The (Unsurprising) Effectiveness of Mathematics in the Natural Sciences

“If nature is really structured with a mathematical language and mathematics invented by man can manage to understand it, this demonstrates something extraordinary. The objective structure of the universe and the intellectual structure of the human being coincide.” – Pope Benedict XVI

In 1960, physicist and Nobel laureate Eugene Wigner published a well-known article entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences“. In it, he explored the mind-boggling usefulness of mathematics in describing and further revealing the physical universe. As an example, he questioned why tools such as complex numbers – foreign as they are to our intuition and everyday experiences – are nonetheless a product of human thought necessary for the formulation of the laws of quantum mechanics. Why is it that elements of mathematics can so perfectly describe seemingly unrelated phenomena, such as the ratio of a circle’s circumference to its diameter (pi) appearing in the Gaussian distribution function used to study population trends? Furthermore, why is it that the human mind is so astonishingly capable of recognizing the language of mathematics and using it to advance our knowledge of the physical world?

Of course, these questions inevitably lead to others. Why is the universe so ordered in the first place? Where did this order come from, if anywhere? This apparent “fine-tuning” of the universe (particularly with respect to the existence of intelligent life) has numerous possible explanations. I’m going to briefly describe three of the most prevalent, but be aware that some of these have sub-variations, and that this isn’t an entirely comprehensive list.

1. Perhaps there are actually multiple universes (or even infinite universes), and we happen to exist in a universe with physical properties that allow us to exist.

2. Perhaps the universe isn’t actually as ordered as it seems.

3. Perhaps the universe “just is”. Maybe some day we’ll know why; maybe we never will.

Of course, the reader will have doubtlessly recognized that all of these explanations avoid what is probably the simplest and most intuitive response: that our seemingly fine-tuned universe was indeed finely tuned by a Fine Tuner. Although many of today’s scientists balk at the notion that the universe may have been designed, it is worth pointing out that this position is no less scientifically defensible than, say, the idea of multiple universes. Neither can be empirically tested. Both can only be accepted on faith. Design is also less problematic, practically speaking, than the idea that the universe’s apparent order is illusory, and it is considerably more satisfying than simply accepting the apparent order as an unknowable brute fact.

All of this brings me back to the Pope Benedict quote that I opened with. If the intellectual structure of the human mind truly does coincide with the objective structure of the universe – as it undoubtedly seems to – then what implications does this carry for the Christian? This is the kind of question that obviously cannot be answered scientifically, but that makes it no less fascinating. I can’t pretend to actually know all the answers, of course, but I do have a few ideas.

Genesis 1:26-28 states that God created mankind in his image, so that man could subdue the earth and rule over its creatures. I think when most people hear the phrase “in God’s image”, they tend to think strictly in terms of physical appearance. They imagine a guy with a flowing white beard breathing life into Adam. But what quality is it, really, that enables man to subdue the earth? Although our physical stature is certainly impressive, it’s clear that we’re NOT the largest, strongest, or fastest creatures on this planet. What makes us unique, rather, is our minds. When we’re told that God created mankind in his image, does it not seem likely that this applies to our intellect as much as it applies to our physical appearance?

Consider what this means. If the God who designed the universe and set in place its mathematical properties also created us in his image, it would be reasonable to expect the human mind to be fluent in the language of mathematics. It would hardly be surprising┬áto learn that we’re inhabiting a finely-tuned universe, or to find that our language of mathematics is so powerfully capable of uncovering the physical laws that govern it. For the Christian, the problems that have so long confounded physicists and philosophers aren’t really problems at all. Man’s intelligence is simply reflecting a small shadow of God’s intelligence.