Happy New Year, everyone!  I tripped over a well-concealed hole and sprained my ankle while carrying my daughter across the grass at Austin’s New Years festival, so am now ringing in 2017 lying in bed immobilized, which somehow seems appropriate.  At least Lily is fine, and at least being bedridden gives me ample opportunity to blog.

Another year, another annual Edge question, with its opportunity for hundreds of scientists and intellectuals (including yours truly) to pontificate, often about why their own field of study is the source of the most important insights and challenges facing humanity.  This year’s question was:

What scientific term or concept ought to be more widely known?

With the example given of Richard Dawkins’s “meme,” which jumped into the general vernacular, becoming a meme itself.

My entry, about the notion of “state” (yeah, I tried to focus on the basics), is here.

This year’s question presented a particular challenge, which scientists writing for a broad audience might not have faced for generations.  Namely: to what extent, if any, should your writing acknowledge the dark shadow of recent events?  Does the Putinization of the United States render your little pet debates and hobbyhorses irrelevant?  Or is the most defiant thing you can do to ignore the unfolding catastrophe, to continue building your intellectual sandcastle even as the tidal wave of populist hatred nears?

In any case, the instructions from Edge were clear: ignore politics.  Focus on the eternal.  But people interpreted that injunction differently.

One of my first ideas was to write about the Second Law of Thermodynamics, and to muse about how one of humanity’s tragic flaws is to take for granted the gargantuan effort needed to create and maintain even little temporary pockets of order.  Again and again, people imagine that, if their local pocket of order isn’t working how they want, then they should smash it to pieces, since while admittedly that might make things even worse, there’s also at least 50/50 odds that they’ll magically improve.  In reasoning thus, people fail to appreciate just how exponentially more numerous are the paths downhill, into barbarism and chaos, than are the few paths further up.  So thrashing about randomly, with no knowledge or understanding, is statistically certain to make things worse: on this point thermodynamics, common sense, and human history are all in total agreement.  The implications of these musings for the present would be left as exercises for the reader.

Anyway, I was then pleased when, in a case of convergent evolution, my friend and hero Steven Pinker wrote exactly that essay, so I didn’t need to.

There are many other essays that are worth a read, some of which allude to recent events but the majority of which don’t.  Let me mention a few.

Let me now discuss some disagreements I had with a few of the essays.

  • Donald Hoffman on the holographic principle.  For the point he wanted to make, about the mismatch between our intuitions and the physical world, it seems to me that Hoffman could’ve picked pretty much anything in physics, from Galileo and Newton onward.  What’s new about holography?
  • Jerry Coyne on determinism.  Coyne, who’s written many things I admire, here offers his version of an old argument that I tear my hair out every time I read.  There’s no free will, Coyne says, and therefore we should treat criminals more lightly, e.g. by eschewing harsh punishments in favor of rehabilitation.  Following tradition, Coyne never engages the obvious reply, which is: “sorry, to whom were you addressing that argument?  To me, the jailer?  To the judge?  The jury?  Voters?  Were you addressing us as moral agents, for whom the concept of ‘should’ is relevant?  Then why shouldn’t we address the criminals the same way?”
  • Michael Gazzaniga on “The Schnitt.”  Yes, it’s possible that things like the hard problem of consciousness, or the measurement problem in quantum mechanics, will never have a satisfactory resolution.  But even if so, building a complicated verbal edifice whose sole purpose is to tell people not even to look for a solution, to be satisfied with two “non-overlapping magisteria” and a lack of any explanation for how to reconcile them, never struck me as a substantive contribution to knowledge.  It wasn’t when Niels Bohr did it, and it’s not when someone today does it either.
  • I had a related quibble with Amanda Gefter’s piece on “enactivism”: the view she takes as her starting point, that “physics proves there’s no third-person view of the world,” is controversial to put it mildly among those who know the relevant physics.  (And even if we granted that view, surely a third-person perspective exists for the quasi-Newtonian world in which we evolved, and that’s relevant for the cognitive science questions Gefter then discusses.)
  • Thomas Bass on information pathology.  Bass obliquely discusses the propaganda, conspiracy theories, social-media echo chambers, and unchallenged lies that helped fuel Trump’s rise.  He then locates the source of the problem in Shannon’s information theory (!), which told us how to quantify information, but failed to address questions about the information’s meaning or relevance.  To me, this is almost exactly like blaming arithmetic because it only tells you how to add numbers, without caring whether they’re numbers of rescued orphans or numbers of bombs.  Arithmetic is fine; the problem is with us.
  • In his piece on “number sense,” Keith Devlin argues that the teaching of “rigid, rule-based” math has been rendered obsolete by computers, leaving only the need to teach high-level conceptual understanding.  I partly agree and partly disagree, with the disagreement coming from firsthand knowledge of just how badly that lofty idea gets beaten to mush once it filters down to the grade-school level.  I would say that the basic function of math education is to teach clarity of thought: does this statement hold for all positive integers, or not?  Not how do you feel about it, but does it hold?  If it holds, can you prove it?  What other statements would it follow from?  If it doesn’t hold, can you give a counterexample?  (Incidentally, there are plenty of questions of this type for which humans still outperform the best available software!)  Admittedly, pencil-and-paper arithmetic is both boring and useless—but if you never mastered anything like it, then you certainly wouldn’t be ready for the concept of an algorithm, or for asking higher-level questions about algorithms.
  • Daniel Hook on PT-symmetric quantum mechanics.  As far as I understand, PT-symmetric Hamiltonians are equivalent to ordinary Hermitian ones under similarity transformations.  So this is a mathematical trick, perhaps a useful one—but it’s extremely misleading to talk about it as if it were a new physical theory that differed from quantum mechanics.
  • Jared Diamond extols the virtues of common sense, of which there are indeed many—but alas, his example is that if a mathematical proof leads to a conclusion that your common sense tells you is wrong, then you shouldn’t waste time looking for the exact mistake.  Sometimes that’s good advice, but it’s pretty terrible applied to Goodstein’s Theorem, the muddy children puzzle, the strategy-stealing argument for Go, or anything else that genuinely is shocking until your common sense expands to accommodate it.  Math, like science in general, is a constant dialogue between formal methods and common sense, where sometimes it’s one that needs to get with the program and sometimes it’s the other.
  • Hans Halvorson on matter.  I take issue with Halvorson’s claim that quantum mechanics had to be discarded in favor of quantum field theory, because QM was inconsistent with special relativity.  It seems much better to say: the thing that conflicts with special relativity, and that quantum field theory superseded, was a particular application of quantum mechanics, involving wavefunctions of N particles moving around in a non-relativistic space.  The general principles of QM—unit vectors in complex Hilbert space, unitary evolution, the Born rule, etc.—survived the transition to QFT without the slightest change.


104 Responses to “State”

  1. Harry Johnston Says:

    I don’t agree with everything Jerry Coyne says in that essay, but I don’t think he’s entirely wrong about the relevance of determinism to criminal punishment. For a start, he doesn’t seem to me to be saying that you shouldn’t tell criminals that they shouldn’t have committed the crime, so the contradiction you mention doesn’t arise, or at least not directly.

    More generally, it strikes me that he’s making the same point Eliezer Yudkowsky makes in Harry Potter and the Methods of Rationality, basically just that unnecessary suffering is sad. In this context, that means that if imposing a harsher punishment than necessary will increase the convict’s suffering but serve no other useful purpose, it is undesirable to do so.

    (He goes too far, perhaps, in suggesting that this should rule out retributory punishment altogether. In some cases, meeting the victim’s and society’s emotional need for revenge might legitimately be considered a useful purpose. That’s a much harder question.)

