I realize these days you won't be extremely interested in things like the fringe festival or the caribana in Toronto. Knowing that Israelis never refuse to discuss politics, you might be interested in some thoughts on politics and democracy, this time from mad mathematician's angle. When I was about 13, I conducted an experiment: I stopped people in the street and asked them how much is a quarter of a quarter. To my amazement, about 40% didn't know or said it is 1/8. You can try it yourself, but it has to be done on the street with random people. My astonishment was even greater when my grandmother, who I still consider a very clever woman, didn't know. It can be argued that the brain is capable of performing complex mathematical tasks like visual processing unconsciously, but is not built for symbolic mathematics. Nevertheless, I was thinking: how come these people are allowed to vote if they don't understand such simple things?
Idan Amit reminded me a real story I like which appeared in SIAM news. At a party, people were asked to select a number in the range 0..100. The one who is the closest to 2/3 of the average of all the numbers wins. A mathematician was thinking: 2/3 of the average will be lower than 67, therefore no one will select a number higher than 67. But then nobody will select a number higher than 67*2/3, etc. so she wrote 0. An economist was thinking: the average will be around 50, so he wrote 30 (close to 50*2/3). Not surprisingly, at that party the economist won.
People who wrote a number greater than 67 were fools. They didn't understand they couldn't win this way. What the mathematician had essentially to do was to gamble on the composition of participants (how many don't understand the game, understand it like the economist, naive mathematicians, or will gamble like himself). So, is democracy the dictatorship of the fools? It really depends who defines what is foolish. Let's take a closer look. Suppose you participate in this game with 100 people. Your a-priory chances of winning are 1%. Assume further you don't really like these brain games. Even more, you believe that those who play these games at universities are wasting the tax-payers money on non-realistic toy problems. Doesn't it reasonable for you to pick a random number understand that you are probably not going to win? The same in real politics. What left wing, right wing, religious and Palestinians do make sense to them. Those who can't get into their head are like the naive mathematician, who believes that everybody will behave by the same logic.
One of the basic concepts in game theory is mixed strategies. For example, suppose you play rock-paper-scissors. If you choose an action by random with probability 1/3, you are guaranteed to win 1/2 of the times on average. However, if your opponent has a different strategy that you know, you can take advantage of it and win more than 1/2 of the times (by the way, it is known that humans are bad at generating large random sequences, but they still outperform the best computer poker program). This principle explain why politicians don't expose their strategies and change their mind often. This prevents their opponents of knowing their moves. There is a small problem here - people like consistent politicians, not zig-zaggers. But straight politicians are too exposed to attacks and don't survive. Professional politicians zig-zag while claiming to be on a straight line.
Now that we understand that politics is a huge game with incomplete information and random events, with many players behaving in ways which are not comprehensible to the other players and politicians that change their mind, it is clear that the final outcome of moves cannot be calculated. Of course, some people will claim they see a straight arrow from the beginning of history and predict the future. Unfortunately, not all these arrows point in the same direction. Some of them will be right, some wrong, and all these long term predictions are not worth more than a long term weather forecast.
The good thing about democracy is that it employs very strong psychological mechanisms. If you vote for the winning candidate, and he changes his mind, you are still more likely to accept his explanations. If your candidate lost, you may accept the winner understanding that the majority thinks differently. At any rate, it gives people a sense of control over their lives, even if realistically the amount of control is minuscule. Given all the known problems with democracy, one wonders if there is a better alternative. There doesn't seem to be one at present, but I believe that in the future countries lead by computers will outperform countries lead by humans. Computers will minimize the bureaucracy and will make decision at least as good as humans do in a fraction of a second. But what about the psychological mechanisms? Well, people will still vote if they want their head computer blue or orange.
Bottom line: I think the Israeli-Arab conflict has no simple, natural, positive solution. If there was one, people would have found it. A negative solution is bad. Rational solution, as I argued above, won't work because there are too many irrational people involved. On the other hand, an irrational solution doesn't make sense. We are left with a complex solution: dividing the land. One side gets the real part. The other gets the imaginary part.
