Stuff That’s Happened

Hi from FOCS’2016 in scenic New Brunswick, NJ!  (I just got here from Avi Wigderson’s 60th birthday conference, to which I’ll devote another post.)

In the few weeks since I last overcame the activation barrier to blog, here are some things that happened.


Friday’s revelation, of Trump boasting on tape to George W. Bush’s cousin about his crotch-grabbing escapades, did not increase my opposition to Trump, for a very simple reason: because I’d already opposed Trump by the maximum amount that’s possible.  Nevertheless, I’ll be gratified if this news brings Trump down, and leads to the landslide defeat he’s deserved from the beginning for 101000 reasons.

Still, history (including the history of this election) teaches us not to take things for granted.  So if you’re still thinking of voting for Trump, let me recommend Scott Alexander’s endorsement of “anyone but Trump.”  I’d go even further than my fellow Scott A. in much of what he says, but his post is nevertheless a masterful document, demonstrating how someone who nobody could accuse of being a statist social-justice warrior, but who “merely” has a sense for science and history and Enlightenment ideals and the ironic and absurd, can reach the conclusion that Trump had better be stopped, and with huge argumentative margin to spare.

See also an interview with me on Huffington Post about TrumpTrading, conducted by Linchuan Zhang.  If you live in a swing state and support Johnson, or in a safe state and support Hillary, I still recommend signing up, since even a 13% probability of a Trump win is too high.  I’ve found a partner in Ohio, a libertarian-leaning professor.  The only way I can foresee not going through with the swap, is if the bus tape causes Trump’s popularity to drop so precipitously that Texas becomes competitive.

In the meantime, it’s also important that we remain vigilant about the integrity of the election—not about in-person voter fraud, which statistically doesn’t exist, but about intimidation at the polls and the purging of eligible voters and tampering with electronic voting machines.  As I’ve mentioned before on this blog, my childhood friend Alex Halderman, now a CS professor at the University of Michigan, has been at the forefront of demonstrating the security problems with electronic voting machines, and advocating for paper trails.  Alex and his colleagues have actually succeeded in influencing how elections are conducted in many states—but not in all of them.  If you want to learn more, check out an in-depth profile of Alex in the latest issue of Playboy.  (There’s no longer nudity in Playboy, so you can even read the thing at work…)


As some of you probably saw, Mohammad Bavarian, Giulio Gueltrini, and I put out a new paper about computability theory in a universe with closed timelike curves.  This complements my and John Watrous’s earlier work about complexity theory in a CTC universe, where we showed that finding a fixed-point of a bounded superoperator is a PSPACE-complete problem.  In the new work, we show that finding a fixed-point of an unbounded superoperator has the same difficulty as the halting problem.

Some of you will also have seen that folks from the Machine Intelligence Research Institute (MIRI)—Scott Garrabrant, Tsvi Benson-Tilsen, Andrew Critch, Nate Soares, and Jessica Taylor—recently put out a major 130-page paper entitled “Logical Induction”.  (See also their blog announcement.)  This paper takes direct aim at a question that’s come up repeatedly in the comments section of this blog: namely, how can we sensibly assign probabilities to mathematical statements, such as “the 1010^1000th decimal digit of π is a 3″?  The paper proposes an essentially economic framework for that question, involving a marketplace for “mathematical truth futures,” in which new mathematical truths get revealed one by one, and one doesn’t want any polynomial-time traders to be able to make an infinite amount of money by finding patterns in the truths that the prices haven’t already factored in.  I won’t be able to do justice to the work in this paragraph (or even come close), but I hope this sophisticated paper gets the attention it deserves from mathematicians, logicians, CS theorists, AI people, economists, and anyone else who’s ever wondered how a “Bayesian” could sleep at night after betting on (say) the truth or falsehood of Goldbach’s Conjecture.  Feel free to discuss in the comments section.

My PhD student Adam Bouland and former visiting student Lijie Chen, along with Dhiraj Holden, Justin Thaler, and Prashant Vasudevan, have put out a new paper that achieves an oracle separation between the complexity classes SZK and PP (among many other things)—thereby substantially generalizing my quantum lower bound for the collision problem, and solving an open problem that I’d thought about without success since 2002.  Huge relativized congratulations to them!

A new paper by my PhD student Shalev Ben-David and Or Sattath, about using ideas from quantum money to create signed quantum tokens, has been making the rounds on social media.  Why?  Read the abstract and see for yourself!  (My only “contribution” was to tell them not to change a word.)

Several people wrote in to tell me about a recent paper by Henry Lin and Max Tegmark, which tries to use physics analogies and intuitions to explain why deep learning works as well as it does.  To my inexpert eyes, the paper seemed to contain a lot of standard insights from computational learning theory (for example, the need to exploit symmetries and regularities in the world to get polynomial-size representations), but expressed in a different language.  What confused me most was the paper’s claim to prove “no-flattening theorems” showing the necessity of large-depth neural networks—since in the sense I would mean, such a theorem couldn’t possibly be proved without a major breakthrough in computational complexity (e.g., separating the levels of the class TC0). Again, anyone who understands what’s going on is welcome to share in the comments section.

Sevag Gharibian asked me to advertise that the Call for Papers for the 2017 Conference on Computational Complexity, to be held July 6-9 in Riga, Latvia, is now up.

81 Responses to “Stuff That’s Happened”

  1. Orin Says:

    My understanding is that there are no current no-go theorems (Bell, Kochen–Specker, etc) that rule out QM emerging from GR + CTCs (basically Einstein’s program). Given that your earlier work showed that quantum computing is possible in a “classical” CTC universe, as well as the ideas surrounding ER=EPR and the fact that CTC universes generically result in non-deterministic distributions over classical trajectories (e.g. see Thorne 1991), do you have an opinion on whether “QM as emergent from pure GR” is an idea worth taking seriously?

  2. Scott Says:

    Orin #1: To whatever extent I understand your question, I would say that the central problem with trying to get quantum mechanics from CTCs is that you “drastically overshoot the target.” More concretely:

    – Sure, you could get Bell inequality violation from CTCs, but you could also get straight-out faster-than-light communication!

    – Sure, you could solve BQP problems with polynomial resources, but you could also solve all problems in PSPACE!

    – Sure, you could get states that behave like superpositions, but you could also get states that behave like superpositions that violate the No-Cloning Theorem and the uncertainty principle!

    And so on, you get the idea.

    Thus, why quantum mechanics has the specific character that it does—why it only gives BQP but not PSPACE, only Bell violation and not superluminal signalling, etc. etc.—would remain totally unexplained. It would need to be postulated by fiat, meaning that Occam’s Razor would tell us to dispense with the CTC part and just say from the beginning that the world is quantum-mechanical.

  3. Ulrik Says:

    Any comments on the recent proof that NP=PSPACE by Gordeev and Haeusler using proof-compression?



  4. Scott Says:

    Ulrik #3: Anyone who’s read the paper and knows something about it is welcome to comment. Dana has forbade me from making any more academic bets, but suffice it to say my prior is so overwhelmingly against this standing as not to be particularly interested in spending time on it.

  5. Matt Leifer Says:

    Re: The logical induction paper

    The paper sets out to solve a problem that I think is a pseudo problem in subjective Bayesian probability, namely, the supposed need for logical omniscience.

