1. It is intended as a complement to undergraduate mathematically-focussed courses. I teach a junior-senior "topics" course on this material. Following the link to the Fall 2008 class-by-class topics gives a bottom-up view of what I actually can do, and draft write-ups of many lectures. This page starts a top-down discussion of what I would like to be able to do.
2. The material is also intended for a general audience -- people who read "serious popular science" books. Though given my track record for actually finishing books, it may just stay forever as a web site. As such it provides a more idiosyncratic complement to two existing web sites: Understanding Uncertainty and Chance News.
This is a beta version cover page, currently used in talks to academics, urging them to consider teaching a course in this style. Later I will do a cover page aimed at the typical reader, if I can ever figure out who that might be!
2. Let's start with the second. Saying "Hamlet is fiction" is not dissing Shakespeare. Similarly, saying
1. Turning to the first part, let me start with a narrow interpretation of "fact":
Of course my students actually do course projects -- in practice, not as sharply focussed as I would prefer -- and here are some interesting student project write-ups.
3. How do "ordinary people" think about chance? This question, with emphasis on risks and investments, has been studied a great deal in psychology and behavioral economics, notably by Amos Tversy and colleagues. A nice source is the book Cognition and Chance. It's fun to talk about this material in class, though I don't have anything new to say so I won't say anything here.
That style of research is mostly based on asking hypothetical questions involving uncertainty, or on volunteers participating in artificial experiments. A rather different, and less thoroughly studied, question about perception is "in what contexts do people think about chance without being prompted? -- and what thoughts do they have?". The links at the bottom go to my discussions of topics ranging from that question to philosophical debate about the interpretation of probability. Even though this is only a small part of the course, thinking how to tackle such questions empirically can lead to creative projects.
Critique of introductory mathematical probability courses A typical introductory textbook, in its introduction or back cover, makes extravagant claims about the usefulness of mathematical probability, but very little in the actual book demonstrates this usefulness -- such demonstation being implicitly postponed to future courses. What one sees in more advanced courses and research literature is "complex fiction"-- models that use technically sophisticated mathematics (compared to the 10 simple models I mention) -- but the vast majority of models are never actually checked against data. So
Critique A: most of the content of introductory mathematical probability courses serves as ``technical prerequisites for complex fiction" rather than saying something interesting about the real world.
The focus of my parts 1-3 is different; I want a course which is satisfactory as a terminal course (analogous to the Freedman et al. Statistics course), while hopefully whetting the curiousity of occasional students and motivating them to study the subject further. Closely related is
Critique B: even in the best textbooks, the majority of examples and exercises are ``just made up" -- see e.g. this list of exercises.
To phrase this more humorously, I urge instructors to
If you really care, here is some more rhetoric about how this course differs from a standard College course.
At some opposite extreme from mathematical probability, one can ask about the Big Picture -- what is the role of probability in Life, the Universe, and Everything? This is the domain of philosophers or writers of popular science style books. My overall opinion of such work is:
Critique C: Writers who claim, explicitly or implicitly, to be dealing with "probability in general" tend in fact to be working within some very narrow vision of the contexts in which Probability arises.
To demonstrate this, I need to exhibit a broader vision, and this is (under construction in) a representative list of perceived instances of chance in the real world.