I recently considered the role that mathematics plays in bringing meaning, or perhaps even story, to our experience. Mathematics is often used to reveal the structure that can be found in large sets of data, or in any number of physical things that change over time, or in the properties of the abstractions themselves. Mathematics, then, sort of tells us what we’re looking at, within what would otherwise be an unwieldy or even meaningless data. In my last post, I took note of the way that mathematics was used to communicate meaning in the structure of cathedral walls – in particular Lincoln Cathedral whose construction began at the end of the 11th century and continued through the Middle Ages. There I shared the suggestion that the geometry of the Cathedral was used to convey, or even to instruct on, the fundamental nature of our being. It happens now that another New Scientist article, Shakespeare: poet, playwright, scientist broadened the issue for me.
The article was written by broadcaster and author Dan Falk, whose most recent book is The Science of Shakespeare. In the article, Falk considers, specifically, evidence in the play’s words that Shakespeare made use of astronomical observations, and explores how he may have known about them.
Galileo’s telescopic observations came toward the end of Shakespeare’s career, but Cymbeline, first performed in 1611, offers tantalizing hints that he was aware of the findings. In the play’s final act, the hero, Posthumus, falls into a dream-like state, and the ghosts of four family members appear and move around him in a circle. The ghosts cry out for Jupiter, the Roman god. On hearing their pleas, he descends onto the stage. So we have Jupiter and four ghosts moving in a circle.
But the book also addresses the emergence of the scientific world view more generally and, in doing so, takes note of the relationship between science and religion. I recently saw a group of students who had gathered on the University of Texas, Dallas campus with posters designed to provoke a debate about truth, science and religion. When I saw them, it occurred to me that mathematics never comes up in these debates, despite the fact that it is so intimately tied to ancient, medieval and modern world views. Reading the history of the relationship between science and religion, as Falk surveys it, encouraged me to pursue my own thoughts about whether an updated philosophy of mathematics might contribute to the science vs. religion debate. Early in his book, Falk makes the following observations:
…the rediscovery of classical texts, via Arabic translations, triggered a new wave of learning across Europe. Those works included the writings of Aristotle and Ptolemy…,as well as the geometry of Euclid, the medical writings of Galen, and much more…This wave of learning was closely linked to the activities of the Roman Catholic Church. The best medieval schools had been those associated with the monasteries and the great cathedrals. By the late Middle Ages these had also become centers of what we would now call science…There were also the universities, the earliest having been founded around 1200; these, too, functioned largely as religious institutions. The highest degree offered was in theology – though to obtain it, the student also had to master mathematics, logic, and natural philosophy.
The close connection between science and faith may seem strange to the modern reader, living at a time when Western society, and Western science in particular, has become a secular endeavor….The evolving relationship between science and religion is a large and complex subject…For one thing, religion was simply part of the fabric of society; all of the key figures of the Scientific Revolution were men of faith of one kind or another.
…As historian Paul Kocher puts it, early modern science “was more often cited as proving God’s existence than disproving it…And as Principe writes, the study of nature was seen as “an inherently religious activity…But the link between science and faith, as Principe stresses, is deeper than this. For the thinkers of early modern Europe, he writes, “the doctrines of Christianity were not personal choices. They had the status of natural or historical facts.”
Mathematics inspired many of the thoughts of an emerging scientific world-view, but it is also closely associated with the more mystical side of things. Kepler, as Falk points out, was obsessed with numerology, like the ancient Pythagoreans. His work relies on observations of the physical as well as the mystical. Quoting Allen Debus, Falk tells us:
His subtle mixture of mathematics and mysticism is “far removed from modern science, but it formed an essential ingredient of its birth.”
Mathematics is often at the beginning of things. The considerations of Shakespeare’s Hamlet explored in Falk’s article, and in his book, should remind us of the complexity of human thought. Relationships among art, science, and religion are inherent. They are all narratives that grow out of the same ground. Their coexistence, it would seem, is just a fact of our existence, and one of the keys to a deeper understanding of who we are.
If mathematics is, as I tend to see it, the mind itself building structure with the elements of thought, then mathematics’ development is like the development of another sense. It is, after all, the structure we give to any sensory data that creates a meaningful thing perceived. And so it is with mathematics. Mathematics, like story and name, brings meaning, not mechanics, to our experience. It increasingly links what we see to what we think we know, as we try to reconcile our immediate experience with what’s ‘out there.’ The evolution of mathematical concepts allows us to probe deeper and deeper into the universe, as well as into our own nature. And this is the subject of both religion and science. So why is mathematics so consistently absent from our debates?