes Stradanus, Nova Reperta (c. 1600): 7 of 22 images: 2. Magnet, 3. Gunpowder, 4. Printing, 5. The mechanical clock, 7. Distillation, 15. Lenses, 19. Copper engraving.
  2. C. J. Scriba, ‘The autobiography of John Wallis’, Notes and Records of the Royal Society, 25 (1970), 17–46, prescribing pp. 22-31, 37-43.
  3. ‘The Foundation of the two Lectureships in the Mathematical Sciences by Henry Savile, 272-84: Oxford University Statutes, trans. Ward, vol. I, 272-4, 277: on
  4. Funerary Monument for Sir Henry Savile (d. 1622), Merton College Chapel.
  5. Schools Quadrangle (1613-24), Bodleian Library, Oxford.
  6. ‘Architectural and Mathematical Model’ (a.k.a. ‘Mathematical pillar’), 1620, MHS Inv. No.  90861.
  7. Tower of the Five Orders (1613-24), Schools Quadrangle, Oxford
  8. Armillary Sphere, Italian?, c. 1580, owned by Henry Percy, 9th Earl of Northumberland (1564-1632), 'The Wizard Earl', presented to the Bodleian Library in 1601 by Sir Josias Bodley, MHS Inv. No. 70229.
  9. Hans Blum, The Booke of Five Collumnes of Architecture, trans. John Thorpe (1608), pp. 1-6.
  10. Oster, Science in Europe, pp. 1-8: extracts from Plato, Timeus. 

Credits: Howard Hotson (September 2018)

Image: Entrance to the Schola naturalis philosophiae, Schools Quadrangle (1613-24), Oxford. Photo: Howard Hotson, 25 Feb. 2017.