    One particularly relevant case is mandatory penalties for traffic accidents, on the assumption that the driver could have “chosen” not to make any mistakes, or to maintain perfect concentration at all times, despite everything we’ve discovered to the contrary.

  2. Charlie Says:

    I think now would be a good time for me to comment here for the first time. I first discovered you and your work back in April when Sean Carroll linked to your John Horgan interview in a tweet. I would like to tell you how much I have enjoyed reading this blog since then. I can’t always follow along as I’m only an amateur scientist (molecular biology), but I can generally judge the quality of many of your quantum computing jokes by their structure. I would say that you are moderately humorous. I hope that in 2017 more people discover and enjoy this blog. Your perspicaciousness is both invaluable and entertaining.

  3. Boaz Barak Says:

    Happy new year and hope you get better soon!

    Very interesting essay but perhaps what you wanted to say is that “state” should be *less* known (or emphasized).

    If I understand you correctly, what you argue is that what matters is the *interface* to a system and state is just some particular representation of the equivalence class of all systems that behave identically under the interface.

    In this sense the choice of a particular representation for a state (equivalence class) seems arbitrary and more having to do with our culture and sensibilities than with reality. But of course we know that representation matters for complexity. For example, suppose that you had a system which we could represent its state as either x or g^x where g is the generator for some finite group with hard discrete log. Both representations make the same predictions but the former might be much easier to work with. We might even be able to cook up some example where the easier to work with description is longer than the most succinct one.
    So one justification to consider a seemingly more complicated state (e.g., “tacking something new”) is if it would make computing on it easier.

  4. wolfgang Says:

    >> yes, there’s a real world, external to our sense impressions

    What exactly do you mean with “real” and I don’t understand “external” here …
    Are you saying our “sense impressions” are not real?

    I also have a problem with “yes”, but I leave that for another debate 😎

  5. Scott Says:

    Boaz #3: Happy new year to you too, and thanks for the comment!

    What I think should be better known, and more emphasized, is the particular concept of “state” that I tried to get across in the essay: not something handed down from God, but something that we deduce from the interface with observation, and which is always subject to revision and pruning.

      state is just some particular representation of the equivalence class of all systems that behave identically under the interface.

    Yes, that’s precisely it! But I wouldn’t say it follows that the choice of representation has more to do with our culture and sensibilities than with reality–after all, it’s severely constrained by the fact that it needs to represent the equivalence class, and ideally no more than that! Take, for example, the density matrix: the mathematical object that we’re talking about is completely determined by the structure of QM, up to the actual way we write it down as a table with rows and columns. (And yes, if one representation of a mathematical object enables polynomial-time computation with it and another doesn’t, we both agree that the former is almost certainly to be preferred. 🙂 )

  6. Scott Says:

    wolfgang #4: Why didn’t you take issue with “is” or “a”? 🙂

    All I was trying to say is that I’m not a solipsist, you shouldn’t be one either, and solipsism isn’t in any way implied by the view I defended, that what we mean by “the state of the world” has to be deduced from Occam’s Razor and the interface to observation. (Indeed, solipsism would presumably deny that there’s such a thing as “the state of the world” at all.)

  7. Miles Mutka Says:

    The Daniel Hook link is to the wrong response, here is the correct link:

    Also Howard Gardner did not write about common sense, Jared Diamond did:

  8. Shecky R Says:

    Safe, healthy New Year to one-and-all (…but honestly, I don’t expect it to be Happy). Am enjoying reading the Edge pieces and your take on some. One additional simple one I enjoyed is Eric Weinstein on “Russell Conjugation,” admittedly because I think it does impinge on the current political scene.

  9. Scott Says:

    Miles #7: (gasp) Thanks so much, and sorry about those goofs! Fixed now.

  10. Jim Holt Says:

    Sorry I “stole” your idea, Scott! Hey, isn’t that what Poincaré and HIlbert said about Einstein?

  11. J Tyson Says:

    I was almost seriously injured or killed by a narrowly-averted misstep into an unmarked hole in Cambridge MA around 2am one night– A manhole cover had been dislodged by the snowplow, and what remained was a 40-50 foot drop into about a foot of icy flowing water on cement. The metal ladder rungs on the way down added the possibility of smacking your chin on the way down.

  12. Scott Says:

    Jim #10: Hilbert, at least, was generous in giving credit (“every boy playing in the streets of Gottingen knows more four-dimensional geometry than Einstein—and yet it is Einstein who did this work, not the mathematicians”). Reading that quote, I always wondered what it must’ve been like to walk down the streets in Gottingen back then. 🙂

  13. wolfgang Says:

    >> Why didn’t you take issue with “is” or “a”?

    You are right, those two are the real issues:

    If you follow Copenhagen or a neo-Copenhagen interpretation, e.g. qbism, then the idea of “a” state is problematic, because wavefunctions are observer dependent.

    If you use a many-worlds interpretation (which does not really work yet) then you would have to include branches with different geometries and the use of “is” becomes problematic, because it is unclear how our time carries over to other branches of the wavefunction. (And furthermore, it would be impossible for us to determine the state of the many-verse from our own branch).

    This leaves us with hidden variables or modifications of quantum theory to save realism, but it is my understanding that you are not a fan of those.

  14. murmur Says:

    Hey Scottie, how do you feel now that your hero Obama allowed an anti-Israel resolution to go forward while Trump resolutely opposed it? Shouldn’t you be ashamed after your constant fear-mongering that Trump is anti-semite?

  15. fred Says:

    In the essay on the second law of thermodynamics.

    “The Second Law defines the ultimate purpose of life, mind, and human striving: to deploy energy and information to fight back the tide of entropy and carve out refuges of beneficial order.”

    But either life/intelligence is just some random fluke equivalent to an egg unscrambling itself (a impossibly rare event), or thermodynamics needs to account for the inevitable appearance of life.

  16. Peter Morgan Says:

    I more-or-less disagree with your comment about Math, “I would say that the basic function of math education is to teach clarity of thought”, in response to Keith Devlin, but then you say something very close to what I was intending to say in riposte, that “Math, like science in general, is a constant dialogue between formal methods and common sense”. So I’d like to modify your first thought to say something like “I would say that the basic function of math education is to teach the worldly use of formal methods”. “Clarity of thought” seems too woolly for the idea.

  17. jonas Says:

    Scott, thank you for pointing to these articles. Several of them were worth to read for me. The most interesting statement is in Jennifer Jacquet’s article, which told me that some oil mining process has caused a series of small earthquakes in the US. This is described in “”. This was very new to me, because I had specifically assumed that currently used technology can’t influence earthquakes.

    How did you react to Bruno Giussani’s article where he says “we’re likely moving away from transistors to a world of quantum computing, which relies on particles instead to perform calculations”. Do you consider it an upsetting misuse of the popular buzzword of quantum computing means; or do you on the other hand feel indifferent because it’s a statement about future computer hardware, which really isn’t your area of competence?

  18. Aram Says:

    Nice essay! I’m not sure that racists appeal to hidden variables, though. Rather I think they exaggerate the significance of superficial variables. Here is my favorite explanation of it:

    Race also is a good example of where our definitions of state are cultural choices.

  19. Jay Says:

    Happy new year! Although I too doubt that…

    >Yes, it’s possible that things like the hard problem of consciousness, or the measurement problem in quantum mechanics, will never have a satisfactory resolution.

    I doubt this correctly describes Gazzaniga’s point. “We’ll never measure both position and momentum at the same time” doesn’t mean we have no satisfactory resolution for these measurements, isn’t it?

