A Book That Confounds Your Expectations
About seven years ago, MathNEXUS included a column of the Banach-Tarski Paradox ...perhaps the strangest "truth" in mathematics. At that same time, I suggested a complementary resource The Pea and the Sun by Leonard Wapner, as it was a great help in my attempts to understand the Banach-Tarski Paradox.
And now, another text by Leonard Wapner is being recommended highly. Unexpected Expectations: The Curiosities of a Mathematicaol Crystal Ball takes on new paradoxes.
The focus of the book is the idea of mathematical expectation, using the associated paradoxes as an impetus to re-examine the "legitimacy" of the notion itself. It begins with a history and introduction of key ideas in probability theory, then introduces the idea of mathematical expectation--a concept that palys a strong role in betting, lotteries, and other decision-making situations.
Other key ideas explored include:
Again, the book is highly recommended as Leonard Wapner has a great witing style that both comforts and challenges the reader in the world of confusing paradoxes. Most of the content was new to me, yet it was enjoyable and helped "un-solidify" my belief in mathematical expectations.
- Roles of aversion and risk
- Envelop problems, which are a class of expected value paradoxes
- Parrondo's Paradox, whereby losing expectations can lead to positive results
- Connections to non-zero sum games, such as Chicken and the Prisoner's Dilemma
- Newcomb's Paradox, which focuses on the idea of free will
- Benford's Law...which is another strange mathematical animal that I have enjoyed exploring for many years (read the book to learn what it is!)
Get the book and read it....if you enjoy being puzzled and discovering new things about what you thought you understood!