Introductions to Popular Combinatorial Games
Mathematics and Go, February 6, 2006, Berkeley
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.
On August 3-4, 2015, the Museum of Mathematics (Momath) in New York sponsored a conference honoring Elwyn Berlekamp, Richard Guy, and John Conway, the authors of "Winning Ways". The conference was held at Baruch College, and was one of the conferences in Momath's long-term MOVES series (Mathematics of Various Entertaining Subjects). This DVD is the lecture Berlekamp gave at the conclusion of that conference.
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, Stanford
On 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.
Gallimaufry of Games, 2000, updated in 2018
This video was shown at the thirteenth Gathering for Gardner on April 12-14, 2018. It discusses a problem I had composed for the fourth Gathering for Gardner in 2000.
The problem includes interesting endgame positions in Go, checkers, chess, and Domineering. The "gallimaufry" is the sum of these four games, in which each player, at his turn, can pick the board on which he chooses to move. The problem's solution provides a compelling illustration of the power of combinatorial game theory.
Winning Ways, circa 1986, Lawrence Livermore National Laboratory
This is an unedited recording of a lecture Berlekamp gave to an audience of scientists at Lawrence Livermore National Laboratory circa 1986. It is an introduction to Combinatorial Game Theory, and a promotion of "Winning Ways", whose first edition, then consisting of two volumes of two parts each, had been published in 1982. Lecture aids included a blackboard with colored chalk and an overhead projector with transparencies, as was common at that time.
This was the annual "Viterbi Lecture" at USC.
Fibonacci Plays Billiards (PPT), Spring 2006, University of Calgary and August 6, 2016 in Columbus, OH
Historical note: In 2006 the University of Calgary established an annual lecture in honor of Richard & Louise Guy. I gave this presentation (of which Richard Guy was the surprise co-author) as the first such lecture. Subsequent lecturers in this series are listed on Slide 2. A couple years earlier, we had driven together from Calgary to a game theory conference in Edmonton. When we stopped en route for lunch, we encountered a computer scientist at the next table who was heading to the same conference. He was engrossed in a problem which proved contagious. Richard and I joined in, and then veered off in our own direction. What follows is the Powerpoint of that talk. It includes some animated movies, of which the animated Slide 65 is the most impressive. If you are not able to view the animations on the slides below, you can download the full Powerpoint file by clicking on the "Fibonacci Plays Billiards" link above.
On April 14th, 2007, a slightly refined version of this talk was given to a meeting of the Pacific Northwest section of the Mathematical Association of America, at Linfield College in McMinnville, OR, with Richard Guy in attendance again. And yet another version was given at the summer joint math meetings in Columbus OH on August 6, 2016, where it was the concluding talk of a special session celebrating Richard Guy's forthcoming 100th birthday on Sep 30, 2016. I discussed the talk privately with Richard the night before, and he told me that he had continued our study of the graph whose nodes are integers from 1 to N, where a branch joins two nodes iff their sum is a perfect square. This corresponds to the portion of the talk subtitled "Pythagoras Plays Billiards Too". Richard said that he had found explicit cycles in such graphs for every N running from the low 30s up to 250, although no pattern generalizable to arbitrary N had yet been found. So I announced that in my talk. He then presented his review/reaction/rebuttal, in which he revealed that following our discussion the night before, he had solved the case of N = 251.
Recreational Mathematics, Fall 1976, Miami University, Oxford, OH