    This derives from the criterion in the Dutch Book and similar arguments that if a bet is guaranteed to lead to a sure loss then a rational agent should not make such a bet. This would imply that one should never bet against a tautology, leading to a the problem that seemingly rational mathematicians do make bets all the time about things like the Reimann hypothesis, e.g. by deciding whether to devote their careers to finding a proof or finding counterexamples, even though they may be tautologies in the formal system they are working in that we just have not found a proof of yet.

    However, I have always read the Dutch book criterion in the following alternative way, “if an agent BELIEVES that a bet is guaranteed to lead to a sure loss then the agent should not enter into it”. “Believes” is a crucial qualifier here. With this wording, it is only when an agent believes that something is certain that they must assign it probability 1. This immediately allows mathematicians to bet on the Reimann hypothesis without violating rationality. It also means, on the converse, that it doesn’t matter if something is actually true, only whether the agent is certain that it is true. For example, a rational Christian who is certain that god exists must assign probability 1 to the existence of god and be willing to stake their life on it, regardless of whether it is actually true.

    This reading of things seems reasonable to me, and preferable to the standard reading that implies logical omniscience. After all, why should we expect that truths that are unknown to an agent should have any bearing on their rationality? Now, I will admit that my reading does do some damage to the standard mathematics of probability theory. For example, we can no longer derive the relationships between the logic of propositions and their probabilities. For example, if A and B are mutually exclusive then we would normally say that P(A or B) = P(A) + P(B). On my reading, this can only be derived if the agent BELIEVES that A and B are mutually exclusive, regardless of whether or not they actually are.

    However, I still think my reading is better. For example, suppose you are asked to bet on whether the next car that comes round the corner is red (R) or green (G). You may believe that R and G are mutually exclusive and thus be bound to assign P(R or G) = P(R) + P(G). However, when the next car that comes round the corner is actually red with green racing stripes you realize that you were wrong about mutual exclusivity. It seems to me that the situation is always like this. When we make a mathematical model of the world we map statements about the world to formal statements in a mathematical system. There is always some uncertainty about how to do this, and hence there is always a possibility that the logical structure we have chosen is wrong. The same thing is true in mathematics, as there is always some uncertainty about which formal system is the “correct” one. If we encounter an undecidable statement, then we may decide to fix up the system in one way or another, and (some) mathematicians actually argue with this. We can go further than this and enter into “What the Tortoise Said to Achilles” style arguments about whether a rational person need even accept the basic laws of logic. From my somewhat radical perspective, all of these laws are basically empirical (a long and controversial argument that I probably shouldn’t rehash here) so I see very little difference between probabilities about mathematical statements and those about the physical world.

    The bottom line is that, on my view, we shouldn’t think of probabilities as being attached to statements in some formal system, but rather to statements in ordinary language. They have to respect the rules of deductive logic so far as the agent believes that they apply, which is the case in most everyday examples of statistical inference, but not in general. If that does damage to the standard mathematics of probability theory then so much the worse for probability theory. Probability theory applies where it applies and doesn’t where it doesn’t (something I believe is a tautology, so I assign it probability 1, but if you believe there is a case where it both does and doesn’t apply then your probability may be different). Our view of reasoning under uncertainty will be artificially narrowed if we start from the assumption that probability theory must always apply in its standard form.

    As for induction, logical or otherwise, that is not really part of the worldview of a subjective Bayesian. We identify characteristics of an agent’s beliefs that imply that inductive reasoning will be valid FOR THEM, such as exchangeability, but there is no situation in which all rational agents MUST regard inductive reasoning as valid. There is a recognition in the theory that the problem of induction, and its statistical cousin, are just insoluble from a logical point of view, so we move from a position of just flatly having to assume it, to one of identifying conditions under which rational agents should apply it. As far as I am concerned the logical induction work simply identifies conditions under which agents should apply inductive-type reasoning to mathematical statements. It is about structures that their beliefs might have that would imply that. It is, in that sense, a kind of counterpart to the excahngeability theorem. It does not solve the problem of logical omniscience, because that was never a real problem in the first place.

  6. Orin Says:

    Thanks for your reply Scott #2. I guess I’ve never seen a proof or careful argument that further work on consistency conditions and/or some minimal additional axiom (motivated by the Cauchy problem of classical CTCs, not tailored to produce QM) wouldn’t provide the necessary constraints “for free”. I know the idea was pretty much discarded in Einstein’s time, but that was before most work on CTCs happened.

  7. Scott Says:

    Orin #6: I’m not aware of any proposal on the table for how to recover the specific features of QM by positing CTCs. If and when there’s a serious such proposal, I’ll be happy to talk about it.

  8. jonas Says:

    That paper by Shalev Ben David and Or Sattath sounds nice. I’ll be interested if it turns out to be a plausible construction for a quantum money scheme, or another unexpected proof for something completely different when it fails like your quantum money paper.

  9. October 2016 Newsletter - Machine Intelligence Research Institute Says:

    […] Shtetl-Optimized and n-Category Café discuss the “Logical Induction” paper. […]

  10. Max Tegmark Says:

    I’m honored that you mentioned my paper with Henry Lin! If you strip away the neural network notation, no-flattening theorems translate into easy-to-understand math. For example, we prove (in v.2) using group theory methods that you can multiply n numbers with flat network using 2^n neurons in the hidden layer – but no less. It boils down to a theorem about polynomials (see Appendix A). Note that we’re only able to prove this exponential cost of abandoning depth for very special function classes – much is left to be done here!

  11. easy Says:

    I also found the Harvard paper mediocre and not worthy of FB share (certainly not as important as Harambe).

    People think Polls are wrong and Trump will triumph (unlikely but what is your take? Even Nate Silver has not given his stamp which he did by this time with Obama against Romney).

  12. David Says:

    On politics, I think the evidence we’re sleepwalking to extinction with climate change is compelling, so I’d like Trump to win because it has a chance of stirring us from this low level trance state. For all Hillary’s advantages in the short term, in the big picture she’s a symptom of complacency. Global extinction would be a black swan event, to avoid it you would want as many eyes open as possible. We need people to feel uncomfortable, feel like their lives are at risk from any angle. I think our next few generations have to take this hit for the ones who come after them.

  13. The Most Conservative Says:

    I don’t understand how people can think that Trump is going to bring about the end of the world, and yet simultaneously be unwilling to take the time to debate reasonable Trump supporters online. I made a list of Trump supporters I find semi-convincing in this comment:

  14. Scott Says:

    David #12: What you’re describing is the Marxist idea of “heightening the contradictions”—or to spell it out plainly, purposefully trying to make the world as horrible as possible in the hopes of “finally waking people up” so that they’ll demand genuine change.

    The trouble is, I can’t think of a single case in human history where a conscious strategy to that effect has ever worked. (Can anyone else?)

    To take one example, I remember talking to Nader supporters in 2000 who said they hoped Bush would defeat Gore, since Bush would be so terrible that he’d naturally cause a nationwide leftist awakening (and, presumably, a Green Party victory) in the next election cycle. How well did that work out?

    Instead, I agree precisely with Scott Alexander’s view: namely, our best hope for surviving the climate crisis, and all the other crises our world faces, is just to keep our civilization sputtering along for long enough that new technologies—i.e., the central things that have actually turned the ratchet of human history for the past few centuries—have time to arrive and to create a new reality. A few possible examples of such technologies, though far from the only ones, are cheap solar energy, cheaper and safer nuclear energy (possibly including fusion), carbon capture and sequestration, geoengineering, genetic engineering, and AI (which wouldn’t need to reach a Singularity to change our world substantially).

