5 ms·

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

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.

TheOtherHobbes 6y ago
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.
- jacquesm 6y ago
  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.
- api 6y ago
  It may in some ways have helped. It forces deep concentration and prioritizes simple and elegant solutions over needlessly complex ones. Information technology is powerful but I sometimes wonder if we are grossly misusing it.
- btrettel 6y ago
  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.
baxtr 6y ago
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?
- stan_rogers 6y ago
  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.
  - waheoo 6y ago
    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.
    - tejohnso 6y ago
      Quotes don't always imply a negative connotation. Could simply mean to call attention to a common phrase, with the typical colloquial meaning intended.
- waheoo 6y ago
  https://en.m.wikipedia.org/wiki/Pierre-Simon_Laplace https://en.m.wikipedia.org/wiki/Pierre-Simon_Laplace 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]

TheOtherHobbes 6y ago

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.

jacquesm 6y ago
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.
api 6y ago
It may in some ways have helped. It forces deep concentration and prioritizes simple and elegant solutions over needlessly complex ones. Information technology is powerful but I sometimes wonder if we are grossly misusing it.
btrettel 6y ago
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.

baxtr 6y ago

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?

stan_rogers 6y ago
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.
- waheoo 6y ago
  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.
  - tejohnso 6y ago
    Quotes don't always imply a negative connotation. Could simply mean to call attention to a common phrase, with the typical colloquial meaning intended.
waheoo 6y ago
https://en.m.wikipedia.org/wiki/Pierre-Simon_Laplace https://en.m.wikipedia.org/wiki/Pierre-Simon_Laplace 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]