Friam

Model of induction

Classic

List

Threaded

41 messages Options

123

Nick Thompson

Model of induction

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

Robert J. Cordingley

Re: Model of induction

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 (cell)
Member Design Corps of Santa Fe

Eric Charles-2

Re: Model of induction

I'll assume you meant something generic like: "focus its play on those wheels with the longest runs [of unusual results, whatever form that might take]."

With that in mind, your test better work. If it doesn't, then casinos and players have wasted a lot of time worrying about loaded equipment.

Or, to phrase it differently, if I'm the casino manager, and you tell me we have a problem with a loaded wheel, you'll have my attention. However, if you also tell me that someone following the proposed plan couldn't possibly detect the difference between the loaded wheel and a non-loaded one, then you'll lose my attention, because apparently you don't know what the word "loaded" means.

Now, you (Nick) might be pointing out that if we spun each wheel a million times, then concluded which one was the loaded one, and made a fortune betting smartly for the next million spins... it is still the case that our conclusion may be drawn into suspicion during the third million spins. That strikes me as a different problem... That is, the question of the best way to make money off of a loaded wheel shouldn't be held up by generic reference to the problem of induction.

-----------
Eric P. Charles, Ph.D.
Supervisory Survey Statistician

U.S. Marine Corps

[hidden email]

On Mon, Dec 12, 2016 at 12:44 PM, 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/
============================================================
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 <a href="tel:(281)%20989-6272" target="_blank" value="+12819896272">281-989-6272 (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

Owen Densmore

Re: Model of induction

Administrator

In reply to this post by Robert J. Cordingley

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/
============================================================
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 <a href="tel:(281)%20989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Frank Wimberly-2

Re: 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" <[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/
============================================================
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 <a href="tel:(281)%20989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Roger Critchlow-2

Re: Model of induction

Seems like the abduction step would be assuming that there are loaded wheels before you have any empirical evidence.

A wheel could be fat-tailed, tending to longer runs, without being biased toward any particular numbers. There would be an incentive to bet on a run continuing, but no particular number would be more likely to have long runs. That wouldn't be a loaded wheel in the usual understanding of crooked gambling devices. But it would be the sort of device to encourage gamblers to believe they have a hot hand.

-- rec --

On Mon, Dec 12, 2016 at 2:06 PM, Frank Wimberly <[hidden email]> wrote:

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" value="+15056709918" target="_blank">(505) 670-9918
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/
============================================================
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 <a href="tel:(281)%20989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Frank Wimberly-2

Re: Model of induction

In reply to this post by Frank Wimberly-2

Example of mathematical induction:

Theorem: The sum of the first n integers is n(n+1)/2.

Proof: If n=1, check. We assume 1+2+...m=m(m+1)/2 we need to show that if n=m+1 then 1+2+...+n = n(n+1)/2. But we know it's = m(m+1)/2 + n which is = (n-1)n/2 + n =

(n^2 - n)/2 +n=n^2/2 -n/2 +n =n^2/2 +n/2=

n(n+1)/2. QED

Frank Wimberly
Phone (505) 670-9918

On Dec 12, 2016 12:06 PM, "Frank Wimberly" <[hidden email]> wrote:

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" value="+15056709918" target="_blank">(505) 670-9918
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/
============================================================
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 <a href="tel:(281)%20989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Steve Smith

Re: Model of induction

In reply to this post by Roger Critchlow-2

Eudamonic Pie anyone?

https://en.wikipedia.org/wiki/The_Eudaemonic_Pie

It seems that (some) roulette wheels (being imperfect, analog devices) can and have been predicted statistically.... by NM boys born and bred... This was all still a fresh story when I met Doyne (and eventually Norm) back in the early 80s.

On 12/12/16 12:23 PM, Roger Critchlow wrote:

Seems like the abduction step would be assuming that there are loaded wheels before you have any empirical evidence.

A wheel could be fat-tailed, tending to longer runs, without being biased toward any particular numbers. There would be an incentive to bet on a run continuing, but no particular number would be more likely to have long runs. That wouldn't be a loaded wheel in the usual understanding of crooked gambling devices. But it would be the sort of device to encourage gamblers to believe they have a hot hand.

