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Text of the page (random words):
cing since the need to resolve it was so powerful and even having written that i continue to underestimate the power of this effect so if you re psychologically anything like me for the sake of motivation alone i suggest you look for ways to manufacture contradictions out of gaps in your knowledge the second thing to pay attention to is what happens when you resolve the paradox on the most benign level you get a fuller picture of why things are the way they are when you see that they couldn t be some other way in a sense no explanation is complete without this going a bit deeper doing this helps you develop a more integrated mental model you don t have recipes for particular calculations but mechanisms that need to be considered wherever applicable explanations can t just be one off descriptions of unexplained phenomena but instead are part of the machinery that keeps everything adding up to normality so when debugging try to prove that your code works if you don t know the answer to a question find a reasonable seeming answer that evidently doesn t work and ask why if you don t know what something is ask how it s different from something that seems like it should be similar imagine counterexamples and attempt proofs by contradiction why do things this way can manufacture questions of the form why not do things this other way even if the other way is overly simple or you don t have a good explanation for doing it the other way either replacing the former question with the latter can be very effective how does the argument for this position work gives you why doesn t your argument go through in this other domain be especially watchful for incomplete explanations the ones that point to the right answer but don t know their own limits the sky is blue rather than red because of the wavelength dependence of rayleigh scattering but why is it blue rather than violet but be careful the feeling of resolving paradoxes can be extremely satisfying and the impression of depth of explanation that you get can be unduly persuasive it s important to avoid accidentally drilling things that seem confusing are always nothing to worry about even if it s by resolving the confusion instead of suppressing it instead you want to frame this kind of pedagogy as things that seem unsatisfactory are worth poking using points of confusion not to show the power of the right simple foundations to resolve them but to expose new ideas and emphasize that they re necessary to make things work out right a lot of e t jaynes s writing works by setting up veridical paradoxes and knocking them down it has a powerful psychological effect on a certain mindset b as exposition it s both engaging and persuasive but it can easily leave one in ignorance of why the advocated approach might be unsatisfactory you begin to feel like anything opaque or confusing has some natural explanation in terms of what you already know you feel safe black boxing any mystery as essentially already resolved as it awaits only the application of the same foundations as everything else this resolving paradoxes as rhetorical style is especially explicit in jaynes s clearing up mysteries from a 1988 maxent workshop the recent emphasis on the data analysis aspect stems from the availability of computers and the failure of orthodox statistics to keep up with the needs of science this created many opportunities for us about which other speakers will have a great deal to say here but while pursuing these important applications we should not lose sight of the original goal which is in a sense even more fundamental to science therefore in this opening talk we want to point out a field ripe for exploration by giving three examples from widely different areas of how scientic mysteries are cleared up and paradoxes become platitudes when we adopt the jeffreys viewpoint once the logic of it is seen it becomes evident that there are many other mysteries in all sciences calling out for the same treatment in his first example diffusion he states a naive paradox our particles have a symmetric velocity distribution so how do we get nonzero flux anywhere he then describes einstein s derivation of fick s diffusion law as unsatisfactory and then gives a clear derivation using bayes theorem i had to look up einstein s argument c and it s true that it derives the diffusion equation in terms of velocity distributions and particle density over time without reference to any instantaneous flux whereas jaynes version is from the perspective of a single particle at a single instant in time the rest coming in through the prior a particle is more likely to have come from a denser region and gives the flux among other results but the derivation presentation i first learned in stat mech d is at least as clear about what i see as the main point given a surface more particles pass through from the denser side without invoking bayes it s also more immediately obvious to me how to adapt it to other problems although that might just be because i m not as used to the methods jaynes likes did jaynes find that one unsatisfactory too he doesn t bring it up maybe because he hadn t seen it or because it made a weaker point than talking about how handicapped einstein was by not knowing the true logic of science i d guess it was unsatisfactory to him since from a certain perspective it still depends on forward integration that jaynes prefers to think about as prior information although it can be trivially rephrased but why should i care about deriving a flux from a probability distribution for a single particle rather than from the perspective of a single surface that seems less important to me than the clarity of the moral lesson and the general adaptability and the paradox is still resolved by the same moral lesson and by noting that while that the statistical velocity distribution of all particles has zero mean you can still have flux across a specified surface the mean velocity only tells you about the motion of the particles center of mass which indeed won t move under free diffusion it s natural that taking some subset of the particles should give you a different distribution and there are natural ways of thinking about it that aren t in jaynes s terms just think of the motion of rocks in saturn s rings e thus a slightly more specific warning a benevolent complete paradox pedagogy needs to remember that the resolution to a paradox e g how do we get net particle flux anywhere if the velocity distribution is symmetric has to explain a correct solution f why other solutions with a claim to correctness are unsatisfactory g why it s not a paradox i e why you shouldn t have expected the naive reasoning to work h ideally making it clear that the reason it s not a paradox is somewhat independent of any particular resolution itself if you only give one or two of these then you re at greater risk of being unduly persuasive regarding the one true way ness of your methods and it s not just a matter of intellectual etiquette or scrupulous hedging you really won t have explained everything there will be lingering confusion noticed or otherwise how far could this be taken could one organize a physics course around rejecting naive arguments for false conclusions of course a lot of classic paradoxes are uninteresting edge cases but you can take care not to make it a game of spot the hidden violated assumption that s never violated in practice