Why Mathematics is Unreasonably Effective at Explaining the Physical World

In his famous article, The Unreasonable Effectiveness of Mathematics, physicist Eugene Wigner pondered how it is that mathematics is so effective at explaining the workings of the physical world.  This is the same topic of the recent NOVA special, The Great Math Mystery, which offers a very well-done and interesting account of how mathematics governs the universe from the smallest particles to the sweeping spiral galaxies of the heavens.

The effectiveness of mathematics in mapping the workings of the universe, however, should also give pause to anyone who believes that materialism is the final word not only on how the world works, but on science itself.

Today, in science, we see highly educated people  pondering the intricate machine-like precision of physical reality yet science has no mechanism to account for how this is possible.  Simply put, since materialists have drained mind, spirit, God, and intelligence from the physical world, they have no force to organize the physical world to the limit of mathematical order.

Following the realist creed, today’s scientists believe they must separate themselves from the world in order to study it.   These particles, according to a strict application of materialism, are left alone to form the picture-perfect universe.

(It might be noted that realism, the notion that what we experience is real and nothing else, glosses over what to do with the human body. If the body is considered part of the physical world, which seems hard to deny, the question becomes what is the “self” that we are separating from the physical world.  Read on.)

When materialists get to this point, they refer to the “laws of nature,”  “natural selection,” or the “self-organizing principle” as if somehow the big bang programmed the original exploding particles with an internal guidance system directing them to parade out into the universe on key and follow a tight mathematical and regular rhythm.

But what is happening here is that materialists hide “Mind” or God within the physical world and for the most part stay away from confronting the question of where the laws of nature come from.  To materialists, the laws of nature equal God.

For example, in his book, Dreams of Reason, Henri Pagels writes, “We can safely drop the traditional idea of a Demiurge, for there is no scientific evidence for a Creator of the natural world, no evidence for a will or purpose in nature that goes beyond the known laws of nature.” This view comes very close to Pantheism, which is the doctrine that “God is not a personality, but that all laws, forces, manifestations, etc. of the self-existing universe are God.” Pantheism is associated with the philosopher Benedict Spinoza, and with none other than Albert Einstein who, in 1954, wrote a letter to a friend where he said,  “We followers of Spinoza see our God in the wonderful order and lawfulness of all that exists and in its soul as it reveals itself in man and animal.”

So if the laws of nature are God, then the question become through what power this scientific god managed to animate the physical world with an organizing ability.

Roger Penrose, in his book, The Emperor’s New Mind, made a calculation that sheds light on why materialistic science must, in the end, invoke some sort of organizing power.   Penrose calculated the odds against the entire solar system, together with all its inhabitants, being created simply through the random collision of particles.  He came up with 10 to the 60th power of 10. (p. 354).   About how long will this particular miracle to occur?  Paul Davies estimates 10 to the 80th power of 10 years, trillions upon trillions of time older than the universe.  (God and the New Physics.) 

And then one may ask the question of whether, if these random particles did somehow join together to form the universe — like a monkey just happening to type Beethoven’s 5th symphony on a piano — what led these pieces to stay together and flow through time like a never-ending movie?

The point here is that chance alone cannot create the universe and, therefore, we must find some way for it not only to get organized, but organized to the limit of mathematical order.

Richard Dawkins and many other materialists write about encountering religious-like feelings when witnessing the splendors of creation.  This is all fine and good, and the spiritual sensation encountered is certainly well-founded, since the mystery of how the “natural” world orginated is of the same category of pondering the mystery of God.

Perhaps they are the same?

Like virtually every other report on the amazing harmonies of the physical world, the NOVA show recognizes the mystery, but stops before coming too close to the depth of the problem: Doesn’t it seem odd that modern science, which is based upon a worldview drained of spirit, Mind, and God, ponders a mystery that can only be explained by ——-spirit, Mind or God?

A common answer to the math mystery is to say that God does it.  But this answer, which tends to stop further inquiry, leaves open the questions of what do you mean by God? and how does this being perform the feat?

So, then, where do the laws of nature come from?

Two of history’s greatest thinkers, David Hume and Immanuel Kant, came close to answering the question posed by the Great Math Mystery and their thinking on the topic indeed provides a logical solution.

David Hume examined the source of the regularity we observe in the physical world — why the sun always rises, food nourishes, and dropped eggs break — and concluded that there is nothing in the experience of these events that imparts necessity.  In other words, we cannot have certainty about laws by simply observing the workings of the physical world; there is no reason “out there” for why the sun might not alway rise; no sunrise is logically possible.  Going further, Hume concluded that what makes us think the world will operate the same tomorrow as it does today is nothing other than our needs and beliefs, a subjective pull that demands the world conform to our inner desires.

Kant did not like this answer, believing something more substantial than needs and beliefs held the world together.  He then concluded that it is the structure of the mind imposing itself upon the world that creates the order we see.  To Kant, our minds do not conform to objects; rather, the objects we perceive conform to the logical structure of our minds.

Both of these views, widely ignored by modern science, put the source of order in the mind: Hume through needs and beliefs, and Kant, through the structure of the mind.

And this is where we find the answer for the unreasonable effectiveness of mathematics in the physical world.  There is one way for the structure of the mind and our needs and beliefs to actually influence the physical world: if the physical world is actually a projection of the mind, a holograph, a dream.

Minds, of course, are connected to dreams.  And so the quest of science to discover why mathematics is so effective at explaining the world turns back upon itself. As Max Planck, the founder of quantum mechanics, wrote, “Science cannot solve the ultimate mystery of nature.  And that is because, in the last analysis, we ourselves are part of the mystery that we are trying to solve.”

Modern science is still on the journey to explain the world without including the mind of the observer in the explanation.  It believes the definition of “science” excludes the observer despite, it might be added, the preeminent role the observer plays in quantum mechanics. And so we see scientists pondering the unreasonable effectiveness of mathematics in explaining the physical world, writing books and starring in TV shows on the topic.  But soon, after the media appearances end, the depth of the mystery still confronts us: we ponder a universe of mathematics but have no way to explain it, unless of course we are part of the final equation.