Subject: summary of suggested readings for freshman seminar
From: "Johanna Hardin"
Date: Tue, 29 Aug 2006 19:07:22 -0700
To:

Hi, all.  I had many requests to pass along the ideas for readings (and other things) that people gave me.  Below I’ve summarized the suggestions.  I also have a website (linked to my homepage which is below) that lists the readings.  It will eventually have more course details.

 

Thanks for all the great ideas!

 

-Jo

 

Jo Hardin

Assistant Professor

Department of Mathematics

Pomona College

610 N. College Ave.

Claremont, CA 91711

909-607-8717

jo.hardin@pomona.edu

http://pages.pomona.edu/~jsh04747

 

 

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Journal Articles about inherent ability to process randomness:

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* A. Tversky and D. Kahneman, "Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment," Psychological Review, 90 (1983), pp. 293-315.

 

* "A 30% Chance of Rain Tomorrow?  How Does the Public Understand Probabilistic Weather Forecasts?"  In Risk Analysis, (2005) volume 25, 623-629.

 

* "Communicating Statistical Information."  In Science (2000) volume 220, 2261-2262.

 

* "How to improve Bayesian reasoning without instructions:  Frequency formats."  In Psychological Review, (1995), volume 102, 684-704.

 

* Judgment under Uncertainty: Heuristics and Biases A Tversky, D Kahneman - Science, 1974

 

* Stuart Oskamp's "Overconfidence in Case Study Judgments" from Kahneman, Slovic, and Tversky (eds) _Judgment Under Uncertainty: 

Heuristics and Biases_.

 

Oskamp reports on a study in which subjects were given bits and pieces of the life story of Joseph Kidd, and asked to answer multiple choice questions about Kidd on the basis of what they knew at that point.  The information was presented in 4 stages; after each stage, subjects answered the same set of questions about Kidd, and also rated their confidence in each answer they gave.  Results showed that as they were given more and more information about Kidd, their confidence level went up, but their accuracy remained little better than chance.  (Subjects included undergrads, grad students in psych, and therapists.  The therapists were no more accurate than the other subjects, but they were on average less

overconfident.)

 

* "The Perception of Randomness" by Maya Bar-Hillel and Willem A. Wagenaar (1991) can be found in Advances in Applied Mathematics, 12, 428-454.  Also look in the PsychInfo data base under "randomness" for articles on human's inability to generate or perceive random sets of data.

 

* Falk, R., & Konold, C. (1997). Making sense of randomness: Implicit encoding as a basis for judgment. Psychological Review, 104, 301-318.

 

A little more accessible version of this is:

 

Falk, R., & Konold, C. (1998). Subjective randomness. In S. Kotz, C.B.

Read, & D.L. Banks (Eds.), Encyclopedia of statistical sciences (pp.

653-659). NY, NY: J. Wiley & Sons.

 

* 'Statistcs as Principled Argument' by Robert P. Abelson

 

* articles and books by Gerd Gigerenzer and Peter Sedlmier that present arguments and research results supporting the claim that humans evolved the ability to track and process frequencies, but not to reason about proportions. They suggest that instructional approaches that start with frequency representations of probability reasoning tasks are more accessible to students.  Gigerenzer also has books and articles that argue against theories and research results of Kahneman and Tversky, and Gigerenzer's arguments are along the lines of evolutionary psychology.

 

 

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Fiction books / stories with chance mechanisms:

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* There were a series of short stories by G. K. Chesterton called the Father Brown mysteries (episodes even appeared on the BBC and PBS).  The plots often involved crimes or events that were interpreted as supernatural when, in fact, the explanation was rather straightforward.  These were written  in the early part of the 20th century when spiritualism (seances, mysticism) was popular in England.

 

* Isaac Azimov's first book in the Foundation Trilogy

 

* The Stochastic Man by Robert Silverberg

 

* Hitcher's Guide to the Galaxy

 

* The Dice Man by Luke Rhinehart about a psychologist who decides to lead his life according to the roll of a dice (every decision).

 

* Music of Chance by Paul Aster.  It's a good title but I didn't enjoy the book as much.  It has some gambling and some consequences of random events.

 

* Jorge Luis Borges called "The Library of Babel".  It is told from the pov of an aging librarian who is one of a uncounted horde of librarians.  Each maintains a section of a vast library where, to his knowledge, every volume has the same number of pages in the same font with the same number of lines per page.  Most of the volumes are gibberish.  He has heard of claims that some of the volumes actually make sense.  Some librarians claim that they have found a book that is a key to all the other volumes.  Factions arise, wars are fought and the history of the library goes on.  The protagonist gives brief accounts of all of this.

 

* "The Law" by Robert M. Coates in which the so-called Law of Averages stops operating, so that (for example) if you went to the grocery store, you would find it mobbed because everyone else just happened to decide to go there at the same time, or you would find it empty except for yourself for the opposite reason. I read this story in an anthology called "The Mathematical Magpie" by Clifton Fadiman; it originally appeared in the New Yorker in 1947.

 

* Jurassic Park by Michael Crichton includes a discussion of the normal distribution (see p. 65) and uses the collected data to conclude that the dinosaurs are reproducing.

