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The Unplanned Impact of Mathematics

76 points by memexy 6y ago

augustt 6y ago
A nice example is that Gauss realized in 1805 that Fourier transforms could be made less tedious by subdividing the problem (n=12=3*4 in his case), 160 years before Cooley-Tukey.
- memexy 6y ago
  Yes, but Gauss was also a perfectionist and he didn't publish anything that weren't up to his standards. He even discovered non-euclidean geometry at some point but didn't think it was worth publishing so Bolyai's son János (and also Lobachevsky) had to re-discover it > Bolyai’s son János was also a mathematician. In 1832, János published his brilliant discovery of non-Euclidean geometry. His father, overjoyed that his son might have achieved something worthy of praise from Gauss, the man he admired more than any other, asked Gauss for his view of the work. There was a bit of a feud and I don't know if it was ever properly settled > Whether Gauss actually fleshed-out non-Euclidean geometry as comprehensively as Bolyai and Lobachevsky is uncertain. -- https://www.famousscientists.org/gauss-and-non-euclidean-geometry/ https://www.famousscientists.org/gauss-and-non-euclidean-geo...
- deleted 6y ago
  [deleted]
37r7u43urr 6y ago
As much as we talk about math literacy here (compared to other platforms anyway), I can't help but feel like the incomprehensibility of high level math to laymen is a feature. It's not talked about outside of academia often, because why would it be, but for a long time philosophy resisted efforts to 'mathmatecize' (my own word) the field because of concern that it would become inscrutible to outsiders. As a result, academic philosophy is much more politically polarized than math. Where would we be if every step forward in mathematics was met with backlash for not paying adequate concern to some arbitrary set of external implications? Anyone can disagree of course but just looking at the political affiliation ratios of educators makes it clear that one aspect of the hard sciences historically has been an ability to stay focused on utility despite post-modernism. I'm probably being unfair though, the humanities continue to produce persuasive arguments (persuasive emphasis being one of the first things most lit and speech majors learn during critical thinking and writing courses in college) they've just dropped the pretense of being truth seeking persuits.
- StandardFuture 6y ago
  Obfuscation is a practice of the entirety of Academia for a long while now. The art of obfuscation is not new at all. A small anecdote, I remember a Taiwanese friend mentioning the history of the complexity of Chinese characters and how they were devised, in part, to ensure that the lower class(es) could not learn them. Obfuscation inherently guarantees a lot of things out of the box: you appear more enlightened, only a class of people can understand and thus judge your work, and all newcomers can only become "in the know" if and only if they are trained by someone who already is "in the know". This is very appealing to anyone with even minor insecurities (most people), and has been widely utilized throughout many areas of human society in time. Math is merely one example where this practice has presence. EDIT: I will admit that the more democratized the internet has made knowledge, and the more prevalent higher-degrees become in society, the more awareness people have of this issue and the more it gets called out. So, all in all, there is the positive side of things that this art of obfuscation is in decline of use for things where it should never be used (like education, science, etc.).
  - augustt 6y ago
    I'd say this is generally not true, at least in math. There's definitely poor notation and misnomers that come from tradition, but it's hardly deliberate as "obfuscation" implies.
    - mkl 6y ago
      I'm not sure I agree (I have a PhD in maths). There are many maths papers and books I've tried to understand where that seems to have been deliberately made more difficult than it needs to be. Sure, you could argue that I didn't have the necessary prerequisite knowledge at that point, or that the authors simply weren't good at explaining things, but I do get the impression that it's sometimes more than that. Using specialised meanings for words without definition or reference (words that are used for other purposes elsewhere so they can't be searched for) is a key problem, as is the same with notation, and as is leaving out crucial steps. If you're already in the know, those things are probably clear.
mathgenius 6y ago
Working in theoretical physics (quantum computing) I think about this a lot: the unreasonable effectiveness of mathematics. I see two ways of understanding this. (1) That mathematicians are in the game of building powerful tools, and therefore these tools inherently capture a wide range of phenomena. (2) When confronted with a difficult problem we become the drunk person looking for their keys under the street light, even if we know the keys are elsewhere. In this case, the street light is whatever good calculations we have at hand, ie. mathematics.
HeOfLittleBrain 6y ago
As I said the first time this topic was posted: This article is ironic coming from such a math phobic publication as Nature: http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...
- memexy 6y ago
  Why is it ironic and why are they math phobic?

