6 ms·

> ...partly because there isn't a whole lot of benefit to his approach if you're just doing things in 2D and 3D— in those cases, the alternative approaches are

> ...partly because there isn't a whole lot of benefit to his approach if you're just doing things in 2D and 3D— in those cases, the alternative approaches are in a sense simpler and more straightforward This is the crux: Grassmann had discovered and explored several mountain passes while others had not yet settled the valleys which they connected? Even if he hadn't been an outsider, he seems to have been (from a career standpoint) "too early". (compare https://news.ycombinator.com/item?id=40312021 https://news.ycombinator.com/item?id=40312021 )

eigenvalue 2y ago
Yes, agreed. But he could have done a better job outlining and explaining the valleys to people first so they would be in a position to appreciate the mountain passes! Luckily, credit in academia tends to reward such people better than the commercial market, even if it ends up happening long after death. Look at Galois for example.
- 082349872349872 2y ago
  True. Even were it to have been making a virtue of necessity, he did note "some day these ideas, even if in an altered form, will reappear and with the passage of time will participate in a lively intellectual exchange. For truth ... remains even if the garments in which feeble men clothe it fall into dust."
  - vinnyvichy 2y ago
    Thanks! Probably approximately no citation needed.
    - vinnyvichy 2y ago
      Since you are possibly not terrible at unearthing obscure but Critical rocksnacks, exactly why, Archangelsk Governorate? I mean, if besides that there it being harder to tell noon from midnight, e.g. neighboring Finnics having obnoxiously dissimilar mythology ) https://en.wikipedia.org/wiki/Lady_Midday https://en.wikipedia.org/wiki/Lady_Midday
    - jasomill 2y ago
      It's from the forward to Grassmann's 1962 Ausdehnungslehre[1]: einst dieſe Ideen, wenn auch in veränderter Form, neu erstehen und mit der Zeitentwickelung in lebendige Wechſelwirkung treten werden. Denn die Wahrheit … bleibt bestehen, wenn auch das Gewand, in welches schwache Menschen ſie kleiden, in Staub zerfälit. The translation is from Kannenberg, Extension Theory, AMS, 2000[2]. [1] https://archive.org/details/dieausdehnungsl05grasgoog/page/n11/mode/2up https://archive.org/details/dieausdehnungsl05grasgoog/page/n... [2] https://www.ams.org/bookstore/pspdf/hmath-19-prev.pdf#page=11 https://www.ams.org/bookstore/pspdf/hmath-19-prev.pdf#page=1...
      - vinnyvichy 2y ago
        Double thanks! (Always glad to see the German taking "Elizabethan" s-f glyph pair to its ambiguous conclusion.) My very earliest exposure to the Ausdehnungslehre was in Sternberg+Bamberg. Until coming across Penrose diagrams, this book staved off the disgust I felt for tensor calculus (as used by physicists). http://ndl.ethernet.edu.et/bitstream/123456789/33770/1/108.pdf.pdf http://ndl.ethernet.edu.et/bitstream/123456789/33770/1/108.p... Mainly shocked by the compression of Maxwell's equations to a single line. Otherwise.. that was.. (regrettably cryptic) a reference to the eerily resonant Kolmogorov option, roughly motivated by Hilbert's slogan "truth does not need martyrs". https://scottaaronson.blog/?p=3376 https://scottaaronson.blog/?p=3376 More precisely, I am sympathetic to the idea that the path that Grassmann took to release his discoveries into the world was actually close to the optimal one. Other paths to consider are thus Grothendieck's,Kaczynski's, Galois' (generalizing to purely social bits, even Nash's) Two-sided intellectual exchange with a finished work across spacetime, that's also something.
        082349872349872 2y ago
