## Game changers: the importance of the puzzle

Looking forward to a few family board games at Christmas? Good, good. Steer clear of Monopoly — a dreadful, grinding game. Settlers of Catan is the game that Monopoly wishes it was although, for committed players, Puerto Rico is even better. (Agricola is the best game. But you knew that already.)

Consider the puzzle of the bridges of Königsberg — 18th-century Königsberg had seven bridges connecting two sides of a river and two large islands. The puzzle was: is there a walking route through the city that crosses each bridge only once? When the great mathematician Leonhard Euler heard about the problem, he found it “banal” but was intrigued by the fact that, despite its apparent simplicity, “neither geometry nor algebra nor even the art of counting” could solve it. And so Euler invented an entirely new branch of mathematics, graph theory.

“That was the beginning of all network analysis,” says Alex Bellos, the author of *Can You Solve My Problems?*, a new book celebrating the joys and history of puzzles. Euler’s graph theory has been enormously fruitful in chemistry, physics, sociology and, of course, computer science. The internet relies on Euler’s analysis. And it all started with a brain-teaser.

Perhaps it’s no surprise that a puzzle might lead to a mathematical breakthrough: after all, puzzles are designed to be intellectual challenges. But other pastimes have also spurred fresh ideas — for example, gambling. Perhaps the first gambler to draw inspiration from this vice was the Renaissance mathematician Girolamo Cardano, who produced the foundations of probability theory.

Three-and-a-half centuries after Cardano died, the smartest man in the world decided to use mathematics to work out how best to play poker. John von Neumann was one of the driving forces behind the development of both the atomic bomb and the computer, and he wanted to apply mathematics to social sciences — for example, analysing the success or failure of negotiations, or the formation of alliances. His contention was that a mathematical theory that could explain life should start by explaining poker: “Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do, and that is what games are about in my theory.”

The result of von Neumann’s musings — first alone, and then with the economist Oskar Morgenstern — was “game theory”, one of the building blocks of modern economics and an important tool in evolutionary biology.

This is an impressive list of ways in which games have inspired us — and we haven’t even touched on the way that computer scientists have used chess as a testing ground for their machines.

But it would do games a disservice to treat them merely as a source of intellectual inspiration. They have inspired us in other ways too. In his new book, *Wonderland*, Steven Johnson makes a convincing case for the transformative power of play and delight — for example, the Victorian designer of paleo-computers, Charles Babbage, was inspired by a captivating mechanical toy dancer.

This wasn’t the last time that pure fun changed the world of computers. The first video game that mattered, Spacewar!, was designed in the early 1960s by enthusiastic students at the Massachusetts Institute of Technology who wanted to demonstrate just what the latest computers could do. And what they could do went way beyond the technical: they could hijack our attention, trigger Pavlovian responses, even addict us, by providing a compelling and engaging challenge.

Silicon Valley visionary Stewart Brand wrote about Spacewar! in Rolling Stone magazine in 1972. He saw what the game represented: computers that ordinary people would come to love. “I saw them having some kind of out-of-body experience,” he said recently of Spacewar!’s players. “Their brains and their fingers were fully engaged.” That curious compulsion felt by every PlayStation junkie or Instagram addict was felt first by the players of this early game.

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Now, researchers at DeepMind, Google’s artificial intelligence outfit, are turning to computer games to train artificial intelligences. The AI is shown the game screen, given access to the score and a controller, and then — with no further information — figures out how to master the game. At first, DeepMind started with simple games such as Atari’s Breakout but it has recently moved on to Starcraft II, a game that requires tactics, military strategy, surprise and economic planning. Like von Neumann’s poker, learning to play Starcraft II is good training for the rigours of reality.

One of Alex Bellos’s puzzling heroes is Hubert Phillips — the man who coined the word “mezzobrow” to refer to “people of the highest intelligence who enjoy such things as crosswords, chess problems, inferential puzzles and parlour games”. Even as a child I knew about Phillips, the author of a veritable bible of card games. Phillips also wrote 200 detective stories, compiled crosswords and championed a number of classic puzzles — including the “logic grid” problems that are such a staple of the genre.

But that is not how Hubert Phillips began his career. He was a noted economist, adviser to the Liberals in the 1920s and the head of Bristol University’s department of economics. All very respectable, but thank goodness he turned to the far more important practice of having fun.

*Written for and first published in the Financial Times.*

*My new book “Messy” is now out and available online in the US and UK or in good bookshops everywhere.*