On Tue, Dec 13, 2016 at 08:41:12PM -0700, Nick Thompson 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? >
Yes - the modern notion of a random string is that it is uncompressible by a Turing machine shorter than itself. Obviously, you can exploit nonuniformity to provide a compression - eg the way that 'e' and 't' are represented by single . and - respectively provides a compression of random English language phrases. Hence why uniformity is one test of randomness That is why non-uniform random, whilst a thing, must be defined by an algorithmic transformation to a uniform random thing (the algorithmically uncompressible things mentioned above). > Is there a halting problem lurking here? > Absolutely. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] 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
