All three (Aaron Clauset and Cosma R. Shalizi and Mark E. J. Newman) have given great courses at the SFI summer school.
On Tue, Dec 13, 2016 at 8:41 PM, Nick Thompson <nickthomp...@earthlink.net> wrote: > 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 >
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