        (was Galois the co-Kaczynski?) If we want to figure out the optimal path to release discoveries, what happens if we set the action to zero?
  - eigenvalue 2y ago
    Yeah, his ultimate confidence in the merit of his ideas is pretty inspiring, even if he never got to see it happen in his own lifetime.
    - 082349872349872 2y ago
      Since the remainder of the thread has been infested by "noonday demons", there's a nice line by a singer-songwriter about a SF novel in the Noon Universe[0]: "of course, freedom and brotherhood[1] will come / But it will happen without us."[2] [0] https://en.wikipedia.org/wiki/Noon_Universe#Description https://en.wikipedia.org/wiki/Noon_Universe#Description [1] aka « liberté et fraternité ». A cynic would say the Arkanarians already have « égalité », in that they're all stuck on a planet cycling endlessly between mere anti-intellectualism and outright theocracy. [2] Конечно, свобода и братство наступят / Но это случится без нас (https://www.youtube.com/watch?v=ufbCnjBYDbI&t=5134s https://www.youtube.com/watch?v=ufbCnjBYDbI&t=5134s)
- vinnyvichy 2y ago
  HMM
  - 082349872349872 2y ago
    For Aaronson's question, I'd suggest that Prof. Dr. Marcus Hutter is far more likely to have an answer than I am to guess one. (or Schmidhuber!) I'm far more into semigroups than Solomonoff Induction these days... As to inflections, there's a fan theory that different Pynchon titles reflect different conic sections: https://www.math.columbia.edu/~woit/wordpress/?p=7479 https://www.math.columbia.edu/~woit/wordpress/?p=7479
    - vinnyvichy 2y ago
      Ah you mean Schmidhuber's speed prior: https://people.idsia.ch/~juergen/speedprior.html https://people.idsia.ch/~juergen/speedprior.html I was more interested in pointing to you the measly followups to Aaronson's question, which consists solely of forays into nonlinear quantum mechanics & superluminal neutrinos. https://www.preposterousuniverse.com/blog/2011/09/24/can-neutrinos-kill-their-own-grandfathers/ https://www.preposterousuniverse.com/blog/2011/09/24/can-neu...
vinnyvichy 2y ago
See the other thread on the Milanovic-Kuznets curve[0-1], then lookup the Wiki Indeed, it's ... Critical .. to identify points with, uh, unexpected curvature. ?HN (?Lagniappe of the halfDay): KidW,o WitH,d? [0]https://scottaaronson.blog/?p=762 https://scottaaronson.blog/?p=762 [1]https://news.ycombinator.com/item?id=40437206 https://news.ycombinator.com/item?id=40437206
- 082349872349872 2y ago
  Hmm... what are the finnic equivalents/dysquivalents of the Południca/полуднице[0]? My poisk-fu will probably be insufficient, but my wild guess at the moment is that due to circumstances mentioned in https://en.wikipedia.org/wiki/Arkhangelsk#Literature https://en.wikipedia.org/wiki/Arkhangelsk#Literature , coincidentally the reference was collected there. (Midnight to me is just a local play on being easier to temporally localise in summer than Noon[1], being just south of the arctic circle[2]. There's another russian folk tale I can't remember specifically in which young folk, on a particular saint's day, go looking for a specific species of flower[3] and if they find a —phenotypically non-existent— colour, it grants invisibility: the rural peasantry's equivalent of ex falso quodlibet?) [0] https://ru.wikipedia.org/wiki/Полудница#/media/Файл:Распространение_мифов_о_полуднице_и_некоторых_типов_русалок_у_восточных_славян.png https://ru.wikipedia.org/wiki/Полудница#/media/Файл:Распрост... shows them only in slavic areas (1) [1] I'll note that in my local laws, 12.00-13.00 are still quiet hours; one doesn't rely on any Mittagsgespenst but instead could just threaten to call the cops on errant workers. [2] compare https://sv.wikipedia.org/wiki/Midnattssol