Once upon a time there was a village in which there lived many married
couples. There were certain qualities about this village, though, that
made this village unique:
Whenever a man had an affair with another man's wife, every woman in the
village got to know about the affair, except his own wife. This happened
because the woman who he had slept with talked about their affair with all
the other women in the village, except his wife. Moreover, no one ever
told his wife about the affair.
The strict laws of the village required that if a woman could prove that
her own husband had been unfaithful towards her, then she must kill him
that very day before midnight. Also, every woman was law-abiding,
intelligent, and aware of the intelligence of other women living in that
village.
You and I know that exactly twenty of the men had been unfaithful to their
wives. However, as no woman could prove the guilt of her husband, the
village life proceeded smoothly.
Then, one morning, a wise old man with a long, white beard came to the
village. His magical powers, and honesty was acknowledged by all and his
word was taken as the gospel truth.
The wise old man asked all villagers to gather together in the village
compound and then announced:
"At least one of the men in this village has been unfaithful to his wife."
Questions:
1. What happened next?
2. And what this got to do with stock market crashes?
Answer 1:
After the wise old man has spoken, there shall be 19 peaceful days
followed by a massive slaughter before the midnight of the 20th day when
twenty women will kill their husbands.
Proof:
We will use backward thinking for the proof. Indeed, the very purpose of
this post is to demonstrate the utility of the backward thinking style.
Let's start by assuming that there is only one unfaithful man in the
village - Mr. A. Later, we shall drop this assumption.
Every woman in the village except Mrs. A knows that he is unfaithful.
However, since no one has told her anything, and she remains blissfully
ignorant. But only until the old man speaks the words, "At least one of
the men in this village has been unfaithful to his wife."
The old man's words are news only for Mrs. A, and mean nothing to the
other women. And because she is intelligent, she correctly reasons that if
any man other than her own husband was unfaithful, she would have known
about it. And since she has no such knowledge in her possession, it must
mean that it's her own husband who is unfaithful. And so, before the
midnight of the day the old man spoke, she must execute her husband.
Now, let's assume that there were exactly two unfaithful men in the
village - Mr. A and Mr. B.
The moment the old man speaks the words, "At least one of the men in this
village has been unfaithful to his wife," the village's women population
gets divided as follows:
Every woman other than Mrs. A and Mrs. B knows the whole truth;
Mrs. A knows about philanderer Mr. B, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. B - who will be executed by Mrs. B that night; and
Mrs. B knows about philanderer Mr. A, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. A - who will be executed by Mrs. A that night.
As the midnight of day one approaches, Mrs. A is expecting Mrs. B to
execute her husband, and vice versa. But, and this is key, none of them do
what the other one is expecting them to do!
The clock is ticking away and passes midnight and day 2 starts. What
happens now is sudden realization on the part of both Mrs. A and Mrs. B,
that there must be more than one man who is unfaithful. And, since none of
them had prior knowledge about this other unfaithful man, then it must be
their own respective husbands who were unfaithful!
In other words, the inaction of one represents new information for the other.
Therefore, using the principles of inductive logic requiring backward
thinking, both Mrs. A and Mrs. B will execute their respective husbands
before the midnight of day 2.
Now, let's assume that there are exactly three unfaithful men in the
village- Mr. A, Mr. B., and Mr. C. The same procedure can be used to show
that in such a scenario, the wives of these three philandering men will
kill them before the midnight of day 3.
Using the same process, it can be shown that if exactly twenty husbands
are unfaithful, their wives would finally be able to prove it on the 20th
day, which will also be the day of the bloodbath.
