INNOVATION: United States government teams up with Coursera

Via the New York Times:

Coursera, a California-based venture that has enrolled five million students in its free online courses, announced on Thursday a partnership with the United States government to create “learning hubs” around the world where students can go to get Internet access to free courses supplemented by weekly in-person class discussions with local teachers or facilitators. 

The learning hubs represent a new stage in the evolution of “massive open online courses,” or MOOCs, and address two issues: the lack of reliable Internet access in some countries, and the growing conviction that students do better if they can discuss course materials, and meet at least occasionally with a teacher or facilitator.

MATHEMATICS: Gathering for Gardner - "How to win at Wimbledon" - additional thoughts

A couple more points : (1) the first related to  Bayesian updating; and (2) the second related to framing of problems.

-+-

I believe that the choice you should make depends on how good you are at tennis (at base level). If your only chance of getting even one point against Federer is if he makes a double fault, then you should choose 6-0, 6-0, 6-6 (6 - 0). If you are good enough to perhaps win a game against Federer with non-vanishing odds, then your optimal strategy may be different. The reason for this is Bayesian updating.

- Supposing you choose 6-0, 6-0, 5- 0 (40 - love). If you are really bad, then Federer will adjust his game once he realizes how bad you are. He may choose to serve differently with an intention to avoid double faults as much as possible at the risk of making a bad serve. He has essentially adjusted his per-point win probability. If you, dear reader, are really bad, then one must adjust one's model to account for this Bayesian updating. Thus, 6-0, 6-0, 6-6 (6-0) might be the more realistic solution. Once FedEx realizes you are terrible, you will be toast.

-+-

Another thing to consider - this one very tricky judgement bias and psychological effect, namely, the "Overconfidence effect". Consider the following two examples :
(1) A survey of 1 million high school students showed that 70 percent think they are above-average leaders (only 2 percent rated themselves below average). [1]
(2) In another study 94 percent of college professors claimed that their research was above average. (See Seed magazine reference below : [1])

People may think that they may actually have a chance of taking even one point off Federer whereas in reality, that probability p may be much, much closer to zero. The "6-0, 6-0, 5- 0 (40 - love)" solution may suffer from this bias for people who are somewhere between the good to great spectrum.

-+-
Another point, this one related to the framing of problems.

A puzzle is not the same as a mathematical problem. Whereas a mathematical problem is in the abstract, a puzzle may add additional constraints because it is set in the real world. In my solution, the chances of Federer actually dying may seem like a humorous suggestion or an aside but such a probability must, in fact, be taken into account in the real world. Another thing to consider is that Federer may be tired (this point, which is Amit Chakrabarti's, is different from the situation of Federer actually dying).

Again, a puzzle is not the same as a mathematical problem. If constrained optimization is what you want, then the puzzle setter would want to state the problem more carefully. Settings in outer space are an oft-used techhnique for framing such problems so as to ensure strict mathematical correspondence. Use them. Robots are another useful device. Use them too.
-+-
References

[1] http://seedmagazine.com/content/article/on_overconfidence/

-+-
Update (July 8): fixed typos. updated the post a bit.

ECONOMICS: Raj Chetty is wrong

Raj Chetty writes in the NYT that economics is a science. He is wrong.

My email to Greg Mankiw.

-+-

As a computer scientist with an interest in the Philosophy of science, I am sad to see this title for an article in the NYT. 

For economics to be a science, it would need to have two capabilities, which it does not possess unlike the core sciences: experimentation and verification.

<stuff deleted>

-+-

Postscript: I love Krugman's elegant response to Raj Chetty's article. Elegant is the word for it. Note the use of the word 'maybe'. The reason why it is 'maybe' a science is that it is based on 'hard data'. The reason why it is 'maybe' not a science is that it is not based on reproducible experiments and verification.

