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Somebody says:

Yours truly replies (mathoverflow.net/a/275825/381):

What makes all this hard to learn in a systematic way is that the theory itself is still incomplete and proceeds in parts via educated guesswork.

In principle perturbative string theory is well defined: This says to pick a 2d super-conformal field theory of central charge 15, collect its n-point functions into one formal power series, interpret this as a loop-wise finite, hence normalized, scattering matrix known from QFT, then study this.

In principle "compactifications, Dualities, D-branes" (though not M-branes) are all well defined parts of this scheme. For instance D-branes are the algebraic data that defines the 2d SCFT at the boundary of the Riemann surfaces, Dualities are correspondences between different 2d SCFTs that miraculously yield isomorphic scattering matrices this way, and compactifications are decompositions of a 2d SCFT as a tensor product with some "finite" factor for instance a rational CFT. The target spacetime geometry that is being compactified thereby is to be read off from the CFT in a way generalizing how spectral Connes-style NCG reads off target geometry from algebraic data. (See the exposition at www.physicsforums.com/insights/spectral-standard-model-string-compactifications/)

The problem at this point is that, while well defined, it is mathematically so hard. The only 2d CFTs that have mathematically been constructed as full CFTs are the "rational" ones, which only describe certain compact factors. For the others there is Segal's axiomatics, but essentially no examples. What one has is the local description in terms of vertex operator algebras. For these many examples are available, but not enough for the purposes of the physicists.

This is the first point where physics parts with a systematic mathematical development. Namely while it is hard to really construct full 2d SCFTs, the folk lore of the path integral allows to think of solutions to supergravity equations of motion as inducing 2d SCFTs via quantization of the "nonlinear sigma-model" with these spacetimes as their targets. So now instead of deducing effective target space geometry from the SCFT algebra, one prescribes classical target space geometry to which one believes SCFTs may be associated. It is from here on that much of string theory is now phrased in terms of classical geometry with some extra stringy effects sprinkled in (modular invariance, anomaly cancellation, brane instanton effects).

The uncertainty as to how well this sigma-model construction is under constrol is the cause of the discrepancy in the perception of how many string vacua are known: A perturbative string vacuum is equivalently that 2d SCFT which gives the scattering matrix, so in principle the "landscape of perturbative string vacua" is the moduli space of 2d SCFTs. But since this is not understood, what people instead scan is the space of target space geometries that are thought to induces 2d SCFTs. This is a subtle business, where one imagines one may incrementally approximate that 2d SCFT by adding alpha-prime corrections, cancelling anomalies, etc. Therefore one finds authors who worry that too many string vacua are known, and other authors who worry that too few string vacua are known.

If this were all there is to it, the solution would in principle be straightforward: mathematicians/mathematical physicists should simply sit down and find means to rigorously construct 2d SCFTs and to understand the moduli space that they form. That would be the mathematics of perturbative string theory, and all the answers as to "compactifications, Dualities, D-branes" would be encoded in there, under some well defined dictionary.

But now there is also the "M-branes", and that's indicative of the real problem: Since the string perturbation series is just a non-converging formal power series, as for a normalized perturbative QFT, it ought to be but the Taylor expansion of some non-perturbative theory about some points of its cofiguration space.

There are many compelling hints for this "theory formerly known as String" but so far they are just hints.

"

We still have no fundamental formulation of “M-theory” - the hypothetical theory of which 11-dimensional supergravity and the five string theories are all special limiting cases. Work on formulating the fundamental principles underlying M-theory has noticeably waned. [...]. If history is a good guide, then we should expect that anything as profound and far-reaching as a fully satisfactory formulation of M-theory is surely going to lead to new and novel mathematics. Regrettably, it is a problem the community seems to have put aside - temporarily. But, ultimately, Physical Mathematics must return to this grand issue.

"

(G. Moore, "Physical Mathematics and the Future", talk at Strings 2014)

The way this is presently being studied is the same mix of classical target spacetime geometry with conjectured "extra effects" sprinkled in. For instance a "black M-brane" is to first approximation a solution to the equations of motion of 11d supergravity which preserves half of the global supersymmetry. By analogy with the D-branes and some other arguments, coincident such M-branes should "carry" a non-abelian gauge SCFT on their worldvolume. There is presently no way to derive this from anything, but superconformal invariance imposes enough constraints that a classical action functional could finally be guessed (the BLG/ABJM model). Now the search is on for the analogue on the M5-brane. Nothing definite is known, there are hints, and whatever one finds will justify itself by plausibility arguments. Because none of this can be derived from first principles

There are presently no first principles for full string theory, aka M-theory. There is no mathematics of M-theory to be learned. Instead, the mathematics of M-theory is waiting to be found.