    My (possibly wrong) understanding is that Gazzaniga considers firing neurons and their emerging properties (conscious thoughts) as ontologically distincts, as (say) a collection of sand grains and a dune. We can count sand grains for dunes and non dunes and of course dunes are made of sand grains, but there is no collection of sand grains that is not a dune to which adding a grain of sand makes it a dune. This famous paradox resolves (?) if we consider that “dune” and “sand grains” do not correspond to the same “layer of reality”, e.g. one can’t mix operations on sand grains and measurement of dunes and expect no internal contradictions.

    I don’t like his appeal to quantum mechanics to make this point (because ontology is the same for position and momentum), but don’t you think this is closer to what Gazzaniga had in mind? If not, maybe you’re adding inputs from some of his other writings, do you remember which ones?

  20. Scott Says:

    fred #15: No, the Second Law is totally, 100% fine with a local increase in complexity along with a general increase in entropy. It doesn’t say that complexity increase will necessarily happen (as, indeed, it doesn’t always happen), but nor does it say it won’t.

    Or as it’s sometimes said: the creationists would actually be completely correct, were it not for all those low-entropy photons that enter the earth in the form of sunlight, and the high-entropy photons that come out.

  21. Jay Says:

    Hey murmurie,

    There are bizare folks for whom blaming Israel for making peace impossible is not antisemitic. Call them nazi if you wish, that can’t be worst than voting for the buffoon you and Putin got elected.

  22. Scott Says:

    Peter #16: But when I think through why I’d like kids to learn math—most kids, not just the ones who will become researchers or whatever—it’s not so they can calculate their income taxes or any other practical thing. In my experience, those arguments are indeed pretty easily knocked down in the computer age. (Steven Weinberg told me recently that he can’t recall an occasion where he’s needed so much as high-school algebra outside of his scientific work. And if he hasn’t… 🙂 )

    Rather, the reason I want kids to learn math is so they can see what clear thinking looks like: how to spot fallacious arguments, isolate what’s being claimed and what’s being assumed, carefully define terms, etc. etc. There are many other fields that can also teach clear thinking, but math is clarity itself distilled and abstracted.

  23. Scott Says:

    murmur #14: On the contrary, I’m ashamed to see the prime minister of Israel cheer the rise of fascism in the United States for short-term political reasons, and bad ones at that. I’ve taken a lot of flak from the far left for saying pro-Zionist things on this blog—and yet my own vision of Zionism is a lot closer to Obama’s and Kerry’s (and, I’d say, to Theodor Herzl’s) than it is to Netanyahu’s and Trump’s.

    Also, if you reread my posts and comments, you’ll see that I never—not once—accused Trump of being antisemitic, because I don’t think he is. He’s almost every other horrible thing one can possibly name, but not that. The issue in that regard isn’t him per se: rather it’s that, by smashing the fortress of Enlightenment norms, he’s allowed all the bottom-dwellers of the US, including the antisemites, to crawl triumphantly out from the mud underneath.

    Though admittedly, I’ve read that some of Trump’s white nationalist fans are a much more affable kind of antisemite than Hitler: their desire is to deport all American Jews to Israel, and thereafter to maintain a great relationship between Israel and the US. Maybe my Israeli in-laws will show up at one of their rallies to cheer them on. 😉

  24. adamt Says:


    You say you are arguing against solipsism, but your argument actually lends itself quite well to arguing FOR solipsism. Solipsism is incredibly simple after all and entirely consistent with the observed state of the observable universe.

    By demanding that there is a real external world aren’t you doing precisely what you argue we ought not do?? Making our scientific theories tailored around our ontology – there is an external world!! – instead of the opposite?

  25. adamt Says:

    Btw, sympathies for the ankle. I am out of commission too with a horrible tooth ache and the dentist won’t be in until Tuesday.

  26. Scott Says:

    adamt #23: No, I don’t think solipsism fits well with a scientific worldview, because of the very fact that observation reveals such a large, stable state at all behind our immediate sense impressions. I.e., I can’t just be dreaming all this, because reality has a stability and coherence to it that isn’t at all dreamlike: when I sprain my ankle one night, it’s still sprained the next morning; it hasn’t magically healed just because I stopped thinking about it. Nor do the words on a page or the numbers on a watch change every time I look at them, nor have I woken up in a cold sweat back in the world where Hillary won, etc. All this state that’s external to my consciousness, in the sense that I can’t affect it except by interacting with it in the ordinary causal ways, is the thing that I call “reality.”

  27. Dan Riley Says:

    The link to Diamond’s piece is wrong too, it links to his bio.

    It’s also funny that Diamond uses special relativity as an example. There are still people convinced that SR must be wrong because it defies common sense, certain that any day now someone will find the critical error. Finding a rule for when common sense should be followed and when not is probably equivalent to proving whether P=NP.

  28. fred Says:

    Scott #20

    “No, the Second Law is totally, 100% fine with a local increase in complexity along with a general increase in entropy.”

    Right, I know that life doesn’t contradict the second principle – my point that tying the second law with the “purpose of life” is a bit stretching it given how little we understand about the rise of ordered systems/complexity. And, to be fair, we still have no proof that life on earth isn’t some fluke.

  29. Sasho Says:

    This may be naive, but it feels like there is some category-theoretic about your essay: the idea of identifying a mathematical object with the homomorphisms it takes part in.

  30. Scott Says:

    Dan Riley #27: Sorry again! Fixed.

  31. Scott Says:

    Sasho #29: LOL, all these years I’ve been a category theorist and didn’t even know it!

  32. Sniffnoy Says:

    This may be naive, but it feels like there is some category-theoretic about your essay: the idea of identifying a mathematical object with the homomorphisms it takes part in.

    I mean, one could talk more generally about the structural point of view; that’s not specifically category-theoretic.

  33. Tarn Somervell Says:

    The Helena Cronin link is broken – it goes to her Edge profile page. Oddly, I can’t find any such response from her there

  34. Scott Says:

    Tarn #33: Sorry again; fixed! (Explanation for the unusually large number of goofs is that I’ve been in bed, doing all this on an iPhone.)

  35. Anonymous Says:


    I think the disagreement with Halvorson is just a matter of terminology. He seems to be implicitly distinguishing “quantum mechanics” from “quantum theory.”

    In the classical context, physicists generally use the word “mechanics” to refer specifically to models of particles or rigid bodies, using instead the more general term “classical theory” or “classical physics” to refer more broadly to everything classical, whether it be particles, rigid bodies, or continuous fields.

    In the quantum context, physicists sometimes use “quantum mechanics” to mean all of quantum theory as you define it: “The general principles of QM—unit vectors in complex Hilbert space, unitary evolution, the Born rule, etc.”

    But other times, by “quantum mechanics,” people mean more narrowly the particle side of quantum theory. When people say, for example, that “(0+1)-dimensional QFT is just quantum mechanics,” they mean quantum mechanics in this latter sense.

    So when Halvorson writes that QFT has replaced quantum mechanics, he doesn’t mean that it’s replaced quantum theory. He just means that QFT has replaced simple particle models in quantum theory, and you and he seem to be in agreement on this point.

  36. John Sidles Says:

    Scott proclaims (in the OP)  “The general principles of QM [quantum mechanics] — unit vectors in complex Hilbert space, unitary evolution, the Born rule, etc. — survived the transition to QFT [quantum field theory] without the slightest change.

