Picture-Perfect Approach to Science
The quon string-genus relation (above) entails the Hopf algebra relation (below).
The linked paper contains the details.
A picture is worth 1,000 words, the saying goes, but a group of Harvard-based scientists is hoping that it may also be worth the same number of equations.
Pictorial laws appear to unify ideas from disparate, interdisciplinary fields of knowledge, linking them beautifully like elements of a da Vinci painting. The group is working to expand the pictorial mathematical language first outlined last year by Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, and postdoctoral fellow Zhengwei Liu.
"There is one word you can take away from this: excitement," Jaffe said. "And that’s because we’re not trying just to solve a problem here or there, but we are trying to develop a new way to think about mathematics, through developing and using different mathematical languages based on pictures in two, three, and more dimensions."
Continue reading "Picture-perfect approach to science" by Peter Reuell in the Harvard Gazette, Jan 24, 2018. https://news.harvard.edu/gazette/story/2018/01/mathematicians-work-to-expand-pictorial-language-into-other-fields/.
Also read the original paper: Arthur M. Jaffe and Zhengwei Liu, "Mathematical picture language program," PNAS (Jan 2, 2018) doi: 10.1073/pnas.1710707114.