Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Goodbye, gjm. The impetus that your posts provided to post thought-provoking mathematical links will be missed. :)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

gjmasserts "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?

A... (read more)

29yActually I clearly and explicitly went out of my way to say I wasn't asserting
that.
Bored of being laughed at out loud now. (Twice in one short thread is enough.)
Bye.

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

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)"

19yIt seems perfectly possible to me -- I make no claims about whether it's
actually true -- that the following could all be the case. (1) Of the various
physical theories in the possession of the human race that are definite enough
to be assessed, one of the clear winners is the Standard Model. (2) Of the
various ways to understand the quantum mechanics involved in the Standard Model,
the clear winner is "many worlds". (3) The known lacunae in our understanding of
physics make it clear that further conceptual advances will be needed before we
can claim to understand everything. (4) Those conceptual advances could take
just about any form, and everything we currently think we know is potentially up
for grabs. (5) "Many worlds" is not uniquely under threat from these future
conceptual advances -- everything is up for grabs -- and the possibility of
future conceptual revolutions doesn't call for any more caution about "many
worlds" than it does for caution about, say, the inseparability of space and
time.
In other words: The fact that science is hard and not yet finished is indeed
reason for epistemic humility -- about everything; but pointing to some
particular thing alleged to be a discovery of modern science and saying "no,
wait, it could turn out to be wrong" is not justifiable by that fact alone,
unless you are happy to do the same for all other alleged discoveries of modern
science.
My guess is that you have some other reasons for being skeptical about the
many-worlds interpretation, besides the very general fact that quantum mechanics
might some day be the subject of a great scientific upheaval. But you haven't
said what they are.
My point about your tone is not concerned with the fact that you include
references and quotations, and taking offence isn't the failure mode you might
need to worry about. The danger, rather, is that you come across as pushing,
with an air of smug superiority, a non-standard view of the present state of
science, and that this is lia

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

gjmavers "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,... (read more)

19yNo, I think it's excellent (though I prefer the PowerPoint version
[http://norvig.com/Gettysburg/]), but it isn't an essay.
That sentence appears to me to embody some assumptions you're not in a position
to make reliably. Notably: That I think, or thought until John Sidles kindly
enlightened me, that Eliezer's QM essays are anything like a complete exposition
of QM. As it happens, that wasn't my opinion; for that matter I doubt it is or
was even Eliezer's.
In particular, when Eliezer says that QM is "non-mysterious" I don't think he
means that everything about it is understood, that there are no further
scientific puzzles to solve. He certainly doesn't mean it isn't possible to pick
a mathematical framework for talking about QM and then contemplate
generalizations. He's arguing against a particular sort of mysterianism one
often hears in connection with QM -- the sort that says, roughly, "QM is
counterintuitive, which means no one really understands it or can be expected to
understand it, so the right attitude towards QM is one of quasi-mystical awe",
which is the kind of thing that makes Chopraesque quantum woo get treated with
less contempt than it deserves.
Even Newtonian mechanics is mysterious in the sense that there are unsolved
problems associated with it. (For instance: What are all the periodic 3-body
trajectories? What is the right way to think about the weird measure-zero
situations -- involving collisions of more than two particles -- in which the
usual rules of Newtonian dynamics constrain what happens next without, prima
facie, fully determining it?) But no one talks about Newtonian mechanics in the
silly way some people talk about quantum mechanics, and it's that sort of
quantum silliness Eliezer is (at least, as I understand it) arguing against.
I think at least one of us has a serious misunderstanding of what's generally
meant by the phrase "not even wrong". To me, it means "sufficiently vague or
confused that it doesn't even yield the sort of t

Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92

**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.

... (read more)Regrettably, tgb, even the redoubtable

Google Booksdoes not provide page-images for Spivak'sPhysics for Mathematicians: Mechanics I. The best advice I can give is to seek this book within a university library

Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92

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. :)

Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92

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?

29yI can't find the particular proofs of Noether theorems that your link refers to.
Can you help me find them? I see no instances of the word "muggle" in Spivak's
paper - in fact no index at all. Is there a different version of it? Please
help, as I would greatly appreciate reading this!
Edit: I see now that the comment was referring to a book by Spivak, and that the
linked PDF is only on 'elementary mechanics.'

Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92

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)

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, wiza

29y1. Both canon and HPMoR have arithmancy. In HPMoR, "Harry and Professor
McGonagall had bought his textbooks from Flourish and Blotts just under the
deadline. With only a slight explosion when Harry had made a beeline for the
keyword 'Arithmancy' and discovered that the seventh-year textbooks invoked
nothing more mathematically advanced than trigonometry." And Harry really
shouldn't have exploded. Many real world Muggle schools don't get as far as
trigonometry by the end of high school, and they don't have to spend any
time on charms or transfiguration.
2. Ryvmvre unf fgngrq gung guvf vf abg na NV fgbel.

99yAbominable Conclusion 1: the AIs that first negotiated with humanity, thousands
of years ago, to levitate objects on command, had insisted that humans speak the
protocol words... Wingardium Leviosa.

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

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 issue... (read more)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

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."

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

The entanglement(s) of hot-noisy-evolved biological cognition with abstract ideals of cognition that Eliezer Yudkowsky vividly describes in *Harry Potter and the Methods of Rationality*, and the quantum entanglement(s) of dynamical flow with the physical processes of cognition that Scott Aaronson vividly describes in *Ghost in the Quantum Turing Machine*, both find further mathematical/social/philosophical echoes in Joshua Landsberg's *Tensors: Geometry and Applications* (2012), specifically in Landsberg's thought-provoking introductory section **Section 0.3: Clas**... (read more)

09yAn 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
[http://www.scottaaronson.com/blog/?p=1438#comment-81146]” (to borrow an apt
phrase from Jaffe and Quinn's arXiv:math/9307227
[http://arxiv.org/abs/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 [http://arxiv.org/abs/0810.1019] (arXiv:0810.1019, 2011), whose
Introduction states:
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! :)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Quantum aficionados in the mold of **Eliezer Yudkowsky** will have fun looking up "Noether's Theorem" in the index to Michael Spivak's **well-regarded** *Physics for Mathematicians: Mechanics I*, because near to it we notice an irresistible index entry "Muggles, 576", which turns out to be a link to:

TheoremThe flow of any Hamiltonian vector field consists of canonical transformations

Proof(Hogwarts version) ...

Proof(Muggles version) ...

**Remark** It is striking that Dirac's *The Principles of Quantum Mechanics* (1930), Feynman's *Lectures on *... (read more)

39yThe thing you link to is not anything by Joshua Landsberg, but another of your
own comments.
That in turn does link to something by 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 and about half of it is a quotation from
Plato. (It also makes no explicit allusion to Spivak's Hogwarts-Muggles
distinction, though I agree it's pointing at much the same divergence.)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

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 ... (read more)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Thank you for your gracious remarks, Paper-Machine. Please let me add, that few (or possibly none) of the math/physics themes of the preceding posts are original to me (that's why I give so many references!)

Students of quantum history will find pulled-back/non-linear metric and symplectic quantum dynamical flows discussed as far back as Paul Dirac's seminal *Note on exchange phenomena in the Thomas atom* (1930); a free-as-in-freedom review of the nonlinear quantum dynamical frameworks that came from Dirac's work (nowadays called the "Dirac-Frenkel-M... (read more)

29yQuantum aficionados in the mold of Eliezer Yudkowsky
[http://tvtropes.org/pmwiki/pmwiki.php/FanFic/HarryPotterAndTheMethodsOfRationality]
will have fun looking up "Noether's Theorem" in the index to Michael Spivak's
well-regarded
[http://mathoverflow.net/questions/51395/a-soft-introduction-to-physics-for-mathematicians-who-dont-know-the-first-thing/51414#51414]
Physics for Mathematicians: Mechanics I, because near to it we notice an
irresistible index entry "Muggles, 576", which turns out to be a link to:
Remark It is striking that Dirac's The Principles of Quantum Mechanics (1930),
Feynman's Lectures on Physics (1965), Nielsen and Chuang's Quantum Computation
and Quantum Information (2000)---and Scott Aaronson's essay The Ghost in the
Turing Machine (2013) too---all frame their analysis exclusively in terms of
(what Michael Spivak aptly calls) Muggle mathematic methods! :)
Observation Joshua Landsberg has written an essay Clash of Cultures
[http://lesswrong.com/r/discussion/lw/hq7/quotes_and_notes_on_scott_aaronsons_the_ghost_in/97m3]
(2012) that discusses the sustained tension between Michael Spivak's "Hogwarts
math versus Muggle math". The tension has historical roots that extent at least
as far back as Karl Gauss' celebrated apprehension regarding the "the clamor of
the Boeotians [http://books.google.com/books?id=vrQLbbxGNMsC&pg=PA54]" (aka
Muggles).
Conclusion Michael Spivak's wry mathematical jokes and Eliezer Yudkowsky's
wonderfully funny Harry Potter and the Methods of Rationality both help us to
appreciate that outdated Muggle-mathematical idioms of standard textbooks and
philosophical analysis are a substantial impediment to 21st Century learning and
rational discourse of all varieties---including philosophical discourse.

