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Physicists avoid highly mathematical work despite being trained in advanced mathematics, new research suggests. The study, published in the New Journal of Physics, shows that physicists pay less attention to theories that are crammed with mathematical details. This suggests there are real and widespread barriers to communicating mathematical work, and that this is not because of poor training in mathematical skills, or because there is a social stigma about doing well in mathematics.
Dr Tim Fawcett and Dr Andrew Higginson, from the University of Exeter, found, using statistical analysis of the number of citations to 2000 articles in a leading physics journal, that articles are less likely to be referenced by other physicists if they have lots of mathematical equations on each page. [...] Dr Higginson said: "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.
"This is an important issue because it shows there could be a disconnection between mathematical theory and experimental work. This presents a potentially enormous barrier to all kinds of scientific progress."
http://phys.org/news/2016-11-physicists-mathematics.html
[Abstract]: Statistical Analysis of the Effect of Equations on Citations
(Score: 2, Insightful) by khallow on Monday November 14 2016, @08:50AM
Formulas aren't even that long - why not expend a few extra letters to clarify meaning?
Because it means a lot more work and overhead for the researcher. In mathematical work, these symbols are used far more often than in computer programs. The researcher is trying to construct a variety of certificates demonstrating certain things and there is plenty of backtracking, dead ends, etc that aren't present in computer programs. I think it would be more like requiring computer programs to make their computations human-readable. That would introduce a fair amount of overhead.
Similarly, it generates work and overhead for any readers confirming the results of the paper. And if the researcher uses one set of symbols for research efficiency and other for discussion of the work, that's more work for everyone.
Finally, what actually is worth communicating in this way? Math is notorious for being a place where meaning creates problems rather than solves them.
A common source of new math is abstraction of a math description of some physical system. The variables and concepts to the physical system lose a lot of their meaning when so abstracted. But often phrases and variables are retained, such as with Lagrangian [wikipedia.org] and Hamiltonian [wikipedia.org] mechanics, where the labels that originally corresponded to physical parameters such as "action" get reused even in contexts where they don't make sense. Compatibility with related material turned out to be more important than a paper that was somewhat more self-contained. (I guess that's another problem with math, its concepts and variables tends to have an overly broad scope compared to programming.)
Alternately, one might wish to strip away meaning. A classic example of this is the Lorenz system [wikipedia.org], something I'm studying at the moment. Edward N. Lorenz, a mathematician and meteorologist was studying chaotic behavior of a model of weather systems he had constructed, and attempted to abstract out what was causing the chaotic behavior. The result is expressed in terms of three completely abstract functions x, y, and z of a single independent variable t (which managed to retain its meaning of "time"). Presumably, the three variables originally meant things like wind speed, temperature, or moisture content, but that has been completely stripped away.
When one assigns a meaning to variables, the reader will usually do so as well. That usually aids in understanding, but it can hinder it as well. Math is patterns promiscuously applied. If a pattern appears or is represented in a system, then the consequences of that pattern appear as well, even if no one is aware of the existence of the pattern in the system!