The Power of Common Knowledge

Sometimes, even the littlest of information gives one a wealth of information. Let me give you a short story.

The story takes place in a benightedly sexist village of uncertain location. In this village there are many married couples and each woman immediately knows when another woman’s husband has been unfaithful but not when her own has. The very strict feminist statutes of the village require that if a woman can prove her husband has been unfaithful, she must kill him that very day. Assume that the women are statute-a biding, intelligent, aware of the intelligence of the other women, and, mercifully, that they never inform other women of their philandering husbands.

As it happens, twenty of the men have been unfaithful, but since no woman can prove her husband has been so, village life proceeds merrily and warily along. Then one morning the tribal matriarch comes to visit from the far side of the forest. Her honesty is acknowledged by all and her word is taken as truth. She warns the assembled villagers that there is at least one philandering husband among them. Once this fact, already known to everyone, becomes common knowledge, what happens ?

The answer is that the matriarch’s warning will be followed by nineteen peaceful days and then, on the twentieth day, by a massive slaughter in which twenty women kill their husbands.

To see this, assume there is only one unfaithful husband, Mr. A. Everyone except Mrs. A already knows about him, so when the matriarch makes her announcement, only she learns something new from it. Being intelligent, she realizes that she would know if any other husband were unfaithful. She thus infers that Mr. A is the philanderer and kills him that very day.

Now assume there are two unfaithful men, Mr. A and Mr. B. Every woman except Mrs. A and Mrs. B knows about both these cases of infidelity. Mrs. A knows only of Mr. B’s, and Mrs. B knows only of Mr. Ns. Mrs. A thus learns nothing from the matriarch’s announcement, but when Mrs. B fails to kill Mr. B the first day, she infers that there must be a second philandering husband, who can only be Mr. A. The same holds for Mrs. B who infers from the fact that Mrs. A has not killed her husband on the first day that Mr. B is also guilty. The next day Mrs. A and Mrs. B both kill their husbands.

If there are exactly three guilty husbands, Mr. A, Mr. B, and Mr. C, then the matriarch’s announcement would have no visible effect the first day or the second, but by a reasoning process similar to the one above, Mrs. A, Mrs. B, and Mrs. C would each infer from the inaction of the other two of them on the first two days that their husbands were also guilty and kill them on the third day. By a process of mathematical induction we can conclude that if twenty husbands are unfaithful, their intelligent wives would finally be able to prove it on the twentieth day, the day of the righteous bloodbath.

I hope you had an ‘aha’ moment.

US College Admission Statistics for 2011

This table includes the Ivy League + 2 and other competitive universities in the United States for applicants in the 2010-2011 pool.

Ivy+2	Admits	Applic	Rate
Brown	2,692	30,946	8.70%
Columb	2,419	34,929	6.93%
Cornell	6,534	36,392	17.95%
Dartmo	2,178	22,385	9.73%
Harvar	2,158	34,950	6.17%
MIT	1,715	17,909	9.58%
Penn	3,880	31,659	12.26%
Princet	2,282	27,189	8.39%
Stanfor	2,427	34,348	7.07%
Yale 	2,006	27,282	7.35%


Select	Admits	Applic	Rate
Chicago	3,446	21,773	15.83%
Duke	3,739	29,689	12.59%
JHU 	3,550	19,388	18.31%
NorthWe	5,575	30,975	18.00%
NotDam	3,995	16,543	24.15%
Tufts	3,735	17,130	21.80%
WUSTL	4,440	28,826	15.40%

LACs	Admits	Applic	Rate
Barnard	1,284	5,154	24.91%
Bates	1,396	5,195	26.87%
Bowdoin	1,022	6,554	15.59%
Buckne	2,161	7,937	27.23%
Carlet	1,474	4,977	29.62%
CMC	619	4,481	13.81%
Colby	1,505	5,175	29.08%
Dickins	2,531	6,061	41.76%
Grinne	1,315	2,966	44.34%
Swart	977	6,547	14.92%

Public	Admits	Applic	Rate
UCLA	15,551	61,513	25.28%
UNC	6,965	23,726	29.36%
UVA	7,750	24,010	32.28%

 

Bookin at 1737 hrs

What a weird time to book in. And no army-related posts for this week as a solemn reminder that I’ll be confined in camp next week.

Boohoo. 🙂

Okay actually I just spent 1.5 days playing Final Fantasy III on my iPhone. The 3D graphics is a refreshing change from the previous version.

Alright got to prep my uniform now.

An Intense Emotion

I have this theory that the more important and intimate the emotion, the fewer the words are required to express it. For instance, in dating,

“Will you go out with me?” Six words.

“I think I care for you.” Five words.

“You matter to me.” Four words.

“I love you.” Three words.

“Marry me.” Two words.

So what’s left? What’s the most important and intimate word you can ever say to somebody?

It’s “goodbye.”

— J. Michael Straczynski