Group Theory in the Bedroom

I work in an inter- (or perhaps multi-) disciplinary field, which means that people come to it from a variety of different backgrounds. So, the lowest common denominator in terms of mathematical techniques and methods that can be assumed of a “typical” audience is rather low indeed. This is particularly true in the classroom because a lot of students first get interested in robotics and AI due to the “gee whiz” factor and then wonder why I am overloading them with other technical concepts – I have been wondering how best to give them a flavor for why they should dig deeper and think more rigorously – and what that lets them do in terms of the problems that come up in this area.

Recently, I came across a book (a collection of articles really) that does a very nice job of explaining some fairly sophisticated ideas in a way that serves exactly this purpose. The book entitled Group Theory in the Bedroom is written by Brian Hayes, based on his column in The American Scientist magazine. The book’s name derives from a very nice article that explains the idea behind rotation and motion groups in a way that even a high school student should be able to appreciate. It is all done using a concrete task – how do you come up with a strategy to flip your mattress so it wears out evenly. In the process, he tells you what a group is, what its properties are, what is the benefit of identifying such symmetries (you can actually make statements about the possible sequences for mattress flipping, you can ‘prove’ what is and isn’t possible, you can design efficient algorithms), etc. If a student were to understand this much and I were to tell her just one bit of further information – that Lie Groups are continuous versions of these elementary objects, then she’d already be able to appreciate the raison d’etre for an essential line of inquiry within robotics. And she may actually agree to listen to, and perhaps even read up on, the more technical material explaining the details.

This is the sort of expository skill I need to develop further, and I am pleased to find existing literature that I can dip into to get started!

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