mathematics God’s native tongue?
If you think that understanding whether mathematics was invented or discovered is not that important, consider how loaded the difference between “invented” and “discovered” becomes in the question: Was God invented or discovered? Or even more provocatively: Did God create humans in his own image, or did humans invent God in their own image?
I will attempt to tackle many of these intriguing questions (and quite a few additional ones) and their tantalizing answers in this book. In the process, I shall review insights gained from the works of some of the greatest mathematicians, physicists, philosophers, cognitive scientists, and linguists of past and present centuries. I shall also seek the opinions, caveats, and reservations of many modern thinkers. We start this exciting journey with the groundbreaking perspective of some of the very early philosophers.
CHAPTER 2
MYSTICS: THE NUMEROLOGIST AND THE PHILOSOPHER
Humans have always been driven by a desire to understand the cosmos. Their efforts to get to the bottom of “What does it all mean?” far exceeded those needed for mere survival, improvement in the economic situation, or the quality of life. This does not mean that everybody has always actively engaged in the search for some natural or metaphysical order. Individuals struggling to make ends meet can rarely afford the luxury of contemplating the meaning of life. In the gallery of those who hunted for patterns underlying the universe’s perceived complexity, a few stood head and shoulders above the rest.
To many, the name of the French mathematician, scientist, and philosopher René Descartes (1596–1650) is synonymous with the birth of the modern age in the philosophy of science. Descartes was one of the principal architects of the shift from a description of the natural world in terms of properties directly perceived by our senses to explanations expressed through mathematically well-defined quantities. Instead of vaguely characterized feelings, smells, colors, and sensations, Descartes wanted scientific explanations to probe to the very fundamental microlevel, and to use the language of mathematics:
I recognize no matter in corporeal things apart from that which the geometers call quantity, and take as the object of their demonstrations…And since all natural phenomena can be explained in this way, I do not think that any other principles are either admissible or desirable in physics.
Interestingly, Descartes excluded from his grand scientific vision the realms of “thought and mind,” which he regarded as independent of the mathematically explicable world of matter. While there is no doubt that Descartes was one of the most influential thinkers of the past four centuries (and I shall return to him in chapter 4), he was not the first to have exalted mathematics to a central position. Believe it or not, sweeping ideas of a cosmos permeated and governed by mathematics—ideas that in some sense went even further than those of Descartes—had first been expressed, albeit with a strong mystical flavor, more than two millennia earlier. The person to whom legend ascribes the perception that the human soul is “at music” when engaged in pure mathematics was the enigmatic Pythagoras.
Pythagoras
Pythagoras (ca. 572–497 BC) may have been the first person who was both an influential natural philosopher and a charismatic spiritual philosopher—a scientist and a religious thinker. In fact, he is credited with introducing the words “philosophy,” meaning love of wisdom, and “mathematics”—the learned disciplines. Even though none of Pythagoras’s own writings have survived (if these writings ever existed, since much was communicated orally), we do have three detailed, if only partially reliable, biographies of Pythagoras from the third century. A fourth, anonymous one was preserved in the writings of the Byzantine patriarch and philosopher Photius (ca. AD