Home >Opinion >Gliding past a century

The mathematician Richard K. Guy is arguably best known for discovering a glider.

Assuming that’s an intriguing-enough opening, let me explain. In 1970, the British mathematician John Conway invented a board game called, simply, “Life". Now, this is not a game in the conventional sense: there’s no way to “win", nor do you play against an opponent. In fact, Life doesn’t even need a player as it proceeds. You just set up an initial state and then watch what happens.

Life happens on a grid of squares that stretch in every direction (imagine an infinite chessboard). Each square, or cell, is either alive or dead (or call it black or white, filled or empty). To start, you choose a certain number of cells to be live—at random, or in a pattern, whatever. Each cell now evolves according to a set of rules that considers its eight neighbours (left, right, above, below, and on the four corners).

If it’s a dead cell which has exactly three live neighbours, it springs to life (think of this as reproduction). If it’s a live cell, these rules apply:

*If it has less than two or more than three live neighbours, it dies (think of starving if you have too few neighbours, or suffocating if you have too many).

* If it has two or three live neighbours, it lives on.

Subject each cell to these rules and obviously you change the state of the game. Then apply the rules again, and yet again, on and on. You will see the patterns on the board morph in different ways. Run it as an animation—and as you watch, as the patterns on the board roam across the board and mutate, you might swear they are actually alive. Not for nothing did Conway call this “Life".

Life, from simple building blocks: a few inked-in squares, a few rules. But how does this happen? This is the endlessly fascinating question Conway’s game raises, and this is why it was and remains today a much discussed favourite among mathematicians and computer scientists.

But it goes deeper too: The game also mimics the way computers work, in the sense that Alan Turing, pioneer of computer science, described their operation. His “Turing machine" was a conceptually simple thought experiment that could simulate the power of any given computer.

Conway’s Life is like that: If you define and interpret the patterns on its board appropriately, you can in theory simulate anything a computer does.

Also fascinating about Life are patterns of cells that do particular things (or nothing: There are four patterns like that). For example, start with a horizontal row of three live cells. One application of the rule turns it into a vertical column of three; another and it switches back to the original row. This pattern is called a “blinker". Another pattern goes through 15 iterations before returning to its initial state.

As you can imagine, this essay could really do with some illustrations. Still, see Wikipedia for several interesting configurations. And you can play the game here, experimenting with your own patterns.

And then Richard Guy discovered the glider, a pattern made up of just five live squares. When you start applying Conway’s rules, it wriggles through four steps and ends up exactly the same as it started, but transposed one square away diagonally. Four more steps, and it moves along one more square. So as you keep iterating, Guy’s glider glides smoothly in that chosen diagonal direction. If you watch it on a sufficiently large board, it’s easy to imagine the glider as an intrepid spaceship, off to explore the unknown on its diagonal path, never to return.

Guy and some MIT colleagues even found a “glider gun"—a pattern of 36 live squares that emits a glider every 30th iteration. Again, if you watch this gun at work, it’s easy to imagine it as a roiling factory of sorts, shooting out a steady stream of gliders that wriggle away diagonally.

Even had he not found the glider in Life, Guy is a thoroughly interesting man. A chess fanatic in his youth, he also got a degree in mathematics. During World War II, he was with the Royal Air Force, stationed in Iceland. Later, he taught mathematics. In the 1960s, he even taught for a spell at the Indian Institute of Technology, Delhi. The 2014 Fields Medal winner, Manjul Bhargava, had an uncle who used to speak endlessly about his terrific mathematics teacher in Delhi. Bhargava was astonished to find this was the same Richard Guy whose explorations in number theory he had himself grown to admire.

Guy wears a button that says “Peace is a Disarming Concept" and still does serious mathematics: he and a Dartmouth College colleague are working on what are known as “amicable numbers". He is also known for his “Strong Law of Small Numbers"— a tongue-in-cheek but half-serious assertion that there are not enough small numbers for all the uses humankind has for them, which is why we have so many seemingly startling coincidences around us (a trivial example I mused about in my youth: For many years, the highest individual score in Test cricket equalled the number of days in a year).

On 30 September, Guy turned 100 years old. This column is my tribute to a long, productive and still-promising life. Or Life.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers explores the joy of mathematics, with occasional forays into other sciences.

Comments are welcome at Read Dilip’s Mint columns at

Subscribe to Mint Newsletters
* Enter a valid email
* Thank you for subscribing to our newsletter.

Never miss a story! Stay connected and informed with Mint. Download our App Now!!

Edit Profile
My ReadsRedeem a Gift CardLogout