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Shminux, there are plenty of writers---mostly far more skilled than me!---who have attempted to connect our physical understanding of dynamics to our mathematical understanding of dynamical flows. So please don't let my turgid expository style needlessly deter you from reading this literature!

In this regard, Michael Spivak's works are widely acclaimed; in particular his early gem *Calculus on Manifolds: a Modern Approach to Classical Theorems of Advanced Calculus* (1965) and his recent tome *Physics for Mathematicians: Mechanics I* (2010) (and in a comment on... (read more)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Gjmasks "Along what vector field V are you taking the Lie derivative?

The natural answer is, along a *Hamiltonian* vector field. Now you have all the pieces needed to ask (and even answer!) a broad class of questions like the following:

Alice possesses a computer of exponentially large memory and clock speed, upon which she unravels the Hilbert-space trajectories that are associated to the overall structure ), where is a Hilbert-space (considered as a manifold), is its metric, is its symplectic form, is the complex structure induced by ), and )

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

JLM, the mathematically natural answer to your questions is:

• the quantum *dynamical* framework of (say) Abhay Ashtekar and Troy Schilling's *Geometrical Formulation of Quantum Mechanics* arXiv:gr-qc/9706069v1, and

• the quantum *measurement* framework of (say) Carlton Caves' on-line notes *Completely positive maps, positive maps, and the Lindblad form*, both pullback naturally onto

• the *varietal* frameworks of (say) Joseph Landsberg's *Tensors: Geometry and Applications*

Textbooks like Andrei Moroianu's *Lectures on Kahler Geometry* and Mikio Nakahara's *Geometry, Topolo*... (read more)

0[anonymous]9y(reposted with proper nesting above
[http://lesswrong.com/r/discussion/lw/hq7/quotes_and_notes_on_scott_aaronsons_the_ghost_in/96su]
)
The natural answer is, along a Hamiltonian vector field. Now you have all the
pieces needed to ask (and even answer!) a broad class of questions like the
following:
* Alice possesses a computer of exponentially large memory and clock speed,
upon which she unravels the Hilbert-space trajectories that are associated to
the overall structure ), where is a Hilbert-space (considered as a manifold),
is its metric, is its symplectic form, is the complex structure induced by ),
and ) are the (stochastic,smooth) Lindblad and Hamiltonian potentials that
are associated to a physical system that Alice is simulating. Alice thereby
computes a (stochastic) classical data-record as the output of her
unraveling.
* Bob pulls-back ) onto his lower-dimension varietal manifold (per Joseph
Landsberg's recipes), upon which he unravels the pulled-back trajectories,
thus obtaining (like Alice) a classical data-record as the output of his
unraveling (but using far-fewer computational resources).
Then It is natural to consider questions like the following:
Is this a mathematically well-posed question? Definitely! Is it a scientifically
open question? Yes! Does it have practical engineering consequences? Absolutely!
What philosophical implications would a "yes" answer have for Scott's freebit
thesis? Philosophical questions are of course tougher to answer than
mathematical, scientific, or engineering questions, but one reasonable answer
might be "The geometric foaminess of algebraic state-spaces induces Knightian
undertainty in quantum unravelings that is computationally indistinguishable
from the dynamical effects that are associated to primordial freebits."
Are these questions interesting? Here is it neither feasible, nor necessary, nor
desirable that everyone think alike!