    And I hope even some Trump supporters would agree that Hillary is the candidate most likely to “keep our civilization sputtering along,” rather than dynamiting it (the latter, after all, is practically Trump’s campaign promise).

    Ironically, then, I find that the grizzled left-leaning establishment view, and the starry-eyed techno-utopian view, reach the same conclusion as far as practical politics are concerned.

  15. Scott Says:

    easy #11:

      People think Polls are wrong and Trump will triumph (unlikely but what is your take? Even Nate Silver has not given his stamp which he did by this time with Obama against Romney).

    I don’t think I can do systematically better than the prediction markets or various statistical models, which are all currently giving a probability of Clinton victory in the 80%-90% range.

  16. gentzen Says:

    Ulrik #3: My comment can be found here.

    Let me clarify that the papers mentioned in my question on amateur reviews were simply selected from the Theory of Computing Blog Aggregator at the moment when I wrote the question, in the hope that such a specific criteria would avoid the most serious biases in selecting sample problems to illustrate the issue. (I also included an older paper, because I had actually read that one.) I didn’t even google the author names, otherwise I would have noticed that a paper by David Rosenbaum might be slightly displaced on such a list …

  17. Fishlips Says:

    Any preliminary look at the Gordeev-Hermann “NP vs PSPACE” paper?

  18. anonymous Says:

    In case anyone hasn’t heard, there are rumors that there is some unreleased footage captured during the filming of the show “The Apprentice”, which shows Trump saying the N word. However, any leaker would be hit with a $5 million leaker’s fine that was written into the apprentice contract. There is now a gofundme campaign to raise $5.1M to reimburse any leaker that comes forward:

  19. Anon Says:

    Where are the women in Avi Widgerson’s academic family? What happened to those 16 women his daughter mentioned -the ones who spoke at a conference he organized?

    Am I the only one in seeing the irony in a group of math/CS folks who make the workplace uncomfortable at best for women and people of color stridently condemn Trump?

    Reminds of an old Jewish saying paraphrased – Men who are good for the world are bad for their family.

  20. Scott Says:

    Anon #19: Not sure I understand. Shafi Goldwasser, Dorit Aharonov, and Toni Pitassi are three renowned female collaborators or students of Avi who spoke at the conference; his daughter Einat (a psychologist) spoke as well. Avi’s record with mentoring female postdocs has been impeccable, and something I aspire to match someday. My impression is that Avi has been both good for the world and good for his family, and is one of the last scientists one could criticize on either count.

  21. Corey Says:

    Matt Leifer #5:

    The bottom line is that, on my view, we shouldn’t think of probabilities as being attached to statements in some formal system, but rather to statements in ordinary language.

    The people who care about probability distributions over logical propositions are trying to understand provable AI safety, so they only care about attaching probabilities to statements in some formal system.

    It seems to me that your knowledge of Bayesian foundations is limited to Dutch book arguments; are you familiar with Cox’s theorem? The content of the theorem is that if you want to extend propositional logic to a real-valued system for quantifying plausibility (and you subscribe to a few fairly reasonable desiderata) then you’re stuck with probability theory. This is more friendly to investigating properties of AIs that Dutch book arguments over ordinary language claims, but it runs into the omniscience problem immediately — the probability-theory-extended principle of explosion says that if a falsehood is assigned a positive probability then any proposition can be given any probability value. Hence MIRI’s work on logical induction.

  22. easy Says:

    Scott #15 they did the same with Brexit?

  23. Scott Says:

    easy #22: With Brexit, I think polls showed clearly that it was extremely close; it was just that pundits refused to believe it. Here the polls (certainly since Friday) show Clinton with a clear lead; the question is whether she’ll maintain that for the next month.

  24. Anon#19 Says:

    Okay. I missed the last few talks. Thanks for clarifying.

  25. easy Says:

    ah I see. ok.

  26. Douglas Knight Says:

    Scott 23, it was not just that the pundits failed to believe the Brexit polls, but that the polls were also off. Look at wikipedia’s list of people synthesizing polls (which I can’t link without being labeled spam). The median prediction was Remain by 2 points. Sure, you can call that “extremely close,” but it was wrong by 4 points, which is a lot (but less than the current US poll gap).

  27. mjgeddes Says:

    I think I now see the outline of a complete, precise solution to the puzzle of consciousness.

    Shockingly, the answer appears to be nothing like what the currently most popular theories propose. I now think that the two leading theories of consciousness, Information Integration (ITT) and ‘Self Modeling’ are well wide of the mark.

    I’d been considering the idea that consciousness is some sort of subtle property of causality for a while, but what really made me think about it more intensely was Sean Carroll’s excellent recent book ‘The Big Picture’. Sean really drives home some excellent points about ‘the arrow of time’ and its close link to subjective experience. Highly recommended, and very much on the right track I believe!

    The way to close the gap between mind and matter is to start from the bottom (elementary particles) and carefully trace a path *up* the complexity hierarchy. At the same time, start from the top (mind) and carefully trace a path *down* the complexity hierarchy. As the gap starts to close, the outline of the answer to the enigma of consciousness begins to appear out of the mist!

    Moving up: Particle Physics > Mechanics > Spatial network and arrow of time emerging

    Moving down: Values > Decision Theory > Cognitive Psychology > Memory > Working Memory > Time perception

    The gap between mind and matter has closed right up!

    Matter-Arrow of time-GAP-Time Perception-Mind

    The gap can be completely closed by making the jump between ‘the arrow of time’ (top-level of matter) and ‘time perception’ (base-level of mind)

    In my view, consciousness is a recursive 3-level symbolic representation of time (past-present-future). This 3-level representational chain is the link that completely closes the gap and provides the solution.

    See wikipedia article on ‘Time Perception’ for some background material:

  28. amy Says:

    Scott #23/Douglas Knight #26, part of the pundit fail had to do with the fact that “secede” votes regularly fail. Narrowly, but they fail. The Danish vote for Maastricht wasn’t quite the same thing, looking for an opt-in.

    I was among those who were shocked by the Brexit vote, and I think it’ll be a long time before we have a good understanding of why it went as it did, particularly since Government-level xenophobia’s been so quick to get formal. I don’t think pointing to the Midlands is enough. I do suspect that economic/trade union is simply not a strong enough matrix to bear the weight of both convenient economic fantasizing ca. 1992 and a massive influx of non-white refugees. There’s a European culture growing on that matrix that didn’t exist in the 1980s, and that includes (included?) the UK, but it’s not robust enough to support all that, I don’t think.

  29. amy Says:

    “non-white” is wrong; “non-European”. Complicated.

  30. Jay Says:

    Scott #NOTS

    Your paper shows (among other things) that unbounded CTCs, either Deutschian or ∞-Postselected, would violate the Church Turing Thesis. It also describes several views on the physicial significance of that result.

    But I’m not sure to get the logical significance. I thought Deutschian CTCs were “CTCs that respect causality”. Is it logically consistent to have Deutschian CTCs (or ∞-Postselected CTCs) that can compute the halt function?

  31. David Roberts Says:


    Any comment on the new NP vs PSPACE paper (or arXiv:1609.09562)? A serious shot or no?