-- rec --
On Mon, Dec 12, 2016 at 2:06 PM, Frank Wimberly <[hidden email]> wrote:
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 moz-do-not-send="true" href="tel:%28505%29%20670-9918" value="+15056709918" target="_blank">(505) 670-9918
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/
============================================================
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 <a moz-do-not-send="true" href="tel:%28281%29%20989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Nick Thompson

Re: Model of induction

In reply to this post by Owen Densmore

O. Everything. Mathematical induction is a form of Deduction. Alas. N

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 Owen Densmore
Sent: Monday, December 12, 2016 11:45 AM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Model of induction

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/
============================================================
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
<a href="tel:(281)%20989-6272" target="_blank">281-989-6272 (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

David Eric Smith

Re: Model of induction

In reply to this post by Robert J. Cordingley

Hi Robert,

I worry about mixing technical and informal claims, and making it hard for people with different backgrounds to track which level the conversation is operating at.

You said:

> A long run is itself a data point and the premise in red (below) is false.

and the premise in red (I am not using an RTF sender) from Nick was:

>> But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased.

Whether or not it is false actually depends on what “probability” one means to be referring to. (I am ending many sentences with prepositions; apologies.)

It is hard to say that any “probability” inherently is “the” probability that the wheel produces those successes. A wheel is just a wheel (Freud or no Freud); to assign it a probability requires choosing a set and measure within which to embed it, and that always involves other assumptions by whoever is making the assertion.

Under typical usages, yes, there could be some kind of “a priori” (or, in Bayesian-inference language, “prior”) probability that the wheel has a property, and yes, that probability would not be changed by testing how many wins it produces.

On the other hand, the Bayesian posterior probability, obtained from the prior (however arrived-at) and the likelihood function, would indeed put greater weight on the wheel that is loaded, (under yet more assumptions of independence etc. to account for Roger’s comment that long runs are not the only possible signature of loading, and your own comments as well), the more wins one had seen from it relatively.

I _assume_ that this intuition for how one updates Bayesian posteriors is behind Nick’s common-language premise that “the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased”. That would certainly have been what I meant in a short-hand for the more laborious Bayesian formula.

For completeness, the Bayesian way of choosing a meaning for probabilities updated by observations is the following.

Assume two random variables, M and D, which take values respectively standing for a Model or hypothesis, and an observed-value or Datum. So: hypothesis: this wheel and not that one is loaded. datum: this wheel has produced relatively more wins.

Then, by some means, commit to what probability you assign to each value of M before you make an observation. Call it P(M). This is your Bayesian prior (for whether or not a certain wheel is loaded). Maybe you admit the possibility that some wheel is loaded because you have heard it said, and maybe you even assume that precisely one wheel in the house is loaded, only you don’t know which one. Lots of forms could be adopted.

Next, we assume a true, physical property of the wheel is the probability distribution with which it produces wins, given whether it is or is not loaded. Notation is P(D|M). This is called the _likelihood function_ for data given a model.

The Bayes construction is to say that the structure of unconditioned and conditioned probabilites requires that the same joint probability be arrivable-at in either of two ways:
P(D,M) = P(D|M)P(M) = P(M|D)P(D).

We have had to introduce a new “conditioned” probability, called the Bayesian Posterior, P(M|D), which treats the model as if it depended on the data. But this is just chopping a joint space of models and data two ways, and we are always allowed to do that. The unconditioned probability for data values, P(D), is usually expressed as the sum of P(D|M)P(M) over all values that M can take. That is the probability to see that datum any way it can be produced, if the prior describes that world correctly. In any case, if the prior P(M) was the best you can do, then P(D) is the best you can produce from it within this system.

Bayesian updating says we can consistently assign this posterior probability as: P(M|D) = P(D|M) P(M) / P(D).

P(M|D) obeys the axioms of a probability, and so is eligible to be the referent of Nick’s informal claim, and it would have the property he asserts, relative to P(M).

Of course, none of this ensures that any of these probabilities is empirically accurate; that requires efforts at calibrating your whole system. Cosma Shalizi and Andrew Gelman have some lovely write-up of this somewhere, which should be easy enough to find (about standard fallacies in use of Bayesian updating, and what one can do to avoid committing them naively). Nonetheless, Bayesian updating does have many very desirable properties of converging on consistent answers in the limit of long observations, and making you less sensitive to mistakes in your original premises (at least under many circumstances, inluding roulette wheels) than you were originally.

To my mind, none of this grants probabilities from God, which then end discussions. (So no buying into “objective Bayesianism”.) What this all does, in the best of worlds, is force us to speak in complete sentences about what assumptions we are willing to live with to get somewhere in reasoning.

