Because Galileo was the first great experimentalist in the history of science people often think of him as if he had the mentality of a research student at MIT or Imperial. He didn’t. He was above all things a man of the Italian neo-Platonic Renaissance. His mentor and guide above all others was Plato. The Italian Christian Platonists took their inspiration from the biblical Wisdom. ‘I was there when he measured the foundations of the earth… when he drew a circle on the face of the deep.” Their core doctrine was that underlying the material things of this earth there is an invisible beauty that is essentially mathematical. It was a view expressed imperishably in Botticelli’s Primavera and Birth of Venus, two paintings that for all their different dimensions might well have been conceived as a diptych. They are paintings (a subject for another blog) in which mathematics, beauty and erotic love are inextricably fused.
The proto-science of the Middle Ages had been largely Aristotelian. It’s watchword was Aristotle’s ‘take a look’. Aristotle was the first great scientist because in between his time in Athens at Plato’s Academy and becoming tutor to the young Alexander in Macedonia he spent some years on the beaches of what is now western Turkey, looking at the animals washed up on the beach more closely than anybody had ever done before. Galileo was the first scientist to think radically differently. Plato inspired him to realise that there is a deeper reality in nature than what you can see – not take a look but take a think – and that deeper reality is mathematical. ‘Nature is a book and its language is mathematics’ he famously wrote. His many experiments with balls rolling down and then up inclines convinced him that they were revealing a reality that they could not themselves directly show. When we think of a feather falling at the same speed as a cannonball we are not thinking of a thought experiment, but of something that is actually happening in nature every time feathers and cannonballs, or anything else for that matter, fall. But that reality is constantly distorted and hidden from us by the conditions under which we live on a material earth, in this case by air pressure. It’s rather like switching on your radio to listen to a performance of Brahms’s violin concerto that is happening in New York and only hearing a cacophonous interference. Your immediate sensation is that of cacophonous interference. But it is only distorting a more fundamental event that is actually happening not only in New York but in your kitchen, even though that is not what you are experiencing. There would be no cacophonous distortion if it were not cacophonously distorting something. Mathematics isn’t just a useful calculating device. It is an invisible reality that actually happens in the depths of nature.
It would be hard to over-estimate the damage that the trial of Galileo by the Church did to humanity, science and the Church itself. Before that science had been almost exclusively a Catholic enterprise. But now fear of the fires of the Inquisition – it had already burnt Giordano Bruno and would undoubtedly have burnt Galileo had he not been so famous – killed science in the Catholic south. It was driven north where it became almost exclusively Protestant. Now Wisdom was not seen as if not God then almost God and inseparable from God (the Word was both with God and was God), but as an idol to be abhorred. Now God is not understood as the ultimate reality in the depths of the universe expressing h(i)rself before all else through mathematics, but, for scientists like Boyle, a creator outside the universe, directing nature externally through abstract laws that could only be understood intellectually. Aesthetic pleasure in the things of nature is now seen not as a direct contact with the mathematical structure of the universe grasped as much through the emotions as through the intellect, as it had been for Botticelli and the Renaissance Platonists, but as no more than a personal predilection. It has been the gradual erosion of this point of view through discoveries, one after another, that have shown that what for Boyle could only be explained by divine creation and guidance, can in fact be explained by nature itself, that has paved the way for modern atheism.
Boyle was wrong and Galileo was right. The deeper into nature that scientists penetrate the more they find that phenomena cannot be separated from the mathematics that describe them. Nevertheless, it is Boyle and Locke not Galileo and Plato who have won. Science, especially physics, is generally seen as a purely intellectual penetration into the deeper aspects of the universe. But our emotions are inseparable from our intellects. We make contact with those depths emotionally as well, and often do it – though not necessarily – through helpful symbolic systems that we call religions. Even though he had been treated so badly Galileo remained a staunch Catholic because he understood this. As Botticelli saw, our engagement with mathematics is essentially erotic, a function of love as much as logic. Not that we generally think when we take pleasure in the beauties of nature and especially the natural beauty we find in human beings, and even seek to penetrate deeper into them as mystics do, that we are engaging with mathematics. But we are. The Renaissance Platonists were right. Have you ever seen both a more mathematical and sexy picture than The Birth of Venus? Beauty is mathematical (Turing is famous for inventing the computer and his work during the Second World War at Bletchley Park, but I’m even more interested in his later work on the mathematical foundations of the beautiful markings we see in animals and plants, especially his interest in the role of the Fibonacci sequence underlying so many of those beauties). If mathematics is not God, then it is as close to God and inseparable from God as anything could be.