https://sv.wikipedia.org/wiki/Midnattssol [3] at least as long as they're not deflowering each other instead. Another just-so story for a Halfday Witch is related: older members of the village can easily be kept in check by threatened retaliation, but when the younger kids (acting as temporary fieldhands for the harvest) might be in danger of intruding upon Masha and Sasha's privacy[4] over midday, they are threatened with the Midday Witch, and if the small kids ask why Masha and Sasha are not afraid of her, they get told M&S are taking their chances but know enough about agronomy to answer her questions — or would Masha's mother be told she didn't make it home for lunch because she had been caught by the Midday Witch and had to recite flax culture 101? [4] probably easier to find by "taking a walk" (Гуляют все девчонки и парни района?) than at home; compare gown-greening: https://www.youtube.com/watch?v=XqX0720VTRY https://www.youtube.com/watch?v=XqX0720VTRY Lagniappe: https://www.youtube.com/watch?v=EnoqvRGc7pk https://www.youtube.com/watch?v=EnoqvRGc7pk (frame story: midnight, framed story: midday)
joe_the_user 2y ago
Sort of. I'd change the metaphor a bit. Math at the start of 19th century was like a country many of whose high mountains (say theorems) had been climbed but whose basic geography (foundations) hadn't been charted. Grassman was perhaps the first to begin the process of true foundational studies - creating structures that formally tied the mountains together (different from intuitively tying the mountains together, notably). Grassman's approach (incorporated as "exterior algebra") was klunky and difficult most likely specifically because he was doing something new, something never done before. That is, he was working when no formal linear algebra and indeed neither formal abstract algebra nor formal foundations of real numbers nor formalization of calculus existed (though many things were talked about informally). And Grassman was resisted because of the (probably necessary) klunkiness, but also because many mathematicians didn't see the need for this and no small number actively resisted the need for formal. IE, saw the qualities of numbers and collections of thing as best handled intuitively rather than formally and especially disliked the way formal formulations allowed and required counter-intuitive structures (transfinite sets, the axiom of choice, etc). This resistance didn't just touch Grassman but affect Cantor and Hilbert, etc. Today, math still has a tension between the provers of hard theorems and the structure builders, that would be the mountain climbers and the geographers, the Erdős' and the Grothendiecks. Moreover, the history of that tension isn't as clear as it could be since fields of math are generally taught as fully formulated systems with few nods to the state of the field before a given formulation (I just learned today that van der Waerden's Moderne Alegebra, published in 1930, was the first text to put abstract algebra in anything like it's present form). More on the history of the formalization of mathematics can found in Jan van Plato's The Great Formal Machinery Works (Grassman is the first writer covered).
- Ar-Curunir 2y ago
  I'm sure you didn't mean to imply this, but Grothendieck definitely used his new structures to prove some hard theorems.
  - eigenvalue 2y ago
    This reminds me of the Grothendieck quote about his approach to solving problems (in contrast with Erdős, who I suppose in this analogy would look for a big hammer with which to smash the nut open quickly!): “I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise, you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marble, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.”

