“A bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?”
If your answer was $0.10, then don’t worry, you join many thousands of people who have made the same mistake. More than half the students asked at some of the worlds top graduate universities answered this wrongly and as much as 80% at less selective universities.
I recently read an interesting book that sheds some light on how the human mind thinks. Its called Thinking Fast and Slow by Daniel Kahneman, in it he argues that we have two distinct ‘systems’ that characterise our thought processes. System 1 is subconscious and automatic, ‘fast thinking’ that you would use to judge the direction of a sound, detect hostility in a voice or complete the phrase “bread and …”.
Whereas System 2 is what we tend to think of as thinking, a slower process, something we have to actively do. For example, when doing mathematical calculations, counting the occurrence of the letter ‘a’ in this post or remembering an address.
We are mostly a slave to our System 1 which runs automatically, as we are more comfortable when System 2 is not exerting much effort. Our System 2 is able to override what System 1 decides, but it tends to be lazy and as a consequence, the actions it thinks it has chosen, are in fact influenced by System 1. We want to be at ‘cognitive ease’, where our System 2 isn’t overburdened.
Now this isn’t speculation, the findings presented in the book are a result of years of tests and experiments designed to find the role that System 1 actually has on our lives. In one such experiment, designed to test the effects on what they called ‘priming’. At an office kitchen that operated an ‘honest box’, if you take milk from the fridge or teabags, you put some money back into the box. Now, in a ten week long experiment, without any explanation they placed a picture above the box, one week it was of flowers, followed by a pair of eyes for a week, alternating. Weirdly enough, on average, the weeks with the eyes picture, they collected three times as much as the weeks with the flower picture. Without any other external factors, they explained this as an example of System 1, influencing the decision your System 2 makes on how much money to put back in the box. A similar effect was seen in a study by Newcastle University who put a picture of staring eyes above a cycle racks and found crime dropped by 62%. You can read more about that here.
In another experiment they tested the effect they described as ‘substitution’, where your System 1 answers questions that your System 2 doesn’t know or finds difficult. When they asked the following questions to college students: “How happy are you these days?” followed by “How many dates did have last month?”, there was no link between the responses to the two, however, when asked in reverse order, dates followed by happiness, they found the responses were nearly perfectly correlated. They explained this as System 1 answering the question about happiness by substituting it with how many dates they had.
Was Gandhi more or less than 144 years old when he died?
How old do you think Gandhi was when he died?
Now, unless you happened to know the precise answer, the framing of the first question, unless completely absurd, actually had an “anchoring” effect on your answer to the second question. (He was in fact seventy-eight if you were wondering). In another experiment such experiment a set of people were asked the following:
Is the height of the tallest redwood more or less than 1,200 feet?
What is your best guess about the height of the tallest redwood?
This of course only works if you don’t happen to be an expert on the height of trees. Now another group of people were asked the same set of questions but instead of 1,200 feet as the anchor, they were asked whether it was more or less than 180 feet, that’s a 1,020 feet difference! Remarkably, the guesses for the higher anchor group gave an average of 844 feet compared to 282 feet for the lower anchor. In multiple experiments, they found that the anchoring effect is actually around 55%, that is, your system 1, on average, is anchored by 55% to the anchor (ie 100% would be if you stick to the anchor). In a more sinister example, they found a similar effect from the sentencing for shoplifting from a group of judges after they were asked to roll a pair of dice.
What I have learned from this book is that my System 1 is generally quite good at what it does. It is the results of human evolution, built deep within our nature, to survey our surroundings, make quick judgments and reactions. But that accuracy is sacrificed for that speed and to compensate for that, System 2 has to work harder when it really doesn’t want to, preferring to let System 1 get by on its own (this has actually been measured, we use more energy when performing mentally strenuous tasks compared to simpler ones, even in something as fundamental as adding 1 or 3 to a number there is a measured difference). In the question at the start about the cost of a bat and ball, even if you did come to the correct answer, you almost certainly thought of $0.10 first, whether your System 2 jumped in to correct your System 1 is somewhat a measure of how ‘sharp’ it is.
I personally believe after reading this, that the difference between people considered intelligent or not is their ability for System 2 to detect and correct System 1‘s mistakes. Our ability to keep our System 1 in check is perhaps the difference between academic success and mediocrity as many exams questions are framed to exploit this.
I found the book fascinating, and the author rightfully won a Nobel prize for his work. If you want to learn more about psychology and human cognition or are just curious about how the mind works, Thinking fast and slow is a must read. It also has good tips and techniques on how to sharpen your System 2 and reduce Systems 1‘s control over it, you will be a better person for it.
Also, what did the ball actually cost? Let us know in the comments.