19y(Who's JLM?)
I don't think you actually answered any of my questions; was that deliberate?
Anyway, it seems that (1) the general description in terms of Kähler manifolds
is a somewhat nonstandard way of formulating "ordinary" quantum mechanics; (2) J
does indeed play the role of i, kinda, since one way you can think about Kähler
manifolds is that you start with a symplectic manifold and then give it a local
complex structure; (3) yes, M is basically a phase space; (4) you see some great
significance in the idea that some Lie derivative of J might be nonzero, but
haven't so far explained (a) whether that is a possibility within standard QM or
a generalization beyond standard QM, or (b) along what vector field V you're
taking the Lie derivative (it looks -- though I don't understand this stuff well
at all -- as if it's more natural to take the derivative of something else along
J, rather than the derivative of J along something else), or (c) why you regard
this as importance.
And I still don't see that there's any connection between this and Scott's stuff
about free will. (That paragraph you added -- is it somehow suggesting that
"dynamic-J methods" for simulation can somehow pull out information that
according to Scott is in principle inaccessible? Or what?)

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

The dynamicist Vladimir Arnold had a wonderful saying:

"Every mathematician knows that it is impossible to understand any elementary course in thermodynamics."

This saying is doubly true of quantum mechanics. For example, the undergraduate quantum physics notion of "multiply a quantum vector by " is not so easy to convey without mentioning the number "." Here's how the trick is accomplished. We regard Hilbert space as a real manifold that is equipped with a symplectic form and a metric . Given an (arbitrary) vector fi... (read more)

39yAre you describing
* a (nonstandard?) formalism equivalent to other standard ways of doing quantum
mechanics?
* an actually existing theory of quantumish mechanics, genuinely different from
others, that makes predictions that match experiment as well as the existing
theories do?
* a sketch of how you hope some future theory might look?
* something else?
It sounds as if your endomorphism J is supposed to play the role of i somehow,
but how? What do you actually do with it, and why?
What is your manifold M actually supposed to be, and why? Is it just a formal
feature of the theory, or is it meant to be spacetime, or some kind of phase
space, or what?

29yI cannot tell whether your writing style indicates an inability to bridge an
inferential gap or an attempt at status smash ("I'm so smart, look at all the
math I know, relevant or not!"). I will assume that it's the former, but will
disengage, anyway, given how unproductive this exchange has been so far. Next
time, consider using the language appropriate for your audience, if you want to
get your point across.

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Thank you gjm. To the best of my understanding, (1) all markup glitches are fixed; (2) all links are live; and (3) an added paragraph (fourth-from-last) now explicitly links dynamic-J methods to Scott's notion of "freebits".

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Gjm, after a round-of-suffering with the LaTeX equation editor, any-and-all markup glitches in the above comment now seem to be fixed (at least, the comment now parses OK on FireFox/OSX and Safari/OSX). Please let me know if you are encountering any remaining markup-relating problems, and if so, I will attempt to fix them.

[This comment is no longer endorsed by its author]

19yNo, it's OK now. The funny thing is that the glitch doesn't seem to have been
near any of your LaTeX bits.
I confess that I don't really see the connection between your comment and
Scott's essay, beyond the fact that both have something to do with Scott's
opinions on quantum mechanics.

Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine"

Rancor commonly arises when STEM discussions in general, and discussions of quantum mechanics in particular, focus upon personal beliefs and/or personal aesthetic sensibilities, as contrasted with verifiable mathematical arguments and/or experimental evidence and/or practical applications.

In this regard, a pertinent quotation is the self-proclaimed "personal belief" that Scott asserts on page 46:

... (read more)"One obvious way to enforce a macro/micro distinction would be via a dynamical collapse theory. ... I personally cannot believe that Nature would

39yI honestly don't understand why you invoke Killing vectors to make your point. I
am also not sure what this "complex structure J" means (is it some tensor?) in
the QM context and what it would mean to take a Lie derivative of J with respect
to some vector field.

19yOoo, looks like LW's comment-parsing code just lets HTML through blindly or
something. I wonder if I can fix the overhanging italics like this: ? [EDIT: no,
apparently not. So whatever did John do?]

[link] Scott Aaronson on free will

Rancor commonly arises when STEM discussions in general, and discussions of quantum mechanics in particular, focus upon personal beliefs and/or personal aesthetic sensibilities, as contrasted with verifiable mathematical arguments and/or experimental evidence and/or practical applications.

In this regard, a pertinent quotation is the self-proclaimed "personal belief" that Scott asserts on page 46:

... (read more)"One obvious way to enforce a macro/micro distinction would be via a dynamical collapse theory. ... I personally cannot believe that Nature would

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.