    Sir Rudolph Peierls’ essay “Some simple remarks on the basis of transport theory” (1974) offers a contrasting perspective:

    In going from the reversible equations of mechanics to this Boltzmann equation, we have already smuggled in the irreversible behavior in some place. This place is the stosszahlansatz of Boltzmann. …

    I mention this because in any theoretical treatment of transport problems, it is important to realize at what point the irreversibility has been incorporated. If it has not been incorporated, the treatment is wrong. A description of the situation which preserves the reversibility of time is bound to give the answer zero or infinity for any conductivity.

    If we do not see clearly where the irreversibility is introduced, we do not clearly understand what we are doing.

    BOSONSAMPLING experiments, for example, couple (dynamically irreversible) photon sources to (dynamically irreversible) photon detectors via (unitary) interferometers. Peierls’ reasoning dictates that we seek to “see clearly where the irreversibility is introduced”, and indeed QFT requires that we design our sources such that their irreversible photon-emitting quantum currents are perfectly correlated with the irreversible photon-absorbing quantum currents of the detectors.

    What’s tricky about Peierls’ advice  — from an engineering perspective — is that the irreversible photon-emitting currents reside in the (causal) past, while the irreversible photon-absorbing currents reside in the (causal future) … and yet far from being dynamically independent, each set of currents is wholly determined by the other set.

    The resulting interlocking set of relativistic / causal / thermodynamical / field-theoretic constraints is sufficiently tricky to reconcile, both in theory and in practice, that quantum supremacists can assert (rightly) that no fundamental theoretical obstruction to scalable BOSONSAMPLING is known. And yet without contradiction, quantum skeptics can assert (with comparably sound theoretical justification) that experimentally demonstrated photon emitter/absorber technologies are far from convincingly scalable.

    Quantum celerians (like me) consider that this tough-to-reconcile Supremacy/Skepticism tension has acted beneficently ever since the early days of quantum science:

    • “The Born Rule”
        (beneficently become thanks to QFT tensions)
          “The Dirac-Fermi Golden Rule”

    • “unitary evolution”
        (beneficently became thanks to QFT tensions)
          “Lindblad/Carmichael dynamical unraveling”

    • “Large-dimension Hilbert spaces”
        (are beneficently compressed via QFT into)
          “Low-dimension tensor-product spaces”

    In summary, the mathematics of quantum dynamics has over the past century become ever-more-subtle and ever-more-useful — and even ever-more-beautiful — thanks in large measure to the beneficent influence of quantum field theory. These evolutionary changes are noticeable year-by-year, and generation-by-generation they are cumulatively transformational. Moreover, the best is yet to come (as future prospects seem to me and many).

    In Feynman’s phrase “It’s gonna be terrific!”. And so these optimistic expectations for a Happy New Year of 2017 are extended to all readers of Shtetl Optimized, without regard for considerations of skepticism versus supremacy! 🙂

  37. mjgeddes Says:

    Max’s ideas about substrate independence could be key for cracking consciousness! The key is to realize that consciousness has a DOUBLE substrate independence.

    I feel by combining the ideas of Max Tegmark, Sean Carroll and Scott Aaronson, consciousness can be cracked!

    *As Scott and Sean have emphasized (and I fully concur), consciousness is strongly connected to the arrow of time (‘consciousness must fully participate in the arrow of time’).

    Key point 1: Consciousness is strongly linked to the arrow of time.

    *Penrose’s metaphysics diagram of ‘3 worlds’ (Math, Physics and Mind), can be put into a more concrete naturalistic form, by appealing to Sean’s ‘poetic naturalism’ – there’s only one natural world but multiple valid vocabularies. I suggested that ‘Information’, ‘Fields’ and ‘Cognition’ are the concrete manifestations of math, physics and mind, respectively.

    Key point 2: There are 3 fundamental vocabularies for explaining reality: Information, Fields, Cognition

    *Max’s critical points; consciousness is connected to information processing (what information feels like from the inside), now the critical idea of a *double* substrate independence.

    Key point 3: Consciousness is ‘twice removed’ from base reality – it involves a DOUBLE substrate independence (2nd order emergence from Fields>Information>Cognition).

    *Scott’s idea of ‘Knightian uncertainty’ (a form of uncertainty that can neither be construed as deterministic, nor as random). Stephen Wolfram’s ‘Principle of Computational Irreducibility’ could be related to this .

    Key point 4: Cognition involves Knightian uncertainty and irreducible unpredictability.

    *Sean’s emphasizes on record-keeping and memory. The notion of ‘information’ can apply to all of mathematics (information), thermodynamics and cognition. (Chairs and tables leave ‘memories’ or records as they interact with the environment, just as brains do).

    Key point 5: Cognition involves the laying down of memories and records (The equivalence of different notions of ‘information’ – mathematical, thermodynamic and cognitive).

    Put all these points together and you’ve got the framework to take down consciousness!

  38. Scott Says:

    Anonymous #35: OK, fair enough. What I suppose confuses matters further is the tangled historical order: first came quantum mechanics (in Halvorson’s sense), then before the ink was dry Dirac and others were already starting to formulate QFT (though of course the details would take several more decades), and only then did Dirac and von Neumann set out the abstract principles of quantum theory, what people most often mean nowadays by “quantum mechanics.” All within the space of 4 or 5 years.

  39. Scott Says:

    John Sidles #36: In principle, QFT is every bit as time-reversible as any other quantum theory (indeed in QFT, besides the bare reversibility that follows from unitarity, one also has the CPT theorem). Of course particular experiments will typically introduce effective asymmetries, e.g. between the sources and the detectors, but that was true even in non-relativistic QM!

  40. Sandro Says:

    A very quotable passage in Steven Pinker’s entry:

    Poverty, too, needs no explanation. […] it is the default state of humankind. Matter does not just arrange itself into shelter or clothing, and living things do everything they can not to become our food. What needs to be explained is wealth. Yet most discussions of poverty consist of arguments about whom to blame for it.

    What an interesting viewpoint shift on who should carry the burden of proof in social policy arguments, ie. that wealth can only exist due to a fortuitous alignment of circumstances among the poor.

  41. Sandro Says:

    There’s no free will, Coyne says, and therefore we should treat criminals more lightly, e.g. by eschewing harsh punishments in favor of rehabilitation.

    Never understood this argument myself. Even assuming we have no free will, if harsh punishment were effective at rehab and deterrence, then it would still be employed and could be justified, ie. if actors only behaved properly because of the harsh punishment they’d suffer if they didn’t. Which obviously is the case in our world. Which isn’t to say it’s the most effective way to achieve this outcome, just that it does work.

    Coyne’s moral dilemma only exists if you make the mistake of conflating determinism with fatalism, whereby an event will happen one way no matter how much we struggle against that outcome. Then obviously there’s no sense in punishing actors that struggled not to commit some murder but somehow ended up killing someone anyway.

    It’s an absurd mistatement of the problem, and experimental philosophy agrees: they’ve shown that most laypeople subscribe to incompatibilist definitions of free will only when they conflate determinism with fatalism. Once that confusion is removed, people largely employ Compatibilist moral reasoning, as found in law, meaning that determinism is completely irrelevant to moral reasoning.

    Justice is one step even further removed from moral blame, so tying determinism into it is an even bigger stretch.

  42. Mike C Says:

    Scott, these two statements of yours seem to be in tension to me:

    (1) But even if so, building a complicated verbal edifice whose sole purpose is to tell people not even to look for a solution, to be satisfied with two “non-overlapping magisteria” and a lack of any explanation for how to reconcile them, never struck me as a substantive contribution to knowledge. It wasn’t when Niels Bohr did it, and it’s not when Harold Pattee does it either.

    (2) To me, this is almost exactly like blaming arithmetic because it only tells you how to add numbers, without caring whether they’re numbers of rescued orphans or numbers of bombs. Arithmetic is fine; the problem is with us.

