The Bat and Ball Problem

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By Herb Wiseman

The promised answer to the puzzle.

In the last issue I wrote about our eyes wide shut and presented the bat and ball problem. I did not include the solution because I wanted people to struggle with the answer. Let me restate the problem, show the solutions and explain what it means.

If a bat and ball have a combined price of $1.10, and the bat has a price of $1 more than the ball, how much is the ball?

Most people automatically answer 10 cents. But inspection quickly reveals that this is the incorrect answer because that would make the bat’s price $1.10 and the combined price $1.20. There are 10 cents too much which means that the ball must be less than 10 cents.

There are two basic ways to solve this problem. One is trial and error. Choose a number less than 10 cents and more than zero and repeat the inspection. If you choose 4 cents as the price of the ball, then the bat is $1.04 and the combined amount is $1.08 or 2 cents shy of the correct total. If you choose 5cents you arrive at the correct answer.

The second way to solve the problem is with algebra which I have not used for almost 50 years but I believe is as follows.

Bat + ball = $1.10

Let x = the price of the ball

Therefore the Bat is $1 + x

Thus the Bat and ball together is $1 + x + x = $1.10 or 100 +2x = 110

Solve for x

2x = 110-100 = 10

x = 10/2 = 5

Once solved people realize how easy it is to do. But to solve this is similar to many other problems we experience in the monetary reform movement with people to whom we speak. The thinking required is what Kahneman called system two and requires more energy than system one which is automatic or intuitive.

Thus, when we send letters to MPs or finance ministers as many of us have done for decades, we experience our message falling on deaf ears.

For us the solution is easy but for those hearing the message for the first time, the energy required to “compute” what we are saying requires more energy than what they want to put into it and more time than they wish to spend. They already have a different ideology that they have absorbed and they prefer the easy answer. If this explanation is wrong then we have to assume that people who refuse to consider our views are malevolent or uninformed.

Too often we assume malice, a lack of intelligence or, more often, ignorance requiring education when it may be the failure to think at a system two level.
Our Comment.

How do we get to a system too level? Is this what John Kenneth Galbraith identified as “the emancipation of belief”?

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