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.
It's a bit like chess the old fashioned way or by using a special purpose computer. If you have limited processing power your optimization heuristic becomes that much more important. At a guess Laplace was very good at choosing what to work on and how to tackle it leading to relatively few computations but all of those contributing to the result.
Our current brute force approach discards the vast majority of the results generated.
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.
> 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.
A bit off topic: I always wondered how people Laplace and his likes made a living. How could he think about these things and get through life? does anyone know?
According to his great-great-grandson,[4] d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care.
Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the École Militaire.[8]
With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy.[9]
Like most of the "great minds" of the age, he was a gentleman scientist. That is, he came from some wealth that was mostly self-maintaining (in his case, family agricultural holdings - not super-rich, but not having to make his own living either). After Napoleon, he was promoted to middling nobility with all of the privileges that entails.
I don't understand the quotes here. Are you saying rich people can't have great minds? Or are you saying they had it easy? If so, whats your point?
Its a bit like saying Jeff Bezos, bill gates, Steve jobs and others are all a product of the time. I'm not going to say they're not, but that doesn't make their achievements any less great to me.
This is not really a "discovery" so much as a reaffirmation of what was previously known. The original paper is more insightful [1]. The Quanta magazine article is interesting but the title overstates the original citation.
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 been correct. Except a few heat waves this summer has been pretty cold. But the effects of global warming persists, and it would seem the Autumn will be pretty nice here in Oslo.
It seems likely those large scale variations correlate with summer temperatures, but from the information you give there, that’s n=1, self-evaluated, after removal of values that do not fit the prediction.
Are you sure this can be used to make predictions for single seasons?
Quite a few tech companies in Norway have an international staff and speak English in the office. I worked for a small Norway-based open source consultancy for a while. We spoke English in the office as most of us were not Norwegian and most Norwegian customers were happy to work with us in English. I spent some time working with QT Software (then part of Nokia) and their office was also English speaking IIRC.
Depends. Some companies do accept English speakers, but not all. I'd call them up about it before applying. Most accept Danish or Swedish, though. If you're just looking for a restaurant job, then most of them accept English only speakers. But that isn't to say that most customers do, so it helps to know at least the basics for your spesific trade. Sad fact: Norwegian is known to be notoriously hard to learn because most Norwegians resort to English with foreigners. So even if you come here, you might not hear the local language enough to actually learn it well.
This isn't a longer gap, but I think it's interesting. Black holes were first hypothesized by someone named John Mitchell in 1783 [0]. Interestingly enough, and back on topic for the article, Laplace also independently came to the same conclusion in 1796 [0].
It's a little fuzzy as to when black holes were "discovered": most sources say 1971, when Charles Bolton identified Cygnus X-1 as a black hole by measuring its mass indirectly using the wobble of nearby star HBE226868 [1], but the first image of a black hole was only taken in 2019 [2]. Yes, it looked just like in Interstellar, because Kip Thorne consulted on the film [3].
The gap from 1783-1971 is "only" 188 years, but 1783-2019 is 236 years. And, from Laplace's rediscovery of the idea, it's 175 and 223 years, respectively. I think that's pretty cool, too.
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 shape and size.
> 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.
They're just trying to be accurate. The most important aspect of Democritus' atoms is indivisibility, so that's why fundamental particles like quarks are technically a better fit.
Are you seriously suggesting that when Democritus referred to "uncuttable things", he meant to describe particles that would in the future be named after his work rather than to describe particles that were indivisible?
> 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.
You can try to identify atoms by his description of them, in which case you'd have to choose fundamental particles. But you've already explicitly chosen to interpret Democritus' "atoms" as identical with our "atoms", despite the fact that they do not exhibit any of the characteristics Democritus described. What can I conclude except that you think Democritus, in the past, named his concept after ours, in the future?
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.
Lacking evidence, scientists didn't accept Democritus's model continued to speculate. My favorite being the "plum pudding" model proposed by JJ Thompson in 1904.
A friend of mine wondered what the RATIO between the four modes of pressure waves are. Waves are essentially a frequency (like pitch), and he was wondering if the ratio between these “frequencies” constitute a similar ratio between the pitches in a chord.
Kind of. Technically these are spherical harmonics, which are the generalisation of the harmonic series on a sphere instead of a line - also used in quantum theory to calculate orbitals.
The math is a bit more complex than the simple harmonic series.
I thought for a second it was related to the recent '26-Second Pulse' XKCD https://xkcd.com/2344/ but that is about seismic waves while this is about atmospheric pressure.
Our current brute force approach discards the vast majority of the results generated.
Information technology is powerful but I sometimes wonder if we are grossly misusing it.
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.
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.
According to his great-great-grandson,[4] d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care.
Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the École Militaire.[8]
With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy.[9]
Its a bit like saying Jeff Bezos, bill gates, Steve jobs and others are all a product of the time. I'm not going to say they're not, but that doesn't make their achievements any less great to me.
Could simply mean to call attention to a common phrase, with the typical colloquial meaning intended.
[1] https://journals.ametsoc.org/jas/article/77/7/2519/347483/An...
[1]: https://en.wikipedia.org/wiki/North_Atlantic_oscillation
Are you sure this can be used to make predictions for single seasons?
It's a little fuzzy as to when black holes were "discovered": most sources say 1971, when Charles Bolton identified Cygnus X-1 as a black hole by measuring its mass indirectly using the wobble of nearby star HBE226868 [1], but the first image of a black hole was only taken in 2019 [2]. Yes, it looked just like in Interstellar, because Kip Thorne consulted on the film [3].
The gap from 1783-1971 is "only" 188 years, but 1783-2019 is 236 years. And, from Laplace's rediscovery of the idea, it's 175 and 223 years, respectively. I think that's pretty cool, too.
---
[0]: https://blackholecam.org/john-mitchell-developed-theory-of-b...
[1]: http://torontodreamsproject.blogspot.com/2012/01/very-first-...
[2]: https://www.jpl.nasa.gov/edu/news/2019/4/19/how-scientists-c...
[3]: https://www.wired.com/2014/10/astrophysics-interstellar-blac...
> 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 shape and size.
The accuracy is uncanny.
[1] https://en.wikipedia.org/wiki/Democritus#Atomic_hypothesis
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.
> 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.
You can try to identify atoms by his description of them, in which case you'd have to choose fundamental particles. But you've already explicitly chosen to interpret Democritus' "atoms" as identical with our "atoms", despite the fact that they do not exhibit any of the characteristics Democritus described. What can I conclude except that you think Democritus, in the past, named his concept after ours, in the future?
https://library.si.edu/digital-library/book/traite-de-mecani...
John Adams was the second US President. 5.3 million people lived in America.
Makes me want to learn more math.
The math is a bit more complex than the simple harmonic series.
https://en.wikipedia.org/wiki/Spherical_harmonics