    I would be inclined to answer your worries about quantum mechanics in (1) in an analogous way to the way you answered the worry about information theory in (2).

  43. Links for December 2016 – foreXiv Says:

    […] Scott Aaronson and Sabine Hossenfelder discuss the 2017 Edge Questions. […]

  44. Scott Says:

    Mike #42: I’m not sure I even understand the tension you’re claiming, let alone being able to formulate a counterargument. What is there in arithmetic (or information theory) that’s at all analogous to the measurement problem in QM? The measurement problem arises because there are two different physical laws (unitary evolution and the Born rule), which on their face seem incompatible, yet which somehow need to coexist in the same physical universe. There are no analogous incompatible rules of arithmetic—there’s just arithmetic, which is perfectly self-consistent, and then my hypothetical person’s complaint that arithmetic can be used for building bombs (as, indeed, it can).

  45. adamt Says:


    To be clear, I think there are very powerful arguments against solipsism, I just don’t think your essay presents one. Nor is your appeal to the stability of the real world vs the instability of your dreams a very good one. So you have dreams of varying levels of stability and coherence… maybe they are even qualitatively and substantionally different, but I don’t see how that lends itself to concluding the external world ^must^ exist.

  46. Scott Says:

    adamt #45: If I had a dream with the same sort of stability and coherence as the real world, I would call it another real world.

    What are your arguments against solipsism?

  47. James Cross Says:

    Wouldn’t an equally good word be “system”?

    No system, no state.

    The problem is when and how do we define a system. In the real world, not the laboratory, boundaries and relationships are often unclear. Systems affect other systems. Their internals are often complex and this limits our ability to predict.

    I liked the choice of “Mysterianism”.

    “What if our faith in nature’s knowability is just an illusion, a trick of the overconfident human mind? T”

  48. JimV Says:

    I very much liked your opinion that “I would say that the basic function of math education is to teach clarity of thought”. It dovetails with my own opinion that math is simply (good) thinking, thinking is (the attempt to do) math.

    E.g., if I have three errands to do (pick up dry-cleaning, mail a package, buy some ice cream for a party), and spend a minute deciding what order to do them in, I have done math (perhaps badly).

    This is also the reason I am not a Platonist. The thought that all my minor math problems, such as the above, exist independently and eternally in some Platonic universe seems too arrogantly far-fetched.

    Thanks a lot for another great blog read.

  49. Scott Says:

    JimV #48: It all depends on what exactly people mean by “Platonism.” Yes, math is just distilled clear thought, but clear thought can have consequences that we don’t get to alter, and that might therefore be said to “exist independently of us.”

    To put it another way: if someone says they believe in a literal heaven of perfect triangles and squares, to which all “triangles” and “squares” in our world are mere inferior approximations, that indeed sounds about as outlandish as the angel/harp kind of heaven.

    On the other hand, if someone says that extraterrestrials would actually disagree with us about whether 17 is prime, then I’m tempted to call myself a “Platonist” just to spite that person.

  50. John Preskill Says:

    Ice, Scott. Put lots of ice on that ankle. Also, great essay!

  51. Scott Says:

    James #47: The trouble is that the phenomenon of computational universality provides such a striking counterexample to the Mysterian view of the world. I.e. sure, it seems intuitively plausible to say, “just as there are natural pheonema that are incomprehensible to a squid or a frog, but comprehensible to us, so too consciousness is probably just a natural phenomenon that’s incomprehensible to us, but that would be comprehensible to an alien superintelligence.”

    Likewise, when I first learned about programming, it seemed obvious to me that, just like GW-BASIC lets you make crappy little games, which is more than you can do with a LEGO set or whatever, so too if you wanted to make better video games, you’d need a language that could express things that could never be expressed in GW-BASIC, even in principle, and so on.

    But then I learned the Church-Turing Thesis, which says that no, that’s not the case at all. Rather, you very quickly hit the ceiling of computational expressive power, and after that it’s “just” questions of efficiency, of time and memory and quantumness and so forth.

    Likewise, in The Beginning of Infinity, David Deutsch defends the view that the reason humans have taken over the world is that, while chimpanzees and dolphins probably came close, humans are the first species to have crossed the threshold of universality—that is, the threshold beyond which, while of course we’re still limited by time and memory and cognitive biases (some of us more so than others), at least in principle we can articulate and understand anything capable of being articulated and understood.

    I don’t know whether Deutsch is right, but it seems at least as plausible to me as the Mysterian thesis.

  52. Anonymous Says:

    Nicholas Humphrey on referential opacity: while I didn’t know the term before, this is precisely the reason why, even if $\mathbf{P}=\mathbf{NP}$, that still wouldn’t imply $\mathbf{P}^A=\mathbf{NP}^A$ for all oracles $A$.

    That seems a bit… opaque. Why is that true?

  53. Scott Aaronson on order and chaos Says:

    […] Yup: […]

  54. Scott Says:

    John Preskill #50: Thanks!!

    My podiatrist uncle told me that the key is “RICE”: Rest, Ice, Compression, and Elevation. It was reassuring to know that the first things Dana and I thought of had indeed brought us to the frontier of medical know-how in this subject.

  55. Scott Says:

    Anonymous #52: It’s because relativization acts on the definition of a complexity class, not on the class itself. And even if P and NP turned out to be equal as classes, they’d still have different definitions, which is what would allow a suitable oracle to separate them.

    An analogy: from “President in 1964 = LBJ” and “if JFK hadn’t been assassinated, he would’ve been President in 1964,” we can’t just blindly substitute to deduce “if JFK hadn’t been assassinated, he would’ve been LBJ.”

  56. Joshua Zelinsky Says:

    Scott, what would it take to convince you that the Mysterian thesis was likely correct? For those in the thread who think it is correct, what would it take to convince you that the Mysterian thesis is wrong?

    (For myself, I’m fairly confident that the Mysterian thesis is wrong, and moreover, that is is wrong specifically in the context of consciousness, but if we don’t have non-upload generals AIs in the next 40 years, I will update in the direction of them being correct.)

  57. Scott Says:

    Joshua #56: If we met aliens who were to us as we are to dogs, I suppose I’d update quite strongly in favor of the Mysterian thesis, and would do so whether or not those aliens were also confused about consciousness. 🙂

  58. James Cross Says:


    “The trouble is that the phenomenon of computational universality provides such a striking counterexample to the Mysterian view of the world.”

    Just because some things – particularly the mathematical and computational – can be completely understood wouldn’t be an argument that everything can be completely understood.

    To the extent we rely on mathematics for science – so much so that science without mathematics is often regarded as non-science – we are particularly vulnerable to the delusion that everything can be modeled or studied mathematically.

    It is self-reinforcing. We study what we can model mathematically; hence, we believe everything can be modeled mathematically. We would never know if there was something beyond that because we would never bother to study or look for it.

  59. adamt Says:


    If you ever had a lucid dream you might well think differently. In fact, one of the practices for generating lucid dreams is in waking life to periodically look around and consider that you might well be dreaming.

    Anyway, beyond the practical difficulties with solipsism – how would one have a coherent ethical framework or conduct oneself in daily life without being absurd? – my main critique of solipsism is that it does not go far enough. Solipsists believe that only *they* are *real* and the whole edifice of the world is just fevered imagination. The fault is that the very arguments they use to refute the real world can be used to refute the inner self as well.

