Whenever I hear someone describe quantum physics as "weird" - whenever I hear someone bewailing the mysterious effects of observation on the observed, or the bizarre existence of nonlocal correlations, or the incredible impossibility of knowing position and momentum at the same time - then I think to myself:  This person will never understand physics no matter how many books they read.

    Reality has been around since long before you showed up.  Don't go calling it nasty names like "bizarre" or "incredible".  The universe was propagating complex amplitudes through configuration space for ten billion years before life ever emerged on Earth.  Quantum physics is not "weird".  You are weird.  You have the absolutely bizarre idea that reality ought to consist of little billiard balls bopping around, when in fact reality is a perfectly normal cloud of complex amplitude in configuration space.  This is your problem, not reality's, and you are the one who needs to change.

    Human intuitions were produced by evolution and evolution is a hack.  The same optimization process that built your retina backward and then routed the optic cable through your field of vision, also designed your visual system to process persistent objects bouncing around in 3 spatial dimensions because that's what it took to chase down tigers.  But "tigers" are leaky surface generalizations - tigers came into existence gradually over evolutionary time, and they are not all absolutely similar to each other.  When you go down to the fundamental level, the level on which the laws are stable, global, and exception-free, there aren't any tigers.  In fact there aren't any persistent objects bouncing around in 3 spatial dimensions.  Deal with it.

    Calling reality "weird" keeps you inside a viewpoint already proven erroneous.  Probability theory tells us that surprise is the measure of a poor hypothesis; if a model is consistently stupid  - consistently hits on events the model assigns tiny probabilities - then it's time to discard that model.  A good model makes reality look normal, not weird; a good model assigns high probability to that which is actually the case.  Intuition is only a model by another name: poor intuitions are shocked by reality, good intuitions make reality feel natural.  You want to reshape your intuitions so that the universe looks normal.  You want to think like reality.

    This end state cannot be forced.  It is pointless to pretend that quantum physics feels natural to you when in fact it feels strange.  This is merely denying your confusion, not becoming less confused.  But it will also hinder you to keep thinking How bizarre!  Spending emotional energy on incredulity wastes time you could be using to update.  It repeatedly throws you back into the frame of the old, wrong viewpoint.  It feeds your sense of righteous indignation at reality daring to contradict you.

    The principle extends beyond physics.  Have you ever caught yourself saying something like, "I just don't understand how a PhD physicist can believe in astrology?"  Well, if you literally don't understand, this indicates a problem with your model of human psychology.  Perhaps you are indignant - you wish to express strong moral disapproval.  But if you literally don't understand, then your indignation is stopping you from coming to terms with reality.  It shouldn't be hard to imagine how a PhD physicist ends up believing in astrology.  People compartmentalize, enough said.

    I now try to avoid using the English idiom "I just don't understand how..." to express indignation.  If I genuinely don't understand how, then my model is being surprised by the facts, and I should discard it and find a better model.

    Surprise exists in the map, not in the territory.  There are no surprising facts, only models that are surprised by facts.  Likewise for facts called such nasty names as "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird".  When you find yourself tempted by such labels, it may be wise to check if the alleged fact is really factual.  But if the fact checks out, then the problem isn't the fact, it's you.

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    Specifically with respect to quantum theory, this advice is bad (see here, here, and subsequent comments). It is one thing to be open to unusual ideas, or to accept unexpected facts. But the prevailing interpretation of quantum theory has thrown out an ontological principle - that to be is to be something, that some properties by their very nature must take determinate values or not exist at all - so basic that it hardly even has a name, and which is nonetheless basic to objective thought. Accepting quantum theory, for most people, is going to mean not jus... (read more)

    That's certainly true if the metaphysics you're accepting is the Copenhagen Interpretation, which for most people it seems to be.

    that some properties by their very nature must take determinate values or not exist at all

    This is not a scientific principle. Science lives or dies only on the accuracy of its predictions - probabilistic or deterministic. Don't be confused by the fact that pre-quantum, pre-thermodynamics laws were deterministic - that was just a lucky fact, that persuaded people that all laws had to be the same.

    As for the "some properties", quantum mechanics asserts (and experiments back it up) that there is no such thing as position, or momentum - that the combination of the two is the actual property that exists.

    As for the different interpretations of quantum mechanics - they're all equivalent, or they differ in ways we can't measure yet. So none of them on their own say anything about how we should view reality. Only the predictions of quantum mechanics tell us about reality, not the models.