All best,

Eric

> On Dec 12, 2016, at 12:44 PM, 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/
>>
>>
>>
>> ============================================================
>> 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 (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

Nick Thompson

Re: Model of induction

In reply to this post by Frank Wimberly-2

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 (505) 670-9918

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/
============================================================
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
<a href="tel:(281)%20989-6272" target="_blank">281-989-6272 (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

Robert J. Cordingley

Re: Model of induction

In reply to this post by David Eric Smith

Hi Eric

I was remembering that if you tossed a perfectly balanced coin and got
10 or 100 heads in a row it says absolutely nothing about the future
coin tosses nor undermines the initial condition of a perfectly balanced
coin. Bayesian or not the next head has a 50:50 probability of
occurring. If you saw a player get a long winning streak would you
really place your bet in the same way on the next spin? I would need to
see lots of long runs (data points) to make a choice on which tables to
focus my efforts and we can then employ Bayesian or formal statistics to
the problem.

I think your excellent analysis was founded on 'relative wins' which is
fine by me in identifying a winning wheel, as against 'the longer a run
of success' finding one which I'd consider very 'dodgy'.

Thanks Robert

On 12/12/16 1:56 PM, Eric Smith wrote:

> Hi Robert,
>
> I worry about mixing technical and informal claims, and making it hard for people with different backgrounds to track which level the conversation is operating at.
>
> You said:
>
>> A long run is itself a data point and the premise in red (below) is false.
> and the premise in red (I am not using an RTF sender) from Nick was:
>
>>> But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased.
> Whether or not it is false actually depends on what “probability” one means to be referring to. (I am ending many sentences with prepositions; apologies.)
>
> It is hard to say that any “probability” inherently is “the” probability that the wheel produces those successes. A wheel is just a wheel (Freud or no Freud); to assign it a probability requires choosing a set and measure within which to embed it, and that always involves other assumptions by whoever is making the assertion.
>
> Under typical usages, yes, there could be some kind of “a priori” (or, in Bayesian-inference language, “prior”) probability that the wheel has a property, and yes, that probability would not be changed by testing how many wins it produces.
>
> On the other hand, the Bayesian posterior probability, obtained from the prior (however arrived-at) and the likelihood function, would indeed put greater weight on the wheel that is loaded, (under yet more assumptions of independence etc. to account for Roger’s comment that long runs are not the only possible signature of loading, and your own comments as well), the more wins one had seen from it relatively.
>
> I _assume_ that this intuition for how one updates Bayesian posteriors is behind Nick’s common-language premise that “the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased”. That would certainly have been what I meant in a short-hand for the more laborious Bayesian formula.
>
>
> For completeness, the Bayesian way of choosing a meaning for probabilities updated by observations is the following.
>
> Assume two random variables, M and D, which take values respectively standing for a Model or hypothesis, and an observed-value or Datum. So: hypothesis: this wheel and not that one is loaded. datum: this wheel has produced relatively more wins.
>
> Then, by some means, commit to what probability you assign to each value of M before you make an observation. Call it P(M). This is your Bayesian prior (for whether or not a certain wheel is loaded). Maybe you admit the possibility that some wheel is loaded because you have heard it said, and maybe you even assume that precisely one wheel in the house is loaded, only you don’t know which one. Lots of forms could be adopted.
>
> Next, we assume a true, physical property of the wheel is the probability distribution with which it produces wins, given whether it is or is not loaded. Notation is P(D|M). This is called the _likelihood function_ for data given a model.
>
> The Bayes construction is to say that the structure of unconditioned and conditioned probabilites requires that the same joint probability be arrivable-at in either of two ways:
> P(D,M) = P(D|M)P(M) = P(M|D)P(D).
>
> We have had to introduce a new “conditioned” probability, called the Bayesian Posterior, P(M|D), which treats the model as if it depended on the data. But this is just chopping a joint space of models and data two ways, and we are always allowed to do that. The unconditioned probability for data values, P(D), is usually expressed as the sum of P(D|M)P(M) over all values that M can take. That is the probability to see that datum any way it can be produced, if the prior describes that world correctly. In any case, if the prior P(M) was the best you can do, then P(D) is the best you can produce from it within this system.
>
> Bayesian updating says we can consistently assign this posterior probability as: P(M|D) = P(D|M) P(M) / P(D).
>
> P(M|D) obeys the axioms of a probability, and so is eligible to be the referent of Nick’s informal claim, and it would have the property he asserts, relative to P(M).
>
> Of course, none of this ensures that any of these probabilities is empirically accurate; that requires efforts at calibrating your whole system. Cosma Shalizi and Andrew Gelman have some lovely write-up of this somewhere, which should be easy enough to find (about standard fallacies in use of Bayesian updating, and what one can do to avoid committing them naively). Nonetheless, Bayesian updating does have many very desirable properties of converging on consistent answers in the limit of long observations, and making you less sensitive to mistakes in your original premises (at least under many circumstances, inluding roulette wheels) than you were originally.
>
> To my mind, none of this grants probabilities from God, which then end discussions. (So no buying into “objective Bayesianism”.) What this all does, in the best of worlds, is force us to speak in complete sentences about what assumptions we are willing to live with to get somewhere in reasoning.
>
> All best,
>
> Eric
>
>
>> On Dec 12, 2016, at 12:44 PM, 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/
>>>
>>>
>>>
>>> ============================================================
>>> 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 (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
>
>

