Comments for Good Math, Bad Math http://scientopia.org/blogs/goodmath Just another Scientopia Blogs site Wed, 22 May 2013 21:08:33 +0000 hourly 1 http://wordpress.org/?v=3.5.1 Comment on New Dimensions of Crackpottery by Ben http://scientopia.org/blogs/goodmath/2013/02/26/new-dimensions-of-crackpottery/#comment-32546 Ben Wed, 22 May 2013 21:08:33 +0000 http://scientopia.org/blogs/goodmath/?p=2131#comment-32546 Here's a funny one from Conservapedia about e=mc^2:

http://www.conservapedia.com/E%3Dmc%C2%B2

]]> Comment on Fuzzy Logic vs Probability by Shawn http://scientopia.org/blogs/goodmath/2011/02/02/fuzzy-logic-vs-probability/#comment-32543 Shawn Fri, 17 May 2013 13:26:10 +0000 http://scientopia.org/blogs/goodmath/?p=1300#comment-32543 In my opinion (and many others) Fuzzy Logic is nothing than a way of thinking of degree of truth of statements. Let's take the example in this post: "degree of tallness". To represent the degree of tallness of two persons, A and B, with 2.5 meters and 2.0 meters respectively, one may simply use the ratio of heights: S1 = "A is tall", S2 = "B is tall", S3 = "the degree of truth of S1 is 1.25 times higher than the degree of truth of S2".

]]> Comment on Probability and Interpretations by eric http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32542 eric Thu, 16 May 2013 17:40:53 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32542 The coin-flip example is interesting because consideration of unfair coins shows how the two interpretations can intermix. A frequentist needs some bayesian concepts to deal with them (i.e., unfair coins make clear that we are starting with ideas about a coin's properties, which we update - we are not starting by accessing a coin's properties directly). Meanwhile, the bayesian is going to have a difficult time making sense of the difference if they don't acknowledge that there are such things as fair and unfair coins.

IMO this is a case where we have two models, both useful in a wide variety of overlapping cases, but each of which deals with some questions more quickly and more intuitively than the other. Sure, we could use one of them to solve all (relevant) math problems, but if flipping between them solves problems quicker and easier, why not do that? I CAN use a claw hammer to screw in a screw, or a screwdriver to drive in a nail...but why would I want to?

]]> Comment on Probability and Interpretations by Bard Bloom http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32541 Bard Bloom Wed, 15 May 2013 14:09:51 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32541 The bitterest fights are between Orthodox vs. Conservative Bayesians.

]]> Comment on Probability and Interpretations by Jonas http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32540 Jonas Tue, 14 May 2013 19:24:56 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32540 What about the propensity interpretation of probabilities? This is a theory Karl Popper vouched for (among others) and tries to explain the origin of observable frequencies. I guess it's more metaphysics than statistics and mathematics.

]]> Comment on Probability and Interpretations by John Miller http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32539 John Miller Tue, 14 May 2013 05:24:06 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32539 http://xkcd.com/1132/ because it need to be done.

]]> Comment on Probability and Interpretations by Brandon Wilson http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32538 Brandon Wilson Tue, 14 May 2013 02:50:36 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32538 E. T. Jaynes' book Probability Theory is a must read for anyone interested in really digging into probability theory.

It derives probability theory from essentially three intuitive properties we'd like probabilities to have.

As a bonus, it shows precisely under what conditions typical frequentist/Bayesian assumptions hold, sort of laying to rest any need for philosophical debates about which is better.

]]> Comment on Probability and Interpretations by John Armstrong http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32537 John Armstrong Tue, 14 May 2013 02:23:01 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32537 Don't worry, Robert. Troll comment is trolly.

]]> Comment on Probability and Interpretations by lily http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32536 lily Tue, 14 May 2013 00:20:57 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32536 This is cool. I did not know that people were so passionate about their interpretations of probability.

Infinite probability distributions are really confusing. I never understand whether the probability of the outcome depends on the number of points corresponding to an outcome or to some measure of that set. shrug.

]]> Comment on Probability and Interpretations by Robert http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/#comment-32535 Robert Tue, 14 May 2013 00:16:53 +0000 http://scientopia.org/blogs/goodmath/?p=2180#comment-32535 What do you mean when you say probabilites are algebraically closed? Under what operation? And what do you mean they satisfy a 2 norm instead of a 1 norm? Are you suggesting that a pdf's L2 norm is 1? If so, this is wrong. Indeed, part of the definition of a pdf is that is 1 in L1 norm. (Of course, when you are dealing with discrete probabilities, the integral is a sum, but if you know measure theory, you will know this is also an integral.)

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