    Actually, I don't think I agree with the thrust of this post. As long as you don't argue "this is weird, hence it is wrong", I think the if you find quantum mechanics strange you're more likely to prosper in the field that if you force your sense of normality to match quantum reality.

    In the first case, you can easily discover a new physical law, find it weird, and cheerfully accept it. In the second case, a new law may be an assault on your feeling of reality, so you may be less willing to accept it - and if you did, you'd have to go through the whole process of updating your instincts again.

    People can develop very good intuition about things they find strange, without having to find them any less strange.


    What is ironic about this posting is your indignation. Offhand it sounds like you are as guilty as those you criticize.

    There is nothing weird about people finding a theory to be weird that does not correspond with their everyday surface perceptions, even when they are able to comprehend it intellectually. Also, and others have noted this more or less, there are a lot of different interpretations out there of what quantum physics "really means," and some are a lot weirder than others. Is it ontological that Schrodinger's Cat does not ei... (read more)

    Wow, great post. Seriously.

    In actuality, the biggest barrier to understanding modern physics is the math. The math models are what generate the "weirdness". Trying to use english to describe what the math models are telling us is what generates the "weirdness".

    But if you suspend disbelief and go where the math takes you, useful things can be done, like nuclear power, solid state physics, etc.

    This is one of the worst posts I've read here.

    If you truly think "This person will never understand physics no matter how many books they read." then you are making great assumptions based on your personal prejudices.

    If you don't find quantum physics weird (or at least understand why someone may), you don't have a grasp on current human intuition. Just because you recognize that quantum physics differs from everyday experience doesn't mean you can't understand quantum physics. It actually means you have a BETTER grasp on understanding human intuition, and has no bearing on whether you know (or have the capability of knowing) less or more about quantum physics.

    Another way of looking at this is to realize that we are all pretty much hard wired to operate in a surface reality that more or less fits a Newtonian-Euclidean model of the world. We now know that this does not hold at high accelerations or at very large or very small scales in a lot of ways. So, these deviations, many of which have been clearly established beyong any doubt, seem weird to most people when they first hear of them, and may even still "feel weird" even after they have long come to intellectually comprehend and accept them.

    Heck, e... (read more)

    "Anyone who is not shocked by quantum theory has not understood it." Neils Bohr. It is not just that one has to greatly revised one's view of what there is in the world; physicists still don't understand very well what quantum theory implies about what in fact there is in a quantum world.

    2Nathan Gillingham
    Exactly the quote and reference I was going to make. Should we believe Bohr didn't understand Physics? 

    Are there data on how many physicists believe in astrology? I can understand how a few would, but I'd be astonished if the percentage weren't a lot lower than for Americans as a whole. Hey, there are PhD biologists who reject evolution--but not many.

    If Richard Feynman can say:

    What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does.

    then it may be strange to the point of being beyond understanding.

    (Nobel Lecture, 1966, The Strange Theory of Light and Matter)

    This is a great post. I just want to add: we might fail to understand physics and mass murderers for different reasons. When a terrorist slams a jet into a skyscraper, someone can say "I don't understand why that person did that? It's bizarre." But they seem to fail in understand because victims have a biased recall of transgressions (according to the work by Baumeister on the myth of pure evil). Perpetrators seem to actually have more accurate and complete understandings of transgressions. This is one of my favorite findings from social science.

    In contrast, we seem to think physics is bizarre for different reasons.

    Well, the main lesson I learned today is:

    Never use quantum mechanics as an example of anything.

    I could have talked about relativity, the counterintuitive mixing of space and time, and non-flat spacetime metrics, but noooo, I had to say "quantum".

    I haven't learned any general relativity yet, but from what I know of special relativity, it actually makes perfect sense. You start with the assumption that no observation can allow you to deduce where you are or how fast you are moving, and then follow that premise to its logical extremes. There are things, if you look at them hard enough, you can understand it intuitively, and they cease to be weird. Quantum mechanics, on the other hand, is one of those things that even if you look at it really, really hard, you still can't understand it. So no, I think quantum mechanics is the only example you could have used here.
    Relativity of simultaneity makes perfect sense to you? I'm prepared to accept that my intuitions are defective and the world really does operate this way... but I can't seem to actually adjust my intuitions accordingly. There's still this little voice in the back of my mind saying, "But which one is the real now?"
    You also need to know that there's something that travels at a finite speed in vacuum, otherwise Galilean relativity is consistent with that assumption too.
    But if you hadn't used that example I would have never read this Wikipedia edit summary, and never heard about you or LessWrong!

