Pi in the Sky

• Email
• Share
• Print

Imagine, one day, that life shows up on another planet. Moreover, it’s intelligent life. Imagine, too, that we’ve a reasonably swift means of communication. We’d need a common language with which to talk. What might that language be? One candidate would be mathematics.

Mathematics seems to be a universal language. Science presumes as much: it works as a descriptive and predictive tool, both on the small scale and at the very large. Moreover, it works for systems that are very close and quite distant — so distant that they reach back to the earliest moments after the Big Bang. And when you stop to think about it, that’s quite remarkable.

It’s not just the universal nature of mathematics that’s striking; it’s that mathematics works at all. The natural world is a complex place. It’s packed with variations and permutations, random events and patterns so complex they are far from obvious to the eye. And yet, mathematics can capture so much of that intricacy. What kind of alchemy transforms the lead of messy reality into the gold of a simple equation? It’s a question that was famously asked by the physicist Eugene Wigner, in 1960. He wrote an essay with a title that says it all: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

Wigner notes the sense that many physicists have: mathematics seems to be discovered, not created. The reason to think this is that discoveries made about the physical world are often, first, discoveries made about mathematics. One of the best known cases concerns Einstein and his work on General Relativity. These equations implied something about the universe that Einstein, at first, refused to believe — that the universe was expanding. It was only later that cosmic expansion was observed by Edwin Hubble. Before then, though, Einstein tried to cancel what the math was implying by adding to his equations what came to be known as the “cosmological constant.” It was designed to cancel out the implication of expansion, though when expansion was shown empirically, Einstein referred to it as “the biggest blunder of my life.”

So, physics is about discovering the laws of nature, and those laws appear to be written in the language of math. Pi really is in the sky. Wigner continues:  “It is … a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered… It is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.”

Those are strong statements. And the extraordinary nature of math can be developed further. After all, do not physicists routinely use criteria such as “beauty” to determine whether they are on the right track or not? The physicist Paul Dirac put it most clearly, in a 1963 article for Scientific American, writing, “It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has a really sound insight, one is on a sure line of progress.” Of course, mathematical predictions must be verified by observation. But that such predictions are verified at all is the nub of the issue. Mathematics looks miraculous.

It’s an ancient idea. The philosopher Gottfried Leibniz mused on the power of mathematics, and it led him to draw theological conclusions. “When God calculates and thinks things through, the world is made,” he thought. The power and beauty of mathematics is exactly what you’d expect if the universe were created by a powerful deity, worthy of worship. The physicist and priest Michael Heller, winner of the 2008 Templeton Prize , captured the thought like this, in his book (co-authored with George V. Coyne), A Comprehensible Universe:

In the human brain, the world’s structure has reached its focal point: the structure of the world has acquired the ability to reflect upon itself… . In this conceptual setting, science appears as a collective effort of the Human Mind to reach the Mind of God… . The Mind of Man and the Mind of God are strangely interwoven.

And yet, is the unreasonable effectiveness of mathematics in the natural sciences really evidence for the existence of a deity? Is the language of math divine? There are good reasons to doubt it.

For one thing, there is the gap between the kind of deity implied by mathematics — a deity not unlike a computer — and the deity worshiped by Christians, Jews and Muslims. This is the living God of Abraham, Isaac and Jacob, not a God who spends eternity manipulating datasets.

So, it’s quite possible to be impressed by the “miracle” of math, and not become a convinced theist. This is the position adopted by the physicist Roger Penrose. He has articled what he refers to as a Platonic view. It can be conceptualized in this way. First, there is the physical world, the natural world that surrounds us. But there’s also a Platonic world — the ideal world of mathematics. The Platonic world maps onto the natural world in some way, perhaps via the imaginative power of human mental activity. And that, if right, means there’s no need to assume that the Platonic and natural world are wrapped up in some kind of divine embrace.

There’s a further reason to question the theistic reading of mathematics. For it’s possible that mathematics is not so unreasonably effective as Eugene Wigner supposed. The idea goes something like this:

At the level of the very, very small, the world is not smooth and continuous. It is lumpy. It’s the world of discrete energy levels and fundamental particles called quantum physics. One way of interpreting the quantum appearance of the very, very small scale is to say that at this level, mathematics is not smooth and continuous. It, too, is lumpy.

This suggests, in turn, that mathematics does not exist in some pure Platonic realm, but that it is just one more messy part of the fabric of the universe. There are, in fact, no universal mathematical laws, and no universal mathematics. Rather, there are local laws — bylaws, if you like. It just depends on where you look. To date, we’ve tended to look on the scale of the everyday and the very large. But as science gazes more and more at the very small, a new kind of math might be the result.

If that turns out to be right, then math may cease to look so unreasonably effective. The miracle, and its perfection, may start to look far less impressive. And if God does exist, future believers may conclude that he is not much of a mathematician after all.

Mark Vernon is a journalist, writer, and former Anglican priest. His books include The Meaning of Friendship, Plato's Podcasts: The Ancients' Guide to Modern Living, and After Atheism: Science, Religion, and the Meaning of Life. He blogs at www.markvernon.com.