Life Is Just A Big Math Problem

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A few iterations of “playing” Conway’s Game of Life from How To Speak Machine

Back in 1985, I took my first computer science course at MIT. We had spent the whole term discussing concepts borne completely in text, numbers, and punctuation marks.

I was so hungry to see something visual. Perhaps it’s because I was one of a handful of freshmen who had brought the new Apple Macintosh computer to campus — and was made fun of because it had pictures on the screen rather than just text. To the upperclassmen and my peers, it all seemed terribly unnecessary.

But then there was a special presentation toward the end of term, where the brilliant, gnome-like instructor, Professor Hal Abelson, slightly aged and slightly balding, figuratively let down his hair. Having a computer science professor with a name reminiscent of the “Hal” computer in Stanley Kubrick’s 2001: A Space Odyssey always got me in an excited mood for the future. Hal took us through some new animated visualizations of The Game of Life as rendered onto a videotape by a colleague of his. Naturally for all of us who grew up on Milton Bradley games, we leaned in excitedly to see our favorite family game being played on the computer.

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But instead of colorful cards and little cars filled with people living out their lives we saw blinking dots on a black and white grid. You have to remember that at the time there was no such thing as computer animation, so our expectations were super low. But this was a new low.

I felt really stupid that day as the other nerds around me seemed to get it way more than me.

I struggled to match Hal’s excitement as he described the importance of these blinking dots. He kept saying how their patterns indicated that there was a new kind of life that could be represented inside the computer. I felt really stupid that day as the other nerds around me seemed to get it way more than me.

Many years later, after I had dipped my mind into the emerging discourse around artificial life, I finally became excited as Hal did that day back in 1984. I realize that the grid of blinking dots wasn’t alive, per se, but it represented life as an emergent property from a simple mathematical model. It wasn’t a “game” in the sense of a board game. It was more a game in the sense of how mathematicians play with complex, multi-step, logical ideas. In other words, it’s not “fun” but it’s still a game. But it definitely got Hal excited as if he were playing a game!

Conway’s Life is a mathematical expression — named after mathematician John Conway (1937–2020) — of the life of cells living on a constrained grid. At each step of the game, one of three things can happen at any point on the grid. A new cell can be born where there wasn’t one before. An existing cell can die. Or an existing cell can remain in the next step of the game. Each space on the grid can only hold one cell. The four rules (via Wikipedia) are as follows:

  1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.
  2. Any live cell with two or three live neighbors lives on to the next generation.
  3. Any live cell with more than three live neighbors dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

These rules are simple to process on a low-end computer because each rule carries a simple computable logic. What makes Conway’s Life so interesting is when it’s played over many cycles; what happens then is completely unexpected. The best way to see it is running in “living” form on a computer. From just these four rules, structures start to appear. Little groups start to move around together. Little groups start to blink together. Little groups collide into other groups, and new little groups spring up.

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Illustration of an emergent “glider pattern” in How To Speak Machine

But what’s important to note is that nowhere in the definition or rules of Conway’s Life is there the idea of a group of cells. All the rules pertain to a single cell on the grid. But because each rule is defined in relationship to its surroundings, the concept of a group emerges as an outcome of how each cell is interdependent upon the others. For me, it quickly visualized how the human body is composed of millions of competing organisms all choosing to sustain cohesion with each other. Each cell is working in relationship to the others, and the macrostructure emerges beyond the definition of its individual parts.

This metaphor can be carried over to the employees within a large corporation.

This metaphor can be carried over to the employees within a large corporation. A corporation retains macroscopic coherence because each individual worker is connected to other workers. And our interactions create different subgroups that behave in ways that are predictable — like forming peaceful subgroups that can last for years in harmony, blinking in unison forever. We can also be predictably defensive, like when organizing a movement to oust the existing leader, forcing them to glide off into the sunset.

Conway’s Game of Life is a great place to start when trying to understand how computational machinery works without actually writing computer programs. And it does a great job of showing you how truly weird computation can be. Mathematical life forms come in all shapes and sizes, from Alexa or Siri talking with you to newsfeeds in your timeline that fully adapt to you to exotic pools of dynamic black and white pixels that are like staring with a microscope into a petri dish of pond water.

Math isn’t just a part of life. It is life.

Is life just a big mathematical simulation in the end? I think so.

Interested in seeing what a “human-powered computer” was like—I posted on that here on Medium a couple weeks back. And if the topic of How To Speak Machine interests you, there’s a book for that. Thank you for tuning in! — JM

Written by

John Maeda: Technologist and product experience leader that bridges business, engineering, design via working inclusively. Happily working at Everbridge☁️ :+).

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