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||An Open Reply to A Letter from DM||

DM, my friend, sent me a mail with this teaser this morning:

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The Simple Problem Einstein Couldn’t Solve … At first

Albert Einstein and Max Wertheimer were close friends. Both found themselves in exile in the United States after fleeing the Nazis in the early 1930s, Einstein at Princeton and Wertheimer in New York.

They communicated by exchanging letters in which Wertheimer would entertain Einstein with thought problems.

In 1934 Wertheimer sent the following problem in a letter.

“An old clattery auto is to drive a stretch of 2 miles, up and down a hill. Because it is so old, it cannot drive the first mile — the ascent — faster than with an average speed of 15 miles per hour. Question: How fast does it have to drive the second mile (on going down, it can, of course, go faster) in order to obtain an average speed (for the whole distance) of 30 miles an hour?”

Einstein fell for this teaser

Wertheimer’s thought problem suggests the answer might be 45 or even 60 miles an hour. But, that is not the case. Even if the car broke the sound barrier on the way down, it would not achieve an average speed of 30 miles an hour. Don’t be worried if you were fooled, Einstein was at first too, replying “Not until calculating did I notice that there is no time left for the way down!”

Gestalt psychologists’ way to solve problems is to reformulate the question until the answer becomes clear. Here’s how it works. How long does it take the old car to reach the top of the hill? The road up is one mile long. The car travels fifteen miles per hour, so it takes four minutes (one hour divided by fifteen) to reach the top. How long does it take the car to drive up and down the hill, with an average speed of thirty miles per hour? The road up and down is two miles long. Thirty miles per hour translates into two miles per four minutes. Thus, the car needs four minutes to drive the entire distance. But, these four minutes were already used up by the time the car reached the top.
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Here is my reply to my friend:

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Dear DM,

Gestalt thinking is NOT just reformulating a problem until its answer becomes clear.

Many a problem has its solution built in some part of it. So, for complete gestalt thinking, one has to go out of the problem, look at it from outside, discover the built-in solution, and then reconstruct the problem to exploit the solution.

It is somewhat like the out-of-body experience some people have when they think they have died, go out of their body, take a look at themselves, and find what was wrong with them. When such people revive, they become better persons, finding a solution to their agonized life in themselves.

The Indians have known it all along, but unfortunately, the two, Einstein and Wertheimer, never gave us a chance with the above problem. At any rate, the British would have intercepted our solution, and claimed it as their own. Now that we are free of the British (have been for quite some time, to be fair to them) let us apply our minds to the problem.

So, taking this problem, and going out of it in true gestalt style, we immediately recognize that the car’s moving slowly, or fast, does not depend upon whether it is going uphill or downhill. The car only moves slowly when facing the peak, but fast with its back turned towards the peak!

(We all do it, when facing a problem, or running away from it. Do we not?)

So, the problem is readily solved by driving the car uphill in reverse, turning it around (without losing any time) upon reaching the peak, and then driving downhill in forward gear, like all cars are supposed to do most of the time. In this manner, the car never faces the peak (its problem), and the task is accomplished; the problem is solved.

I hope, by this illustration, I have not only explained the application of true gestalt thinking, but also revealed an insight into the truly ingenious Indian mind. I hope that you (and legion) will be encouraged to try out a few such problems at your end. Otherwise, you all know whom to approach.

Mikupa
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