eigenvalue 2y ago

Yes, agreed. But he could have done a better job outlining and explaining the valleys to people first so they would be in a position to appreciate the mountain passes! Luckily, credit in academia tends to reward such people better than the commercial market, even if it ends up happening long after death. Look at Galois for example.

082349872349872 2y ago
True. Even were it to have been making a virtue of necessity, he did note "some day these ideas, even if in an altered form, will reappear and with the passage of time will participate in a lively intellectual exchange. For truth ... remains even if the garments in which feeble men clothe it fall into dust."
- vinnyvichy 2y ago
  Thanks! Probably approximately no citation needed.
  - vinnyvichy 2y ago
    Since you are possibly not terrible at unearthing obscure but Critical rocksnacks, exactly why, Archangelsk Governorate? I mean, if besides that there it being harder to tell noon from midnight, e.g. neighboring Finnics having obnoxiously dissimilar mythology ) https://en.wikipedia.org/wiki/Lady_Midday https://en.wikipedia.org/wiki/Lady_Midday
  - jasomill 2y ago
    It's from the forward to Grassmann's 1962 Ausdehnungslehre[1]: einst dieſe Ideen, wenn auch in veränderter Form, neu erstehen und mit der Zeitentwickelung in lebendige Wechſelwirkung treten werden. Denn die Wahrheit … bleibt bestehen, wenn auch das Gewand, in welches schwache Menschen ſie kleiden, in Staub zerfälit. The translation is from Kannenberg, Extension Theory, AMS, 2000[2]. [1] https://archive.org/details/dieausdehnungsl05grasgoog/page/n11/mode/2up https://archive.org/details/dieausdehnungsl05grasgoog/page/n... [2] https://www.ams.org/bookstore/pspdf/hmath-19-prev.pdf#page=11 https://www.ams.org/bookstore/pspdf/hmath-19-prev.pdf#page=1...
    - vinnyvichy 2y ago
      Double thanks! (Always glad to see the German taking "Elizabethan" s-f glyph pair to its ambiguous conclusion.) My very earliest exposure to the Ausdehnungslehre was in Sternberg+Bamberg. Until coming across Penrose diagrams, this book staved off the disgust I felt for tensor calculus (as used by physicists). http://ndl.ethernet.edu.et/bitstream/123456789/33770/1/108.pdf.pdf http://ndl.ethernet.edu.et/bitstream/123456789/33770/1/108.p... Mainly shocked by the compression of Maxwell's equations to a single line. Otherwise.. that was.. (regrettably cryptic) a reference to the eerily resonant Kolmogorov option, roughly motivated by Hilbert's slogan "truth does not need martyrs". https://scottaaronson.blog/?p=3376 https://scottaaronson.blog/?p=3376 More precisely, I am sympathetic to the idea that the path that Grassmann took to release his discoveries into the world was actually close to the optimal one. Other paths to consider are thus Grothendieck's,Kaczynski's, Galois' (generalizing to purely social bits, even Nash's) Two-sided intellectual exchange with a finished work across spacetime, that's also something.
      - 082349872349872 2y ago
        (was Galois the co-Kaczynski?) If we want to figure out the optimal path to release discoveries, what happens if we set the action to zero?
- eigenvalue 2y ago
  Yeah, his ultimate confidence in the merit of his ideas is pretty inspiring, even if he never got to see it happen in his own lifetime.
  - 082349872349872 2y ago
    Since the remainder of the thread has been infested by "noonday demons", there's a nice line by a singer-songwriter about a SF novel in the Noon Universe[0]: "of course, freedom and brotherhood[1] will come / But it will happen without us."[2] [0] https://en.wikipedia.org/wiki/Noon_Universe#Description https://en.wikipedia.org/wiki/Noon_Universe#Description [1] aka « liberté et fraternité ». A cynic would say the Arkanarians already have « égalité », in that they're all stuck on a planet cycling endlessly between mere anti-intellectualism and outright theocracy. [2] Конечно, свобода и братство наступят / Но это случится без нас (https://www.youtube.com/watch?v=ufbCnjBYDbI&t=5134s https://www.youtube.com/watch?v=ufbCnjBYDbI&t=5134s)
vinnyvichy 2y ago
HMM
- 082349872349872 2y ago
  For Aaronson's question, I'd suggest that Prof. Dr. Marcus Hutter is far more likely to have an answer than I am to guess one. (or Schmidhuber!) I'm far more into semigroups than Solomonoff Induction these days... As to inflections, there's a fan theory that different Pynchon titles reflect different conic sections: https://www.math.columbia.edu/~woit/wordpress/?p=7479 https://www.math.columbia.edu/~woit/wordpress/?p=7479
  - vinnyvichy 2y ago
    Ah you mean Schmidhuber's speed prior: https://people.idsia.ch/~juergen/speedprior.html https://people.idsia.ch/~juergen/speedprior.html I was more interested in pointing to you the measly followups to Aaronson's question, which consists solely of forays into nonlinear quantum mechanics & superluminal neutrinos. https://www.preposterousuniverse.com/blog/2011/09/24/can-neutrinos-kill-their-own-grandfathers/ https://www.preposterousuniverse.com/blog/2011/09/24/can-neu...

vinnyvichy 2y ago

See the other thread on the Milanovic-Kuznets curve[0-1], then lookup the Wiki Indeed, it's ... Critical .. to identify points with, uh, unexpected curvature. ?HN (?Lagniappe of the halfDay): KidW,o WitH,d? [0]https://scottaaronson.blog/?p=762 https://scottaaronson.blog/?p=762 [1]https://news.ycombinator.com/item?id=40437206 https://news.ycombinator.com/item?id=40437206

