Humans: not optimised for logic

Below is a puzzle that will soon be 50 years old. It was developed in 1966 by Peter Wason, a cognitive psychologist interested in the often illogical nature of human reasoning. The puzzle is a very simple logic puzzle and involves no tricks. Yet, across multiple studies less than 10% of people give the correct answer. See how you do:

Logic puzzle 1

There are four cards with a number on one side and a colour on the other. If the number is even, the card must be red on the other side.

Which cards need to be turned over to check if the above rule is followed?

Which cards could violate the rule?

Keen for the answer? Well… just wait a moment. Let’s try another puzzle:

Logic puzzle 2

You work at a licensed restaurant. Your boss asks you to make sure all patrons who are served alcoholic drinks are over 18.

Which patrons do you need to check?

Okay. Now let’s check how you did.

• The correct answer to logic puzzle 1 is the first card (number 4) and the last card (green).
• The correct answer to logic puzzle 2 is patron 2 and patron 4

Chances are, if you are like most of us, you had the answer to puzzle 1 wrong but were correct for puzzle 2. If you got both right then, congratulations! You are an unusually logical thinker.

But here’s the really interesting thing: From a logic point of view, these are both the exact same puzzle. Both puzzles involve testing a rule of the form “If P then Q”. The most common answer to puzzle one is to select the cards named in the rule — the 4 and the red. This would be logically equivalent to a bottleshop owner asking for ID from anyone buying alcohol who looks older than 18.

Often there is some degree of misinterpretation of the rule as if it read “all even cards, and only even cards, will be red on the other side”. However, the answer most commonly provided is incorrect even for that interpretation: for that rule you would need to turn over every card to confirm the rule.

Somehow the nature of the content of the second puzzle makes the correct answer “pop out”, while the first puzzle exposes limitations of our human reasoning. There are several theories about why we are so much better at the second variation of the same puzzle.

One theory is that our brains are optimised to detect violations of social rules — in this case the rules prohibiting underage drinking. Being good at detecting and enforcing social rule violations may have significant survival value — whereas being able to detect violations of arbitrary logical rules may have very few implications for survival. Another theory is that the effect is a feature of how we process information by relevance while minimising cognitive effort.

Whatever the explanation, here is what I would see as the important take-home lesson: Humans aren’t logical. We can be absolutely convinced we are right while being at the same time obviously wrong. We jump to conclusions. We ignore information that contradicts what we already think. We are messy creatures, and we can’t change that. However, by understanding our nature, and limitations, we can be a little less vulnerable to some of their consequences — perhaps a little less hurt by assuming, when our friend says “You’re five minutes late”, that it means “I’m angry with you”, for example.