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People who are that far removed from "what is going on" aren't going to think about it at all. This is a popular article about math which uses a suggestive anal

People who are that far removed from "what is going on" aren't going to think about it at all. This is a popular article about math which uses a suggestive analogy. Analogies are not "misconceptions", and are not infections that anyone is "allowing" to "fester". Your concern for the quality of our discourse is admirable, but your handwringing is not. I don't think the cult-prone read articles about polynomials, ever; and I don't believe that misunderstanding such articles makes one more susceptible to QAnon, flat-Earth, anti-vax, etc.

lisper 6y ago
I think you may have forgotten what it's like to be a young person encountering new technical concepts for the first time. Or maybe you were fortunate enough never to have encountered a misleading description, or maybe you were smart enough to think beyond every misleading decription on your own every time. Most people are not so fortunate. The problem here is not that the article uses an analogy, the problem is that it doesn't present it as an analogy, it presents it as literal. The headline says that mathematicians have measured a force. That's nonsense. They did no such thing. But in order to realize that they did no such thing and that the "repulsive force" idea is an analogy you have to already know what is going on. Here is another example from the body of the article: "“You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said. No, you can't. If you could, then the "force" that these "particles" exerted on each other would cause them to move in accordance with Newton's first law. So not only is it an analogy presented as literal, it's actually a bad analogy.
- twangist 6y ago
  >> “You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said. > No, you can't. Well, yes, you can, and a professional mathematician just said so, yet it seems you insist that mathematics is all about dotting the i's and crossing the t's. Thinking of the roots in the way described is exactly what Dmitrov did: he explored this analogy, worked with a formalized version of it, and used it to prove a significant theorem. I agree that the article writer's intro takes the analogy much too far, to the point of being just false — mathematicians don't look at the number line and see "forces" at work maintaining the distances between the integers.

lisper 6y ago

I think you may have forgotten what it's like to be a young person encountering new technical concepts for the first time. Or maybe you were fortunate enough never to have encountered a misleading description, or maybe you were smart enough to think beyond every misleading decription on your own every time. Most people are not so fortunate. The problem here is not that the article uses an analogy, the problem is that it doesn't present it as an analogy, it presents it as literal. The headline says that mathematicians have measured a force. That's nonsense. They did no such thing. But in order to realize that they did no such thing and that the "repulsive force" idea is an analogy you have to already know what is going on. Here is another example from the body of the article: "“You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said. No, you can't. If you could, then the "force" that these "particles" exerted on each other would cause them to move in accordance with Newton's first law. So not only is it an analogy presented as literal, it's actually a bad analogy.

twangist 6y ago
>> “You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said. > No, you can't. Well, yes, you can, and a professional mathematician just said so, yet it seems you insist that mathematics is all about dotting the i's and crossing the t's. Thinking of the roots in the way described is exactly what Dmitrov did: he explored this analogy, worked with a formalized version of it, and used it to prove a significant theorem. I agree that the article writer's intro takes the analogy much too far, to the point of being just false — mathematicians don't look at the number line and see "forces" at work maintaining the distances between the integers.