The title might also have been "The Mathematics of Amazons" or the more general "The Mathematics of Games".Following the presentation of the play of a particular game of Amazons on a 6x6 board, the lecture provides a post-mortem analysis which reveals the last fatal mistake, and the position at which the game on the board splits into the sum of two disjoint battles. The introduction of coupons facilitates the analysis of each battle separately, and provides insights into good play in their combined sum. Similar use of coupons facilitates "orthodox" analysis of several other "hot" combinatorial games, including the Asian board game called Go.
Popular Misconceptions, April 5, 2013, StanfordOn the occasion of Prof. Thomas Kailath's 70th Birthday in 2005, a group of his former students and associates endowed a fund to support an annual lecture at Stanford University by a distinguished contributor of mathematics-based solutions to challenging problems in engineering. Elwyn Berlekamp was the 2013 Kailath Lecturer.
Following Tom Kailath's introduction, Berlekamp discusses four "Popular Misconceptions" about applications of mathematics and probability: 1) confusing "average" with "typical," 2) underestimating variance, 3) overuse of integers, and 4) simplistic quantization. In the last portion of the lecture, Berlekamp sketches a more sophisticated "Stretched String" quantization methodology. This technique can be used to characterize the output stream from a Poisson process whose dynamic mean changes with time, incurring occasional big jumps as well as gradual drifts. In many situations, it offers more insight than traditional "moving averages." Applications include studies of accident rates and of financial data.
This DVD is a recording of a presentation Berlekamp gave on February
6, 2006 at the Faculty Club of the University of California at
Berkeley. The audience consisted of a very select group, including
several Nobel Prize winners. Some members of the audience had almost
no prior knowledge of Go.
Following a 4 minute introduction by Berkeley's Dean of Letters & Science Mark Richards, Berlekamp's 27 minute talk gives a fascinating high-level overview of both Go and mathematics, including both history and some of the recently discovered connections between them. It is followed by a questions and answer period and a bibliography.