    One thing that happens with new theories is that at first they seem strange, but then gradually the concepts filter into the popular consciousness and then they are easier to accept. It's commonplace to say, "everything is relative", or "the observer affects what he observes". Also, better ways are found to instruct students in the principles, which also helps with acceptance. QM and relativity do not seem all that odd to me, because I have known about them for so long.

    One theory that still baffles me is the holographic principle, which... (read more)

    Don't jump the gun; we have no experimental confirmation of the holographic principle. Unlike say the Schrodinger equation, which is one of the most precisely verified equations in the history of physics.

    Shakespeare, Feynman wrote that in 1966, which was before Everett's absolutely essentialy (and stunningly obvious in retrospect) insight spread through the physics community. Feynman's claim in 1966 that "Nobody understands QM" thus inadvertantly illustrates one of the other great truths, which is that nobody knows what nobody knows. The accumulated pool of scientific knowledge is far too vast for any one human mind to hold more than a tiny fraction. There are six billion people in the world, and you don't know what they know. Feynman should have stuck to saying "I don't understand QM", to which he could have attested of his own knowledge.

    Quantum mechanics really was a very poor choice as my first example, because the application of "Think like reality" to QM is nontrivial. Before you conform your intuitions to reality, you should be very sure of what reality is.

    Quantum mechanics tells us unambiguously that reality is over points in configuration space and that quarks and photons have no individual identities - if you pretend that a point in configuration space with photon 1 at A and photon 2 at B is different from a point in configuration space w... (read more)

    "Which branch am I in?" is clearly not a nonsensical question, because I actually have these memories which follow a sequence of single events---things being here and not over there. You can say it's a pointless question, because there is another me somewhere in the other branches; but it's clearly not meaningless, because we only experience and remember one result from each experiment.
    I don't think he was actually trying to say nobody understands quantum, I'm pretty sure he was actually saying (albeit in less words): "just because you don't understand quantum, does not mean that you are unintelligent, or that the theory is incorrect". I believe that as you pointed "nobody knows what nobody knows", implies that he wouldn't make such a statement with the intentions that it should be take literally, and consequently it seems significantly more probable that the intentions of the statement were something else entirely. I would also like to note that the statement "nobody knows what nobody knows" has only one piece of evidence attached to it, and I am curious were else you noticed it taking effect.

    Questions like "How are amplitudes converted to subjective probabilities?" are not automatically dictated by the theory

    You might find this paper by David Deutsch interesting. Although, equation 14 bugs me, it seems to me |Psi_2> as defined doesn't necessarily exist.

    Stuart, I said determinate, not determinist. I was objecting to the notion of an objectively indeterminate property - as if it made sense to say of a particle that it has a position, but no particular position... You yourself say "there is no such thing as position, or momentum... the combination of the two is the actual property that exists." I would be very surprised if that is anything more than a slogan. Can you explain to me the exact nature of this 'combination' that is the actual property? (Please don't just say that the formalism provides... (read more)

    Presumably the actual property is the state of the wavefunction. So for instance we could have a Gaussian wavefunction... and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it's a Fourier transform the momentum would grow ever more indeterminate. Interestingly, there are apparently ways of working around this, by carefully choosing your observables to be operators that commute. http://arstechnica.com/science/2010/08/quantum-memory-may-topple-heisenbergs-uncertainty-principle/

    as if it made sense to say of a particle that it has a position, but no particular position

    That might or might not make sense (mathematicians have been tearing their hair out about non-computable numbers, see Chaitin's constant). But most quantum mechanists do not say that a particle has a position. In fact if you interpret Quantum mechanics in terms of "hidden variables" (there are underlying values for the objects, like spin and momentum, but we can't get at them) then you will generally come unstuck.

    Can you explain to me the exact nature of th... (read more)

    And so, like kudzu, the thread is taken over by the Great Quantum Debate... but Mitch, do you agree with the central point of the original post, that true facts cannot be "weird" or "bizarre" except insofar as we think like primates and not like reality? That we are always faced with a dilemma to eventually discard either the mistaken intuition or the mistaken fact?

    As to your quantum-question: as I understand it, the presences of particle species at particular locations are the dimensions of the configuration space, points within which... (read more)

    Eliezer, If a theory seems bizarre to your intuitions, then either the theory is wrong or your intuitions need reshaping.