-+-


Maybe Economics Is A Science, But Many Economists Are Not Scientists

Raj Chetty stands up valiantly for the honor of his and my profession, arguing that economics is too a science in which careful research is used to falsify some hypotheses and lend credibility to others. And in many ways I agree: there is a lot of good research in economics, maybe more than ever as the focus has shifted somewhat from theoretical models loosely inspired by observation — which, as he suggests, was my forte — to nitty-gritty empirical work.

MATHEMATICS: Gathering for Gardner - "How to win at Wimbledon" - solution

My email to Peter Winkler.

-+-

This is in reference to the "How to Win at Wimbledon" puzzle at :

http://www.math.dartmouth.edu/~pw/solutions.pdf

I have a better solution to your problem. In fact, you can win at Wimbledon with probability 1.

My belief is that the theory advanced by Amit Chakrabarti (who I happen to know actually :) ) is correct. I can see that he is a man after my own heart. The only thing about his theory is that it does not go far enough. The number N that was chosen may not be large enough - assuming that the players can come back for the match if it goes beyond a certain limit, the players may not even be all that tired.

The ideal scores, then, are :

(i) 6-6 (LargeNumberN - LargeNumberNMinus2), 6-6 (LargeNumberN' - LargeNumberN'Minus2), 6-6 (6-0)

(ii) 6-0 , 6-6 (LargeNumberN - LargeNumberNMinus2), 6-6 (6-0)

(iii) 6-6 (LargeNumberN - LargeNumberNMinus2), 6-0, 6-6 (6-0)

Under (ii) and(iii), one needs to choose a sufficiently large N. In particular, one must choose an N that is so large that Roger Federer is at the brink of death. In fact, N is so large and the man is so close to death that if he serves even once more, he will die. Furthermore, it is his turn to serve. That is the situation to find oneself in. 

I believe that I and Amit, *we* are the Ones we have been waiting for. :)

- Anand

-+-

MATHEMATICS: Gathering for Gardner - Winning at Wimbledon

As part of the Gathering For Gardner (G4G) celebrations worldwide, we will be pondering the following puzzle:

-+-

As a result of temporary magical powers, you have made it to the Wimbledon finals and are playing Roger Federe for all the marbles. However, your powers cannot last the whole match. What scoare do you want it to be when they disappear, to maximize your chances of hanging on for a win?

-+-

MISCELLANEOUS: Global warming slowdown linked to cooler Pacific waters

From the BBC:

Scientists say the slow down in global warming since 1998 can be explained by a natural cooling in part of the Pacific ocean. 

Although they cover just 8% of the Earth, these colder waters counteracted some of the effect of increased carbon dioxide say the researchers. 

But temperatures will rise again when the Pacific swings back to a warmer state, they argue.

DIET: The Classical Sanskrit Diet idea, or Decision Analysis for Diets - a summary

I would like to close out (or, at least begin to close out) the series of posts on the Classical Sanskrit diet by stating what you should take out of this exercise.

First of all, I must note that the Classical Sanskrit diet is not a diet per se. It is a set of tools to help you make good dietary decisions. Secondly, elements of the Classical Sanskrit Diet can be applied to a number of other diets and so you may want to think about how you can use the fundamental "Decision Analysis ideas", as it were, to your own diet. Thirdly, one of the basic ideas in the Classical Sanskrit Diet is that if we went back to eating like people did prior to the twentieth century, our dietary outcomes would improve. This seems to be a sound idea, generally speaking.

And finally, another of the basic ideas in the Classical Sanskrit Diet is that we should eat plenty of fruits and vegetables. Fruits and vegetables comprise the largest portion of this diet. Indeed, the set of foods to eat is directly borrowed from Dean Ornish's books. There is a list of foods listed in one of his books that essentially can be eaten in unlimited quantities. So, my thinking was that if all you did was to simply eat two out of three meals consisting only of foods in that list, you are probably already better off than you are right now. The diet I adopted was pretty simple : for breakfast and lunch, simply eat as much of the foods you want as long as they come from the list of foods that you can eat in unlimited quantities. By the time, it is time for dinner, you are probably already so full that you won't overeat. So, for dinner, I essentially allowed myself to eat anything I wanted - as long as the items were not in the "OUGHT NOT TO EAT" list. Items in the "OUGHT NOT TO EAT" list are reserved for special occasions.

