Is Ultimate Truth an Equation? Nah. The Stute – The Stute

My friend, Richard is a curmudgeonly physicist, who sends me science-y things he finds online. Richard loves making the point that if you dont understand something mathematically, you dont understand it. This claim bugs me, perhaps because I studied literature in college and teach humanities here at Stevens. My rebuttal follows.

Richard is in fancy company when he contends that the deepest truths are mathematical. Pythagoras and Plato both implied as much, and Galileo famously wrote that you can only read the grand book of the universe if you understand the language in which the book is written: mathematics. In 1931 James Jeans, a British physicist, proposed that the Great Architect of the universe, that is, God, seems to be a mathematician.

Richard sent me the Galileo and Jeans quotes, plus similar comments from physicist Richard Feynman. To those who do not know mathematics, Feynman wrote in The Character of Physical Law, it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. But heres an irony: Feynmans comments on quantum physics contradict the claim that mathematics illuminates nature.

In a book on quantum electrodynamics, which he helped formulate, Feynman reiterates that you cant comprehend quantum theory without the math. But he adds that you cant understand it with the math either! I dont understand quantum physics, Feynman confesses. Nobody does. He suggests that physicists advanced mathematical tricks, although they make calculations easier, can obscure what is actually happening in nature.

Also, if God is a mathematician, in what dialect does She/He/They/It speak? Quantum phenomena are described with differential equations, matrices and path integrals, a method invented by Feynman. Each of these dialects employs imaginary numbers, which are constructed from the square roots of negative numbers.

Moreover, quantum theory accounts for electromagnetism and the nuclear forces, and general relativity describes gravity. Quantum theory and general relativity are conveyed in radically different lingos that are hard to translate into each other. Some physicists still dream of a unified theory, possibly embodied in a single formula, that describes reality. That is the theme of Michio Kakus recent bestseller The God Equation: The Quest for a Theory of Everything.

But Kakus vision of a mathematical theory of everything seems increasingly quaint, given all weve learned about the limits of mathematics. In the 1930s, Kurt Gdel proved that all but the simplest mathematical systems are inconsistent, posing problems that cannot be solved within the axioms of that system. Extending the work of Gdel, mathematician Gregory Chaitin points out that mathematics, rather than being a unified, logically consistent whole, is riddled with randomness, contradictions and paradoxes.

Philosopher Bertrand Russell, early in his career, revered mathematics, which he thought is our best route to absolute truth. Toward the end of his life, perhaps because of the influence of Gdel, Russell arrived at a darker view of mathematics. I fear that, to a mind of sufficient intellectual power, he wrote, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.

Thats far too bleak a view. If mathematics reduces to a tautology, 1 = 1, it is a fantastically fecund tautology. Mathematics has led to countless intellectual, aesthetic and material advances, on which our civilization depends. But mathematics, like ordinary language, is a human invention, a powerful but limited tool, not a divine gift. Many mysteries resist mathematical analysis, especially those related to the human mind. And some great scientific advances have been non-mathematical. Charles Darwins On the Origin of Species does not include a single equation.

For all these reasons, we should doubt physicists who say that truth must be expressed in equations. Physicists would say that, wouldnt they? Thats like a poet saying that truth can only be expressed in meter and rhyme, or an economist saying that everything comes down to money.

Back for a moment to my grouchy pal Richard. Although a math-o-phile, Richard does not share the belief of Kaku and others that there ismust be!a single, true mathematical description of the world. Richard adheres to a position called theoretical pluralism. There can be many ways to model nature and to solve a scientific problem, Richard says, and insisting that there must be one correct way can impede scientific progress. On this point, Richard and I agree.

John Horgan directs the Stevens Center for Science Writings. This column is adapted from one posted on johnhorgan.org.

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Is Ultimate Truth an Equation? Nah. The Stute - The Stute