    I'm leaning towards embracing your point more, but still two issues: 1) "need". If my intuition tell me something, but I know it's wrong, and I can deal with it without letting my intuition interfere, why do I need to reshape my intuition - shouldn't I just go with "don't trust my intuition"? 2) As a mathematician, I have good mathematical intuition. It helped me when I took a course on quantum mechanics and relativit... (read more)

    So does MWI actually bring anything to the table in terms of testable predictions that differ from Copenhagen et. al.?

    Yes, in that it doesn't postulate this weird non-unitary indeterministic "collapse" business which is never actually observed.

    There is an interesting critique of MWI here that I just finished reading. An fascinating topic to be sure. . .

    Matthew C: My criticisms of Kent's criticisms of MWI (as formulated by Everett), in the paper you link to:

    A Hilbert space has an inner product by definition, so mu is already an entity of the theory without needing any extra postulates.

    In the example given, decoherence will result in the two terms of the RHS of (2) not being able to interfere with one another, which justifies considering them to be independent worlds, no intuition required.

    Kent's talk about bases seems confused, the dimensionality of a basis is fixed by the dimensionality of the state spac... (read more)


    I think it's unfortunate that this thread has veered off into debates about the inner workings of quantum theory and indignant defenses of what is and is not known in physics. Eliezer used quantum mechanics as an example to illustrate a larger point which has scarcely been mentioned here, a point which connects very clearly to the name of this blog -- Overcoming Bias, and yet everyone seems more interested in the metaphor than what it represents; they are mistaking the map for the terrain, as Eliezer might say =)

    As I understand it, Eliezer is making a point about how short-sighted and self-centered it is to label a phenomena "weird". To call something weird is, in essence, identifying it as an outlier in our (woefully limited) data set of experiences. As Eliezer points out, this is a shortcoming of our model and not an inherent “eccentricity” in reality. Now I believe that being surprised is completely natural and in fact unavoidable, but what I believe Eliezer is really railing against is how fixated people can become with the “weirdness” of a universe which refuses to conform to our simple models and heuristics.

    In cognitive psychology, there is a theory of cognitive gro... (read more)

    Does anyone have a book they can recommend that explains the actual math of quantum mechanics? Once I actually see the equations, things always start making sense to me. For example, my introductory modern physics course talked about the Schroedinger equation and had an optional section on operators and wave functions. Having suffered through Fourier analysis in my electrical engineering courses, the way the Heisenberg uncertainty principle comes from the application of transformations to wave functions made a kind of intuitive sense. I know an awful lot o... (read more)

    You could try "The structure and interpretation of quantum mechanics" by R I G Hughes or "The Interpretation of quantum mechanics" by Roland Omnes. Either has enough math to articulate the problem. I also really liked "Quantum mechanics and experience" by David Z Albert - it was this book that led me to realize that many-worlds is obviously true (as it now seems to me). Albert himself does not believe in many-worlds but he explains it really well. I'm now working through the university physics texts because none of the above cover relativistic QM. They physics texts though are - to a man - in the "shut up and calculate" school of thought. It is claimed that many a promising physicist has disappeared down the rat-hole of the philosophical interpretation of QM. You may also enjoy "A Different Universe: Reinventing Physics from the Bottom Down" by Robert Laughlin. He argues that so-called fundamental physics is just the lowest layer of emergent froth that we are able to see. Quantum Field Theory shows that "empty space" is full of stuff for example.

    You write: "There are no surprising facts, only models that are surprised by facts."

    That's deterministic thinking. Surprising facts happen every once in awhile. Rarely, but occasionally.

    But I agree with your general point. Surprise is an indication that you have a problem with your model, or that you have prior information that you have not included in your model.

    but Mitch, do you agree with the central point of the original post, that true facts cannot be "weird" or "bizarre" except insofar as we think like primates and not like reality? That we are always faced with a dilemma to eventually discard either the mistaken intuition or the mistaken fact?

    The reality is that possibilities are very large in number and actual knowledge is shockingly small. To genuinely "think like reality" might mean to maintain as constant and thorough an awareness as possible of every uncertainty in your exi... (read more)

    A few more words on quantum theory. In effect, there is a prevailing myth and a rising heresy. The prevailing myth is the Copenhagen interpretation, the rising heresy is the many-worlds interpretation. They have this much in common, that both are full of fuzzy thinking but their acolytes believe them to be exact. Therefore, when you press the acolytes for details, you never get quite the same answers, because the belief that the interpretation does provide answers comes first, and then the details are invented in response to scrutiny, in faith that they ar... (read more)

    My feeling is that Bohm escapes these problems, at the cost of requiring nonlocal information transfer (a high price, but one I'm willing to pay).
    Can't this be answered by an appeal to the fact that the initial state of the universe is supposed to be low-entropy? The wavefunction corresponding to one of the worlds, run back in time to the start of the universe, would have higher entropy than the wavefunction corresponding to all of them together, so it's not as good a candidate for the starting wavefunction of the universe.
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    Have you heard of the Pondicherry interpretation of QM?

