JohnSidles
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Goodbye, gjm. The impetus that your posts provided to post thought-provoking mathematical links will be missed. :)
gjm asserts "Of the various ways to understand the quantum mechanics involved in the Standard Model, the clear winner is "many worlds"
LOL ... by that lenient standard, the first racehorse out of the gate, or the first sprinter out of the blocks, can reasonably be proclaimed "the clear winner" ... before the race is even finished!
That's a rational announcement only for very short races. Surely there is very little evidence that the course that finishes at comprehensive understanding of Nature's dynamics ... is a short course?
As for my own opinions in regard to quantum dynamical systems, they are more along the lines of here are some questions that are mathematically well-posed and are interesting to engineers and scientists alike ... and definitely not along the lines of "here are the answers to those questions"!
gjm avers: 'When Eliezer says that QM is "non-mysterious' ... He's arguing against a particular sort of mysterianism"
That may or may not be the case, but there is zero doubt that this assertion provides rhetorical foundations for the essay And the Winner is... Many-Worlds!.
A valuable service of the mathematical literature relating to geometric mechanics is that it instills a prudent humility regarding assertions like "the Winner is... Many-Worlds!" A celebrated meditation of Alexander Grothendieck expresses this humility:
... (read more)"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 marl, resisting penetration ... the sea
gjm avers "Landsberg that has a section headed "Clash of cultures" but it could not by any reasonable stretch be called an essay. It's only a few paragraphs long."
LOL ... gjm, you must really dislike Lincoln's ultra-short Gettysburg Address!
More seriously, isn't the key question whether Landsberg's essay is correct to assert that "there are language and even philosophical barriers to be overcome", in communicating modern geometric insights to STEM researchers trained in older mathematical techniques?
Most seriously of all, gjm, please let me express the hope that the various references that you have pursued have helped to awaken an appreciation of the severe and regrettable mathematical limitations that are inherent in... (read more)
Edit 1: Kudos to "gjm" (see above) for pointing to Spivak's page on Amazon!
Edit 2: Spivak's Hogwarts proof implicitly uses a fundamental theorem in differential geometry that is called Cartan's Magic Formula ... this oblique magical reference is Spivak's joke ... as with many magical formulas, the origins of Cartan's formula are obscure.
Regrettably, tgb, even the redoubtable Google Books does not provide page-images for Spivak's Physics for Mathematicians: Mechanics I. The best advice I can give is to seek this book within a university library system.
LOL --- perhaps a chief objective of the Ministry of Magic is to conceive and require obfuscating interfaces to magic! That would explain a lot!
Parallels to real-world high-school and/or undergraduate mathematical education ... are left as an exercise. :)
For a professional-grade comment on "muggle math" versus "Hogwarts math", see Michael Spivak's Physics for Mathematicians: Mechanics I.
To express this point another way ... how likely is it, that Harry's final understanding of magic will be non-mathematical? What grade of mathematical abstraction capabilities will Harry need to acquire?
Conspicuously absent from the canon, and from Methods of Rationality (so far) --- and absent entirely from the Hogwarts curriculum --- are two fundamental elements of rational cognition:
Therefore
... (read more)Postulate 1 "Magic" is the name that witches, wizards, and muggles alike give to the practice of manipulating physical reality by negotiation with agents that are (artificial? primordial? evolved? accidentally created?) intelligences.
Postulate 2 "Magical Spells" is the name that witches, wizards, and muggles alike give to an evolving set of protocols for negotiating with an existing community of (mysterious) intelligences. These protocols are designed to minimize the risks and harms associated to the practice of magic, by concealing the physical
An elaboration of the above argument now appears on Shtetl Optimized, essentially as a meditation on the question: What strictly mathematical proposition would comprise rationally convincing evidence that the key linear-quantum postulates of "One Ghost in the Quantum Turing Machine* amount to “an unredeemed claim [that has] become a roadblock rather than an inspiration” (to borrow an apt phrase from Jaffe and Quinn's arXiv:math/9307227).
Readers of Not Even Wrong seeking further (strictly mathematical) mathematical illumination in regard to these issues may wish to consult Arnold Neumaier and Dennis Westra's textbook-in-progress Classical and Quantum Mechanics via Lie Algebras (arXiv:0810.1019, 2011), whose Introduction states:
... (read more)"The book should serve as an appetizer, inviting the reader to go
A preprint would be terrific too.
A tough(?) question and a tougher(?) question: When self-modifying AI's are citizens of Terry Tao's Island of the Blue-Eyed People/AIs, can the AIs trust one another to keep the customs of the Island? On this same AI-island, when the AI's play the Newcomb's Paradox Game, according to the rules of balanced advantage, can the PredictorAIs outwit the ChooserAIs, and still satisfy the island's ProctorAIs?
Questions in this class are tough (as they seem to me), and it is good to see that they are being creatively formalized.