tag:blogger.com,1999:blog-8666091.post5954378640678025378..comments2019-01-10T01:42:37.015+01:00Comments on The Reference Frame: All proofs in natural and social sciences ultimately depend on probabilitiesLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-8666091.post-31850129070058782332013-06-18T21:31:39.602+02:002013-06-18T21:31:39.602+02:00How often does this universe repeat? What is the p...How often does this universe repeat? What is the probability that a universe like this one existed? We can define the properties of this universe as the physical laws and constants that define its symmetries, but we can't test the number of repetitions this universe occurs over the whole number of equivalent repetitions of the probable universes. Therefore, string cosmology or string inflationary models are not statistically testable, so they must be tagged as pseudo-science ;-)Albert Zotkinnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-28074301446342629172013-06-18T19:18:35.981+02:002013-06-18T19:18:35.981+02:00I was eager to express that thought, and so I wrot...I was eager to express that thought, and so I wrote the comment before reading the rest of the article. <br /><br />Sorry :DAngularMannoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-32112872102547430562013-06-18T19:08:32.094+02:002013-06-18T19:08:32.094+02:00Exactly but I actually wrote this thing in the tex...Exactly but I actually wrote this thing in the text above, too. ;-DLuboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-69529977134015222852013-06-18T18:56:32.281+02:002013-06-18T18:56:32.281+02:00In reality even mathematical proofs are not noise-...In reality even mathematical proofs are not noise-free, since they depend on the verification by humans or computers, and there is always a (very tiny) chance of error in those verifications. They just appear rigorous because the significance is so high.AngularMannoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-61821928693470854632013-06-18T15:58:19.965+02:002013-06-18T15:58:19.965+02:00This justification sounds really crazy because in ...This justification sounds really crazy because in the normal formulation of the "Bayesian vs frequentist controversy", it's the Bayesians who should accept the notion of probability in a wider, more inclusive set of situations, in particular, they include various really subjective notions of probability.<br /><br /><br />I can't imagine how someone could reject the frequentist interpretation of probabilities, because it's the more indisputable one.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-27934335359329398472013-06-18T14:38:21.891+02:002013-06-18T14:38:21.891+02:00Briggs and many other Bayesians reject the frequen...Briggs and many other Bayesians reject the frequentist approach in its entirety and regard confidence intervals and p values to be patent absurdities. It's not clear how they would apply Bayes Theorem to the the LHC results. It's also not clear whether Bayesians do not become effective frequentists once the results are in. They seem to be pure Bayesians only for the prior probability.BobSykesnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-2525127968262061152013-06-18T13:43:26.194+02:002013-06-18T13:43:26.194+02:00There is always " some " noisy factor in...There is always " some " noisy factor in nature and therefore is statistics important. As I say there are no exactly two same things in universe. According to my lecture from basic statistics but other area as quantum physics, match cutting machine ,I know that there are no same matches with 30 mm exactly as set up of machine, there is always some difference due to machine. But if there is 28- 32 mm it is OK due to quality (match box properties, burning time). If I interprete it to quantum physics this noise could be due to test equipment performance ... ... But question is how many sigma are adequate to proof theory? This I think in future math should be deal with 8)Peter Golianhttp://www.petervesely.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-90779503493160547902013-06-18T04:23:09.823+02:002013-06-18T04:23:09.823+02:00Thanks. I'll study up.Thanks. I'll study up.lukeleanoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-39784894692062316142013-06-17T22:19:45.175+02:002013-06-17T22:19:45.175+02:00Dear Luke, I wrote the explanation but I understan...Dear Luke, I wrote the explanation but I understand that in order to explain such things, one would have to pedagogically spend about 30 times longer time.<br /><br />The odds become so extreme with the number of sigmas so quickly because the probability is the integral of exp(-x^2) which is faster than exponential.<br /><br />Please think about it or try to study some standardized page/introduction to it, like<br /><br />http://en.wikipedia.org/wiki/Normal_distribution#Standard_deviation_and_tolerance_intervalsLuboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-26088174687948421602013-06-17T21:17:24.961+02:002013-06-17T21:17:24.961+02:00If the chance of a two sigma event is 1 out of 20 ...If the chance of a two sigma event is 1 out of 20 and a three sigma event is 1 out of 300, how does a 5 sigma event get all the way up to 1 out of 3,000,000?<br /><br />To betray my ignorance, in IQ studies the average is 100 and the standard deviation is 15. Roughly one out of seven people have an IQ of 115 or higher, and one out of fourty-nine 130 or higher. Continuing that trend I was under the impression that you keep multiplying by 1/7 to get the chances for each higher sigma: approximately one out of 350 for 3 sigma, one out of 2500 for four sigma, and one out of 17,500 for 5 sigma, corresponding to an IQ of 175, which is already pretty meaningless or so I gather from something you once said because the tests aren't really that good.