how much thermodynamics can you get with why doesn t this perpetual motion device work what do we lose by presenting quantum mechanics by fiat do we beat into students an instinct for suppressing their confusion and accepting non explanations my experience is that typical undergrad courses tend to leave students confused about what exactly is special or surprising about quantum mechanics at least until they start trying to show whether various experimental results have semi classical explanations i it certainly feels like a lot of my new insights come from asking why i can t just do the stupid obvious thing or how two vaguely contradictory things can be compatible in contrast to say thinking really hard about how to solve a given problem but it s not the answer to everything plenty of approaches are better than just thinking real hard and you can get even trickier you notice that pressure lowers the freezing point so if you re operating at the right point on the phase diagram you can freeze the water by decreasing pressure above it thus lifting your weight and doing work then you let it warm up and melt then increase the pressure and cool it back down to get where you started in the liquid phase giving you a different engine cycle where it s arguably harder to show why it can never give perfect or better efficiency back as it sounds like eliezer yudkowsky experienced and i think unfortunately tried to emulate back section 4 in his brownian motion paper which is roughly how i learned to think about transport in condensed matter i think mostly because it gives a good entry point into the sommerfeld approximation back which is basically the one on wikipedia and more recent than einstein s but still prior to 1988 back from this perspective jaynes avoids making clear why you shouldn t have expected the total velocity distribution alone to tell you about flux back you can incorporate information about where a particle came from to get a velocity distribution from the perspective of a single particle which can be used to calculate the flux back forward integration at least to jaynes back the overall mean velocity tells us about the motion of the mean of the particle distribution involving total flux across all surfaces which is indeed zero in the absence of boundaries or the density going off to infinity and is totally consistent with nonzero flux across any given surface but for a given surface nearby particles may be more likely to have come from one direction so it doesn t make sense to reason from just the overall distribution without incorporating that additional information from the particles of interest back jaynes himself spent a while attempting a semiclassical account of the lamb shift which despite some progress ended with losing his 100 bet on it back and you can get even trickier you notice that pressure lowers the freezing point so if you re operating at the right point on the phase diagram you can freeze the water by decreasing pressure above it thus lifting your weight and doing work then you let it warm up and melt then increase the pressure and cool it back down to get where you started in the liquid phase giving you a different engine cycle where it s arguably harder to show why it can never give perfect or better efficiency as it sounds like eliezer yudkowsky experienced and i think unfortunately tried to emulate section 4 in his brownian motion paper which is roughly how i learned to think about transport in condensed matter i think mostly because it gives a good entry point into the sommerfeld approximation which is basically the one on wikipedia and more recent than einstein s but still prior to 1988 from this perspective jaynes avoids making clear why you shouldn t have expected the total velocity distribution alone to tell you about flux you can incorporate information about where a particle came from to get a velocity distribution from the perspective of a single particle which can be used to calculate the flux forward integration at least to jaynes the overall mean velocity tells us about the motion of the mean of the particle distribution involving total flux across all surfaces which is indeed zero in the absence of boundaries or the density going off to infinity and is totally consistent with nonzero flux across any given surface but for a given surface nearby particles may be more likely to have come from one direction so it doesn t make sense to reason from just the overall distribution without incorporating that additional information from the particles of interest jaynes himself spent a while attempting a semiclassical account of the lamb shift which despite some progress ended with losing his 100 bet on it leave a comment december 2 2017 january 14 2019 whales no comments link on proof and progress in mathematics william thurston s on proof and progress in mathematics 1994 17 page pdf is good unassuming philosophy of science i think it s pretty well known but given my goals for link posts i m not worried about being redundant leave a comment july 15 2017 whales no comments the whaaales political spectrum quiz 1 you are analyzing diffraction of fullerenes buckyballs are a particles b waves continue reading leave a comment june 25 2017 july 15 2017 whales no comments a partial taxonomy of aesthetic compressibility some art doesn t need to be experienced to be mostly apprehended a a good enough description suffices maybe the thing follows convention too closely or the author is in a rut but less redundant art can still internally have a variety of flavors of compressibility signposting rather than do the thing loudly proclaim that you re doing the thing candidates open world crpgs inception guardians of the galaxy a lot of experimental things pretension may be a subset of this inflation anything you can say in a sentence say in a paragraph anything you can say in a paragraph say in an essay chapter post anything you can say in a blog post say in a book examples most popular nonfiction a lot of tv also seems to do this mostly out of lack of confidence that people will get it commodification package your work such that it becomes fungible with similar work examples insert thing from genre you don t like gimmickry distinguish yourself by doing something whose main feature is that it distinguishes yourself examples i can t actually think of any that i agree with seasoning use drop in elements that have the same effect regardless of context the context insensitivity lets it feel manipulative even if it works the seasoning elements don t need to be clichés which i d instead describe as conveying the same meaning regardless of context both do generally rely on external conventions examples some pixar shorts and movies lots of movie and game soundtracks whether or not these are bad depends on your goal done right you can use these as tools to cheaply make things more powerfully affect a broader audience it isn t trickery it s effective artistry moreover the above terms are just ways of pointing to what didn t work for you and the sense in which it failed and pretty much can t themselves constitute criticism a gimmick is usually intended to have an effect but for whatever reason it was outweighed for you by its own distinctiveness by calling it a gimmick you haven t actually explained how it failed to have that effect by calling something seasoning you re just asserting that it failed to connect with the work s substance why is the thing inflated and not taking advantage of the effe...