gepr

probability vs. statistics (was Re: Model of induction)

In reply to this post by Nick Thompson

I have a large stash of nonsense I could write that might be on topic. But the topic coincides with an argument I had about 2 weeks ago. My opponent said something generalizing about the use of statistics and I made a comment (I thought was funny, but apparently not) that I don't really know what statistics _is_. I also made the mistake of claiming that I _do_ know what probability theory is. [sigh] Fast forward through lots of nonsense to the gist:

My opponent claims that time (the experience of, the passage of, etc.) is required by probability theory. He seemed to hinge his entire argument on the vernacular concept of an "event". My argument was that, akin to the idea that we discover (rather than invent) math theorems, probability theory was all about counting -- or measurement. So, it's all already there, including things like power sets. There's no need for time to pass in order to measure the size of any given subset of the possibility space.

In any case, I'm a bit of a jerk, obviously. So, I just assumed I was right and didn't look anything up. But after this conversation here, I decided to spend lunch doing so. And ran across the idea that probability is the forward map (given the generator, what phenomena will emerge?) and statistics is the inverse map (given the phenomena you see, what's the generator?). And although neither of these really require time, per se, there is a definite role for [ir]reversibility or at least asymmetry.

So, does anyone here have an opinion on the ontological status of one or both probability and/or statistics? Am I demonstrating my ignorance by suggesting the "events" we study in probability are not (identical to) the events we experience in space & time?

On 12/11/2016 11:31 PM, Nick Thompson wrote:
> 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.

--
☣ glen

============================================================
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

uǝʃƃ ⊥ glen

Robert Wall

Re: Model of induction

In reply to this post by Robert J. Cordingley

Eric,

(I am ending many sentences with prepositions; apologies.)

Modern language usage manuals, for example, Garner's Modern American Usage [2009: 3rd Edition, page 654], advise that you no longer have to worry about ending a sentence with a preposition. As Winston Churchill once quipped when criticized for occasionally ending a sentence with a preposition, "This is the type of errant pedantry up with which I will not put." 🤐

Cheers,

Robert W.

On Mon, Dec 12, 2016 at 3:21 PM, Robert J. Cordingley <[hidden email]> wrote:

Hi Eric

I was remembering that if you tossed a perfectly balanced coin and got 10 or 100 heads in a row it says absolutely nothing about the future coin tosses nor undermines the initial condition of a perfectly balanced coin. Bayesian or not the next head has a 50:50 probability of occurring. If you saw a player get a long winning streak would you really place your bet in the same way on the next spin? I would need to see lots of long runs (data points) to make a choice on which tables to focus my efforts and we can then employ Bayesian or formal statistics to the problem.

I think your excellent analysis was founded on 'relative wins' which is fine by me in identifying a winning wheel, as against 'the longer a run of success' finding one which I'd consider very 'dodgy'.

Thanks Robert

On 12/12/16 1:56 PM, Eric Smith wrote:

Hi Robert,

I worry about mixing technical and informal claims, and making it hard for people with different backgrounds to track which level the conversation is operating at.

You said:

A long run is itself a data point and the premise in red (below) is false.

and the premise in red (I am not using an RTF sender) from Nick was:

But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased.

Whether or not it is false actually depends on what “probability” one means to be referring to. (I am ending many sentences with prepositions; apologies.)

It is hard to say that any “probability” inherently is “the” probability that the wheel produces those successes. A wheel is just a wheel (Freud or no Freud); to assign it a probability requires choosing a set and measure within which to embed it, and that always involves other assumptions by whoever is making the assertion.

