Reader Matt Bunkers raised the issue of the tilde (~) in scientific writing. Some use it for “proportional to”. Others use it for “order of magnitude”. Still others use it for “approximately”.
Given the wide variety of uses for the tilde, why not just write out what you mean? Doing so will make your writing more accessible to your audience.
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David M. Schultz is a Professor of Synoptic Meteorology at the Centre for Atmospheric Science, Department of Earth and Environmental Sciences, and the Centre for Crisis Studies and Mitigation, The University of Manchester. He served as Chief Editor for Monthly Weather Review from 2008 to 2022. In 2014 and 2017, he received the University of Manchester Teaching Excellence Award, the only academic to have twice done so. He has published over 190 peer-reviewed journal articles.
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There is nothing fundamentally wrong with the tilde, just as there is nothing fundamentally wrong with the millibar (mb)! Long live the millibar. So much easier to say that hecto-Pascal…
Since you asked a “why” question, I’ll try to answer. Most folks using the tilde (proper symbol for “on the order of”) and the double tilde (“approximately”) are trying to be concise. The more uses of “approximately” or “on the order of” are in the paper, the longer it gets. Using symbols in place of often-reused words, when appropriate (and obviously there’s disagreement on what’s appropriate) is a way to pack the same information into a smaller space.