This may not be as bad as it may sound. Maybe "M-theory" is easier to deduce following mathematical principles, than the historical route of the perturbtive string. I just wrote an exposition of such a point of view over at PF-Insights:

http://www.physicsforums.com/insights/super-p-brane-theory-emerging-super-homotopy-theory/

So it seems not out of the question that, conversely, it will in the end be the physicists who will learn M-theory from the mathematicians.

**"I'm a mathematician. I want to understand compactifications, Dualities, D-branes, M-branes etc."**(mathoverflow.net/q/116251/381)Yours truly replies (mathoverflow.net/a/275825/381):

What makes all this hard to learn in a systematic way is that the theory itself is still incomplete and proceeds in parts via educated guesswork.

In principle perturbative string theory is well defined: This says to pick a 2d super-conformal field theory of central charge 15, collect its n-point functions into one formal power series, interpret this as a loop-wise finite, hence normalized, scattering matrix known from QFT, then study this.

In principle "compactifications, Dualities, D-branes" (though not M-branes) are all well defined parts of this scheme. For instance D-branes are the algebraic data that defines the 2d SCFT at the boundary of the Riemann surfaces, Dualities are correspondences between different 2d SCFTs that miraculously yield isomorphic scattering matrices this way, and compactifications are decompositions of a 2d SCFT as a tensor product with some "finite" factor for instance a rational CFT. The target spacetime geometry that is being compactified thereby is to be read off from the CFT in a way generalizing how spectral Connes-style NCG reads off target geometry from algebraic data. (See the exposition at www.physicsforums.com/insights/spectral-standard-model-string-compactifications/)

The problem at this point is that, while well defined, it is mathematically so hard. The only 2d CFTs that have mathematically been constructed as full CFTs are the "rational" ones, which only describe certain compact factors. For the others there is Segal's axiomatics, but essentially no examples. What one has is the local description in terms of vertex operator algebras. For these many examples are available, but not enough for the purposes of the physicists.

This is the first point where physics parts with a systematic mathematical development. Namely while it is hard to really construct full 2d SCFTs, the folk lore of the path integral allows to think of solutions to supergravity equations of motion as inducing 2d SCFTs via quantization of the "nonlinear sigma-model" with these spacetimes as their targets. So now instead of deducing effective target space geometry from the SCFT algebra, one prescribes classical target space geometry to which one believes SCFTs may be associated. It is from here on that much of string theory is now phrased in terms of classical geometry with some extra stringy effects sprinkled in (modular invariance, anomaly cancellation, brane instanton effects).

The uncertainty as to how well this sigma-model construction is under constrol is the cause of the discrepancy in the perception of how many string vacua are known: A perturbative string vacuum is equivalently that 2d SCFT which gives the scattering matrix, so in principle the "landscape of perturbative string vacua" is the moduli space of 2d SCFTs. But since this is not understood, what people instead scan is the space of target space geometries that are thought to induces 2d SCFTs. This is a subtle business, where one imagines one may incrementally approximate that 2d SCFT by adding alpha-prime corrections, cancelling anomalies, etc. Therefore one finds authors who worry that too many string vacua are known, and other authors who worry that too few string vacua are known.

If this were all there is to it, the solution would in principle be straightforward: mathematicians/mathematical physicists should simply sit down and find means to rigorously construct 2d SCFTs and to understand the moduli space that they form. That would be the mathematics of perturbative string theory, and all the answers as to "compactifications, Dualities, D-branes" would be encoded in there, under some well defined dictionary.

But now there is also the "M-branes", and that's indicative of the real problem: Since the string perturbation series is just a non-converging formal power series, as for a normalized perturbative QFT, it ought to be but the Taylor expansion of some non-perturbative theory about some points of its cofiguration space.

There are many compelling hints for this "theory formerly known as String" but so far they are just hints.

"

We still have no fundamental formulation of “M-theory” - the hypothetical theory of which 11-dimensional supergravity and the five string theories are all special limiting cases. Work on formulating the fundamental principles underlying M-theory has noticeably waned. [...]. If history is a good guide, then we should expect that anything as profound and far-reaching as a fully satisfactory formulation of M-theory is surely going to lead to new and novel mathematics. Regrettably, it is a problem the community seems to have put aside - temporarily. But, ultimately, Physical Mathematics must return to this grand issue.