Under typical usages, yes, there could be some kind of “a priori” (or, in Bayesian-inference language, “prior”) probability that the wheel has a property, and yes, that probability would not be changed by testing how many wins it produces.

On the other hand, the Bayesian posterior probability, obtained from the prior (however arrived-at) and the likelihood function, would indeed put greater weight on the wheel that is loaded, (under yet more assumptions of independence etc. to account for Roger’s comment that long runs are not the only possible signature of loading, and your own comments as well), the more wins one had seen from it relatively.

I _assume_ that this intuition for how one updates Bayesian posteriors is behind Nick’s common-language premise that “the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased”. That would certainly have been what I meant in a short-hand for the more laborious Bayesian formula.

For completeness, the Bayesian way of choosing a meaning for probabilities updated by observations is the following.

Assume two random variables, M and D, which take values respectively standing for a Model or hypothesis, and an observed-value or Datum. So: hypothesis: this wheel and not that one is loaded. datum: this wheel has produced relatively more wins.

Then, by some means, commit to what probability you assign to each value of M before you make an observation. Call it P(M). This is your Bayesian prior (for whether or not a certain wheel is loaded). Maybe you admit the possibility that some wheel is loaded because you have heard it said, and maybe you even assume that precisely one wheel in the house is loaded, only you don’t know which one. Lots of forms could be adopted.

Next, we assume a true, physical property of the wheel is the probability distribution with which it produces wins, given whether it is or is not loaded. Notation is P(D|M). This is called the _likelihood function_ for data given a model.

The Bayes construction is to say that the structure of unconditioned and conditioned probabilites requires that the same joint probability be arrivable-at in either of two ways:
P(D,M) = P(D|M)P(M) = P(M|D)P(D).

We have had to introduce a new “conditioned” probability, called the Bayesian Posterior, P(M|D), which treats the model as if it depended on the data. But this is just chopping a joint space of models and data two ways, and we are always allowed to do that. The unconditioned probability for data values, P(D), is usually expressed as the sum of P(D|M)P(M) over all values that M can take. That is the probability to see that datum any way it can be produced, if the prior describes that world correctly. In any case, if the prior P(M) was the best you can do, then P(D) is the best you can produce from it within this system.

Bayesian updating says we can consistently assign this posterior probability as: P(M|D) = P(D|M) P(M) / P(D).

P(M|D) obeys the axioms of a probability, and so is eligible to be the referent of Nick’s informal claim, and it would have the property he asserts, relative to P(M).

Of course, none of this ensures that any of these probabilities is empirically accurate; that requires efforts at calibrating your whole system. Cosma Shalizi and Andrew Gelman have some lovely write-up of this somewhere, which should be easy enough to find (about standard fallacies in use of Bayesian updating, and what one can do to avoid committing them naively). Nonetheless, Bayesian updating does have many very desirable properties of converging on consistent answers in the limit of long observations, and making you less sensitive to mistakes in your original premises (at least under many circumstances, inluding roulette wheels) than you were originally.

To my mind, none of this grants probabilities from God, which then end discussions. (So no buying into “objective Bayesianism”.) What this all does, in the best of worlds, is force us to speak in complete sentences about what assumptions we are willing to live with to get somewhere in reasoning.

All best,

Eric

On Dec 12, 2016, at 12:44 PM, 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/

============================================================
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

<a href="tel:281-989-6272" value="+12819896272" target="_blank">281-989-6272 (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

--
Cirrillian
Web Design & Development
Santa Fe, NM
http://cirrillian.com
<a href="tel:281-989-6272" value="+12819896272" target="_blank">281-989-6272 (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

Nick Thompson

Re: Model of induction

In reply to this post by Robert J. Cordingley

Robert,

I want to get back to you eventually concerning what kind of -duction we are
talking about here.

But before that< I want to clear up any other confusions I may have.

Let's take your coin example; it's all my poor civilian brain can really
handle.

You are quite right that if coin is a balanced coin, a run of 100 heads is
no reason to believe that the next flip will be a heads. On the other hand,
after 100 heads, what is the probability that the coin is balanced? I used
to play a game in my freshman class in which I would bring in "my own
special" coin, and flip it for them. After each flip, I would ask them
whether they still believed that the coin was fair. What amazed me was with
what consistency people fell off the wagon between .10 and .05. The would
help to answer the question, later on. Why psychologists tended to use the
.05 level of significance.

