Is God a Mathematician_ - Mario Livio [38]
Simplicio appears to agree and he introduces the comparison with logic:
Simplicio: Truly I begin to understand that although logic is a very excellent instrument to govern our reasoning, it does not compare with the sharpness of geometry in awakening the mind to discovery.
Sagredo then sharpens the distinction:
Sagredo: It seems to me that logic teaches how to know whether or not reasoning and demonstrations already discovered are conclusive, but I do not believe that it teaches how to find conclusive reasoning and demonstrations.
Galileo’s message here is simple—he believed that geometry was the tool by which new truths are discovered. Logic, on the other hand, was to him the means by which discoveries already made are evaluated and critiqued. In chapter 7 we shall examine a different perspective, according to which the whole of mathematics stems from logic.
How did Galileo arrive at the idea that mathematics was nature’s language? After all, a philosophical conclusion of this magnitude could not have suddenly materialized out of thin air. Indeed, the roots of this conception can be traced all the way back to the writings of Archimedes. The Greek master was the first to use mathematics to explain natural phenomena. Then, via a tortuous path passing through some medieval calculators and Italian court mathematicians, the nature of mathematics gained the status of a subject worthy of discussion. Eventually, some of the Jesuit mathematicians of Galileo’s time, Christopher Clavius in particular, also acknowledged the fact that mathematics might occupy some middle ground between metaphysics—the philosophical principles of the nature of being—and physical reality. In the preface (“Prolegomena”) to his Comments on Euclid’s “Elements,” Clavius wrote:
Since the mathematical disciplines deal with things which are considered apart from any sensible matter, although they are immersed in material things, it is clear that they hold a place intermediate between metaphysics and natural science, if we consider their subject matter.
Galileo was not satisfied with mathematics as the mere go-between or conduit. He took the extra bold step of equating mathematics with God’s native tongue. This identification, however, raised another serious problem—one that was about to have a dramatic impact on Galileo’s life.
Science and Theology
According to Galileo, God spoke in the language of mathematics in designing nature. According to the Catholic Church, God was the “author” of the Bible. What was one to make then of those cases where the mathematically based scientific explanations seemed to contradict the scriptures? The theologians of the 1546 Council of Trent answered in no uncertain terms: “No one relying on his own judgment and distorting the Sacred Scriptures according to his own conception shall dare to interpret them contrary to that sense which Holy Mother Church, to whom it belongs to judge of their true sense and meaning, has held or does hold.” Accordingly, when in 1616 theologians were asked to give their opinion on Copernicus’s heliocentric cosmology, they concluded that it was “formally heretical, since it explicitly contradicts in many places the sense of the Holy Scripture.” In other words, what was truly at the heart of the Church’s objection to Galileo’s Copernicanism was not so much the removal of the Earth from its central position in the cosmos, but rather the challenge to the church’s authority in interpreting the scriptures. In a climate in which the Roman Catholic Church was already feeling embattled by controversies with Reformation theologians, Galileo and the Church were on a clear collision course.
Events started to unfold rapidly toward the end of 1613. Galileo’s former student, Benedetto Castelli, made a presentation of the new astronomical discoveries to the grand duke of Tuscany and his entourage. Predictably, he was pressured to explain the apparent discrepancies between the Copernican cosmology and some