  32. Tsvi Benson-Tilsen Says:

    Matt Leifer #5:

    The paper sets out to solve a problem that I think is a pseudo problem in subjective Bayesian probability, namely, the supposed need for logical omniscience.

    There is a key problem in modeling bounded rational reasoners. Namely, a good reasoner R should have beliefs about logical facts, such as the outputs of long-running computations. However, if R is computable, then there are computations that are too complicated for R to predict their results in advance with certainty. I think we both agree that the correct response here is the subjectivist point of view: you can still reason about logical facts, even if you are uncertain about them—you just use probabilities, which might be in (0,1) even for facts that are logically determined by things you already believe.

    The “problem of logical omniscience” is just that it doesn’t work to extend logic to probability in the natural way. Roughly, if you believe in all the axioms of first-order logic (assign P(“A”)=1 and P(“not A”)=0 for axioms A), and your probabilities respect logical connectives (so that P(“A or B”) + P(“A and B”) = P(“A”) + P(“B”)), then your beliefs are uncomputable. So we have to relax these constraints.

    This doesn’t argue against subjectivism, I don’t think. But it does mean we need a new notion of “good reasoning”. In the case of empirical uncertainty, we have what appears to be the correct theory of how to update on evidence (probabilistic conditioning). In the case of logical facts, we have a satisfying theory of computationally unbounded reasoning: logical deduction over recursively axiomatizable theories.

    But in the case of logical uncertainty, we need a notion of how to arrive at correct beliefs about logical facts in cases where you can’t just compute those facts. I hope that at some point this problem is completely solved in the framework of Bayesian probability theory, for example by having a computationally easy prior and then updating it on the results of non-trivial computations. The contribution of the paper is to give a candidate criterion for “good reasoning under logical uncertainty”.

    I have always read the Dutch book criterion in the following alternative way, “if an agent BELIEVES that a bet is guaranteed to lead to a sure loss then the agent should not enter into it”.

    This is one way to relax the constraint of logical coherence. Hacking [1] proposed something much like this. However, as pointed out by Eells [2], this criterion seems extremely weak: it only penalizes reasoners for reporting beliefs that are incoherent with respect to facts they already know, so it doesn’t incentivize them to discover new facts.

    The paper gives a less radical weakening of the Dutch book criterion: instead of requiring that reasoners report beliefs that are completely unexploitable by any bookie, we can require only that their beliefs not be repeatedly exploitable by efficiently computable bookies. This requirement turns out to be feasible, and to incentivize reasoners to satisfy a variety of desirable properties. Unfortunately, although the Garrabrant induction criterion is firmly subjectivist, it does not seem particularly Bayesian; it’s an active area of research to understand logical induction in a more interpretable and philosophically clean light.

    […] there is always some uncertainty about which formal system is the “correct” one.

    Even if we assume that we only care about computations, which can be unambiguously referred to using logic, there remains the problem of reasoning under computational limitations about long-running computations. If we fix any formal system that represents computations (in the technical sense), logical deduction in that system is slow: sometimes the quickest way to “predict” the output of a computation using logical deduction is to directly simulate every step of the computation in your formal system.

    all of these [logical] laws are basically empirical […]

    I somewhat agree with this—perhaps we should only care about logic insofar as it composes or models good reasoning in practice. However, there is something intuitively very fundamental about logical relationships, where logical structure feels like part of the territory rather than just part of the map, and I’m still confused around this.

    […] there is no situation in which all rational agents MUST regard inductive reasoning as valid

    I might have some bets I’d like to make with you 🙂 More seriously, there is a sense in which Garrabrant induction performs objectively successful subjective reasoning. In empirical uncertainty, there is a prior in the background by which a reasoner is judged, and there need not be a canonical prior. However, in the case of logical uncertainty, there is a canonical objective territory against which reasoners can be judged: which statements are provable and which are refutable.

    [1] Hacking, Ian. “Slightly more realistic personal probability.” Philosophy of Science (1967): 311-325.
    [2] Eells, Ellery. “Bayesian problems of old evidence.” Scientific Theories 14 (1990): 205-223.

  33. Scott Says:

    amy #28: Good to have you here as always!

    I certainly don’t want to instigate another gender-politics mega-thread (!), but the comment of Anon #19 reminded me of something that’s been bugging me greatly. I was saddened, though not surprised, when Trump’s vile tape was met not only with the anger and disgust it richly deserved, but with editorials about how virtually all men everywhere are just like Trump, so are hypocrites if they criticize him. Lindy West, in the NYT, provided one particularly explicit example:

      But here is the thing, the big thing, that Paul D. Ryan and Reince Priebus and Mike Pence and all the spineless Billy Bushes of the world (and plenty of progressive men too, for that matter) don’t understand: Most of you are no better than Mr. Trump; you are just more subtle…

    Obviously I will never, ever support Trump, not if he showed up at my doorstep promising a trillion dollars for theoretical computer science research. But if anyone could persuade me to see the positive in Trump, it would be Lindy West and those who’ve expressed similar sentiments. It’s like, do they not see the logical implication of their argument? If even progressive men, men who spend their lives trying to be as un-Trump-like as possible, are still tarred with the original sin of having been born male … well then, what’s the point of trying? This seems like a perfect example of one of the central phenomena of the modern world, namely progressives (the ones on “our” side) doing everything they can to shoot themselves in the foot and alienate their potential allies.

  34. easy Says:

    do you think 5% more white males will be boosted to go to the voting booths than normal?

  35. Douglas Knight Says:

    Amy 28, there are two separate issues: why Brexit won and why the pundits failed. If secessions always fail, well, that doesn’t seem to me a useful category. But if secessions always underperform their polls, that seems like something for the pundits to adjust for, and a good excuse for the pundits getting it wrong. But that rule failed, so maybe you shouldn’t apply it to Trump, not that he’s a secession in the first place.

    As for whether pundits could have done better, wikipedia’s graph of polls make it look to me that undecideds broke 70:30 in favor of leave. That was true as undecided dropped from 20 to 10 on the eve of the election and it was true of the final 10 points (assuming that they actually voted and polls didn’t just fail to capture the demographics of who would actually vote). Should a pundit have made that extrapolation? I don’t know. Nate Silver says that momentum doesn’t exist in elections, but he’s talking about people switching positions. Maybe it’s different with undecideds, who probably aren’t actually waiting to the last minute.

  36. Daniel Seita Says:

    Anon #19

    Out of curiosity, but do Asians count as people of color under your interpretation?

    (Not saying this in a confrontational tone.)

  37. gentzen Says:

    The logical induction paper is nicely written from a scholarly perspective. Its section on related work traces both the historical relevant predecessors, as well as the recent relevant work on the topic. I have to admit that I am not really qualified to judge this, as I am not even an amateur probabilist. (Sniffnoy keeps repeating that he is not a logician, and he is the one who drew me into this…)

    So I learned that Ramsey had written something about probability, and decided immediately that I had to read that. Ramsey’s paper had 5 sections:
    (1) The Frequency Theory
    (2) Mr Keynes’ Theory
    (3) Degrees of Belief
    (4) The Logic of Consistency
    (5) The Logic of Truth
    Especially section (4) and (5) turned out to be just wonderful, sections (1) and (2) are nice and short too. Section (3) is a bit long, less convincing, and perhaps less worth reading (even so certainly important from a historical point of view). Section (3) may even unintentionally highlight just how one-dimensional naive Bayesian reasoning actually is.

