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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.

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:

"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 advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet it finally surrounds the resistant substance."

Surely in regard quantum mechanics, the water of our understanding is far from covering the rocks of our ignorance!

As for the tone of my posts, the intent is that people who enjoy references and quotations will take no offense, and people who do not enjoy them can simply pass by.

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 the essays of Less Wrong's Quantum Physics Sequence, including in particular Eliezer_Yudkowsky's essay Quantum Physics Revealed As Non-Mysterious.

The burgeoning 21st century literature of geometric dynamics helps us to appreciate that the the 20th century mathematical toolkit of Less Wrong's quantum essays perhaps will turn out to be not so much "less wrong" as "not even wrong," in the sense that Less Wrong's quantum essays are devoid of the geometric dynamical ideas that are flowering so vigorously in the contemporary STEM literature.

This is of course very good news for young researchers! :)

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:

  • mathematics, and
  • artificial intelligences (AIs)


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 origins of magic.

Postulate 3 The chief organizing objective of the Hogwarts curriculum is to preserve the social fictions that are associated to Postulates 1 and 2.

Postulate 4 Harry Potter is regarded as dangerous because he seeks to evade the restrictions associated to Postulates 1, 2, and 3, by inquiring into the true nature of magic and its actions.

Literary Remark Harry Potter would do well to reflect upon the words and fate of Captain Ahab:

"All visible objects, man, are but as pasteboard masks. But in each event — in the living act, the undoubted deed — there, some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask. If man will strike, strike through the mask! How can the prisoner reach outside except by thrusting through the wall? To me, the white whale is that wall, shoved near to me. Sometimes I think there's naught beyond. But 'tis enough. He tasks me; he heaps me; I see in him outrageous strength, with an inscrutable malice sinewing it. That inscrutable thing is chiefly what I hate; and be the white whale agent, or be the white whale principal, I will wreak that hate upon him. Talk not to me of blasphemy, man; I'd strike the sun if it insulted me. For could the sun do that, then could I do the other; since there is ever a sort of fair play herein, jealousy presiding over all creations. Ohg abg zl znfgre, zna, vf rira gung snve cynl. Jub'f bire zr? Gehgu ungu ab pbasvarf."

Conclusion Harry Potter's quest to restore Hermione Granger may be leading him and the Hogwarts crew to a similarly disastrous fate as Ahab and the Pequod crew.

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:

"The book should serve as an appetizer, inviting the reader to go more deeply into these fascinating, interdisciplinary fields of science. ... [We] focus attention on the simplicity and beauty of theoretical physics, which is often hidden in a jungle of techniques for estimating or calculating quantities of interest."

That the Neumaier/Westra textbook is an unfinished work-in-progress constitutes proof prima facie that the final tractatus upon these much-discussed logico-physico-philosophicus issues has yet to be written! :)

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