Michael Berry is the Melville Wills Professor of Physics Emeritus at the University of Bristol, United Kingdom.
A fellow of the Royal Society of London and a foreign associate of the National Academy of Sciences, Berry has received numerous awards including the Moët Hennessey-Louis Vuitton Science for Art prize, the Wolf Prize in Physics and the Lorentz Medal of the Royal Netherlands Academy of Arts and Sciences.
He holds 13 honorary degrees from universities around the world and serves on advisory committees for the International Institute for Physics, Natal, Brazil, and the Harvard Center for Mathematical Sciences and Applications. He is a member of the Institute for Quantum Studies at Chapman University, Orange, California, and serves on the International Board of the Weizmann Institute of Science, Rehovot, Israel.
On April 5, 2018, Berry delivered the Eugene P. Wigner Distinguished Lecture on the topic “Making Light of Mathematics.” His talk reflected on Wigner’s 1960 paper, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” This is an edited transcript of our conversation following his lecture.
1. How do visually stunning and beautiful phenomena such as rainbows or twinkling starlight illustrate the value of mathematics?
It was known for centuries—Galileo emphasized it—that if we want to understand the physical world, the natural language is mathematics.
Many of the things we discover and we study in science are things that you can't perceive directly. Nobody’s seen an atom. Nobody's felt a gravity wave pass by. So, the relationship between the mathematics and the phenomenon is often quite obscure. We scientists understand the principle of it, but not always the details.
But with some visual phenomena, like rainbows and the sparkling of the sun on the sea, you can describe the mathematics in a way that directly relates to what people see, and that's helpful.
2. How are these concepts useful for promoting science and research?
They say a picture is worth a thousand words. That's true, but as scientists we know that an equation summarizes, economically, infinitely many pictures. So why do we need pictures? The reason is that the extreme compactness of equations makes it hard to understand what they contain. Pictures can help make that clear to people. So I think pictures are as important as visual phenomena that you can see directly.
3. How do these concepts echo Wigner’s article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”?
In a curious way. In that article, there are very many sensitive observations about how the mathematics that’s in our heads is related to the world that’s outside.
But I don't quite agree with him. He's talking about the unreasonable effectiveness as though there's no reason why that should happen. But I think there is a reason. We are creatures recently evolved. We haven't been around for more than a tiny sliver of cosmic time. We are still developing. We know a little more than dogs, but not that much more in the grand scheme of things.
We understand bits and pieces of this inscrutable universe. How? We can only understand what we are capable of understanding. Thus, we can only understand those aspects of the universe that reflect the most sophisticated constructs that our minds can make.
What are those constructs? They are mathematical. So, it's inevitable that the most recent mathematics is going to find its echo—or be necessary—in order to understand things in the physical world.
Sometimes, the maths comes first—almost as though it’s waiting for us. Einstein had learned that there is something called the geometry of curved spaces. Nobody thought it was any use, but there it was, just waiting for him to pick it up and use it in his gravity theory. Sometimes, physicists do the mathematics first, and the mathematicians then elaborate it. But whether the physics or the mathematics comes first, it seems inevitable that sophisticated mathematics would describe aspects of the universe. It's because of the way we are made. So, I don't think the effectiveness of mathematics is unreasonable; I think it's inevitable. But it is wonderful!
4. Machine learning and artificial intelligence are able to find patterns in data without a mathematical underpinning. What does that say about the role of mathematics in future scientific research?
Machine learning is relatively recent, and within physics it hasn't yet contributed much that is fundamental. There are some interpretations of data and detection of patterns in pictures. My reaction is that although it’s a different kind of discovery, once you see the patterns, you want to understand them, and then you need maths again.
5. Why was it important to visit ORNL, meet with researchers here, and participate in the Wigner Lecture Series?
For me the main reason is, what an honor! We all have boundless admiration for Wigner, and to be associated even in this way with his name is a wonderful thing. Of course, it's intimidating, given the list of all the people who came before. Visiting ORNL is like visiting any other excellent place where scientific research is done. You meet people you don't know. You learn surprising things. And you take them away with you. ORNL is indeed a place of great excellence. It's part of the great patchwork of organizations where great science is done.