intro’d to Cohl via this wired article:
Cohl Furey, a mathematical physicist at the University of Cambridge, is finding links between the Standard Model of particle physics and the octonions, numbers whose multiplication rules are encoded in a triangular diagram called the Fano plane.
Complex numbers, suitably paired, form 4-D “quaternions,” discovered in 1843 by the Irish mathematician William Rowan Hamilton,..John Graves, a lawyer friend of Hamilton’s, subsequently showed that pairs of quaternions make octonions: numbers that define coordinates in an abstract 8-D space.
There the game stops. Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided. The first three of these “division algebras” would soon lay the mathematical foundation for 20th-century physics, with real numbers appearing ubiquitously, complex numbers providing the math of quantum mechanics, and quaternions underlying Albert Einstein’s special theory of relativity. This has led many researchers to wonder about the last and least-understood division algebra. Might the octonions hold secrets of the universe?
“Octonions are to physics what the Sirens were to Ulysses,” Pierre Ramond, a particle physicist and string theorist at the University of Florida, said in an email.
Driven by a profound intuition that the octonions and other division algebras underlie nature’s laws, she told a colleague that if she didn’t find work in academia she planned to take her accordion to New Orleans and busk on the streets to support her physics habit. Instead, Furey landed a postdoc at the University of Cambridge in the United Kingdom. She has since produced a number of results connecting the octonions to the Standard Model that experts are calling intriguing, curious, elegant and novel.
Furey, who is 39, said she was first drawn to physics at a specific moment in high school, in British Columbia. Her teacher told the class that only four fundamental forces underlie all the world’s complexity—and, furthermore, that physicists since the 1970s had been trying to unify all of them within a single theoretical structure. “That was just the most beautiful thing I ever heard,” she told me, steely-eyed. She had a similar feeling a few years later, as an undergraduate at Simon Fraser University in Vancouver, upon learning about the four division algebras. One such number system, or infinitely many, would seem reasonable. “But four?” she recalls thinking. “How peculiar.”
After breaks from school spent ski-bumming, bartending abroad and intensely training as a mixed martial artist, Furey later met the division algebras again in an advanced geometry course and learned just how peculiar they become in four strokes. When you double the dimensions with each step as you go from real numbers to complex numbers to quaternions to octonions, she explained, “in every step you lose a property.”
The octonions’ seemingly unphysical nonassociativity has crippled many physicists’ efforts to exploit them, but Baez explained that their peculiar math has also always been their chief allure. Nature, with its four forces batting around a few dozen particles and anti-particles, is itself peculiar. The Standard Model is “quirky and idiosyncratic,” he said.
[image: LUCY READING-IKKANDA/QUANTA MAGAZINE]
“The question is, is there an obvious way to go from the one-generation picture to the three-generation picture? I think there is.”
This is the main question she’s after now.
“Accordions are the octonions of the music world,” she said—“tragically misunderstood.” She added, “Even if I pursued that, I would always be working on this project.”
she is taken with the mystery of why the property of division is so key.
hard to believe .. history would forget about this fourth number system.. the quaternions:
her site: https://www.furey.space/
The standard model of particle physics is the result of decades of collaboration, which began roughly in the 1930s, and converged finally on its current state in 1979, . It is a perfected set of rules that tells us how the known fundamental particles behave. In the decades since 1979, the standard model has seen little in the way of alterations, and yet has survived rigorous experimental testing, nearly completely unscathed.
However, despite its long string of victories, the standard model is in some ways hollow, or incomplete. Roughly speaking, we know how to use the model to make predictions, but we do not know why it is the way it is.
To be more explicit, we do not know why the standard model is based on the gauge group SU(3)xSU(2)xU(1)/Z_6, and not some other gauge group. Even given that gauge group, the standard model does not specify why it uses such a long, apparently arbitrary, list of particles to represent that group. The standard model does not explain why its quarks and leptons are organized into three generations. It does not explain why SU(2) weak isospin acts only on left-handed states. Finally, the standard model does not explain the values of its 19 parameters. These questions, and others, have gone unanswered now for nearly 40 years.
The main goal of my work is to try to answer questions like these.
her page on cambridge site: http://www.damtp.cam.ac.uk/people/nf252/
Cohl Furey is a Canadian mathematician and physicist. She earned her PhD in 2015 from the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, and the University of Waterloo, Canada.
She is currently a research fellow at the University of Cambridge, where she is a member of the Department of Applied Mathematics and Theoretical Physics high energy physics research group. Her main interests are division algebras, Clifford algebras, Jordan algebras, and their relation to particle physics. Her work focuses on finding an underlying mathematical structure to the Standard Model of particle physics. She is most noted for her work on octonions.