N

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/

-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Robert J.
Cordingley
Sent: Monday, December 12, 2016 3:21 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Model of induction

Hi Eric

I was remembering that if you tossed a perfectly balanced coin and got
10 or 100 heads in a row it says absolutely nothing about the future coin
tosses nor undermines the initial condition of a perfectly balanced coin.
Bayesian or not the next head has a 50:50 probability of occurring. If you
saw a player get a long winning streak would you really place your bet in
the same way on the next spin? I would need to see lots of long runs (data
points) to make a choice on which tables to focus my efforts and we can then
employ Bayesian or formal statistics to the problem.

I think your excellent analysis was founded on 'relative wins' which is fine
by me in identifying a winning wheel, as against 'the longer a run of
success' finding one which I'd consider very 'dodgy'.

Thanks Robert

On 12/12/16 1:56 PM, Eric Smith wrote:
> Hi Robert,
>
> I worry about mixing technical and informal claims, and making it hard for
people with different backgrounds to track which level the conversation is
operating at.
>
> You said:
>
>> A long run is itself a data point and the premise in red (below) is
false.
> and the premise in red (I am not using an RTF sender) from Nick was:
>
>>> But the longer a run of success continues, the greater is the
probability that the wheel that produces those successes is biased.
> Whether or not it is false actually depends on what "probability" one
> means to be referring to. (I am ending many sentences with
> prepositions; apologies.)
>
> It is hard to say that any "probability" inherently is "the" probability
that the wheel produces those successes. A wheel is just a wheel (Freud or
no Freud); to assign it a probability requires choosing a set and measure
within which to embed it, and that always involves other assumptions by
whoever is making the assertion.
>
> Under typical usages, yes, there could be some kind of "a priori" (or, in
Bayesian-inference language, "prior") probability that the wheel has a
property, and yes, that probability would not be changed by testing how many
wins it produces.
>
> On the other hand, the Bayesian posterior probability, obtained from the
prior (however arrived-at) and the likelihood function, would indeed put
greater weight on the wheel that is loaded, (under yet more assumptions of
independence etc. to account for Roger's comment that long runs are not the
only possible signature of loading, and your own comments as well), the more
wins one had seen from it relatively.
>
> I _assume_ that this intuition for how one updates Bayesian posteriors is
behind Nick's common-language premise that "the longer a run of success
continues, the greater is the probability that the wheel that produces those
successes is biased". That would certainly have been what I meant in a
short-hand for the more laborious Bayesian formula.
>
>
> For completeness, the Bayesian way of choosing a meaning for probabilities
updated by observations is the following.
>
> Assume two random variables, M and D, which take values respectively
standing for a Model or hypothesis, and an observed-value or Datum. So:
hypothesis: this wheel and not that one is loaded. datum: this wheel has
produced relatively more wins.
>
> Then, by some means, commit to what probability you assign to each value
of M before you make an observation. Call it P(M). This is your Bayesian
prior (for whether or not a certain wheel is loaded). Maybe you admit the
possibility that some wheel is loaded because you have heard it said, and
maybe you even assume that precisely one wheel in the house is loaded, only
you don't know which one. Lots of forms could be adopted.
>
> Next, we assume a true, physical property of the wheel is the probability
distribution with which it produces wins, given whether it is or is not
loaded. Notation is P(D|M). This is called the _likelihood function_ for
data given a model.
>
> The Bayes construction is to say that the structure of unconditioned and
conditioned probabilites requires that the same joint probability be
arrivable-at in either of two ways:
> P(D,M) = P(D|M)P(M) = P(M|D)P(D).
>
> We have had to introduce a new "conditioned" probability, called the
Bayesian Posterior, P(M|D), which treats the model as if it depended on the
data. But this is just chopping a joint space of models and data two ways,
and we are always allowed to do that. The unconditioned probability for
data values, P(D), is usually expressed as the sum of P(D|M)P(M) over all
values that M can take. That is the probability to see that datum any way
it can be produced, if the prior describes that world correctly. In any
case, if the prior P(M) was the best you can do, then P(D) is the best you
can produce from it within this system.
>
> Bayesian updating says we can consistently assign this posterior
probability as: P(M|D) = P(D|M) P(M) / P(D).
>
> P(M|D) obeys the axioms of a probability, and so is eligible to be the
referent of Nick's informal claim, and it would have the property he
asserts, relative to P(M).
>
> Of course, none of this ensures that any of these probabilities is
empirically accurate; that requires efforts at calibrating your whole
system. Cosma Shalizi and Andrew Gelman have some lovely write-up of this
somewhere, which should be easy enough to find (about standard fallacies in
use of Bayesian updating, and what one can do to avoid committing them
naively). Nonetheless, Bayesian updating does have many very desirable
properties of converging on consistent answers in the limit of long
observations, and making you less sensitive to mistakes in your original
premises (at least under many circumstances, inluding roulette wheels) than
you were originally.
>
> To my mind, none of this grants probabilities from God, which then end
discussions. (So no buying into "objective Bayesianism".) What this all
does, in the best of worlds, is force us to speak in complete sentences
about what assumptions we are willing to live with to get somewhere in
reasoning.
>
> All best,
>
> Eric
>
>
>> On Dec 12, 2016, at 12:44 PM, 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/
>>>
>>>
>>>
>>> ============================================================
>>> 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 (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
>
>

