Rudolf Taschner

I'd like this book a lot better if the author had gotten away from home more often.

Game Theory is one of those branches of mathematics that has a very specific starting point, and also some very obvious milestones. The starting point is von Neumann's and Morgenstern's The Theory of Games and Economic Behavior, and some of the milestones include the publications of John Nash, the Prisoner's Dilemma tournament of Robert Axelrod, the founding of the RAND corporation, and the sneaky ideas of Martin Shubik. It's a field for which a biographic history is a natural.

And this book... is about half of it. I particularly liked the description of von Neumann's and Morgenstern's early interaction, where von Neumann demonstrated the need for mixed strategies (those in which one randomly chooses between two or more strategies) by modeling a game of poker with just two players and two cards. I knew that von Neumann had made his big insights while trying to come up with a better poker strategy; I didn't know how he had done it. (In poker terms, a mixed strategy is one in which one sometimes bluffs, but not always. Von Neumann proved that this was the only way one could reliably win -- if you never bluff, but always bet based on the actual value of your hand, your opponents will know exactly when to bet and when to fold.)

On the other hand, the book does not include von Neumann's proof of the minimax theorem, which doesn't have any such fun application as poker but which is the underlying basis of the whole thing.

Similarly, there is a brief mention of Axelrod's Prisoner's Dilemma tournament, and of Anatol Rapoport's winning "Tit for Tat" strategy -- but no discussion of the other strategies (which are often fascinating in the behavioral assumptions which underlie them), or of Axelrod's discussion of the same, or of who Axelrod was (and not much about Rapoport, either).

Such omissions could perhaps be justified if the goal was to keep the book short -- but there is also a lot of stuff that is not game theory. I will grant that some of it, such as the discovery of the mathematics of probability, is useful; you can't really do game theory if you can't assign probabilities to the events. But what about the second-to-last chapter, about Ludwig Wittgenstein? This has nothing to do with game theory. The only justification I can see for it is that this book is by a professor from Vienna, and the author wanted to bring in some Austrians in a field that is mostly English-speaking. But that chapter doesn't teach us anything.

Similarly the last chapter, on Blaise Pascal and Pascal's Wager -- the idea that you should bet on the existence of God, because if God exists, it pays off, and if God doesn't exist, it doesn't matter what you believe. This sounds like a problem in strategy, and in a sense it is: if there are only two strategies possible (believe in God/don't), and only two outcomes (there exists a God who wants to be believed in and rewards those who do/God doesn't exist), then Pascal's choice is the optimal strategy.

The problem is that Pascal's Wager cannot be shown to correspond to reality. What if, for instance, there is a God, and that God will forgive those who don't believe in God but will punish people who believe in the wrong God? Then Pascal's payoff matrix is dead wrong and Pascal's strategy is disastrous. It doesn't matter what you believe to be true; Pascal's Wager is not a valid game. And yet the book ends with it.

So what we have is a mix of very good, very interesting material about game theory and... other stuff. Maybe you will find the other material interesting. I didn't, but I don't care for philosophy, and I wanted more math. Tastes vary, but be sure you know what you're getting with this book.… (meer)

Rudolf Taschner is Austria's great "math is cool" promoter. This book offers a nice to read easy introduction to a few math puzzles and presents some the great mathematicians. Unfortunately, it always stops well before the math is getting hard. It isn't really possible to truly learn to swim in never venturing beyond the non-swimmer's pool. Granted it is difficult to interest a wider public about mathematics.

Nevertheless, it would have been nice to find a few more new ideas or challenging approaches in this book. Its effect is similar to a "Math is cool" Barbie doll.… (meer)

Mathematik ist nicht bloß ein Fach, das in der Schule bei vielen auf wenig Gegenliebe stößt. Mathematik durchdringt vielmehr unseren Alltag und liefert Erklärungsmodelle für unsere Welt. Buchautor und Mathematikprofessor Rudolf Taschner unternimmt eine spannende Reise, bei der man mit allem rechnen muss. In insgesamt zehn Kapiteln zeigt er auf, wo die Mathematik überall ihre Finger im Spiel hat. Verknüpft mit interessanten Kurzbiografien der jeweils wichtigsten Wissenschafter erfährt der Leser zum Beispiel, warum Sterne den Zahlen gehorchen, wie die Geometrie die Kunst beeinflusst, weshalb die Spieltheorie für die Wirtschaft wichtig ist, worin sich Wahrscheinlichkeit und Zufall unterscheiden oder wie ein perfekter Fußball konstruiert wird. Mit Hilfe der Unendlichkeit nähert sich Taschner auch der Religion an und spannt so den Bogen von der exakten Naturwissenschaft zur Philosophie. Ein Buch zum Entdecken, Verstehen und Staunen.… (meer)