    I also tried to read what de Finetti and Carnap had written on probability, but their writings turned out to be not so short after all. I also went back to take another look at Jaynes “Probability Theory: The Logic of Science,” which argues against certain technical points by de Finetti and Carnap, and was also mentioned in passing “(as argued extensively by Jaynes [2003])” in the logical induction paper. This showed to me just how scholarly well the logical induction paper is actually written. Jaynes text didn’t mention Ramsey anywhere, and instead delivered a totally wrong “essence” of Gödel’s theorem:

    Now, whatever T may assert, the fact that T can be deduced from the axioms cannot prove that there is no contradiction in them, since, if there were a contradiction, T could certainly be deduced from them!

    This is the essence of the Gödel theorem, as it pertains to our problems. As noted by Fisher (1956), it shows us the intuitive reason why Gödel’s result is true. We do not suppose that any logician would accept Fisher’s simple argument as a proof of the full Gödel theorem; yet for most of us it is more convincing than Gödel’s long and complicated proof.

    The logical induction paper on the other hand correctly relates Gödel’s theorem with “self-trust” of the logical inductor, and demonstrates that the proposed approach is able to handle the “self-trust” issue raised by Gödel.

  38. Giorgio Castriota Scanderbeg Says:

    1) As just twitted to Sean Carrol for the cited paper of Ben-David and Sattath I suggested him to encourage his colleagues (so I suggest you) in writings little stories, fables, metaphors in their papers that can help the “non-technical” platea to better appreciate the work. You know that the “non-technical platea” is becoming larger and larger (I’m a writer that literally spend one, two hours per day reading yours exceptional works and admittedly not understand quasi-nothing) so I think a very huge work you have to do is (a part to kidnap some guys in your literature departments and force them to “shut up and—metaphorize”) to open a possibility to write some little parallel or “oracle” traslation in literally term in your papers.
    2) Regarding your CTC’s Paper I really cannot understand how to conceptualize the Deutsch ½ probabilities to kill my grandfather. So I set-up the following: my grandmother narrated me how his husband died just after they ehm…did it! (my grandfather was a stunning stuntmen that at that particular moment was working on a Buster Keaton movie). In the narration of my grandmother she told me that he was poisened by his fierce enemy named Novikov (another stuntman in the movie). Now my grandmother is passed over and then I found a very huge amount of “titillating” Novikov’s love letters to my grandmother. So I really believe in this love affair! (Could it be the reason why my father is dead in searching to construct a time machine to recover the wasting time to make it?). Equipped with my own time machine (rounding on the CTC and hoping not to dissipate…Time), I popped up in the middle of the Keaton set movie, looking for the poisoned glass of wine of my grandfather, exchange it and wait for the night hidden behind a wooden little house. Now As I know I have a real, actual, classical, non-Deutsch huge ½ probabilities to survive (if my granfather is really my grandfather I survive, if not I will die (when?). How now it needs to be implemented the Deutsch probabilities in this (admittedly, very doofus) scenario?

  39. Scott Says:

    Giorgio #38: Sorry, I didn’t understand your scenario. Narrative has its place, but would it be possible to state your question more plainly?

    Deutsch is a diehard proponent of the Many-Worlds interpretation, so the way he thinks about a “1/2 probability of killing your grandfather” is simply that you do so in a 1/2 fraction of worlds. But personally, I wouldn’t say you need to subscribe to MWI to say that Deutsch has given a valid mathematical procedure to get fixed points of CTCs. The central issue, as Bennett et al. pointed out, is that because of nonlinearity, these “probabilities” couldn’t get mixed up with ordinary subjective probabilities, but would need to be treated as fully objective parts of the state of the universe.

  40. John Sidles Says:

    Does Donald Trump represent the best of conservatism, any more than Lindy West represents the best of progressivism (per comments #19, #28, #33)?

    Yet in the long run, isn’t the best of conservatism and progressivism — along with the best of mathematics, science, medicine, etc. — what matters most?

    After all, peer review would scarcely make sense otherwise. Would it make any sense for the STEAM’s community’s gatekeepers to publicize only the worst works, and only the most abusive criticisms of those works? Yet that’s what contemporary political debate too often resembles.

    Here’s Wendell Berry, speaking in the Afterword to the (recent) third edition of his The Unsettling of America: Culture & Agriculture (1977 & 2015)

    [One] reason that my book has received no vigorous counterargument, I fear, is that in centers of learning and power, argument itself has become virtually obsolete, a lost art.

    Public discourse of all kinds now tends to pattern itself either upon the arts of advertisement and propaganda (that is, the arts of persuasion without argument, which lead to reasonless and even unconscious acquiescent, or upon the allegedly objective or value-free demonstrations of science.


    What are the parallels between agri-culture and STEAM-culture? What lessons does Berry’s analysis have for mathematicians, scientists, engineers, and physicians? In ducking Berry’s tough questions, haven’t the rhetoricians of the cherry-picking left and the cherry-picking right evolved to be not opposed, but rather mutually complicit?

    This considerations are why (as it seems to me) we all of us owe a debt of appreciation and gratitude to transgressive works like Wendell Berry’s Jefferson Lecture “It all turns on affection” (2012) and Jonathan Israel’s Benjamin Franklin Medal Lecture “Changing the world: the Enlightenment and basic human rights” (2010).

    Concretely, these lectures recall to our minds the transgressively transformative legacies that were bequeathed to humanity by two outstanding scientist-citizens: Thomas Jefferson and Benjamin Franklin.

    Needless to say, the era of transgressive STEAM-legacies is far from ended … and for this reason, in coming decades, we will each and all of us be irretrievably and transformationally made to care for these matters, in all of the diverse and even frighteningly dangerous senses that the phrase “made to care” has for us. Because yes, the 21st century’s STEAM enterprise is dangerous.

  41. easy Says:

    I think that 5%+ white male participation is what their only strategy has been all along. Krugman thinks the ground game is not strong enough (but it ain’t over until it is right?).

  42. Sniffnoy Says:

    Tsvi #32: Thank you for writing this comment, as I was about to write a similar but worse one. 🙂

    Corey #21: Personally, I find Cox’s theorem somewhat unsatisfying, as it relies on the assumption that we want to use real numbers in the first place; to me that seems a pretty big assumption. I prefer Savage’s theorem, which based on decision-theoretic concerns gives a foundation for both probability and utility simultaneously. I mean, the downside there is that I guess not everyone likes that it’s grounded in decision-theoretic concerns rather than pure degrees of belief; but what is a “degree of belief”, anyway? Savage interprets this the Bayesian way — it’s the odds you’d bet at.

    Anyway, the point is, Savage’s theorem doesn’t assume real numbers anywhere; it does make an Archimedean assumption, which one might argue is hardly any different, but I think it’s considerably better, as it’s actually listing out a constraint on how the agent will act, one which we might expect a “rational” agent might follow, as opposed to just assuming that we’re using real numbers for no real apparent reason.

  43. Sniffnoy Says:

    Anon #19:

    Am I the only one in seeing the irony in a group of math/CS folks who make the workplace uncomfortable at best for women and people of color stridently condemn Trump?