--
Cirrillian
Web Design & Development
Santa Fe, NM
http://cirrillian.com
281-989-6272 (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

Eric Charles-2

Re: probability vs. statistics (was Re: Model of induction)

In reply to this post by gepr

I don't have an answer per se, but I have some relevant information:

Back in the early days of statistics, one could become a pariah in the eyes of the field if it became suspected one had surreptitiously used Bayes' Theorem in a proof. This was because the early statisticians believed future events were probable. They really, deeply believed it. They were defining a new world view, to be contrasted with the deterministic world view. If you smoked, there was a probability that in the future you might get cancer; it was not certain, nothing was predetermined. In such a context, any talk of backwards-probability is nonsensical. After you have lung cancer, there is not "a probability" that you smoked. Either you did or you did not; it already happened! Thus, at least for the early statisticians, people like Fisher, time was inherent to claims about probability.

Now, it is worth noting that one can wager on past events of any kind, given someone willing to take the bet. And in such a context, Bayes' Theorem can be mighty useful. The Theorem is thus quite popular these days, but that is a different matter. Whatever the results of such equations are --- between 1 and 0, having certain properties, etc. --- so long as the results refer to past events, Fisher and many others would have insisted that the result is not "a probability" that said event occurred.

Also, from what I can tell, as mathematicians became more prevalent in statistics, as opposed to the grand tradition of scientist-philosophers who happened to be highly proficient in mathematics, such ontological/metaphysical points seem to have become much less important.

-----------
Eric P. Charles, Ph.D.
Supervisory Survey Statistician

U.S. Marine Corps

[hidden email]

On Mon, Dec 12, 2016 at 6:47 PM, glen ☣ <[hidden email]> wrote:

I have a large stash of nonsense I could write that might be on topic. But the topic coincides with an argument I had about 2 weeks ago. My opponent said something generalizing about the use of statistics and I made a comment (I thought was funny, but apparently not) that I don't really know what statistics _is_. I also made the mistake of claiming that I _do_ know what probability theory is. [sigh] Fast forward through lots of nonsense to the gist:

My opponent claims that time (the experience of, the passage of, etc.) is required by probability theory. He seemed to hinge his entire argument on the vernacular concept of an "event". My argument was that, akin to the idea that we discover (rather than invent) math theorems, probability theory was all about counting -- or measurement. So, it's all already there, including things like power sets. There's no need for time to pass in order to measure the size of any given subset of the possibility space.

In any case, I'm a bit of a jerk, obviously. So, I just assumed I was right and didn't look anything up. But after this conversation here, I decided to spend lunch doing so. And ran across the idea that probability is the forward map (given the generator, what phenomena will emerge?) and statistics is the inverse map (given the phenomena you see, what's the generator?). And although neither of these really require time, per se, there is a definite role for [ir]reversibility or at least asymmetry.

So, does anyone here have an opinion on the ontological status of one or both probability and/or statistics? Am I demonstrating my ignorance by suggesting the "events" we study in probability are not (identical to) the events we experience in space & time?

On 12/11/2016 11:31 PM, Nick Thompson wrote:
> 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.