    Nothing is real, all is dream… even the dreamer. That probably sounds absurd or incoherent but I believe it and it grounds my spiritual beliefs. Solipsists raise themselves up and consider only themselves ontologically real whereas I view all the world as lacking ontological reality including the ^I^ that is typing this. At least that is what I believe intellectually even if I have not truly internalized it. When it is truly internalized and deeply felt I think this manifests as enlightenment: a literal waking up.

  60. Jay Says:

    Joshua #56: me too, but if we don’t have upload AIs in the next 40 years, I will die trying to update.

  61. gentzen Says:

    Gazzaniga’s implicit reference to the Heisenberg cut hinted at by his words “what the physicist Werner Heisenberg called the Schnitt” is unfortunate, since his real goal is to explain interesting thoughts of Howard Pattee (not Harold Pattee). He wants to talk about a gap between complementary descriptions of a system, but relating this complementarity to Niels Bohr’s complementarity is far fetched, and translating “Schnitt” as gap made me wonder whether I totally misunderstood the intention behind the Heisenberg cut. After reading von Neumann’s description of the cut, I was relieved that I am at least not alone in considering the relative arbitrariness and “movability” of the cut to be significant, as well as the “recommendation” to not try to move the cut out of the physical world and into the consciousness of an observer.

    The actual thoughts of Howard Pattee are probably not really infected by Bohr’s principle of complementarity (to tell people not even to look for a solution, to be satisfied with two “non-overlapping magisteria”). At least some summaries of his thoughts suggest rather an original contrarian thinker and searcher for hidden truths.

  62. Ajit R. Jadhav Says:

    Wow, Scott, you read a lot! (and apparently very fast too!). […Hope this remark doesn’t trigger yet another avalanche “papers” by amateurs in your inbox, claiming to have “proved” the P-vs-NP issue one way or the other…]

    … I know you couldn’t possibly mention every interesting article, but the one I don’t see mentioned here and really appreciated was: “Ansatz” by Neil Greshenfeld. (

    …In graduate school, I spent months fighting my way through some really long analyses (seemingly endless, running over tens of pages full of equations), before eventually realizing that the real clue lied in this one “dirty” little trick.

    I first “discovered” it in the sub-fields Greshenfeld doesn’t mention: elasticity and fracture mechanics. I discovered it when I noticed that the specific solutions for the stresses and strains for the same problem were given differently in different books/hand-books (and that the original papers were even worse in this regard!). I was writing a literature review, and wanted it to be both comprehensive and reliable. So, one day I just decided to dig through all these complex-potential analyses (just to find out which one was more credible, even they all came from most reputed sources)… Days, may be weeks later, I realized that the ansatzs they were using were all different! [Yes, it was one of those “Oh God! these mathematicians!!” moment for me!]

    Later on, I anyway learnt that ansatzs are the staple diet in FEM and method of weighted residuals (which means, in engg. simulations), and then, even more generally, in the variational principles—which means, virtually anywhere wherever differential equations are used.

    …Anyway, thanks for pointing out the appearance of the new Edge question… Also, hope you get well very soon.



  63. Daniel Weissman Says:

    Ha, Cochrane says that more people should understand the breeder’s equation, and then makes a very compelling argument by demonstrating that he doesn’t understand it himself! Pretty impressive, ignoring all the actual important applications in agriculture, and instead going for a trait (IQ) that is famous for having dynamics that are far too fast to be explained by selection. Especially since he was apparently responding to a prompt that specifically mentioned cultural evolution, the actual driver.

  64. Daniel Weissman Says:

    Ouch, Cronin’s article also screws up the biology. Hopefully, the part about “only one sex was able to inherit the mitochondria” is just a typo (everybody has to inherit mitochondria, but they typically do so from only one parent). But fundamentally, she’s mixing up anisogamy (eggs & sperm) with dioecy (two sexes). All you have to do is glance out the window at some plants to see the difference. (Or look at Wikipedia: Especially weird since it’s all irrelevant to her actual point.

    Oh, and it’s annoying how she deliberately misinterprets the opening Larkin quote.

  65. mjgeddes Says:

    I don’t believe humans have crossed the threshold for universality.

    Years ago, I worked out that there are 3 kinds of modelling ability:

    (1) Models of the world (Animals clear this threshold)
    (2) Models of the self (Only humans and a very few animals)
    (3) Models of the ‘big picture’ – full ontology of reality (No humans- glimmers only for a rare few)

    We’ve only cleared level.2 I think Scott. Level 1 awareness gives us our physical senses, level 2 awareness is social awareness. But most of us are entirely missing the machinery for level.3 (‘big picture’ awareness).

    I determined that beings on ‘level 3’ would directly see an ‘ontology-scape’, which is the collection of concepts forming all explanatory knowledge as a *unified* whole. This I think is also similar to Sean Carroll’s conception of ‘poetic naturalism’ (multiple vocabularies of reality for multiple knowledge domains that all fit together into a coherent whole).

    Now I still think there’s hope, because I don’t think the threshold for this sort of ‘universality’ is an all-or-nothing thing. Perhaps a rare few humans with unusually strong reflective abilities *could* acheive a few ‘glimmers’ of this sort of awareness from time to time, analogous to (for example) how monkeys might occasionally manage to catch a few glimmers of human (level 2) self-awareness.

    If you want to catch a ‘glimmer’ of level.3 , look here:

  66. James Cross Says:

    #56, 57

    I think the Mysterian thesis is just a useful corrective that tells us there is always more to learn and understand, that ideas we are sure about might be wrong.

    In principle, I don’t think it can be proven or disproven. The only way it could be disproven would be if we finally reached the point where we were supremely confident we did know everything worth knowing.

    I would be surprised, however, if there have not been or ever will be aliens that are to us as we are to dogs.

    We already know from looking at the brains of crows that nature has discovered ways of compacting neurons more tightly than they are packed into the human brain. An alien or perhaps a future human (if we last long enough) might very well have an order of magnitude greater intelligence and perhaps emotional and perceptual capablities beyond what we might dream.

    When we look at the series of evolutionary steps that produced humans, I think we will see that there is much room for Nature to produce some much better.

  67. Jair Says:

    I don’t think there is any coherent argument against solipsism. Yes, the world does seem consistent and surprising to me, and it sure doesn’t seem like it’s part of my consciousness. But the solipsist would probably reply that consciousness is large and complicated, and may parts of it may be obscured as in a dream. Consider the zero-dimensional King of Pointland in Abbott’s ‘Flatland’, which believes it is the only thing in the universe. When he hears an outside voice, something that should be impossible according to its own worldview, he responds

    “Ah, the joy, ah, the joy of Thought! What can It not achieve by thinking! Its own Thought coming to Itself, suggestive of Its disparagement, thereby to enhance Its happiness! Sweet rebellion stirred up to result in triumph! Ah, the divine creative power of the All in One! Ah, the joy, the joy of Being!”

    This kind of conversation can go on for hours. For every seemingly sensible bit of “evidence” for an outside world, the solipsist could reply that it’s just another game that was invented to amuse the one mind.

    The only ‘argument’ against solipsism is that it’s very dull, and goes nowhere. I mean, I guess if I was a solipsist I could try controlling things with my mind for a while, but I’d quickly get bored when it doesn’t work. That’s not an argument against solipsism, but without some kind of extra power over the world what’s the point? I’d eventually forget about this and go back to a more practical philosophy.

  68. Raoul Ohio Says:

    The Mysterians have produced one concrete data point:

  69. Ehud Schreiber Says:

    Dear Scott,

    I’ve also sprained my ankle about a month ago. My wife and her mother are physiotherapists, and they made me start walking and exercising as soon as possible – it hurts, but then one returns to normal much quicker. You should only make sure beforehand, e.g. using X ray imaging, that there is no broken bone. The acronym of treatment used to be RICE – Rest, Ice, Compression, Elevation – but is now changed to MICE – Mobilization instead of Rest. Try googling something like “sprain RICE MICE”.