    I had, but I had the wrong idea about it. At a glance, Mohrhoff's ontology appears to be as follows. There is a fundamental reality which is standard-issue Formless Infinite Oneness, and then there is a multiplicity of elementary physical facts ('observables' taking definite values) out of which everything physical is made. Every single one of those facts is utterly uncaused, both with respect to location in space and time, and the specific value taken. But quantum mechanics gives us the probabilities.

    I do not, so far, see anything illuminating in what he ... (read more)

    My point about probabilities may not be clear. If individual events are genuinely uncaused, then there is equally no explanation for the distribution they exhibit collectively. Statistical reasoning in domains outside of fundamental physics can be justified by distributional hypotheses, e.g. that events are normally distributed, and that hypothesis may have a causal explanation arising in another domain. But when you get to fundamental physics there's no more scope for passing the buck. Justifications for fundamental probabilistic laws can be imagined: for... (read more)

    Indeed, a well-defined probability distribution cries out "deterministic complex system!"; it doesn't really support indeterminism at all. We know how a die roll manages to obey a probability distribution, because it's designed specifically to have several stable states reachable through highly unstable bifurcation points, and the whole thing is made to be as symmetric as possible. But how could the universe manage to obey a probability distribution?
    How could it not? The Kolmogorov axioms are not very restrictive. Obviously, the probability distribution over the state of the universe is not going to be as easy to characterize as the die's Multinomial(1/6,1/6,1/6,1/6,1/6,1/6).


    What I find particularly interesting reading his papers is his emphasis that space and time are features of the macroscopic world, and don't go "all the way down".

    They seem absolute and real to us because of our evolutionary psychology and especially the "space and time" orientation of the visual maps in our brains. He contrasts his view with interpretations which postulate an infinitely sliced spatial manifold which is fundamentally real, but cannot be measured at the finest scales. I'm assuming by that he is referring to MW... (read more)

    interpretations which postulate an infinitely sliced spatial manifold which is fundamentally real

    Strictly speaking, I suppose that is part of the interpretation, but it's a pretty mild part of the interpretation of QM, or at least QFT. Many people expect that this to stop being true in a unification with GR, but that's about physical law, not interpretation.

    Wow...intellectual elitism turned sour and venomous. Your indignation is palpable and, frankly, quite off-putting. I'm not sure what the point of this post is....we should watch our syntax when we express awe?


    Who else has the guts to talk to the audience like this? And hasn't your ratio of surprises gone down as you've learned more about the world?

    The flagrant breaking of rule #12 in this post is one of the things that really makes it priceless. The other is just that it makes a valid point.

    I agree with James Somers. Best post on this blog I've read so far. Best short writing that I've read in a while anywhere, Eliezer.

    I see the point of the post, but it's too harsh. Naive physics (like folk etymology) is important, a facet of the human mind worth studying and paying attention to. It should be overcome, but it can't be replaced by some higher form of intuition. No one can force themselves (him/herself?) to intuit quantum physics. Naive physics can and should be superseded by real physics, but our original intuitions remain intact. The two forms of understanding can live side by side, each with its proper function. Reminded me of a recent piece by Chomsky. Excerpt:

    ... (read more)

    I see the point of the post, but it's too harsh. Naive physics (like folk etymology) is important, a feature of the human mind deserving of study. It is indeed the case that some beliefs arising from intuition should be overcome, but they can't be replaced by some higher form of intuition (no one can force himself to intuit quantum physics). Naive physics can and should be superseded by real physics, but our original intuitions remain intact. The two forms of understanding can live side by side, each with its proper function. See this recent piece by Chomsky, about (among other things) how we've been forced to believe in apparent "absurdities" since Newton.

    This post makes a valuable point, but the point is weakened by too much hyperbole -- or rather by hyberbole that seems like a plausible non-hyperbolic statement that the writer might actually believe.

    Whenever I hear someone describe quantum physics as "weird" - whenever I hear someone bewailing the mysterious effects of observation on the observed, or the bizarre existence of nonlocal correlations, or the incredible impossibility of knowing position and momentum at the same time - then I think to myself: This person will never understand physics... (read more)


    Don't confuse scientific models with truth or reality.