082349872349872 2y ago
Hmm... what are the finnic equivalents/dysquivalents of the Południca/полуднице[0]? My poisk-fu will probably be insufficient, but my wild guess at the moment is that due to circumstances mentioned in https://en.wikipedia.org/wiki/Arkhangelsk#Literature https://en.wikipedia.org/wiki/Arkhangelsk#Literature , coincidentally the reference was collected there. (Midnight to me is just a local play on being easier to temporally localise in summer than Noon[1], being just south of the arctic circle[2]. There's another russian folk tale I can't remember specifically in which young folk, on a particular saint's day, go looking for a specific species of flower[3] and if they find a —phenotypically non-existent— colour, it grants invisibility: the rural peasantry's equivalent of ex falso quodlibet?) [0] https://ru.wikipedia.org/wiki/Полудница#/media/Файл:Распространение_мифов_о_полуднице_и_некоторых_типов_русалок_у_восточных_славян.png https://ru.wikipedia.org/wiki/Полудница#/media/Файл:Распрост... shows them only in slavic areas (1) [1] I'll note that in my local laws, 12.00-13.00 are still quiet hours; one doesn't rely on any Mittagsgespenst but instead could just threaten to call the cops on errant workers. [2] compare https://sv.wikipedia.org/wiki/Midnattssol https://sv.wikipedia.org/wiki/Midnattssol [3] at least as long as they're not deflowering each other instead. Another just-so story for a Halfday Witch is related: older members of the village can easily be kept in check by threatened retaliation, but when the younger kids (acting as temporary fieldhands for the harvest) might be in danger of intruding upon Masha and Sasha's privacy[4] over midday, they are threatened with the Midday Witch, and if the small kids ask why Masha and Sasha are not afraid of her, they get told M&S are taking their chances but know enough about agronomy to answer her questions — or would Masha's mother be told she didn't make it home for lunch because she had been caught by the Midday Witch and had to recite flax culture 101? [4] probably easier to find by "taking a walk" (Гуляют все девчонки и парни района?) than at home; compare gown-greening: https://www.youtube.com/watch?v=XqX0720VTRY https://www.youtube.com/watch?v=XqX0720VTRY Lagniappe: https://www.youtube.com/watch?v=EnoqvRGc7pk https://www.youtube.com/watch?v=EnoqvRGc7pk (frame story: midnight, framed story: midday)

joe_the_user 2y ago

Sort of. I'd change the metaphor a bit. Math at the start of 19th century was like a country many of whose high mountains (say theorems) had been climbed but whose basic geography (foundations) hadn't been charted. Grassman was perhaps the first to begin the process of true foundational studies - creating structures that formally tied the mountains together (different from intuitively tying the mountains together, notably). Grassman's approach (incorporated as "exterior algebra") was klunky and difficult most likely specifically because he was doing something new, something never done before. That is, he was working when no formal linear algebra and indeed neither formal abstract algebra nor formal foundations of real numbers nor formalization of calculus existed (though many things were talked about informally). And Grassman was resisted because of the (probably necessary) klunkiness, but also because many mathematicians didn't see the need for this and no small number actively resisted the need for formal. IE, saw the qualities of numbers and collections of thing as best handled intuitively rather than formally and especially disliked the way formal formulations allowed and required counter-intuitive structures (transfinite sets, the axiom of choice, etc). This resistance didn't just touch Grassman but affect Cantor and Hilbert, etc. Today, math still has a tension between the provers of hard theorems and the structure builders, that would be the mountain climbers and the geographers, the Erdős' and the Grothendiecks. Moreover, the history of that tension isn't as clear as it could be since fields of math are generally taught as fully formulated systems with few nods to the state of the field before a given formulation (I just learned today that van der Waerden's Moderne Alegebra, published in 1930, was the first text to put abstract algebra in anything like it's present form). More on the history of the formalization of mathematics can found in Jan van Plato's The Great Formal Machinery Works (Grassman is the first writer covered).

Ar-Curunir 2y ago
I'm sure you didn't mean to imply this, but Grothendieck definitely used his new structures to prove some hard theorems.
- eigenvalue 2y ago
  This reminds me of the Grothendieck quote about his approach to solving problems (in contrast with Erdős, who I suppose in this analogy would look for a big hammer with which to smash the nut open quickly!): “I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise, you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marble, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.”