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Most of the time people are impressed by analytical skills, it's not really justified in my view. Those skills aren't taught as much as they used to be. You can

Most of the time people are impressed by analytical skills, it's not really justified in my view. Those skills aren't taught as much as they used to be. You can still pick them up, but it's mostly on your own now. (Probably still easier than Laplace had it, though.) Anyway, just skimming the article, it sounds like Laplace simply applied standard normal mode analysis for the wave equation in the atmosphere. This is rather basic stuff that you can learn in an undergraduate partial differential equations class. In my Master's (8 years ago), I took a class on perturbation methods and asymptotic expansions (e.g., "method of matched asymptotic expansions"). These are approximation methods that were very common before computers became mainstream and can be very accurate. These methods are becoming rarer and rarer in fluid dynamics. I think they're still used extensively in theoretical quantum mechanics.

kardos 6y ago
> These methods are becoming rarer and rarer in fluid dynamics. Why are they becoming rarer is the question. Have all the tractable asymptotic problems been solved?
- btrettel 6y ago
  > Have all the tractable asymptotic problems been solved? Definitely not. I think it's more that these approaches are viewed as not necessary as numerical approximations (implemented on a computer) are more accurate, often easier, and allow one to consider complications that would be impossible to handle analytically. Though analytical methods do have major advantages. Computations are made only for special cases. You'll need a lot of computations to see functional dependencies clearly, for instance. If the computations are expensive (and they often are), people are unlikely to do the parametric studies needed to see functional dependencies clearly. Ultimately an analytical expression contains much more information than an array of numbers.

kardos 6y ago

> These methods are becoming rarer and rarer in fluid dynamics. Why are they becoming rarer is the question. Have all the tractable asymptotic problems been solved?

btrettel 6y ago
> Have all the tractable asymptotic problems been solved? Definitely not. I think it's more that these approaches are viewed as not necessary as numerical approximations (implemented on a computer) are more accurate, often easier, and allow one to consider complications that would be impossible to handle analytically. Though analytical methods do have major advantages. Computations are made only for special cases. You'll need a lot of computations to see functional dependencies clearly, for instance. If the computations are expensive (and they often are), people are unlikely to do the parametric studies needed to see functional dependencies clearly. Ultimately an analytical expression contains much more information than an array of numbers.