Is God a Mathematician_ - Mario Livio [37]
This text beautifully demonstrates the fine line that Jesuit mathematicians had to walk at the beginning of the seventeenth century. On one hand, Grassi’s criticism of Galileo was entirely justified and penetratingly insightful. On the other, by being forced not to commit to Copernicanism, Grassi had imposed upon himself a straitjacket that impaired his overall reasoning.
Galileo’s friends were so concerned that Grassi’s attack would undermine Galileo’s authority that they urged the master to respond. This led to the publication of The Assayer in 1623 (the full title explained that in the document “are weighed with a fine and accurate balance the contents of the Astronomical and Philosophical Weighing Scales of Lothario Sarsi of Siguenza”).
As I noted above, The Assayer contains Galileo’s clearest and most powerful statement concerning the relation between mathematics and the cosmos. Here is that remarkable text:
I believe Sarsi is firmly convinced that it is essential in philosophy to support oneself by the opinion of some famous author, as if when our minds are not wedded to the reasoning of someone else they ought to remain completely barren and sterile. Perhaps he thinks that philosophy is a book of fiction created by some man, like the Iliad or Orlando Furioso [an epic sixteenth century poem by Ludovico Ariosto]—books in which the least important thing is whether what is written in them is true. Sig. Sarsi, this is not how matters stand. Philosophy is written in that great book which ever lies before our eyes (I mean the universe) but we cannot understand it if we do not first learn the language and grasp the characters in which it is written. It is written in the language of mathematics, and the characters are triangles, circles and other geometrical figures, without which it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth. [emphasis added]
Mind-boggling, isn’t it? Centuries before the question of why mathematics was so effective in explaining nature was even asked, Galileo thought he already knew the answer! To him, mathematics was simply the language of the universe. To understand the universe, he argued, one must speak this language. God is indeed a mathematician.
The full range of ideas in Galileo’s writings paints an even more detailed picture of his views on mathematics. First, we must realize that to Galileo, mathematics ultimately meant geometry. Rarely was he interested in measuring values in absolute numbers. He described phenomena mainly with proportions among quantities and in relative terms. In this again, Galileo was a true disciple of Archimedes, whose principle of the lever and method of comparative geometry he used effectively and extensively. A second interesting point, which is revealed especially in Galileo’s last book, is the distinction he makes between the roles of geometry and logic. The book itself, Discourses and Mathematical Demonstrations Concerning Two New Sciences, is written in the form of lively discussions among three interlocutors, Salviati, Sagredo, and Simplicio, whose roles are quite clearly demarcated. Salviati is effectively Galileo’s spokesman. Sagredo, the aristocratic philosophy lover, is a man whose mind has already escaped from the illusions of Aristotelian common sense and who can therefore be persuaded by the strength of the new mathematical science. Simplicio, who in Galileo’s previous work was portrayed as being under the spell of Aristotelian authority, appears here as an open-minded scholar. On the second day of the argument, Sagredo has an interesting exchange with Simplicio:
Sagredo: What shall we say, Simplicio? Must we not confess that the power of geometry is the most potent instrument of all to sharpen the mind and dispose it to reason perfectly, and