Math is hard, even for physicists. New research suggests physicists are less likely to lend their focus to theories underpinned by complex mathematical details.Maybe physicists are intimidated by the math, and do not read and understand the papers with heavy math.
The findings -- detailed in the New Journal of Physics -- are compelling because they suggest a "fear," or at least an avoidance, of math is prevalent even among scientists well-trained in high-level mathematics.
"We have already showed that biologists are put off by equations but we were surprised by these findings, as physicists are generally skilled in mathematics," study co-author Andrew Higginson, a researcher at the University of Exeter, said in a news release.
The new study and resulting hypothesis is based on analysis of 2,000 papers published in a leading physics journal. The researchers tallied citations of previous studies in each paper. They found studies with an abundance of mathematical equations on each page were less likely to be referenced in new papers.
But there are other possibilities. Maybe the math-heavy papers are of poorer quality. Maybe they are more likely to be obscure technical results that are not of use to anyone. Maybe the math is used to disguise the intellectual weakness of the papers.
Maybe a lot of papers get cited just to provide a source for some background material. For example, suppose you are writing a physics paper and you know that black hole entanglement is a hot topic, so you find a contrived way to tie it in. Then you will need a reference on black hole entanglement, even tho you know little about the subject. Are you going to cite a paper that is mostly math or mostly English? You will take the paper in English because you can skim it in about 10 minutes and determine that it is relevant. A paper with technical math results will be less likely to be cited.
So this finding may not mean anything.
Correct. What we find out is that even the mathematicians don't do the math right. David Hestenes, in particular, has pointed out that linear algebra textbooks can't even teach geometric algebra. A recent book by Alan Macdonald does both in 220 pages! Hestenes affirms Poincare invocation of math as convention (map) and that flat-space GR is not only possible but somewhat natural. This makes Poincare's insights into special relativity definitively correct before Einstein! Like Evy Galois, no one listened to Grassmann (both never were mathematicians) but he invented linear algebra and exterior algebra. Even Clifford came before the 20th century. The mathematics departments are WAY BEHIND!ReplyDelete
"A new gauge theory of gravitation on flat spacetime has recently been developed by Lasenby, Doran, and Gull in the language of Geometric Calculus. This paper provides a systematic account of the mathematical formalism to facilitate applications and extensions of the theory. It includes formulations of differential geometry, Lie derivatives and integrability theorems which are coordinate-free and gauge-covariant. Emphasis is on use of the language to express physical and geometrical concepts."
Hestenes has admitted himself that he had written books too hard for most to understand: http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf
Maxwell's equations become one equation, along with many theorems of calculus. It's absurd to stick with coordinates. Ignorance of history and fifth-rate mathematics instruction leads people astray. They can't even master p-values in statistics!