 

* “Improbable” by Adam Fawer  It was a great read and has some probability and statistics in it. It begins with the protagonist playing Texas Hold ‘Em, which should engage your students from the beginning. I think that it also deals with some issues that are good for discussions of morality (experiments gone wrong) and mental issues (schizophrenia). There’s a great website for the book itself at http://www.improbablebook.com/.

 

* the first scene of Tom Stoppard’s Rosencrantz and Guildenstern are Dead

 

* Charlie Nam’s “The Golden Door.” Charlie is a retired demographer from Florida State and he wrote the story after doing genealogical searches for his family and “randomly” ran across a “random” mystery involving people from the same village in Russia who were on the ship’s manifest coming to the US but don’t show up in the immigration in-take statistics after the ship arrived at Ellis Island.  Charlie then made up a fictional story on this “random event.”

 

*  “State of Fear” by Michael Crichton

 

* two short stories in "The World of Mathematics", ed. Newman.  1. Inflexible Logic by Russell Maloney (takeoff on monkeys at typewriters) 2. The Law by Robert Coates (takeoff on the law of large numbers)

 

* Nabokov's Pale Fire, in which the lament by small college prof. John Shade abut his unattractive, socially rejected, daughter - dead by her own hand, is marvellously perverted into the solipsistic story of Kingdom, banishment, and refuge by the insane (?) Kimbote, through an interpretation so wild it may be seen as the result of "noise" upon Shade's literary signal, (until the actual present of one and fabulous past of the other (with the Truth somewhat out of bounds) merge together ...

 

* this biblical passage -- Ecclesiastes [ I think at 9.11 ]

 

I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favor to men of skill; but time and chance happeneth to them all.

 

* A Murakami story out of a collection called "The Elephant Vanishes." The story is called 'On seeing the 100% perfect girl one beautiful April morning'. Apparently quite a few of his works (at least the stories) are of people barely missing each other (or finding each other).

 

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Non-fiction books on these topics:

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* Brian Hayes (2001), “Randomness as a Resource”, The American Scientist, vol 89, pages 300-304.

 

*  'How To Lie With Statistics' by Darrell Huff (W.W. Norton Co. 1954)

 

* "Fooled By Randomness: The hidden role of chance in life and markets" by Nassim Nicholas Taleb

 

* What is Random? by Edward Beltrami- Copernicus-imprint of Springer

 

* Chance in Biology: Using Probability to Explore Nature. Mark W. Denny and Steven Gaines.

 

* Stephen Senn, 2003: «Dicing with death. Chance, risk and health». Cambridge

UK: Cambridge University Press.

 

* Peter L. Bernstein, 1996: «Aginst the Gods. The remakable stroy of risk.» New York NY: John Wiley & Sons.

 

* What are the Chances? By Bart Holland

 

* "How We Know What Isn't So" by Thomas Gilovich

 

* Chapter 14 of _The Psychology of Judgment and Decision Making_  by Scott Plous

 

* Peck, Statistics: A Guide to the Unknown 4th edition


* "Beyond Coincidence: Amazing Stories of Coincidence and the Mystery and Mathematics Behind Them" by Martin Plimmer & Brian King (Thomas Dunne Books, 2005); "Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas" by Edward B. Burger & Michael Starbird (W.W. Norton, 2005).

 

* Small Worlds: The Dynamics of Networks Between Order and Randomness By Duncan J. Watts

 

* "Arcadia", also by Tom Stoppard, esp. the biologists lament about his inability to find a pattern in some grouse (?) population

data due to randomness.  Chaos and entropy also figure prominently.

 

* "Gravity's Rainbow": randomness and the poisson distribution for the landing pattern of German missles in london play a major role.

 

* A mystery novel by a Polish writer - I can't recall the author or the name of the book :-)  The plot involves around a conjunction

of rare events - which given enough time are bound to occur.

 

* I read a mystery novel some years back where the culprit turned out to be chance.  Aha, Stanislaw Lem "The Chain of Chance".  here is a review

 

    "A series of mysterious deaths in a southern Italian seaside resort baffles the Italian police. A dozen tourists disappear or die. All

    are men, all are middle-aged, all are foreigners. A former astronaut is dispatched to Italy as private investigator. He sets

    himself up as a decoy, and is assailed by strange events – but what do they mean? Lem charges his plot with a dimension new to

    the genre, as death is revealed as a product of chance. Brilliantly inventive, immensely readable."

 

 

 

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Other suggestions:

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* The movie "Being There" (1979) starring Peter Sellers is about a simple gardner named Chance who just utters random statements from TV shows and is mistaken for a profound thinker.  He eventually becomes a political insider and (I think) even a presidential candidate.

 

* You might want to consider a couple of movies :  " Sliding door"   which essentially is about how a small change in an event ( in this case leaving work a few minutes earlier) could affect so many consecutive  events and " Run Lola Run" a German movies which has the same theme.

 

* The Angels in America play alludes to double-blind experiments. A nurse tells a patient with AIDS to not sign on with any studies "They'll wind up published and you'll wind up dead." Or something like that is her/his line.

 

* There was an episode of Star Trek: Deep Space 9 (please, keep reading) which had a really interesting plot.  There was some guy who was locked

away in the brig, playing a hand-held game.  He was complaining about his bad luck, when he finally gets a winning hand on the game, and dies.

His cellmate takes the game, and starts playing, and his luck begins to change.  It turns out that the game affects the probability field surrounding

the player, and the more one plays the game, the more likely unlikely events are to occur.

 

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