Hi, Russell S., It's a long time since the old days of the Three Russell's, isn't it? Where have all the Russell's gone? Good to hear from you.
This has been a humbling experience. My brother was a mathematician and he used to frown every time asked him what I thought was a simple mathematical question. So ... with my heart in my hands ... please tell me, why a string of 100 one's , followed by a string of 100 2's, ..., followed by a string of 100 zero's wouldn’t be regarded as random. There must be something more than uniform distribution, eh? Is there a halting problem lurking here? Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -----Original Message----- From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Russell Standish Sent: Tuesday, December 13, 2016 7:59 PM To: 'The Friday Morning Applied Complexity Coffee Group' <friam@redfish.com> Subject: Re: [FRIAM] Model of induction On Mon, Dec 12, 2016 at 02:45:11PM -0700, Nick Thompson wrote: > > > Let’s take out all the colorful stuff and try again. Imagine a thousand > computers, each generating a list of random numbers. Now imagine that for > some small quantity of these computers, the numbers generated are in n a > normal (Poisson?) distribution with mean mu and standard deviation s. Now, > the problem is how to detect these non-random computers and estimate the > values of mu and s. > Your question comes down to: given a set of statistical distributions (ie models), which model best fits a given data source. In your case, presumably you have two models - a uniform distribution and a normal (or Poisson - they're two different distibutions resulting from additive versus multiplicative processes respectively) distribution. The paper to read on this topic is @Article{Clauset-etal07, author = {Aaron Clauset and Cosma R. Shalizi and Mark E. J. Newman}, title = {Power-law Distributions in Empirical Data}, journal = {SIAM Review}, volume = 51, pages = {661-703}, year = 2009, note = {arXiv:0706.1062} } Almost everyone doing work in Complex Systems theory with power laws has been doing it wrong! The way it should be done is to compare a metric called "likelihood" calculated over the data and a model, for the different models in question. I was scheduled to give a talk "Perils of Power Laws" at a local Complex Systems conference in 2007. Originally, when I proposed the topic, I planned to synthesise and collect some of my war stories relating to power law problems - but a couple of months before the conference, someone showed me Clauset's paper. I was so impressed by it, not only superseding anything I could do on the timescale, but also I felt was so important for my colleagues to know about that I took the unprecedented step of presenting someone else's paper at the conference. With full attribution, of course. I still feel it was the most important paper in my field of 2007, and one of the most important papers of this century. Even though it didn't officially get published until 2009 :). Nick's question is unrelated to the question of how to detect whether a source is random or not. A non-uniform random source is one that can be transformed into a uniform random source by a computable transformation, so uniformity is not really a test of randomness. Detecting whether a source is random or not is not a computational feasible task. All one can do is prove that a given source is non-random (by providing an effective generator of the data), but you can never prove a source is truly random, except by exhaustive testing of all Turing machines less than the data's complexity, which suffers from combinatoric computational complexity. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
