The Universe as a Mathematically-designed Machine

"To the divine understanding, all phenomena are coexisting and are comprehended in one mathematical structure. The senses, however, recognize events one by one and regard some as the causes of others. We can understand now, said Descartes, why mathematical prediction of the future is possible; it is because the mathematical relationships are preexisting. The mathematical relationship is the clearest physical explanation of a relationship. In brief, the real world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. Moreover, many philosophers, including Descartes, insisted that these mathematical laws are fixed because God had so designed the universe and God's will is invariable. Whether or not humans could decipher God's will or penetrate God's design, the world functioned according to law, and lawfulness was undeniable, at least until the 1800s."

-- Morris Kline (in "Mathematics and the Search For Knowledge")