5 ms·

The article is interesting, and probably right -- albeit maybe slightly unfair to da Vinci -- but I don't really buy this premise: > We live in times of great

by dvt 6y ago

The article is interesting, and probably right -- albeit maybe slightly unfair to da Vinci -- but I don't really buy this premise: > We live in times of great disaggregation, and yet, seem to learn increasingly from generalists. Most teaching is done by non-generalists -- be it in schools, on TV, in documentaries, in courtrooms, or basically anywhere of any import. There's quite a bit of irony in the author quoting Wikipedia though. On first reading, I thought that was some sort of punch-line. > Having a variety of interests is no more a sign of generalized intelligence than being able to walk and chew gum. This is a reductive oversimplification, and I really wish the author were more fair. There's something pretty incredible about someone contributing to multiple fields of study. It's rare, but it happens. The fact that some Twitter personality has surface knowledge about X and Y doesn't imply that there aren't people out there with actual deep knowledge about both X and Y.

gilleain 6y ago
The point about Leonardo da Vinci makes sense, but is definitely unfair. Of course, an art historian might assume Leonardo's mathematics was as great as his artistic ability. In practice, no one has the time or the ability to be equally great in all fields of knowledge. This paper : https://link.springer.com/content/pdf/10.1007/s00004-007-0055-9.pdf https://link.springer.com/content/pdf/10.1007/s00004-007-005... talks about what mathematics he did > . The equation a^n + b^n = c^n does not have a solution in integers for n > 2 . But this theorem had yet to be demonstrated. It was not before 1753 that Leonhard Euler demonstrated that the equation a^3 + b^3 = c^3 does not have a solution. And the final demonstration of the so-called “Fermat’s third theorem”, which is that the general equation does not have a solution for n > 2 , was given by Andrew Weil in 1993. So its fairly impressive that Leonardo was on a path that leads to Euler and then to Weil. Of course, Euler himself was a 'mathematical polymath' as it were, with a wide range of proofs across a number of fields. To critise Leonardo da Vinci for not being good enough at mathematics is a little like complaining about Euler's drawing skills.
- codpiece 6y ago
  I have written that last sentence in my journal to record for posterity.
- tzs 6y ago
  > And the final demonstration of the so-called “Fermat’s third theorem”, which is that the general equation does not have a solution for n > 2 , was given by Andrew Weil in 1993 That should be Andrew Wiles [1]. There was a mathematician who did important work in number theory named Andre Weil [2]. I wonder if they got him mixed up with Wiles? [1] https://en.wikipedia.org/wiki/Andrew_Wiles https://en.wikipedia.org/wiki/Andrew_Wiles [2] https://en.wikipedia.org/wiki/Andr%C3%A9_Weil https://en.wikipedia.org/wiki/Andr%C3%A9_Weil
  - jwilk 6y ago
    And I'm pretty sure it's "last", not "third" theorem.
  - gilleain 6y ago
    Good spot, I should really have noticed that - seems that was not the greatest source! Yeah, they probably did get Weil mixed up with Wiles. Another good example of the difficulty of trying to analyse a polymath's work.
onecommentman 6y ago
> Most teaching is done by non-generalists -- be it in schools, on TV, in documentaries, in courtrooms. So you believe K-8 teaching, the greatest amount of teaching by far globally in the modern era, is done by non-generalists? Who specializes in arithmetic (number theorists and spreadsheet wizards aside)? If you define “pedagogy” as a specialty, perhaps, but that’s not the generalist/specialist discussion here. Even high school teachers generally only require a Bachelor’s degree...two years of content study (Junior-Senior...first two years is general education) out of an adult lifetime of, say, 50 years. Any “working professional” in a discipline wouldn’t count that for much. The media and courtroom teaching...you’d have to expand that discussion a bit for me to believe it. Law school, media studies...well, that’s another matter. It’s not that rare to contribute across multiple disciplines...the entire discipline of systems engineering is predicated on it. BTW: Can anyone summarize the thesis? This isn’t a tl;dr situation. I’m too old to read articles that look like the argument, if any, hinges on semantics with evidence that is, at best, anecdotal. (Frankly, we all are.) And so I don’t. PS: I really like the “>” indent style for quotations for block text in this UI.
- gerdesj 6y ago
  This is an experiment (I think) along the lines of the Turing test. I am quite pissed at the moment so take what I say with a pinch of salt! The text I see may not be the same as you. I see this nonsense: "It’s not difficult to imagine how this happened. The flip side of disaggregation is that each would-be expert is able to read broadly as well. The world of atomized content through hyper-specialization isn’t a stable equilibrium. We are all casual polymaths now." It is bollocks. Complete and utter rubbish. It superficially looks like ... something but it is cobblers.
- dvt 6y ago
  > So you believe K-8 teaching, the greatest amount of teaching by far globally in the modern era, is done by non-generalists? I think you're smart enough to know what I meant (and I even made the "of import" qualification). You don't need to hold a PhD in mathematics to teach kids their multiplication tables.
  - 6y ago

