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0410 the monty hall problem.html
Interesting Posts from 2008 18 november, 2008 Programming Tutorials and Eggshells I have been learning to use the Pylons web framework, based on the Python programming language. I have no experience in either. To do this, I have followed several tutorials on the subject. They are like cookie recipes, and make the setup process look simple. However, though meant for beginners, they do require background knowledge. Take the recipe for Toll House Cookies. Nowhere does it tell you to remove the eggshells before adding the eggs. 27 october, 2008 Beautiful Primitive Man Whenever you see primitive people on TV or in movies, they're ugly. I'm not talking about surviving tribes, but about depictions of neanderthal and cro magnon men and women. They're dirty and unkempt, have lumpy faces and make ugly sounds, but why should they be ugly? Animals are beautiful -- there are very few ugly primates. The human tribes that could be considered the most primitive may seem bizarre to us, but they're never dirty or unkempt. Why this insistance on the fact that primitive man was dirty? In all likelhood, he was magnificent -- clean, well-groomed, and in great shape. In this post-Baconian world, perhaps we seek to reassure ourselves that all this progress is really worth something. 18 october, 2008 Women's Razors Work Better Razor blades made for women work better than men's blades for men who shave irregularly. Razor blades made for men are oriented towards permanently clean-shaven guys who shave every day. Women's razors, on the other hand, have blades at a steeper angle and have more space between blades (on a three-blade Wilkinson Sword, for example). Women's razors are made for cutting longer bristles, since women tend to shave their legs less frequently. For men this means that they clog less and cut a three-day growth more easily. The only question is: are you comfortable using a pastel pink or green razor blade? 20 august, 2008 Opportunity Cost & Addiction It is interesting to consider the concept of opportunity cost in addiction. What we are looking for is a way to describe the moment that the addict (who would like to stop using) caves in and decides to once again take his drug. The junky shoots up when the opportunity cost of taking the drug becomes low enough. Here is a scenario: Week 1: J (the junky) gets out of rehab. He is full of optimism, and has a new lease on life. He goes home and cleans his apartment, and starts his new job (thanks to a government program for helping addicts get a new start). At this time, the opportunity cost of using is far too high, and J does not seriously consider shooting up. Week 2: things are going a little less smoothly. His job is tiring, and J has not consistantly done the dishes or put things away. J's apartment is getting a little messy. It turns out that J's new boss has a tendency to micromanage. J's girlfriend has a lot of ideas about how he should do things differently, and although J tries to go along, it's a lot of work and he doesn't always agree. J starts to think about shooting up, how nice it would be. He really wants things to work out, to stay on the wagon, but boy is it frustrating. His quality of life is significantly lower than it was during week 1, and the opportunity cost of using (losing most of what he has) has dropped significantly. Week 3: J really wants things to work out. He's doing his best to make his boss happy and implement all of his girfriend's ideas. That doesn't really leave him with a lot of energy for himself, and his apartment is slowly turning into a catastrophe. No matterwhat he does, he doesn't feel like his boss will really like him. J feels guilty that he's not doing better at keeping those people around him happy. At this point J has invested a significant amount of energy in the people around him. Everyone knows that junkies are selfish, and J is trying really hard to be selfless. It just doesn't seem to be working out. He doesn't have enough energy, and he can't seem to satisfy everyone. He's stopped taking care of himself in order to be good to other people. You can see where we are going with this. The more that J tries to "be good" and "help others" the faster his life spirals downward. The lower his quality of life, the lower the cost of opportunity of using. There comes a moment when J thinks: ah fuck, it's not worth it. I tried everything, and I can't win. My life is shit anyway, so I might as well shoot up and feel good for a few minutes. It is obvious from this example that although he was trying to be good, everything J did lead to a decreased opportunity cost for using. When the opportunity cost was low enough, J shot up. Imagine another scenario where J gets out of rehab, and instead of trying to "be good", he just tries to have a good life. He takes a vacation in the caribbean, starts working out, learns to draw, learns to cook, decides not to take the advice of his girlfriend just because he doesn't feel like it. Etc. etc. The quality of J's life goes up consistently. The opportunity cost of using drugs also goes up, and as time goes by J is less and less tempted (although he never was really tempted once he got out of rehab). The important thing here is that even by trying to do right for everyone else, the junky can dig his own grave by lowering the opportunity cost of his drug by not taking care of himself. Only by increasing his OWN quality of life can the junky increase the opportunity cost of using. Only by doing things that make HIMSELF happy. 15 august, 2008 Opportunity Cost & Web Design One way to think of Opportunity Cost is as "losing interest". When the Opportunity Cost of an activity becomes too high, you lose interest; you start to feel that you are wasting time. This idea is useful in understanding web site design. A site that is beautifully designed but which is too slow or complicated to use has a high opportunity cost -- the user starts to feel that he or she could be doing better elsewhere. It is therefore extremely important in designing a web site that the user experience feel concentrated and useful, keeping the opportunity cost as low as possible. If the reason for the user's visit is to get something done, anything that slows him or her down raises the opportunity cost. This is true regardless of how beautiful or interesting the site is by other criteria. 