    Even if we take your claim at face value[0] (and Scott has already given some reasons why we shouldn’t), there is zero irony here.

    Trump is awful for a large number of reasons; Scott has discussed a few that are almost entirely unrelated to anything you’re talking about. There’s nothing ironic about voting against a candidate without agreeing that every reason given for voting against that candidate is a valid one. Similarly, there’s nothing ironic about voting for a candidate without agreeing that every reason given for voting for that candidate is a valid one. Indeed, if you ever find yourself thinking that literally every reason you’ve heard for voting for or against a given candidate is valid, that’s the point where you should say “Hm, maybe I’ve got some tribalism bias here I need to work on”.

    And… like, I know psychologizing is bad form, but… I’m having a hard time explaining your comment other than as a product of outgroup homogeneity bias. It definitely looks to me like you’ve lumped things into people-who-agree-with-you and people-who-disagree-with-you and are acting like everyone who disagrees with you thus agrees with each other. Rather than there just being a lot of disparate groups out there whose beliefs don’t have any sytematic relations to one another. Group A who disagrees with you, and group B disagrees with you, are not necessarily closer to one another than either is to you.

    (Relatedly, this is why I think “political axes” are usually unhelpful; people always seem to draw them up with one of the axes being “agrees with me / disagrees with me”, leading to unnatural and outgroup-homogeneity-biased classifications. I’m sure in a sufficiently high-dimensional space you could have a decent classification of political beliefs, but in practice the axes people draw rarely seem to be that helpful.)

    (By the way, have I mentioned how much I like the system of colors in Magic: The Gathering? 🙂 The actual colors themselves are not actually much good as a way of making sense of real-world ideas, of course, there’s a lot that it misses ther; but I think the system of relations between is… well, it has some nice clean symmetry that real life doesn’t, real life is much messsier, but it’s a good antidote to looking at axes, IMO. This point shamelessly stolen from Taymon Beal here.)

    [0]OK, actually here I’m not really talking about taking it just at face value, but throwing in as well some of what you seem to be trying to imply as well. And by the way, might I suggest that it’s really not a good thing to try to argue by hinting like that? If you’ve got a claim to make, spell it out so it can be properly argued with.

  44. Jon Lennox Says:

    Scott @#7: Mark Hadley has had some proposals about deriving QM from GR: see, particularly his thesis.

    I’m not knowledgeable enough about the topic to know if there’s any “there” there, though.

  45. Scott Says:

    Fishlips #17 and David Roberts #31: Sheesh! I already addressed this in comment #4.

    I get proofs of P=NP, NP=PSPACE, P vs. NP is independent of set theory, etc. in my inbox every week. Every single one has been wrong. Not one has even contained useful new ideas. So my prior is so massively, overwhelmingly against these things that, like Oded Goldreich, I don’t elect to spend my time on them, unless someone convinces me that there’s at least a new idea worth understanding, or I have no choice (e.g. because of media coverage).

  46. John Sidles Says:

    David remarks (#15) “I think the evidence we’re sleepwalking to extinction with climate change is compelling …”

    Here on Shtetl Optimized such assertions receive more respect if they’re continued along along evidence-based lines as follows

    “…  [in that] comparison of the new temperature reconstruction with radiative forcing from greenhouse gases estimates an Earth system sensitivity of 9 degrees Celsius (range 7 to 13 degrees Celsius, 95 per cent credible interval) change in global average surface temperature per doubling of atmospheric carbon dioxide over millennium timescales.”

    The continuation is quoted from Carolyn W. Snyder’s new survey “Evolution of global temperature over the past two million years” (Nature, Sept. 26 2016).

    In terms of relevance to ongoing political debates, Snyder’s analysis compels committed climate-change denialists to entirely reverse their worldview, from foundational rejection of climate-modeling science, to foundational acceptance of climate-modeling science.

    The necessity for this transformational shift arises because a strictly Bayesian, strictly evidence-based analysis of the paleo-climate data — unmodified by dynamical climate-models — yields estimates of climate sensitivity that are not lower, but rather are many times higher than the consensus climate-sensitivity estimates.

    In light of these findings, the public can appreciate that only by a broad-band acceptance of consensus climate-modeling methods can alt*Trumpian climate-change skepticism be salvaged as any sort of rational worldview.

    It’s good to see ongoing scientific advances providing such solid grounds for the rapprochement of rational conservatism with thoughtful progressivism. Donald Trump, take notes!  🙂

  47. MIRI October 2016 Newsletter – DailyNews Artificial Intelligence Says:

    […] Shtetl-Optimized and n-Category Café discuss the “Logical Induction” paper. […]

  48. Vitruvius Says:

    The Obama administration has, in the matter of Mrs. Clinton’s e-mail handling, corrupted the DOJ and the FBI in order to conceal the complicity of Mr. Obama and Mrs. Clinton as culprits in that matter, in one role or another — certainly in contempt, probably in perjury, possibly in treason for personal profit. Along with many other instances of the US Federal government and the political machines overstepping their responsibilities & authorities, los Federales have reached or already crossed the Rubicon in terms of descending again into a condition of gangster government.

    Given the hand that has been dealt, Mr. Trump proxies, to many honest citizens, into the flawed saviour of saner government; Mrs. Clinton proxies into the problem incarnate. Perhaps bizarrely, it is Mrs. Clinton who is sabre rattling, and Mr. Trump who is, relatively speaking, the peacenik. While arguments can be made for and against both perspectives, to the degree that either side holds the other in contempt, they do nothing but strengthen the argument of said other side. When the side that claims the higher ground in such a matter is found to be themselves complicit in the very behaviour they were denigrating, it sets off the hypocrisy detectors in we the people.

    The better the times, the more the establishment can get away in terms of such behaviour, but when sufficient numbers of we the people see the situation as declining and get to feeling, rightly or wrongly, that the government is failing to do the job they have been hired to do, instead doing the alternative job of serving themselves, it is not surprising that throughout history the people have from time to time taken up their pitchforks & torches.

    Justice must not only be done, it must be seen to be done. So those of us who may be more likely to think rather than to feel should be leery of belittling the feelings of our fellow citizens, at least past some point, or the eventual revolution will be against those belittling by those being belittled. Y’all will not defeat human nature with logic or anything else, it’s not going away, and you can’t get rid of it by fiat or otherwise. When you’re old enough you will look back on this realization and say to yourself: oy, what was I thinking.

  49. MIRI AMA, and a talk on logical induction - Machine Intelligence Research Institute Says:

    […] some recent discussions of the new framework, see Shtetl-Optimized, n-Category Café, and Hacker […]

  50. jonas Says:

    @Vitruvius #48, in the thread two before this, I already linked to the two recent articles in the Slate Star Codex, and . I think those articles address some of the points you’ve brought up.

  51. Anatoly Says:


    >So my prior is so massively, overwhelmingly against these things that… I don’t elect to spend my time on them…

    If someone were to write to you and offer money for finding a nontrivial mistake in their proof of NP=PSPACE or whatever (“nontrivial” meaning “one that creates a real inferential gap that you don’t see how to fix after giving it 10 minutes of a genuine effort, as judged by you”). The terms are, if you find an error you get the money, if you don’t, you write a blog post saying you couldn’t find an error and recommending that more serious people check it. Would you agree to that, and what would be the sum of money?

