Lost in Math: How Beauty Leads Physics Astray

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

For the most part, physicists and mathematicians have settled on a fine division of labour in which the former complain about the finickiness of the latter, and the latter complain about the sloppiness of the former.

It took twenty-five years from the prediction of the neutrino to its detection, almost fifty years to confirm the Higgs boson, a hundred years to directly detect gravitational waves. Now the time it takes to test a new fundamental law of nature can be longer than a scientist’s full career. This forces theorists to draw upon criteria other than empirical adequacy to decide which research avenues to pursue. Aesthetic appeal is one of them. In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.

What failed physicists wasn’t their math; it was their choice of math. They believed that Mother Nature was elegant, simple, and kind about providing clues. They thought they could hear her whisper when they were talking to themselves. Now Nature spoke, and she said nothing, loud and clear.

If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

Theoretical physicists used to explain what was observed. Now they try to explain why they can't explain what was not observed

In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie.

The sense of beauty of a physical theory must be something hardwired in our brain and not a social construct. It is something that touches some internal chord. When you stumble on a beautiful theory you have the same emotional reaction that you feel in front of a piece of art.

When asked to judge the promise of a newly invented but untested theory, physicist draw on the concepts of naturalness simplicity or elegance and beauty. These hidden rules are ubiquitous in the foundations of physics. They are invaluable. And in utter conflic with the scientific mandate of objectivity.

if you quote this, you can be the first person to quote someone quoting someone quoting himself quoting someone

While I was in school I hated history, but since then I have come to recognize the usefulness of quoting dead people to support my convictions.

Data don’t come to us anymore—we have to know where to get them, and we can’t afford to search everywhere. Hence, the more difficult new experiments become, the more care theorists must take to not sleepwalk into a dead end while caught up in a beautiful dream.

The main reason we use math in physics, however, is because we can.

Their theories, they believe, are too good to not be true.

Arguments from beauty have failed us in the past, and I worry I am witnessing another failure right now. “So what?” you may say. “Hasn’t it always worked out in the end?” It has. But leaving aside that we could be further along had scientists not been distracted by beauty, physics has changed—and keeps on changing. In the past, we muddled through because data forced theoretical physicists to revise ill-conceived aesthetic ideals. But increasingly we first need theories to decide which experiments are most likely to reveal new phenomena, experiments that then take decades and billions of dollars to carry out. Data don’t come to us anymore—we have to know where to get them, and we can’t afford to search everywhere. Hence, the more difficult new experiments become, the more care theorists must take to not sleepwalk into a dead end while caught up in a beautiful dream. New demands require new methods. But which methods? I hope the philosophers have a plan.

After evidence forced him to give up the beautiful polyhedra, Kepler, in later life, became convinced that the planets play music along their paths. In his 1619 book Harmony of the World he derived the planet’s tunes and concluded that “the Earth sings Mi-Fa-Mi.” It wasn’t his best work. But Kepler’s analysis of the planetary orbits laid a basis for the later studies of Isaac Newton (1643–1727), the first scientist to rigorously use mathematics.

foundational physics, which is far from experimental test as science can be while still being science

More important is that besides these four families, there are five “exceptional” Lie groups, named G2, F4, E6, E7, and the largest one, E8. And it can be proved that these are all the simple Lie groups there are, period. To appreciate how bizarre this is, imagine you visit a website where you can order door signs with numbers: 1, 2, 3, 4, and so on, all the way up to infinity. Then you can also order an emu, an empty bottle, and the Eiffel Tower. That’s how awkwardly the exceptional Lie groups sit beside the orderly infinite families.