--
☣ glen

============================================================
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

Roger Critchlow-2

Re: Model of induction

In reply to this post by Nick Thompson

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" value="+15056709918" target="_blank">(505) 670-9918
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/
============================================================
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
<a href="tel:(281)%20989-6272" target="_blank">281-989-6272 (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

Eric Charles-2

Re: Model of induction

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

[hidden email]

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?
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/
============================================================
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
<a href="tel:(281)%20989-6272" target="_blank">281-989-6272 (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

gepr

Re: probability vs. statistics (was Re: Model of induction)

In reply to this post by Eric Charles-2

Excellent! My opponent will be very happy when I make that concession. It's interesting that, for this argument, I've adopted the Platonic perspective despite being a constructivist myself. And it's interesting that my current position (that the math world is extant and static) seems to rely a bit on viewing probability theory as a special subset of math overall. But that perspective seems to encourage me to think about the ontological/metaphysical aspects. Perhaps it's only because I'm not a mathematician.

Thanks!

On 12/13/2016 05:00 AM, Eric Charles wrote:

> I don't have an answer per se, but I have some relevant information:
>
> Back in the early days of statistics, one could become a pariah in the eyes
> of the field if it became suspected one had surreptitiously used Bayes'
> Theorem in a proof. This was because the early statisticians believed
> future events were probable. They really, deeply believed it. They were
> defining a new world view, to be contrasted with the deterministic world
> view. If you smoked, there was a probability that in the future you might
> get cancer; it was not certain, nothing was predetermined. In such a
> context, any talk of backwards-probability is nonsensical. After you have
> lung cancer, there is not "a probability" that you smoked. Either you did
> or you did not; it already happened! Thus, at least for the early
> statisticians, people like Fisher, time was inherent to claims about
> probability.
>
> Now, it is worth noting that one can wager on past events of any kind,
> given someone willing to take the bet. And in such a context, Bayes'
> Theorem can be mighty useful. The Theorem is thus quite popular these days,
> but that is a different matter. Whatever the results of such equations are
> --- between 1 and 0, having certain properties, etc. --- so long as the
> results refer to past events, Fisher and many others would have insisted
> that the result is not "a probability" that said event occurred.
>
> Also, from what I can tell, as mathematicians became more prevalent in
> statistics, as opposed to the grand tradition of scientist-philosophers who
> happened to be highly proficient in mathematics, such
> ontological/metaphysical points seem to have become much less important.

uǝʃƃ ⊥ glen

Nick Thompson

Re: probability vs. statistics (was Re: Model of induction)

Glen and Eric, In my role as the Fool Who Rushes In, let me just say that according to an experience monist, past experience, present experience, and future experience are all on the same footing. We come to know them as different because they prove out in different ways. This should fit nicely with your constructivism, Glen, although you may see it as too much of a good thing. We can have expectations about the past, just as well as we can have expectations of the future, and those expectations can prove out or not in subsequent experience.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/

-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of ?glen?
Sent: Tuesday, December 13, 2016 8:37 AM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] probability vs. statistics (was Re: Model of induction)

Excellent! My opponent will be very happy when I make that concession. It's interesting that, for this argument, I've adopted the Platonic perspective despite being a constructivist myself. And it's interesting that my current position (that the math world is extant and static) seems to rely a bit on viewing probability theory as a special subset of math overall. But that perspective seems to encourage me to think about the ontological/metaphysical aspects. Perhaps it's only because I'm not a mathematician.

Thanks!

On 12/13/2016 05:00 AM, Eric Charles wrote:

> I don't have an answer per se, but I have some relevant information:
>
> Back in the early days of statistics, one could become a pariah in the
> eyes of the field if it became suspected one had surreptitiously used Bayes'
> Theorem in a proof. This was because the early statisticians believed
> future events were probable. They really, deeply believed it. They
> were defining a new world view, to be contrasted with the
> deterministic world view. If you smoked, there was a probability that
> in the future you might get cancer; it was not certain, nothing was
> predetermined. In such a context, any talk of backwards-probability is
> nonsensical. After you have lung cancer, there is not "a probability"
> that you smoked. Either you did or you did not; it already happened!
> Thus, at least for the early statisticians, people like Fisher, time
> was inherent to claims about probability.
>
> Now, it is worth noting that one can wager on past events of any kind,
> given someone willing to take the bet. And in such a context, Bayes'
> Theorem can be mighty useful. The Theorem is thus quite popular these
> days, but that is a different matter. Whatever the results of such
> equations are
> --- between 1 and 0, having certain properties, etc. --- so long as
> the results refer to past events, Fisher and many others would have
> insisted that the result is not "a probability" that said event occurred.
>
> Also, from what I can tell, as mathematicians became more prevalent in
> statistics, as opposed to the grand tradition of
> scientist-philosophers who happened to be highly proficient in
> mathematics, such ontological/metaphysical points seem to have become much less important.

--
␦glen?

============================================================
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

123