21 june, 2008 Expensive Dishes "The next time you sit down for a nice meal at your favorite dining spot, take a close look at the prices of entrees. More often than not, there are one or two really expensive items, and then there are a bunch of mid-level ones and then there are a few inexpensive ones. "The reason those really expensive items are there -- say, $50 for a seafood platter -- is that they are the reference point. You will consider them, then perhaps consider them too expensive, but instead of trading all the way down for the cheapest options ($19), you will likely settle at the middle ($30), thinking you got a deal relative to the pricey entrée. The important part here the idea of anchoring -- establishing a high reference price (the original iPhone) and then offering reduced price choices. Without the initial high-priced offering (that may never be bought), the reduced-price choice would have seemed expensive. Since many people will intentionally choose the middle of a given price range in order to be "reasonable", we can push this middle range up considerably by artifically offering higher-priced merchandise. The Washington Post 11 april, 2008 The Monty Hall Problem and Monkeys The question here is if you have a group of monkeys who like red, blue and green M&M's about equally, experiments have shown that: 1. if you give the monkey a choice of two M&M's of two colors at first 2. then give him a choice of two M&M's not the same color as he chose 3. he will reject the same color twice For example, you give a monkey a red M&M and a blue M&M, and he picks the red one. Then you give him a blue M&M and a green one. Two-thirds of the time, he will reject the blue M&M the second time as well. Psychologists have made a big deal about this, claiming that having rejected the blue M&M the first time, the monkey will reject it the second time, "rationalizing" that he doesn't like blue M&M's anyway, to avoid the thought that maybe he made the wrong choice. This is a mis-reading of statistical evidence. Even the smallest difference in the monkey's preferences will account perfectly for the statistical results found in these experiments. To see how this works, let's take a more obvious example: There are three items: 1. a sugar cube 2. a lettuce leaf 3. a pepper corn Let's assume that the monkey loves sugar, will eat lettuce, and hates pepper. We try the three possible scenarios with the monkeys countless times, and statistically we see that if he rejected something the first time, he rejected it the second time exactly 67% of the time. Here's why. There are three possible pairs of articles offered as a first choice: 1. sugar & lettuce 2. sugar & pepper 3. pepper & lettuce The guiding principle is that the monkey will NOT eat the pepper. For the three cases above, here are the first two choices made by the monkey: round 1 round 2 1. sugar / lettuce (doesn't reject the same thing twice) 2. sugar / lettuce (rejects pepper both times) 3. lettuce / sugar (rejects pepper both times) Two-thirds of the time, the monkey will reject the same thing the second round that he rejected the first round. Is it because he's trying to rationalize his choice? Or just that he doesn't want to burn his tongue? It is obvious from this example that there is no deep psychological phenomenon at work. It's just simple preference for one thing over another. In order for such an experiment to have psychological implications, it would be necessary to prove that the monkey has an absolutely equal preference for the three articles. This would be the case if the element he chose first varied randomly. For example, if the same monkey, when tested on separate occasions, chose the lettuce, the sugar, and the pepper with equal frequency, then we would be closer to some sort of psychological discovery. The New York Times 10 april, 2008 The Monty Hall Problem The situation is like a classic cups problem. There are three cups, and under one of them is a nut. You pick a cup, and the presenter then proceeds to turn over one of the "wrong" cups, under which there is nothing. At this point, you can either stay with your choice, or pick the third cup. Question: are you better off staying with your choice or switching to the third cup, that neither of you has chosen? Intuitively, you might think that you're better off staying with your choice: there's a 50/50 chance you're right,isn't there? The answer is no. There's only a 33% chance that you've picked the right cup, and there's a 67% chance that the third cup is the right one. So you're much better off choosing the third cup. You don't believe me. To see how it works, here are two ways to visualize the problem differently: 1. When you make your first choice, there is a 67% chance you picked the wrong cup. Nothing changes that. So, when you are in the second round, with two cups to choose from, you know that still, there is a 67% chance your first choice was wrong. It follows logically that there is a 67% chance that the other cup is the right one. 2. Changing the scale of the problem makes things more obvious. Let's say that there are 1000 cups. You choose a cup, then the presenter takes away 998 other cups. That leaves the cup you chose, and one other one. Do you still think that there's a 50/50 chance your choice is right, just because there are two cups? Isn't it obvious that although you chose at random, the presenter will usually be certain that of the 1000 cups, only that one he left is the right one? So you can see that choosing one out of two cups doesn't at all imply that you have a 50/50 chance of being right. The fact that the presenter left you a cup implies that there is a better than even chance that it's the right one. For more information, see "The Monty Hall Problem and Monkeys."