by dvt 6y ago

gilleain 6y ago

The point about Leonardo da Vinci makes sense, but is definitely unfair. Of course, an art historian might assume Leonardo's mathematics was as great as his artistic ability. In practice, no one has the time or the ability to be equally great in all fields of knowledge. This paper : https://link.springer.com/content/pdf/10.1007/s00004-007-0055-9.pdf https://link.springer.com/content/pdf/10.1007/s00004-007-005... talks about what mathematics he did > . The equation a^n + b^n = c^n does not have a solution in integers for n > 2 . But this theorem had yet to be demonstrated. It was not before 1753 that Leonhard Euler demonstrated that the equation a^3 + b^3 = c^3 does not have a solution. And the final demonstration of the so-called “Fermat’s third theorem”, which is that the general equation does not have a solution for n > 2 , was given by Andrew Weil in 1993. So its fairly impressive that Leonardo was on a path that leads to Euler and then to Weil. Of course, Euler himself was a 'mathematical polymath' as it were, with a wide range of proofs across a number of fields. To critise Leonardo da Vinci for not being good enough at mathematics is a little like complaining about Euler's drawing skills.

codpiece 6y ago
I have written that last sentence in my journal to record for posterity.
tzs 6y ago
> And the final demonstration of the so-called “Fermat’s third theorem”, which is that the general equation does not have a solution for n > 2 , was given by Andrew Weil in 1993 That should be Andrew Wiles [1]. There was a mathematician who did important work in number theory named Andre Weil [2]. I wonder if they got him mixed up with Wiles? [1] https://en.wikipedia.org/wiki/Andrew_Wiles https://en.wikipedia.org/wiki/Andrew_Wiles [2] https://en.wikipedia.org/wiki/Andr%C3%A9_Weil https://en.wikipedia.org/wiki/Andr%C3%A9_Weil
- jwilk 6y ago
  And I'm pretty sure it's "last", not "third" theorem.
- gilleain 6y ago
  Good spot, I should really have noticed that - seems that was not the greatest source! Yeah, they probably did get Weil mixed up with Wiles. Another good example of the difficulty of trying to analyse a polymath's work.

onecommentman 6y ago

> Most teaching is done by non-generalists -- be it in schools, on TV, in documentaries, in courtrooms. So you believe K-8 teaching, the greatest amount of teaching by far globally in the modern era, is done by non-generalists? Who specializes in arithmetic (number theorists and spreadsheet wizards aside)? If you define “pedagogy” as a specialty, perhaps, but that’s not the generalist/specialist discussion here. Even high school teachers generally only require a Bachelor’s degree...two years of content study (Junior-Senior...first two years is general education) out of an adult lifetime of, say, 50 years. Any “working professional” in a discipline wouldn’t count that for much. The media and courtroom teaching...you’d have to expand that discussion a bit for me to believe it. Law school, media studies...well, that’s another matter. It’s not that rare to contribute across multiple disciplines...the entire discipline of systems engineering is predicated on it. BTW: Can anyone summarize the thesis? This isn’t a tl;dr situation. I’m too old to read articles that look like the argument, if any, hinges on semantics with evidence that is, at best, anecdotal. (Frankly, we all are.) And so I don’t. PS: I really like the “>” indent style for quotations for block text in this UI.

gerdesj 6y ago
This is an experiment (I think) along the lines of the Turing test. I am quite pissed at the moment so take what I say with a pinch of salt! The text I see may not be the same as you. I see this nonsense: "It’s not difficult to imagine how this happened. The flip side of disaggregation is that each would-be expert is able to read broadly as well. The world of atomized content through hyper-specialization isn’t a stable equilibrium. We are all casual polymaths now." It is bollocks. Complete and utter rubbish. It superficially looks like ... something but it is cobblers.
dvt 6y ago
> So you believe K-8 teaching, the greatest amount of teaching by far globally in the modern era, is done by non-generalists? I think you're smart enough to know what I meant (and I even made the "of import" qualification). You don't need to hold a PhD in mathematics to teach kids their multiplication tables.
- 6y ago