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Thursday, September 05, 2019

Can maths predict the universe? | Arts & Books - Prospect

Explaining the unreasonable effectiveness of the natural sciences in mathematics, says Marcus Chown, Prospect Magazine.

Galileo and Emmy Noether’s discoveries broke ground in mapping how maths corresponds to the Universe.
Photo: Science History/Alamy Stock Photo, SSPL &Getty Images
Galileo was one of the first to realise a profound truth about the Universe: mathematics expresses perfectly the behaviour of the physical world. “Philosophy is written in the grand book (I mean the Universe) which stands continually open to our gaze,” he wrote. “But it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. This book is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it.”

Since the 17th century, mathematics has time and time again demonstrated that Galileo was right—it is indeed the unique language of the Universe. Among its spectacular successes have been the predictions of the existence of radio waves, black holes, antimatter, the Higgs boson and gravitational waves. In 1960, the Austrian physicist Eugene Wigner articulated what many had been thinking since the time of Galileo when he remarked on “the unreasonable effectiveness of mathematics in the natural sciences.”

So why is mathematics so effective in distilling the essence of the world? How is it possible that someone sitting at a desk can write down an arcane mathematical formula that predicts the existence of something previously unsuspected—something that people later discover actually exists in the real world? To put it more bluntly: why does the Universe have a mathematical twin that appears to mimic it in every way? “The astonishing effectiveness of mathematics in physics has enthralled me since I was a schoolboy,” says the former scientist and science writer Graham Farmelo. And now it has prompted him to explore the connection in his book The Universe Speaks in Numbers...

Physicists are perfectly happy to accept that they cannot describe many things in the Universe. However, they would say this is simply because our current mathematical tools are inadequate and, in the future, maybe in the 22nd century, we will obtain better tools. Wolfram, however, believes we will never obtain such tools because most of what the Universe is doing is not mathematical (he believes it is computing things—shades of The Hitchhiker’s Guide to the Galaxy).

Farmelo does not cover Wolfram’s views. However, he points out an extraordinary and under-appreciated thing that appears to bolster the view that the connection between mathematics and physics is more than an illusion. The extraordinary thing is that mathematics is not only effective in physics but that physics is also effective in mathematics. When, in the 1970s, the British mathematician Michael Atiyah saw the mathematical potential of local gauge theories, says Farmelo, he inspired a generation of mathematicians to work with physicists on a joint enterprise that has been dubbed “physical mathematics.” Since then, whole new fields of mathematics are being opened up, with gauge theory and string theory spawning insights into topology, the study of geometrical shapes.
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The Universe Speaks in Numbers:
How Modern Maths Reveals Nature's Deepest Secrets
Source: Prospect