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[1] https://journals.ametsoc.org/jas/article/77/7/2519/347483/An...
Earlier quoted context omitted.
Holy cow, he predicted way more than just indivisible constituents of matter [1]: > The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible, and have always been and always will be in motion; that there is an infinite number of atoms and of kinds of atoms, which differ in s…
Uncanny indeed, especially when you consider that Democritus's understanding of atoms is a mostly sufficient underpinning for the science of chemistry, at least up through the end of the 19th century.
Laplace had an amazing mind. He connected so many dots, and everything I've done in the last four years with respect to digital signal processing ends up rooted in something he discovered or postulated or analyzed. Fascinating, but not too surprising, that he shows up in the weather as well.
What's more amazing is that all his math was done with pen and paper - no computer assistance of any kind. Log tables were available, but all the analysis was done by hand. And brain.
Information technology is powerful but I sometimes wonder if we are grossly misusing it.
Laplace had an amazing mind. He connected so many dots, and everything I've done in the last four years with respect to digital signal processing ends up rooted in something he discovered or postulated or analyzed. Fascinating, but not too surprising, that he shows up in the weather as well.
What's more amazing is that all his math was done with pen and paper - no computer assistance of any kind. Log tables were available, but all the analysis was done by hand. And brain.
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.
Earlier quoted context omitted.
Do you want to count Democritus and indivisible constituents of matter?
Holy cow, he predicted way more than just indivisible constituents of matter [1]: > The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible, and have always been and always will be in motion; that there is an infinite number of atoms and of kinds of atoms, which differ in s…
Well, that bit is wrong. Especially if you take the fundamental constituents of what are now called atoms: 6 quarks, 6 antiquarks, 6 leptons (counting neutrinos), 6 antileptons, 5 gauge bosons, 1 scalar boson. Only 30, possibly + whatever dark matter and dark energy are.
Earlier quoted context omitted.
Holy cow, he predicted way more than just indivisible constituents of matter [1]: > The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible, and have always been and always will be in motion; that there is an infinite number of atoms and of kinds of atoms, which differ in s…
> that there is an infinite number of atoms and of kinds of atoms Well, that bit is wrong. Especially if you take the fundamental constituents of what are now called atoms: 6 quarks, 6 antiquarks, 6 leptons (counting neutrinos), 6 antileptons, 5 gauge bosons, 1 scalar boson. Only 30, possibly + whatever dark matter and dark energy are.
Earlier quoted context omitted.
> that there is an infinite number of atoms and of kinds of atoms Well, that bit is wrong. Especially if you take the fundamental constituents of what are now called atoms: 6 quarks, 6 antiquarks, 6 leptons (counting neutrinos), 6 antileptons, 5 gauge bosons, 1 scalar boson. Only 30, possibly + whatever dark matter and dark energy are.
We don't know how many kinds of atoms there are, and infinite is pretty damn accurate all things considered. And it's pretty disingenuous to go out of your way to take quarks to mean what he called atoms just so you can claim he's wrong.
Earlier quoted context omitted.
What's more amazing is that all his math was done with pen and paper - no computer assistance of any kind. Log tables were available, but all the analysis was done by hand. And brain.
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 r…
Why are they becoming rarer is the question. Have all the tractable asymptotic problems been solved?
Earlier quoted context omitted.
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 r…
> 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?
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.
Not sure if it's completely related, but I found the phenomena of the North Atlantic Oscillation [1] to be particulary useful in predicting long-term weather around the South of Norway. This time around, in December 2019, I predicted a rather cold summer in Norway. I made that prediction because the winter was particularly warm and snow-less in the South East between late 2019 and early 2020. For the most part I've b…