76 points by memexy 6y ago

A nice example is that Gauss realized in 1805 that Fourier transforms could be made less tedious by subdividing the problem (n=12=3*4 in his case), 160 years before Cooley-Tukey.

memexy 6y ago
Yes, but Gauss was also a perfectionist and he didn't publish anything that weren't up to his standards. He even discovered non-euclidean geometry at some point but didn't think it was worth publishing so Bolyai's son János (and also Lobachevsky) had to re-discover it > Bolyai’s son János was also a mathematician. In 1832, János published his brilliant discovery of non-Euclidean geometry. His father, overjoyed that his son might have achieved something worthy of praise from Gauss, the man he admired more than any other, asked Gauss for his view of the work. There was a bit of a feud and I don't know if it was ever properly settled > Whether Gauss actually fleshed-out non-Euclidean geometry as comprehensively as Bolyai and Lobachevsky is uncertain. -- https://www.famousscientists.org/gauss-and-non-euclidean-geometry/ https://www.famousscientists.org/gauss-and-non-euclidean-geo...
deleted 6y ago
[deleted]

37r7u43urr 6y ago

As much as we talk about math literacy here (compared to other platforms anyway), I can't help but feel like the incomprehensibility of high level math to laymen is a feature. It's not talked about outside of academia often, because why would it be, but for a long time philosophy resisted efforts to 'mathmatecize' (my own word) the field because of concern that it would become inscrutible to outsiders. As a result, academic philosophy is much more politically polarized than math. Where would we be if every step forward in mathematics was met with backlash for not paying adequate concern to some arbitrary set of external implications? Anyone can disagree of course but just looking at the political affiliation ratios of educators makes it clear that one aspect of the hard sciences historically has been an ability to stay focused on utility despite post-modernism. I'm probably being unfair though, the humanities continue to produce persuasive arguments (persuasive emphasis being one of the first things most lit and speech majors learn during critical thinking and writing courses in college) they've just dropped the pretense of being truth seeking persuits.

StandardFuture 6y ago
Obfuscation is a practice of the entirety of Academia for a long while now. The art of obfuscation is not new at all. A small anecdote, I remember a Taiwanese friend mentioning the history of the complexity of Chinese characters and how they were devised, in part, to ensure that the lower class(es) could not learn them. Obfuscation inherently guarantees a lot of things out of the box: you appear more enlightened, only a class of people can understand and thus judge your work, and all newcomers can only become "in the know" if and only if they are trained by someone who already is "in the know". This is very appealing to anyone with even minor insecurities (most people), and has been widely utilized throughout many areas of human society in time. Math is merely one example where this practice has presence. EDIT: I will admit that the more democratized the internet has made knowledge, and the more prevalent higher-degrees become in society, the more awareness people have of this issue and the more it gets called out. So, all in all, there is the positive side of things that this art of obfuscation is in decline of use for things where it should never be used (like education, science, etc.).
- augustt 6y ago
  I'd say this is generally not true, at least in math. There's definitely poor notation and misnomers that come from tradition, but it's hardly deliberate as "obfuscation" implies.
  - mkl 6y ago
    I'm not sure I agree (I have a PhD in maths). There are many maths papers and books I've tried to understand where that seems to have been deliberately made more difficult than it needs to be. Sure, you could argue that I didn't have the necessary prerequisite knowledge at that point, or that the authors simply weren't good at explaining things, but I do get the impression that it's sometimes more than that. Using specialised meanings for words without definition or reference (words that are used for other purposes elsewhere so they can't be searched for) is a key problem, as is the same with notation, and as is leaving out crucial steps. If you're already in the know, those things are probably clear.

mathgenius 6y ago

Working in theoretical physics (quantum computing) I think about this a lot: the unreasonable effectiveness of mathematics. I see two ways of understanding this. (1) That mathematicians are in the game of building powerful tools, and therefore these tools inherently capture a wide range of phenomena. (2) When confronted with a difficult problem we become the drunk person looking for their keys under the street light, even if we know the keys are elsewhere. In this case, the street light is whatever good calculations we have at hand, ie. mathematics.

HeOfLittleBrain 6y ago

As I said the first time this topic was posted: This article is ironic coming from such a math phobic publication as Nature: http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...

memexy 6y ago
Why is it ironic and why are they math phobic?