"

(G. Moore, "Physical Mathematics and the Future", talk at Strings 2014)

The way this is presently being studied is the same mix of classical target spacetime geometry with conjectured "extra effects" sprinkled in. For instance a "black M-brane" is to first approximation a solution to the equations of motion of 11d supergravity which preserves half of the global supersymmetry. By analogy with the D-branes and some other arguments, coincident such M-branes should "carry" a non-abelian gauge SCFT on their worldvolume. There is presently no way to derive this from anything, but superconformal invariance imposes enough constraints that a classical action functional could finally be guessed (the BLG/ABJM model). Now the search is on for the analogue on the M5-brane. Nothing definite is known, there are hints, and whatever one finds will justify itself by plausibility arguments. Because none of this can be derived from first principles

There are presently no first principles for full string theory, aka M-theory. There is no mathematics of M-theory to be learned. Instead, the mathematics of M-theory is waiting to be found.

This may not be as bad as it may sound. Maybe "M-theory" is easier to deduce following mathematical principles, than the historical route of the perturbtive string. I just wrote an exposition of such a point of view over at PF-Insights:

http://www.physicsforums.com/insights/super-p-brane-theory-emerging-super-homotopy-theory/

So it seems not out of the question that, conversely, it will in the end be the physicists who will learn M-theory from the mathematicians.

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*"Despite a Democratic member of Congress initiating the process to remove Trump from office,*

*there's almost no chance at all that the president would be impeached this year, no matter what happens.**"*

*"Why? Politics. Impeachment takes the form of a trial, but it isn't one. It's a political vote by politicians, all of whom would like to themselves avoid the fate of being thrown out of office. And Trump's political career both relied on and thrives because of the nature of the moment that he launched it."*

http://www.smh.com.au/world/no-matter-how-bad-it-gets-heres-why-donald-trump-isnt-getting-impeached-this-year-20170714-gxbsj3.html

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+Gmail is being problematic.

It never used to ask me to approve logins to gmail (not this account, my main account), and now insists I tap ok on my mobile phone to be logged in.

What is wrong with just password from keypass? Like I logged in for years, and like I logged into this account? It didn't ask any~~stupid~~ questions when logging into this account.

It never used to ask me to approve logins to gmail (not this account, my main account), and now insists I tap ok on my mobile phone to be logged in.

What is wrong with just password from keypass? Like I logged in for years, and like I logged into this account? It didn't ask any

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h/t +Boris Borcic. Looks like a must read post.

**Scientists slash computations for deep learning**

*Rice University computer scientists have adapted a widely used technique for rapid data lookup to slash the amount of computation—and thus energy and time—required for deep learning, a computationally intense form of machine learning. "This applies to any deep-learning architecture, and the technique scales sublinearly, which means that the larger the deep neural network to which this is applied, the more the savings in computations there will be," said lead researcher Anshumali Shrivastava, an assistant professor of computer science at Rice. The research will be presented in August at the KDD 2017 conference in Halifax, Nova Scotia. It addresses one of the biggest issues facing tech giants like Google, Facebook and Microsoft as they race to build, train and deploy massive deep-learning networks for a growing body of products as diverse as self-driving cars, language translators and intelligent replies to emails. Shrivastava and Rice graduate student Ryan Spring have shown that techniques from "hashing," a tried-and-true data-indexing method, can be adapted to dramatically reduce the computational overhead for deep learning. Hashing involves the use of smart hash functions that convert data into manageable small numbers called hashes. The hashes are stored in tables that work much like the index in a printed book. "Our approach blends two techniques—a clever variant of locality-sensitive hashing and sparse backpropagation—to reduce computational requirements without significant loss of accuracy," Spring said. "For example, in small-scale tests we found we could reduce computation by as much as 95 percent and still be within 1 percent of the accuracy obtained with standard approaches."*

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Strange light headache. I can place it near left top back of head. Near where the left thalamus was. Go in just above and back from the left ear and you wouldn't miss much.

I think the dead part of the left thalamus is still settling.

I think the dead part of the left thalamus is still settling.

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https://www.dailydot.com/irl/mushrooms-safe-drug/

Except for two Victorian mushrooms these might be ok. Mycologists may butt in anytime :-)

Except for two Victorian mushrooms these might be ok. Mycologists may butt in anytime :-)

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