two thoughts for one so dear

sūryaṃ cakṣurgachatu vātamātmā dyāṃ ca gachapṛthivīṃ ca dharmaṇā |
apo vā gacha yadi tatra te hitamoṣadhīṣu prati tiṣṭhā śarīraiḥ ||
(Rg Veda X.16.3)

na jāyate mriyate vā kadācin
nāyaṃ bhūtvā bhavitā vā na bhūyaḥ |
ajo nityaḥ śāśvato ‘yam purāṇo
na hanyate hanyamāne śarīre ||
(Gita II.20)

paper a day : games people don’t play

Games People Don’t Play
Peter Winkler
Puzzlers’ Tribute, David Wolfe and Tom Rodgers, eds., A K Peters Ltd. (2001)

This is a short note on 4 little games that people don’t really play. Some are unfair, some are violent, but the interesting question arises for each — what is the best strategy for each player? I’ll describe two of them (with variants) — the other two are equally interesting, but there’s no point in repeating everything!

In “Larger Or Smaller”, Paula writes two numbers on different slips of paper. Victor picks one and has to guess if its the larger or smaller, winning $1 if he’s right. In one version the numbers are just different integers and in the other the numbers are drawn from a uniform distribution on [0,1] and Paula picks which one Victor sees.

Victor can do better than even (if only by a tiny amount) by adopting a clever threshholding strategy proposed by Cover. He guesses “larger” or “smaller” based on a comparison to his threshhold and will win slightly more than half the time (think about it). In the random version, the game is completely fair, with a simple strategy for Paula to choose which number to reveal.

In “Colored Hats” a dictator gives blue and red hats to a roomful of dissidents. They cannot communicate. Each can see the hats of the others and the simultaneously guess their own hat color. If they are wrong they are executed. How do we maximize the number of survivors? As a variant, the dissidents are lined up and guess from the back of the line to the front, so they can see all the hats ahead of them and hear the guesses from those behind them.

It turns out you can save floor(n/2) of the dissidents by having them pair up and guess their partner’s hat color. In the sequential version you can save all but 1 by having the first person guess based on the parity of the red hats in front of them. This provides enough bias for everyone to guess their own hat color.

This hat problem is particularly interesting because of its relation to some of the work in my Master’s thesis. So this paper is actually relevant (albeit tangentially) to my research. Plus it’s a fun and entertaining read. Recreational math and little games like this was what really got me interested in mathematics when I was younger. That and Raymond Smullyan, of course.


Via Amardeep Singh, an article in the NY Times by Kwame Anthony Appiah on cosmopolitanism. His argument (and it’s a good one) is that movements to “preserve traditional culture” are misguided:

Talk of cultural imperialism “structuring the consciousnesses” of those in the periphery treats people like Sipho as blank slates on which global capitalism’s moving finger writes its message, leaving behind another cultural automaton as it moves on. It is deeply condescending. And it isn’t true.

He talks about the reception of soap operas in different cultures — because of their own local values and beliefs, a show like Dallas does not have the same meaning and interpretation to critics in the US as it does to viewers in other countries. It’s a nice complement to the reader-response theory I’m getting in the book I’m reading now. The essay is an excerpt from a forthcoming book, which I may just have to read.

Broiled shrimp with chanterelles and champagne reduction

This is a dish I made for the New Year’s Iron Chef : Battle Champagne party at my friend Usama’s swank pad. Champagne is used thrice in the recipe. The initial idea was given to me by Alexandra, and the fresh chanterelles were generously donated by Michael and Elizabeth (he picks them fresh in the Berkeley hills). Here’s what it looks like:
Broiled Shrimp with Chanterelle Champagne Cream

1 cup champagne or cava
1/4 cup extra virgin olive oil
3 Ttbsp shallots
1/2 tsp fresh ground black pepper
2 lbs raw shrimp, deveined and peeled, leaving tails

  1. Mix marinade ingredients together with shrimp in a large plastic bag. If you’re like me and are bag-deficient, use a tupperware and toss the shrimp every once in a while to be fair. Let them marinate for around an hour.
  2. Take out the shrimp and skewer them (if grilling) or place them on a lightly oiled broiling pan (if broiling). Make sure the broiler rack is high. Discard the marinade and bag (it is tainted with disgusting shrimp cooties).
  3. Broil them for 2-4 minutes on each side until they look cooked/grilled. Let them cool and transfer to a serving dish or bowl.

3 tbsp shallots
1.5 cups champagne or cava
5 tbsp champagne vinegar
1.5 cups heavy cream
1/2 lb fresh chanterelle or other fancy-pants mushrooms
1 tsp olive oil
1 tsp thyme (or more to taste)
2 tbsp honey (or less to taste)
salt and pepper

  1. Put shallot, champagne, and vinegar in a saucepan over medium heat util it boils and reduces to 1/2 to 2/3 of its original volume.
  2. In the meantime, chop the chanterelles roughly and sautee in olive oil until they give up some juice. Once they are cooked, take them off the heat.
  3. After the sauce reduces, add the heavy cream and return it to a boil until it reduces to about 3/4 of its original volume. Add the mushrooms, thyme, honey, salt, and pepper. Reduce it until it’s thick and creamy. You can add a little flour to thicken it up if things aren’t working quite right.

Serve the shrimp with the sauce on the side. Spoon a little onto the shrimp and munch away. Of course you can make any substitutions you like, especially to lower the fat content…