<br /><br />I feel really dumb asking this question but would like to clear up my confusion.lukeleanoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-18303789540472940702013-06-17T20:16:57.486+02:002013-06-17T20:16:57.486+02:00Thanks Lubos, I have been hoping you would comment...Thanks Lubos, I have been hoping you would comment on this since reading WM Briggs' praise for Ziliak. I think there is plenty of bad science backed up with bad statistics, but these guys are not helping.<br /><br />http://wmbriggs.com/blog/?p=8295SteveBrooklineMAnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-62194589302149615402013-06-17T17:52:13.646+02:002013-06-17T17:52:13.646+02:00Lubos You say
" In fact, as we have often em...Lubos You say<br /> " In fact, as we have often emphasized on this blog, all predictions of fundamental theories of physics ultimately have to be probabilistic (even if you remove all the technological limitations of measurement devices etc.) because quantum mechanical postulates have to be universally valid in the whole Universe and every small or large corner of it." and "Statistical significance is absolutely paramount in the verification of hypotheses in all natural sciences as well as all social sciences that more or less successfully try to emulate the scientific character and success of the natural sciences."<br />I think science should abandon the idea of laws being "valid " which is a human construct which gives an illusion of certainty which most people need.The important thing about laws is simply are they useful. This is the root cause of the division between classical physics at one end and quantum mechanics at the other. Its really a question of complexity Classical physics works by simplifying idealising and isolating systems - thus Newton - Einstein gravity works well enough with small masses eg the solar sysem but does very poorly at the Galactic scale. Similarly a statistical stochastic approach works well for particle physics and quantum mechanical processes at the other end.In between at an intermediate level of complexity neither approach works too well. When studying systems eg climate science and cosmology which consist of multiple resonating oscillatory interacting variables probably which have a secular evolution a different approach is requiered.Such systems are usually inherently untestable and outcomes can only be forecast for relatively small periods of future time by the recognition of patterns (wavelet analysis) that repeat for some periods of time on a scale of interest to humanity.In other words the " validity" of "Laws" in this area is inherently unknowable and is a meaningless concept. This is why Einstein couldn't come up with a UFT- nature isn't designed in in such a way that such a concept is meaningfulNorpagnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-43664160572213937962013-06-17T17:35:42.091+02:002013-06-17T17:35:42.091+02:00What about prior probabilities? By Bayes' Theo...What about prior probabilities? By Bayes' Theorem, if someone assigns a low enough prior to e.g. the existence of the Higgs boson, that person may still obtain a less than 50% probability that it exists even after a succesful 5 sigma test.<br /><br />One might of course argue that it's implausible to arbitrarily assign extremely low probabilities to scientific hypotheses, but "intuitive plausibility" does not seem to be a very rigorous framework to estimate prior probabilities. Is there some way around this problem or am I seeing things incorrectly?Orpheusnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-23037683395016617242013-06-17T17:31:07.985+02:002013-06-17T17:31:07.985+02:00Since economists rarely include error bars isn'...Since economists rarely include error bars isn't this evidence that it is not much of a science? I've been mightily impressed by Morgenstern's book on the much neglected measurement problem in economics. Even something as simple as "the" price of an article is difficult to determine and may not even exist. Which is why I think the employment of calculus in economics is spurious: there are no functions, let alone continuous ones, let alone continuous ones which we can measure. I would go further and say that mathematical equations (using the = sign) also have no place in economics except as a heuristic device (Eg. quantity theory of money). The only thing you are left with is the law of diminishing returns in its various manifestations, which is about the shape (convexity, concavity) of certain curves -- oops, not curves, there are no lines, only fuzzy lines whose fuzziness is not based on a normal distribution.<br /><br />Does this mean that economics is useless? Not at all. You can squeeze a lot out of that little that you have. Adam Smith showed the tendency towards general equilibrium in a free market economy, later refined by the marginal revolution. Also you can make certain predictions involving these two signs: < and >. Just not =<br /><br />At least this is my considered view of the subject, which I happen to love.lukeleanoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-17492612359412664752013-06-17T17:27:51.292+02:002013-06-17T17:27:51.292+02:00Without a thorough understanding of statistics it ...Without a thorough understanding of statistics it would be impossible to develop new pharmaceuticals. Without pharmaceuticals I would be dead. He denies statistical significance! My God!Gene Daynoreply@blogger.com