Location: Bizzell Memorial Library, 5th floor Exhibit Hall.
What does it mean to say that mathematics is the language of nature?
Galileo’s controversy over the comets illustrates how difficult it may be to implement novel research methods in science.
Galileo asserted that mathematics is the language of nature. He challenged the established discipline of natural philosophy, or physics, which relied upon non-mathematical methods. Physicists were not trained in mathematics, any more than theologians. Practitioners of both physics and theology regarded mathematics as unable to reach true conclusions about the physical world.
Paradoxically, Galileo’s polemics about mathematics as the language of nature occurred in the midst of controversies with fellow mathematicians. Even for mathematicians, mathematical methods alone proved unable to resolve the enigmas they faced.
Section 1: Systems of the World
Early modern astronomers experimented with geometrically equivalent cosmic systems, debating diverse systems of the world. Given that the competing systems produced identical planetary predictions, astronomers searched for other kinds of observations that might decide between them. Comets seemed to cross through multiple spheres. The spheres of Mars and the Sun seemed likely to intersect. Several systems predicted that Venus might show phases. The Copernican system predicted “stellar parallax,” that stars should appear to slightly shift in position, which was not observed. Definitive evidence that could decide the true system of the world proved elusive.
1. Athanasius Kircher, Iter exstaticum (Würzburg, 1660), "Ecstatic Journey through the Heavens"
2. Valentin Naibod, Astronomicarum institutionum (Venice, 1580), "Principles of Astronomy"
3. Christoph Clavius, In sphaeram Ionnis de Sacro Bosco commentarius (Rome, 1570), "Commentary on the Sphere of Sacrobosco"
4. "Galileo shows the satellites of Jupiter to the Venetian Senators,” from Louis Figuier, Vies des Savants Illustres (Paris, 1870)
5-10. Tycho Brahe, portrait (5), framed prints: Copenhagen (6); Hven (7); Gardens (8); Uraniborg (9); architectural plan (10).
11. Tycho Brahe, Astronomiae instauratae mechanica (Nuremberg, 1602), ”Instruments for the Restoration of Astronomy"
12. Tycho Brahe, Epistolarum astronomicarum (Uraniborg, 1596), ”Astronomical Letters"
13. Tycho Brahe, Opera omnia (Frankfurt, 1648), "Complete Works"
14. Simon Mayr, Mundus Iovialis (Nuremberg, 1614), "The World of Jupiter"
15. Giuseppe Biancani, Sphaera mundi (Bologne, 1620), "Sphere of the Universe"
16. Nicolaus Reimarus Ursus, Fundamentum astronomicum (Strassburg, 1588), "Astronomical Foundation"
17. David Origanus, Novae motuum coelestium ephemerides Brandenburgicae (Frankfurt on the Oder, 1609).
18. Giambattista Riccioli, Almagestum novum (Bologna, 1651), Part 2, "The New Almagest" (Part 1)
19. Gabriele Beati, Sphaera triplex (Rome, 1662), "The Three Spheres"
20. Nicolas Bion, L’Usage des Globes Caeleste et Terrestre, et des Sphaeres, suivant les diffaerens Systaemes du Monde (Paris, 1710), "The Use of Celestial and Terrestrial Globes, and Spheres, according to the different Systems of the World"
Section 2: Comets
Since antiquity, comets posed an enigma. They appear without warning. They do not stay within the Zodiac like the planets. They come from different directions. Their speed and brightness change radically. Their tails always point away from the Sun. Parallax was observed for the Moon but not for comets. This implied that comets are farther away than the Moon, contrary to Aristotle’s argument that comets are fiery vapors in the upper atmosphere.
21. Abbildung und Beschreibung deß wunderwürdigen unvergleichlichen Cometen (Nuremberg, 1680), broadsheet; "Illustration and Description of the Incomparably Great Comet"
22. Johann Hevelius, Cometographia (Gdansk, 1668), "On Comets"
23. Johann Hevelius, Annus climactericus (Gdansk, 1685), "The Climactic Year"
Section 3: Controversy
While mathematicians resisted the attempts of physicists and theologians to discount their conclusions, even mathematical methods alone were not able to resolve the enigmas of comets, parallax, and diverse systems of the world. Galileo engaged in polemics against the system of Tycho Brahe that went beyond the evidence available at the time.
24. Oratio Grassi, De tribus cometis anni MDCXVIII (Rome, 1619), "On the Three Comets of 1618"
25. Johann Kepler, De cometis qui annis 1607 & 1618 (Augsburg, 1619), "On the Comets of the years 1607 & 1618"
26. John Bainbridge, An astronomicall description of the late Comet (London, 1619)
27. Galileo (Mario Guiducci), Discorso delle Comete (Florence, 1619), "Discourse on the Comets"
28. Oratio Grassi, Libra astronomica (Perugia, 1619), "The Astronomical Balance"
29. Giovanni Battista Stelluti, Scandaglio sopra La Libra Astronomica (Terni, 1622), "A Probing of the Astronomical Balance"
30. Galileo, Il Saggiatore (Rome, 1623), 1st ed., early state, "The Assayer"
31. Galileo, Il Saggiatore (Rome, 1623), 1st ed., later state, "The Assayer"
32. Oratio Grassi, Tractatus de sphaera (Rome, 1623), ms., "Treatise on the Sphere"
33. Johann Kepler, Tychonis Brahei dani Hyperaspistes (Frankfurt, 1625), "The Shield-Bearer for Tycho Brahe"
34. Oratio Grassi, Ratio ponderum librae et simbellae (Naples, 1627), ”A Comparison of the Weights for The Astronomical Balance and the Small Scale"
- Christopher M. Graney, Setting Aside All Authority: Giovanni Battista Riccioli and the Science Against Copernicus in the Age of Galileo (Notre Dame, 2015).
- Stillman Drake, ed. and trans., The Controversy on the Comets of 1618.