So, I am not sure which part of my reply was uncharitable...
The part where you accuse him of a “status smash” after he directly answered what J was (that is, the composition of those two maps) and why it was important (that is, because it reflects the symplectic structure). The only lack of productivity is this thread is yours.
Anyway, JS is now on my rather short list of people not worth engaging with in an online discussion.
These sorts of declarations always remind me of Sophist:
STRANGER: The attempt at universal separation is the final annihilation of all reasoning; for only by the union of conceptions with one another do we attain to discourse of reason.
Thurston’s gentle, thoughtful, and scrupulously polite response On proof and progress in mathematics (Bull. AMS 1994, arXiv:math/9307227, 389 citations) has emerged as a classic of the mathematical literature, and is recommended to modern students by many mathematical luminaries (Terry Tao’s weblog sidebar has a permanent link to it, for example).
Conclusion It is no bad thing for students to be familiar with this literature, which plainly shows us that it is neither necessary, nor feasible, nor desirable for everyone to think alike!
Shminux, it may be that you will find that your concerns are substantially addressed by Joshua Landsberg’s Clash of Cultures essay (2012), which is cited above.
“These conversations [are] very stressful to all involved … there are language and even philosophical barriers to be overcome.”
The part where you accuse him of a “status smash” after he directly answered what J was (that is, the composition of those two maps) and why it was important (that is, because it reflects the symplectic structure). The only lack of productivity is this thread is yours.
These sorts of declarations always remind me of Sophist:
Huh, I guess I am not alone in being Sidles-averse, for the same reasons.
Shminux, perhaps some Less Wrong readers will enjoy the larger reflection of our differing perspectives that is provided by Arthur Jaffe and Frank Quinn’s ‘Theoretical mathematics’: Toward a cultural synthesis of mathematics and theoretical physics (Bull. AMS 1993, arXiv:math/9307227, 188 citations); an article that was notable for its biting criticism of Bill Thurston’s geometrization program.
Thurston’s gentle, thoughtful, and scrupulously polite response On proof and progress in mathematics (Bull. AMS 1994, arXiv:math/9307227, 389 citations) has emerged as a classic of the mathematical literature, and is recommended to modern students by many mathematical luminaries (Terry Tao’s weblog sidebar has a permanent link to it, for example).
Conclusion It is no bad thing for students to be familiar with this literature, which plainly shows us that it is neither necessary, nor feasible, nor desirable for everyone to think alike!
That’s a little out of context...I think the stranger literally means the union of concepts, not the union of opinions or points of view.
I see. Well, I very much appreciate your feedback, it’s good to know how what I say comes across. I will ponder it further.
Shminux, it may be that you will find that your concerns are substantially addressed by Joshua Landsberg’s Clash of Cultures essay (2012), which is cited above.