-+-

Enough of that. Let us get to business. Let us see how "Decision Analysis ideas" are applied in the Classical Sanskrit diet:

• Parsimony in decision making: Do not make the process of deciding what to eat a very laborious process. Make it as parsimonious as possible. 
• In the Classical Sanskrit Diet, you basically have to memorize the list of foods in the Sanskrit language just once. Once you do that, your analysis of which food to buy in the supermarket is not dependent on the following variables: what foods you have already eaten that week, what foods you have sitting in the refrigerator, et cetera. You simply have to check whether the foods you ate are part of this Classical Sanskrit Diet list.
• Minimize decision time and minimize variable costs: Minimize variable costs of decision making. Allow for considerable flexibility in fixed costs.
• Again, in the Classical Sanskrit Diet, you basically have to memorize the list of foods in the Sanskrit language just once. That is a fixed cost. Once you do that, everything else is just about referring to a fixed list. That should not be hard. 
• Employ distinctions between SHOULD and COULD, employ distinctions between SHOULD and SHOULD NOT, employ distinctions between MAY and COULD: Try to invest a certain amount of "fixed costs" in terms of what foods you COULD eat, what foods you SHOULD try to eat and what foods you SHOULD NOT eat.
•  It is a good idea to divide what you eat into four parts - the whitelist, the blacklist, a third list, which can perhaps be called the "ought to eat list", and a fourth list which can be called the "ought not to eat list". 
• The blacklist consists of foods you absolutely should not eat. This may be because of dietary restrictions due to illness. e.g. sugary foods for a diabetic. You can come up with this list based on advice from your doctor.
• The whitelist consists of the set of foods that is within the realm of possibility for the dieter. It is important to say, for instance, that a steak is part of a diet even if it is to be consumed very rarely. Save the steak for special occasions by all means, but put it on your whitelist. By doing so, you have identified the set of foods that are permissible. If you are a vegetarian, you would probably not put steak on there. Creating these distinctions creates "Clarity of Thought".
• The "Ought to eat" list consists of the set of foods that the dieter ought to eat : to create this list, identify a set of foods that you think should be on the "ought to eat" list. Americans generally don't eat enough fresh fruits and vegetables, so if you are anything like the typical American, you probably want to add a number of fresh fruits and vegetables to the "ought to eat" list. Again, creating this sort of distinction creates "Clarity of Thought"
• The "Ought not to eat" list consists of the set of foods that the dieter ought not to eat : this is the list in which most people get stuck. The production process of foods in America is a very sophisticated one. A very large number of new foods are created and it is seldom recognized that many of them are not easy to analyze by means of conventional diet. The big mistake many diets make, including the Atkins diet, is that they don't sufficiently clarify what is on the "Ought not to eat" list. This again is a very important distinction to make.    
• The problem of "known unknowns" : The problem with most diets is essentially that new foods are not correctly factored in. Consider a new food - say, deep fried Tootsie rolls - that comes on to the market. This new food is factored into the diet only by means of certain variables such as calorie content. However, certain other important variables such as the constituents of the food are actually not take into consideration at all. This is obviously flawed. Think about it. A new food has jus come on the market. We don't know what lecithin or tannin or whatever else the food contains actually does to your body. Why then should diets not take into consideration the fact that there is a significant "known unknown" about these new foods?
• Employ mnemonics: It is very hard to keep all the above lists straight. So employ mnemonics.
• In the Classical Sanskrit Diet, we utilize Sanskrit as a way of remembering the names of foods on various lists. However, you are free to employ other mnemonics.

It is important for you to realize that what I am offering is not a new diet. Instead what I am offering is a new way of thinking about diets. 

Every day, you make a large number of choices about what you eat. Why not get more intelligent about that? Why not make better decisions?