    Quantum mechanics, relativity, Newtonian and Aristotilian dynamics are all models that, in certain situations, do a good job of predicting reality. Light is not a probabilistic model any more than it is a particle or a wave. It is light and every way we currently have of understanding is an inperfect model -- even if we don't understand just how it's imperfect yet. If the history of science has taught us anything, it's that.

    I think the real issue here is not that it is unacceptable to perceive real phenomena as weird or bizarre, but that it is unacceptable to think that something real ought not be so (based on some model of reality) and continue without updating the model or understanding why the weirdness or bizarreness leaks in.

    To pick on C.S. Lewis and the religious in particular, Lewis conflates many times the Laws of Nature with the 'Laws' of Morality. Laws of nature cannot be broken; those of morality most definitely can be and are. And perhaps as another facet of the n... (read more)

    Sometimes people use words like "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird" to mean "counterintuitive". Is that really all that different from noticing that you're confused but not yet deciding whether your model is at fault or your perception of the new information is? When you hear about something that seems like it's at odds with everything you've ever observed, saying that it's "unexpected" at the very least is truthful, isn't it? Whether or not you intend to investigate further and integrate it (or not) into your map is another matter.

    Surprising facts seems like too useful a term to have it be defined out of existence.

    In practice, the term seems to refer to facts that many people find to be surprising.

    When the world turns out to be counter-intuitive you can be surprised by how sucky your intuition is ("An absolute time frame? Seriously?") rather than by the state of the world.
    4Paul Crowley
    No, it makes sense to be surprised by the world - when that surprise is the sound of you updating to a theory that will be less surprised next time. Pedantry codicil: information-theoretic surprise doesn't always indicate that your model needs to be updated. I wasn't expecting the lottery numbers to be what they were on Saturday.

    “That’s weird” is a colloquialism for “I notice that I am confused.” Saying so is an important intermediate step towards understanding... or so I’ve heard. Once you understand, then weirdness is a non-issue -- you are no longer confused.

    Yes, quantum mechanics is weird. It violates my intuitions, and the intuitions of (nearly?) every human. No, we can't rewrite our intuitions, and knowing quantum mechanics is weird is important because if it wasn't weird we might think we didn't have to shut up and integrate. I won't simply accept that reality is weird just because a scientific theory like quantum mechanics implies it is. Especially since there is such a good chance of quantum mechanics being wrong -- since it clashes with General Relativity. I can't say that the successor to quantum-GR wi... (read more)

    It's interesting how we use the word "model" to mean two different, perhaps even opposite things. In this post we have "models" describing "reality", and in logic we have "theories" describing "models".

    For some reason it felt like a big insight to me to realize that computers aren't identical to any particular piece of math, but rather are a model of that math, which can also be studied with other math. Any given piece of computer-related math might ignore some properties of computers that another formalism would bring to the forefront.

    A weak theory could have both reality and mathematically simple structures as its models, from the point of view of an informal metatheory that allows talking about reality (and motivates the theory). A familiar structure (as a "model") can be used both to study a complicated formal system (natural numbers for PA with its other nonstandard models), and a vaguely defined reality (classical mechanics for the real world with its black holes and quantum mechanics).

    Well, speaking your own language, the reality is supposedly not "weird", but nothing prevents a good map of reality to be still weird. There were a lot of moments in development of science when the current, working picture looked weird, until a deeper understanding came. Take, say the expression of quantum basics given by people who failed to "shut up" http://lesswrong.com/lw/q5/quantum_nonrealism/ or just how it was at sufficiently young state. It was the physics of that time (not a reality) and as we agree now it is weird.

    So what do... (read more)

    "What many people refer to as common sense is nothing more than a collection of prejudices accumulated before the age of eighteen." -- Einstein (first quote I ever memorized, at age nine)


    Actual physical reality is "out there" somewhere, and quantum mechanics is a map we use to find our way around parts of it. Often in physics two maps can be identical in their predictions, but differ substantially in the presentation. Hilbert-space quantum mechanics gives us a presentation of complex amplitudes in configuration space. Phase space quantum mechanics is mathematically equivalent, but the presentation is in terms of (possibly negative) probability fields in "real" x,y,z,px,py,pz,t phase space.

    Quantum mechanics does indeed model some real measu... (read more)

    Surprise exists in the map, not in the territory.

    Surprise exists in the territory because the territory contains the map.