    (I’m not “asking, um, for a friend” or even asking for a friend, just curious)

  52. Anon#19 Says:

    Daniel Seita Says: “Out of curiosity, but do Asians count as people of color under your interpretation?”

    This is a good question Daniel. People of color refers specifically to African Americans and Africans. Asia is a big continent with a wide array of skin color sometimes in the same country. The middle east is full of people with very dark complexions. The census considers them Caucasians. Hispanics are considered Caucasians too. But it must be noted that are Asians and Hispanics who could be mistaken for African American.

    Sniffnoy I read your comment in detail. You too are asking a good question by asking for a clearer statement.

    Let me put it this way. I am so thoroughly disgusted with the abusive, name-calling, stereotyping, hostility expressed toward women I can’t stand to see mathematicians take a holier-than-though attitude towards Trump. It is hypocrisy beyond imagination. While any individual male may truthfully say this is not how he behaves, as a group have the decency and the courage to take a stand against your sexist colleagues (overt and covert ones) before you take a stand against Trump. It is easy and cowardly to rant against the misogynist who may become President while ignoring the misogynist who is your colleague, neighbor, coauthor and friend. Beyond disgusting! Is this clear enough?

  53. Mitt Romney's Dog Says:

    #48 – Clinton was correct. Trump and his supporters live in an alternative universe, where truth and reality don’t matter. Thanks for the nth example.

  54. Daniel Seita Says:

    Anon #52,

    I have fortunately not seen any overt sexism in person in my work. If I do see it, I will do my best to mention it to the relevant people.

    Yes, it’s easy for an academic to oppose Trump, but that’s better than supporting him, right? (I am not aware of any fellow collaborator/student who has publicly supported Trump.)

  55. Anon#19, 52 Says:

    Daniel, Yes, I certainly hope on Election Day people don’t vote for Trump. Trump is a loose-lipped and foolish misogynist and easier to spot that the tight-lipped and smart ones.

  56. John Sidles Says:

    Anon (#19) calls upon mathematicians to “as a group have the decency and the courage to take a stand against your sexist colleagues (overt and covert ones) before you take a stand against Trump.”

    It is natural to wonder whether today’s mathematicians, as a community, have already mustered the “decency and courage” whose necessity in electoral politics Anon’s comment so rightly commends.

    Trumpish comments that were posted recently on Shtetl Optimized — posted by an inappropriately self-denominated commenter “Emmy Noether” — have already directed the attention of Shtetl Optimized readers toward Emma Noether as concrete example of mathematical decency and courage.

    For today’s mathematicians, Emmy Noether is iconic: not only as a great mathematician, not only for the adventure of her life and the nobility of her character, not only for tragically dying too young; but also (and especially) for the intensity of the discrimination she faced for her gender, race, and nationality, and for Emma’s decency and courage in standing against that discrimination.

    So unbounded was the discrimination that Emma Noether endured, that throughout her life she was even frumpishly-Trumpishly fat-shamed. Yikes!

    Seen in the light of Emma Noether’s life, among the very best replies to Anon is the “decency and courage” of Hermann Weyl’s “Funeral oration by for Emma Noether” (which is available on-line in a translation by Peter Roquette).

    Your heart knew no malice; you did not believe in evil, indeed it never occurred to you that it could play a role in the affairs of man. …

    When you were not allowed to use the [Heidelberg] institute’s lecture halls you gathered your students in your own home.

    Even those in their brown shirts were welcome [here Weyl refers to the Sturmabteilung (SA) uniform that was worn by Noether’s student Ernst Witt]; never for a second did you doubt their integrity.

    Without regard for your own fate, openhearted and without fear, always conciliatory, you went your own way.

    Many of us believed that an enmity had been unleashed in which there could be no pardon; but you remained untouched by it all.

    Is Emmy Noether today appreciated as an pioneering, iconic, outstandingly effective warrior for social justice? Oh yes.

    In publicly embracing Emmy Noether’s example and moral principles, is the world’s mathematical community already exhibiting sufficient decency and courage, as to morally qualify the near-unanimous stand of the world’s mathematicians against Trumpish ignorance and prejudice? Yes, absolutely.

  57. Scott Says:

    Anon: Your argument reminds me of someone during WWII who says that the Allies are disgusting hypocrites unworthy of support, because they denounce Hitler even though so many of them are racist, sexist, militaristic assholes themselves.

    For me, the problem with this stance is not merely that it prioritizes purity over real-world consequences. It’s not merely the refusal to accept that subconscious, implicit biases against women and minorities, which the people who hold them are ashamed of and try to suppress, are an unbelievably massive improvement over explicit biases shouted from the rooftops, which was the status quo for most of human history.

    Rather, for me there’s a deeper problem. Namely, history suggests that it’s nearly impossible to defeat the worst assholes without having (so to speak) a bit of asshole in yourself. Lincoln suspended the rule of law, brutally laid waste to the South, and espoused shockingly racist sentiments. Churchill was a cigar-chomping sexist colonialist right-wing aristocrat. Both were despised by many of the leftist activists of their time—but could those activists have won the wars?

    So then, were Lincoln and Churchill “disgusting, holier-than-thou hypocrites”? If so, then I personally treat your accusation of the same against the (white? male?) mathematicians who denounce Donald Trump as a high compliment. On this Yom Kippur, this day of reflection, may each of us aspire to be worthy of being a disgusting hypocrite in your eyes.

  58. Anon#19, 52 Says:

    Interesting that you bring up this argument and adopt this stance. There were many someones who said this one of whom was Elie Wiesel.

    Read this essay from beginning to end and then reread what he has to say, and understand his point carefully about indifference being inhuman.

    Are you a name-calling, stereotyping person hostile to women? I don’t know you. So you answer that. If yes, then you are a disgusting hypocrite. If no, then take a stand against those around you who behave in that manner

    You assumed we are of a different religious background. Wrong assumption! On this Yom Kippur you have demonstrated your “indifference” quite clearly or is it that you just don’t understand. Hard to tell.

    I am certainly thankful for all the men and women who stand up for the injustices heaped on women around them. Less so for the men who are good for the world and bad for their families, broadly defined.

  59. Scott Says:


      Are you a name-calling, stereotyping person hostile to women?

    No. And I regret that I’m now banning you from this thread, since that’s such a bad-faith question.

      You assumed we are of a different religious background.

    No, I assumed no such thing.

  60. Sniffnoy Says:

    Well, if Anon#19 is banned from this thread, I guess that’s a good reason for me not to waste my time writing further replies to them! 😛

  61. jonas Says:

    @Amy: did people still believe that votes for secession always fail after the one in Montenegro succeeded? Sure, it was a bit hard to pay attention to referendums when there’s a civil war going on at the same time, but still.

  62. Giorgio Castriota Scanderbeg Says:

    Scott#39. I am a real ill-mannered man and I apologize for this lack of respect for your very kind response to my questions and for my delayed reply. I will do my best and my answer will be succinct. As one day one of my favorite writer, Giorgio Manganelli, said that there is more “literature” in the simple word “feldspar” or in the “Zorn Lemma” than in any 200-pages novels (probably relying on an “evocative” power for the former and for a huge possibility to extract constructive analogies for the latter), so I hope that there will be a “single verb” that is worth 100 mathematical formulas. My dream is to see one day one of you, physics or mathematicians or scientist from all the fields, winning a Nobel Prize for….literature!! (I’ll take the opportunity to say goodbye to our Literature Nobel Prize, Dario Fo, who just today has passed away). Thank you

  63. Giorgio Castriota Scanderbeg Says:

    ….and sure, Bob Dylan!!