    So, I would recommend going to the doctor for checkup, and then to physiotherapy for treatment, instead of just staying in bed.

    Feel well,
    and thanks for the blog,

  70. Michael Nielsen Says:

    On the holographic principle: I’m sympathetic to the choice. Yes, many ideas in physics are in seeming contradiction to everyday intuition. But only a few are so radically in contradiction.

  71. Scott Says:

    Jair #67: This actually ties in perfectly with what I was trying to say in the “State” essay. If my experience, like the King of Pointland’s, were to be alone with my thoughts forever, save for an occasional interruption that might be someone else but might also be a previously-unknown aspect of my own thoughts, solipsism would be a pretty good theory. Instead my experience is that of being a small creature in an enormous universe, most of which I’m powerless to affect but which can nevertheless affect me, and which follows laws that I didn’t invent but can sometimes with great effort understand, and which contains several billion other beings that give every external appearance of being conscious—different from me in detail, but also different from each other. That this has been my experience, is all that I mean in saying that (for me, anyway) solipsism is a terrible theory. I deny that there’s an additional question I need to answer, about whether it’s “real” reality, or a dream that behaves completely indistinguishably from a reality.

  72. James Cross Says:

    Solipsism may be a terrible theory but all we know and experience comes to us through the lens of consciousness and it is impossible to know how much the lens distorts what we see. There is hope in this too that we may be able to modify more of what we believe reality to be than we currently think possible.

  73. Scott Says:

    James #66:

      I think the Mysterian thesis is just a useful corrective that tells us there is always more to learn and understand, that ideas we are sure about might be wrong.

    The trouble with that view is that the Mysterian thesis involves its own brand of arrogance, in its claim to know that certain specific things are unknowable. I think one is perfectly justified to respond: how do you know that? The danger is that you’ll prematurely close off the paths to learning more, and do so under the guise of humility. (I feel the same way about, e.g., the people who express confidence or even certainty that P vs. NP is independent of the axioms of set theory.)

  74. Scott Says:

    gentzen #61: Thanks, and sorry about that! On reflection, I removed the reference to Pattee entirely from the post, since I wasn’t responding to his ideas firsthand, but only to Gazzaniga’s rendering of them, which might or might not be accurate.

  75. Scott Says:

    James #58:

      Just because some things – particularly the mathematical and computational – can be completely understood wouldn’t be an argument that everything can be completely understood.

    Actually, I never said that mathematical and computational things can be “completely understood,” and there are several important senses in which they can’t be! (First, that there are infinitely many of them; second, that understanding them often requires solving an instance of an uncomputable problem; third, that some of them are independent even of very strong formal systems…)

    What’s important about math and CS for this discussion is simply that they appear to admit universal languages—that is, languages that can express anything that’s expressible at all. There might still be plenty of things that are inexpressible, but that doesn’t seem to be a defect of our languages; we’d face the same problem with other languages.

    Motivated by that, we should clearly distinguish between two very different questions:

    1. Can everything be understood?

    2. Could humans, if given unlimited time and memory, understand anything that any other entity could understand?

    I don’t know the answer to either, but I’m certainly more optimistic about the second than about the first.

  76. Raoul Ohio Says:

    I want to second Udi Schreiber’s comment. Having played basketball into my 60’s, I am very familiar with the traditional idea that when someone sprains an ankle, you pull them back to their feet, and encourage them to continue playing. This works pretty well and helps you learn to ignore moderate pain.

    When you get old and continue to play sports, you are often tempted to not go to the gym because something hurts. After you play, it doesn’t hurt anymore. Something else hurts.

    My advice to everyone: try to walk a lot every day and never take the elevator.

  77. Richard Gsaylord Says:

    i agree that the second law of thermodynamics needs to be better known and better understood. however, Pinker’s discussion of entropy seems pretty abysmal. statements that ” the second law implies that misfortune may be no one’s fault.” and “poverty, too, needs no explanation. in a world governed by entropy and evolution, it is the default state of humankind.” are simply nonsense. it would have far more useful for pinker to have pointed out that contrary to what is often stated in science courses and science books, entropy is NOT greater in a disordered (micro)state than in a disordered (micro)state; rather, entropy is based on the number of microstates available to a system (pinker does seem to understand this as indicated by his statement that “order could be characterized i’n terms of the set of all microscopically distinct states of a system but he fails to emphasize this point adequately IMO).

  78. Sniffnoy Says:

    This kind of conversation can go on for hours. For every seemingly sensible bit of “evidence” for an outside world, the solipsist could reply that it’s just another game that was invented to amuse the one mind.

    At the cost of making the solipsistic theory more and more complex.

    You can’t entirely rule out solipsism with 100% certainty, but you can’t entirely rule out anything with 100% certainty. All knowledge is probabilistic. By any reasonable standard of evidence, we can say solipsism is false.

    (relevant old LW sequence link 😛 )

  79. srp Says:

    Regarding math and common sense, wasn’t it Von Neumann who said “Young man, in mathematics you don’t understand things. You just get used to them.”?

  80. Richard Gsaylord Says:

    comment #76 your advice to everyone to “try to walk a lot every day and never take the elevator.” isn’t very helpful advice to those of us who are disabled and unable to walk, let alone climb stairs.

  81. James Cross Says:


    I didn’t mean to imply that everything mathematical and computational could be completely understood. Only that if we could point to any realm where we could say something is completely understood it would be in those areas.

    Nor do I think Mysterianism has something to do with a lack of intellectual parity among entities. Other entities might be as limited as we are, although perhaps in ways different from us.

  82. venky Says:

    It is interesting to see that many of the social science entries ultimately rely on the concept of higher order beliefs (see Scott’s essay on Aumann). E.g., higher order beliefs are key to coalitions, etc.

  83. C Murdock Says:

    “The question about the envelopes can be resolved by noticing that your decision on earth, to open your envelope or not, doesn’t affect the probability distribution over envelope contents that would be perceived by an observer on Pluto.”

    I’m a little confused. Isn’t this just restating the premise on which the paradox is constructed which *makes* it a paradox in the first place? I don’t understand how anything is “resolved” there.

  84. Scott Says:

    C Murdock #83: Suppose Alice is on earth and Bob is on Pluto. Then the original statement of the “paradox” considers Alice’s perspective, which makes it look like the state on Pluto gets updated instantaneously based on something that happens on earth. By contrast, the “resolution” considers Bob’s local view only, according to which the state is probabilistic (or in the quantum case, a density matrix). Then the important point is that Alice’s conditioning operation, despite how drastic it looks from her perspective, has no effect—none whatsoever—on Bob’s local probabilistic state.

  85. C Murdock Says:

    I’m confused, because I still don’t understand how that prevents Alice from opening her envelope at 12:00 AM and finding “heads” and Bob opening his at 12:05 AM (6 hours before the wave front from Earth hits him) and finding “tails”.

  86. Scott Says:

    C Murdock #85: I’m confused about what you’re confused about, so maybe someone else should take a crack at explaining it?

  87. Leon Says:

    From Carroll on Bayes’ theorem:

    If you say, “I have no idea whether that’s true or not,” you’re really just saying, “My prior is 50%.”

    This view seems widespread, but I don’t know that it makes much sense, even if taken normatively.

    E.g. I don’t think it’s irrational to simultaneously have “no idea” whether 1. A is true or not, 2. B is true or not, and 3. (A & B) is true or not.

