You have left the model for the untainted computers unspecified, but let's say that they are producing uniform pseudo-random numbers over some interval, like 0 .. 1. Then your question becomes how do we distinguish the tainted computers, which are only simulating a uniform distribution?
This problem encapsulates the history of pseudo-random number generation algorithms. A researcher named George Marsaglia spent a good part of his career developing algorithms which detected flaws in pseudo-random number generators. The battery of tests is described here, https://en.wikipedia.org/wiki/Diehard_tests, so I won't go over them, but it's a good list. But, as Marsaglia reported in http://www.ics.uci.edu/~fowlkes/class/cs177/marsaglia.pdf, we don't even know all the ways a pseudo-random number generator can go wrong, we discover the catalog of faults as we go merrily assuming that the algorithm is producing numbers with the properties of our ideal distribution. This was discovered because the random numbers were used in simulations which failed to simulate the random processes they were designed to simulate. -- rec -- On Mon, Dec 12, 2016 at 4:45 PM, Nick Thompson <nickthomp...@earthlink.net> wrote: > Everybody, > > > > As usual, when we “citizens” ask mathematical questions, we throw in WAY > too much surplus meaning. > > > > Thanks for all your fine-tuned efforts to straighten me out. > > > > 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. > > > > Let’s leave aside for the moment what kind of –duction that is. I > shouldn’t have thrown that in. And besides, I’ve had enough humiliation > for one day. > > > > > > Nick > > > > Nicholas S. Thompson > > Emeritus Professor of Psychology and Biology > > Clark University > > http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > > *From:* Friam [mailto:friam-boun...@redfish.com] *On Behalf Of *Frank > Wimberly > *Sent:* Monday, December 12, 2016 12:06 PM > *To:* The Friday Morning Applied Complexity Coffee Group < > friam@redfish.com> > *Subject:* Re: [FRIAM] Model of induction > > > > Mathematical induction is a method for proving theorems. "Scientific > induction" is a method for accumulating evidence to support one hypothesis > or another; no proof involved, or possible. > > > > Frank > > Frank Wimberly > Phone (505) 670-9918 > > > > On Dec 12, 2016 11:44 AM, "Owen Densmore" <o...@backspaces.net> wrote: > > What's the difference between mathematical induction and scientific? > > https://en.wikipedia.org/wiki/Mathematical_induction > > > > -- Owen > > > > On Mon, Dec 12, 2016 at 10:44 AM, Robert J. Cordingley < > rob...@cirrillian.com> wrote: > > Based on https://plato.stanford.edu/entries/peirce/#dia - it looks like > abduction (AAA-2) to me - ie developing an educated guess as to which might > be the winning wheel. Enough funds should find it with some degree of > certainty but that may be a different question and should use different > statistics because the 'longest run' is a poor metric compared to say net > winnings or average rate of winning. A long run is itself a data point and > the premise in red (below) is false. > > Waiting for wisdom to kick in. R > > PS FWIW the article does not contain the phrase 'scientific induction' R > > > > On 12/12/16 12:31 AM, Nick Thompson wrote: > > Dear Wise Persons, > > > > Would the following work? > > > > *Imagine you enter a casino that has a thousand roulette tables. The > rumor circulates around the casino that one of the wheels is loaded. So, > you call up a thousand of your friends and you all work together to find > the loaded wheel. Why, because if you use your knowledge to play that > wheel you will make a LOT of money. Now the problem you all face, of > course, is that a run of successes is not an infallible sign of a loaded > wheel. In fact, given randomness, it is assured that with a thousand > players playing a thousand wheels as fast as they can, there will be random > long runs of successes. But **the longer a run of success continues, the > greater is the probability that the wheel that produces those successes is > biased.** So, your team of players would be paid, on this account, for > beginning to focus its play on those wheels with the longest runs. * > > > > FWIW, this, I think, is Peirce’s model of scientific induction. > > > > Nick > > > > Nicholas S. Thompson > > Emeritus Professor of Psychology and Biology > > Clark University > > http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > > > > ============================================================ > > 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 > > > > -- > > Cirrillian > > Web Design & Development > > Santa Fe, NM > > http://cirrillian.com > > 281-989-6272 <(281)%20989-6272> (cell) > > Member Design Corps of Santa Fe > > > ============================================================ > 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 > > > > ============================================================ > 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
