Re: Model of induction

Posted by Nick Thompson on Dec 12, 2016; 9:45pm
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588446.html

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 [phone]

 

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