  64. Mitchell Porter Says:

    It looks like a second Clinton administration will feature a major escalation in “Cold War 2.0”.

  65. Scott Says:

    Mitchell #64: But if Putin is going to continue to threaten/invade Russia’s neighbors, interfere with US elections, etc., then how much choice does the US have?

    (Incidentally, the irony is almost too much to bear, that now it’s the “conservatives” who are cheering on the expansionist plans of USSR 2.0, while the “liberals” oppose them. But for an anti-authoritarian liberal like myself, this certainly makes everything ideologically simpler.)

  66. amy Says:

    Hey, Scott. (#33) Ordinarily, I’d say yeah, that line of hers went weirdly over the line. Go back and take a look, though, at the comments. Any of the comment-torrents with women telling their stories. Just take a look at the volume of them, the sheer number. I actually can’t read any more of them for a while.

    At that point it might be time to set aside “but you’re implicitly saying *I’m* that guy!” and take a look at the scale and quality of the problem, and see that the moment is not about you, and that if people are sloppy with the accusations as they’re crying out, there might be a reason for it. And that in a calmer moment, after the reality of all these women’s experiences is recognized and absorbed, there’s time to say “I went too far, I’m sorry.”

    Also, when you consider that over half of US men polled still choose Trump as their candidate despite all this, then Lindy’s “most” seems accurate enough to me.

    As for the question of alienating allies: well, you know I don’t like viewing this in terms of armies and allies. I don’t live that way. But I don’t think I’ve seen a civil-rights sort of movement that’s succeeded by constraining their speech so as not to offend the sensibility of sympathetic members of a rights-denying group. Primarily because it seems to me that a genuinely sympathetic person will ask, first, “is it true? All defensiveness aside, is it true, in me?” and then, if the answer is no, ask the person: “Do you mean me, too, and if so why?” And if the answer seems to you substantially bats, keep in mind that you might still be wrong, but ask whether this is the view of the movement you have in mind, or just of this person. And whether you support what they’re after regardless of how they view you. I suppose that’s what it comes down to.

    As for me, though, I don’t believe there’s any movement that’s a monolith, and in the end I deal in people and ideas, not political movements. Which is part of why I haven’t been involved in party politics or activist groups or government for decades. You have to go pick your mob to march with if you’re going to do that, and the mob is invariably stupid and brutal. It’s also why I didn’t apply for the assistant director spot at the local women’s center when the AD moved up to D, and asked me to apply — I love working with her, we’d done some good projects together, but my views are decidedly right of the the usual there, and even though she said it didn’t matter, I knew it’d wind up mattering. A lot.

    I’ll be very glad when this travesty’s over. The headlines are, daily, less imaginable for a presidential campaign, and all these stories…they’re reminding me things from every stage of my life that were unpleasant and quickly forgotten, and I’d be perfectly happy not to remember them again. It’s a bad time.

  67. David Roberts Says:

    @Scott #45 ah, my apologies and sorry for the noise. Somehow that didn’t register. And elsewhere people quickly poured water on the paper, shortly after I asked here…

  68. Another Trump Democrat Says:

    You talk about Russia. But what about Mexico invading its northern neighbor by sending in several million agents, draining the economy, undermining infrastructure, and interfering with US elections by subverting about 1.5 out of 2 major political parties into a treacherous collusion with a hostile foreign invader. Mexico is on the brink of destroying American democracy, and there’s only one election to stop it. The Russians are harmless teddy bears by comparison.

  69. Scott Says:

    ATD #68: You’re seriously proposing that the Mexican government hatched a diabolical plan to send “agents” to “invade” the US and corrupt its political parties—as opposed to a bunch of laborers making individual decisions to look for work over the border, driven by forces any econ textbook would explain?

  70. Another Trump Democrat Says:

    The Mexican government calculates where its interests lie, it believes that illegal immigration of millions of Mexicans in the US is advantageous economically and politically to Mexico, even though it is hostile and adversarial to the US, and the Mexican government is fully complicit in this invasion. Comments by Mexican government officials, such as President Nieto himself, make it clear that the Mexican government officially endorses and encourages millions of Mexican’s to commit crimes against the United States. It is not unreasonable to view this as a form of warfare by Mexico against the United States, and so all the propaganda supporting illegal immigration is merely wartime propaganda. You can quibble about the detals of this argument, but the basic truth of it is there for all to see.

  71. easy Says:

    I think the polls are wrong. Why would a ‘normal’ and ‘typical’ (IQ between 70 and 130) white male not vote for Trump?

  72. easy Says:

    Sorry but consider the margin of difference in and I think today the difference could be even more twisted.

  73. John Sidles Says:

    easy wonders  “Why would a ‘normal’ and ‘typical’ (IQ between 70 and 130) white male not vote for Trump?”

    Respects Grandma, Mom and Sis?
    Marines “just one color”?
    Listens to Bob (congrats!)?

  74. amy Says:

    Oddly enough, the only local evidence I see of a Mexican invasion are blazingly fast roofing jobs, harvests, and spottily-educated first-generation kids in my classes working six times harder than their all-American classmates. If this is the crime you’re talking about, I’d like more of it, please.

  75. easy Says:

    Dr. Sidles though you are white your IQ is at least 130.01. So I wonder if I should take your opinion here and I have a funny feeling Trump will win.

  76. Another Trump Democrat Says:

    Your comments seem to be motivated by the kind of racial prejudice which is essentially monopolized by The Left these days.

    Entering or remaining in a country illegally is a very serious crime. Anyone who does this should be convicted of a felony, and deported and permanently banned from returning. A country has a right to have rules and boundaries, and to act against those who violate them. Anyone providing support for this illegal activity, and/or providing any support to illegal immigrants, including failing to report illegal immigrants to the authorities, should be convicted of a felony for their involvement in this massive criminal enterprise. There are also more subtle ways that this massive criminal enterprise is supported such as using terms like “undocumented” to try to distract from the criminality, or trying to treat “immigration” as a single topic, instead of clearly demarcating between LEGAL and ILLEGAL.

    The reality is that The Left is strongly supportive of various kinds of criminal, anti-social, damaging activity. The Left should be regarded as occupying the moral low ground, but yet they piously claim the moral high ground and condemn those who want a better, safer, smarter, fairer world of dogwhistle bigotry.

    The Left has pushed society to the precipice. It’s time to push back.

  77. amy Says:

    ATD #76, I’ve said nothing at all about race. That appears to be your bag, baby.

    I’m quite happy to have the immigrants and their children here. I particularly enjoy having their kids in my classes because those kids are heart-attack serious about making something of themselves, and they will take and make use of, and value, any opportunity you offer. They’re also aware of what their parents have done for them. Next time you risk your life crossing a border so that you can work like a dog for the rest of your life in order to better your children’s opportunities, I’m happy to talk to you about just how damaging and anti-social all this is.

  78. John Sidles Says:

    Progressives like ⌈⌈⌈amy⌋⌋⌋ sap and impurify our American essence and are rigging our precious elections — so SAD!

  79. amy Says:

    It hasn’t learned! Is there any way to make it play itself?

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