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Re: Model of induction

Posted by Eric Charles-2 on Dec 13, 2016; 1:49pm
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588449.html

Roger, this seems to get the heart of the matter! I think we must wonder your final sentence is not begging the question: "This was discovered because the random numbers were used in simulations which failed to simulate the random processes they were designed to simulate."

I'm not saying that is it begging the question, I'm just saying it seems to me like we are peering deep into the rabbit hole. Presumably, we must have rather extreme confidence that the process we are trying to simulate is, in fact, "truly random", AND rather extreme confidence that our simulation it is not simply having a "bad run", as one would expect any random system to have every so often.  Maybe our simulation is doing great, but the process we are trying to simulate is not random in several subtle ways we have not anticipated. How would we know?

(P.S. In hindsight, this is either right at the heart of the matter, or a complete tangent, and I'm not as confident which it is as I was when I started replying.)




-----------
Eric P. Charles, Ph.D.
Supervisory Survey Statistician
U.S. Marine Corps

On Tue, Dec 13, 2016 at 8:24 AM, Roger Critchlow <[hidden email]> wrote:
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 <[hidden email]> 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:[hidden email]] On Behalf Of Frank Wimberly
Sent: Monday, December 12, 2016 12:06 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
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 <a href="tel:(505)%20670-9918" target="_blank" value="+15056709918">(505) 670-9918

 

On Dec 12, 2016 11:44 AM, "Owen Densmore" <[hidden email]> wrote:

What's the difference between mathematical induction and scientific?

 

   -- Owen

 

On Mon, Dec 12, 2016 at 10:44 AM, Robert J. Cordingley <[hidden email]> 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/

 

 

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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
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