  88. Leon Says:

    From Carroll on Bayes’ theorem:

    Whether you admit it or not, no matter what data you have, you implicitly have a prior probability for just about every proposition you can think of. If you say, “I have no idea whether that’s true or not,” you’re really just saying, “My prior is 50%.”

    I don’t think this is true, even if taken normatively.

    Counterexample: “I have no idea about A” and “I have no idea about B” are compatible with “I have no idea about (A and B)” without A and B being equivalent.

  89. Jay Says:

    Leon #88,

    It seems Caroll doesn’t care to discuss it, but yes that’s a well known loophole.

  90. Scott Says:

    Leon #87: As a believer in the concept of Knightian uncertainty, I also disagree with that particular statement.

  91. wolfgang Says:

    >> universality and superintelligence

    I am quite proud to be a human being, after all we have figured out how most of the universe actually works – from the standard model to the big bang.
    Sure there are some open problems and perhaps some aliens have an easier time with superstrings or the measurement problem than we do. But we have decades of research ahead of us (if we are lucky).

    In my opinion there are actually two independent miracles here:
    i) It is quite amazing that a bunch of apes, after a few million years of brain evolution on a tiny planet, was able to figure out math and physics.
    ii) It is perhaps even more amazing that the world is such that it can be figured out. This is mostly due to the fact that the basic laws of nature are simple and elegant in a certain way (this includes the 2nd law btw) and a priori it could be quite different imho.

    If one wants to look for meaning in this world, this is where one could start.

  92. mjgeddes Says:

    Leon and Scott,

    Yes I too have become a believer in ‘Knightian uncertainty’. That means Carroll is simply wrong here.

    Bayesian inference is not the foundation of rationality, because even *before* any probability assignments can be made, you need to have an underlying model or vocabulary for talking about a particular domain , and there will always be some irreducible fuzziness or imprecision in the model itself. So you need an extra measure (not itself a probability) to handle this meta-uncertainty in the model itself.

    The measure you need is ‘conceptual coherence’, the degree to which the concepts or vocabulary you’re using *coherence* into a integrated explanatory whole.

    The correct foundation of rationality is categorization (or reflection), not Bayesian inference.

    This can be clearly be seen in my top-level ‘domain model of reality’ at link here:

    Here I treat reality as a ‘language’, and you can clearly see a grand pattern whereby knowledge domains arrange themseleves hierarchically into a fractal structure, with a ‘3-level recursion’ – any language of unbounded complexity always needs 3-levels of recursion (object, meta and meta-meta).

    At link above, go to left-hand column, look to middle grouping of 3 domains , and there’s the 3-level recursion for rationality :
    Categorization (Reflection), Probability Theory and Logic

    It’s clear that categorization is the root and probability theory is on the 2nd level.

  93. James Gallagher Says:

    #64 Daniel

    The mitochondria are inherited only from the mother, not “one parent” as you said – I guess you know what you meant but your sentence is perhaps a little sloppy just like Helena Cronin’s in her courageous contribution (Which seems mostly sensible to me)

    Get well soon Scott. As for solipsism, can we not just ask someone something which we couldn’t possibly know (eg translate this sentence into Japanese), or something simple like “what’s around the corner?” before you get there. Other minds have to exist or else we are omniscient – not a proof, I don’t think there can be absolute proof against idealism, but convincing enough for little me.

  94. Scott Says:

    James #93: Fortunately, my ankle is mostly healed—I can walk and only feel it occasionally! Thanks for asking.

    Yes, you’re pointing to special cases of the autonomous, non-dreamlike nature of the external world, which is the general fact that I think makes solipsism such a terrible theory. Even if you’re arrogant enough to think that everyone besides you is a mindless automaton or philosophical zombie—even so, they’re not zombies that you just imagined, for example because they too often know things that you don’t know but can verify later.

  95. JimV Says:

    “,,, aliens who say that 17 is not a prime …”

    Octopodal aliens might well say that.

  96. Scott Says:

    JimV #95: No, if you really want to be intellectually consistent about it, they would not say “17 is not a prime.” They would say “zorflik logeboo tuza’irg oostne,” or however you say in alien language that 17 is a prime and that 15=178 is not one.

  97. Adam Stephanides Says:

    I’m confused by your reference to “the strategy-stealing argument in go” as something that violates common sense. Am I wrong in believing that the strategy-stealing argument works in go without komi (since passing is allowed) but fails with komi?

  98. Scott Says:

    Adam #97: Sorry, I should’ve said “the strategy-stealing argument in Hex.” Alas, I don’t know Go well enough to answer your question.

  99. Max K. Goff Says:

    Your essay inspired me to write a blot post, which may or may not be of interest. Awesome work, Scott. I’m a fan.

  100. Scott Says:

    Max #99: Thanks—but you seem to have misunderstood.

    In my essay, I explicitly said that a state might only determine the probabilities of various observations, not the observations themselves. And because of (e.g.) Bell’s theorem, and the experiments that it led to, and the “nonlocal cosmic conspiracy” that’s needed to explain those experiments in a deterministic way, I personally regard the indeterminism of quantum measurement outcomes as a settled fact, to pretty much the extent anything in physics is a settled fact.

    Hidden-variable theories, like Bohmian mechanics, are sometimes interesting stories that you can tell. But there are infinitely many different such stories, all leading to exactly the same outcomes for every experiment allowed by the rules of quantum mechanics. And the whole point I was trying to make, in the essay, is that there is a real world with a real state, but experience has shown that we constantly need to revise our conception of that state, to cut things out from it (whether coordinate systems, reference frames, gauges, purifications of mixed states, hidden variables…) that our intuition might rely on but that then turn out to make no difference for observations.

  101. Max K. Goff Says:

    Thank you for clarifying your views on Bohmian mechanics. From your essay I got a different impression, but upon rereading your essay in light of your comment above, I stand corrected. Again, thank you for your views! I do admire your work.

  102. Scott Says:

    Max #101: I sincerely apologize if I was unclear. In my defense, I did only have a thousand words…

  103. James Cross Says:


    I am not a pure solipsist but nevertheless your argument is a little simplistic, I think.

    The problem is that entities in dreams can also tell us things we don’t know in the context of the dream. Other entities in dreams also seem to have minds such as other entities in waking life seem to have. We also have scientific discoveries and inventions that have occurred in dreams. The discovery of the structure of benzene and the invention of the needle for the sewing machine are examples.

    I think a revised and updated solipsism that allows for an objective world but still insists that the world we know and perceive is created in the brain might be closer to the truth and in line with science. This is not pure solipsism (you might say it is not solipsism at all) but it validates the fundamental feeling of solipsism.

    Of course, this is not a world where anything is possible. I can’t fly in the waking world, although I might be able to fly in a dream. There are rules and limitations that arise from objective rules and limitations that exist outside the brain and the evolutionary adaptations of our perceptual and neurological systems. Deciding what comes from what isn’t all that simple. What would our physics and geometry be like if we did not have eyes? What would it be like if we had four eyes or a hundred eyes?

  104. Scott Says:

    James #103:

      What would our physics and geometry be like if we did not have eyes?

    In some sense, we already know the answer to that question. Beings who had x-ray vision, or the ability to see individual atoms, could just as well have asked: what would our physics and geometry be like if we didn’t have those abilities? But as humans, we could tell them the answer: it would take a hell of a lot longer, but assuming you developed a long-lasting technological civilization at all, eventually you’d build sensors to compensate for the limits of your bodies, and your physics would converge to what it would’ve been otherwise—namely, to the correct physics that describes our world.

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