Back to some puzzles:

A modern version of the old question, “What happens when irresistible force meets an immovable object?” goes something like this:

With all the tensions in the world, the government funds two research programs. One is to make a new missile that can penetrate any defense, and the other is to make a shield that can withstand any possible missile strike. Both contractors claim success in their research. The government decides to fire the missile at the impermeable shield. What happens?

Many puzzles of this nature (as well as many political and religious arguments) can be solved by stepping back before attempting to answer, and asking just what is the model that has been presented. Without thinking much about it, we are puzzled by the irresistible force meeting the immovable object. A standard answer is that there is a large explosion. Nice try, but that is not right. That breezy answer is the moral equivalent of shrugging your shoulders and walking away. The issue is that we have been suckered in by the language used. When you look at the content of the terms used in the puzzle, you see that immovable objects and irresistible forces are mutually exclusive. If you have one, you can’t have the other. At least you can’t in a logical world. To have both is logically equivalent to saying you have both “A” and “not A” at the same time. So much for pure logic.

In the real world, we can only approximate the absolute conditions, so the government could get such contracts and could conduct such a test which would most likely indeed produce a large explosion, but which of the sides would win - the missile or the shield - depends on the unstated details (as in “the devil is in the details”).

Tricking listeners into accepting illogical premises and then drawing favorable conclusions from them is a favorite way of swaying public opinion.

My Grandfather used to proudly show his axe and state that it had belonged to Thomas Jefferson. Of course it had been in use all those years and had two new heads and three new handles, but it was the same one.

Some speaker whose name I forget claimed to have a sample of the Olympic flame. He had lit a small stick from one of the torches as it passed through his town, and he used that flaming stick to light the pilot on his water heater, where it is to this day. If you doubt it, you can go look at his water heater.

Back to puzzles that rely on assuming - but you have to be careful about what you assume. In this case, two mathematicians are given slips of paper by a third colleague.

To the first mathematician, he says, “The number on your slip is the product of two numbers. They can be the same number or different, but they are whole integers.” To the second mathematician he says, “The slip I gave you has the sum of the same two numbers.”

The first mathematician says, “Well, I don’t know what the two numbers are.”

The second mathematician says, “Yeah, I don’t know either.”

Then the first one says, “Now I know what they are.”

The second one says, “And so do I.”

What are the numbers? (BTW, this puzzle, like many came to me from a friend. If anyone knows the origin of it, I would like to give credit where credit is due.) The answer and analysis will follow in due course.

For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.