The Thinking Page · since 1997

Think better, on purpose.

The web's original home for thinking better — since 1997. Systems thinking, creativity, cybernetics, and cognition: four lenses on a single question — how do we see more clearly, and decide more wisely?

“A truly great intellect takes a connected view of old and new, past and present, far and near.”

— Fred Scott & Joseph Denney
A thinking trap, in miniature

The four-card problem

Four cards, each with a letter on one side and a number on the other, show E · K · 4 · 7. The rule to test: if a card has a vowel on one side, it has an even number on the other.

Which cards must you turn over to catch the rule being broken? Most people are confident — and most people are wrong.

Show the lesson (not the answer) →

The pull is to flip the vowel and the even number — the cards that could confirm the rule. But the card that can actually break it is the odd one: turn over the 7, and if a vowel hides behind it, the rule is false. Better thinking means looking for the evidence that would prove you wrong.

Play the full puzzle →

About

Daniel Aronson

The Thinking Page began in the late 1990s and became, for a time, the #1 result on the web for “thinking.” It has always had one aim: to bring complementary perspectives on how we think into a single place, so each can learn from the others — and so can we.

More about Daniel →

The book

The Value of Values

How leaders can grow their businesses and enhance their careers by doing the right thing. (MIT Press.)

Learn more