Life
Is Binary
THE MATHEMATICAL BIOLOGY OF JOHN HORTON CONWAY
IN THE
YEAR
1970, John Horton Conway invented Life.
___Or more accurately, the Game of Life.
Not the one where you spin the wheel and accumulate plastic kids, but
a mathematical construct governing the behavior of cellular automata.
Fifty-dollar words aside, J.H.C. made a set of rules.
___Before we get to those rules, a little
background for those of you too young, or too stoned, to remember 1970:
Two years earlier, Stanley Kubrick’s film 2001: A Space Odyssey
had introduced the masses to a believable form of artificial intelligence
(AI). Also in ’68, scientists at Stanford University identify the
fundamental particles known as quarks. Then, in 1969, Neil Armstrong
walks on the moon, Intel Corporation develops the microprocessor, and
James Shapiero and Johnathan Beckwith isolate the first gene. Not long
afterward, Intel, with the help of Texas Instruments, unveils the first
silicon chip. Concurrent with all of these technological achievements,
Vietnam rages and the Cold War simmers.
___In his office at Cambridge University,
mathematician John Conway was not only aware of these events, he was
part of the simultaneity of them — part of a geometric progression
of knowledge and invention, accelerating, bumping and growing. Such
awareness led him to suspect that the key to artificial life (Alife)
could hide in a game.
___Being an expert in number theory, group
theory and logic, Conway was drawn to games. He studied games; he wrote
about games; he invented games. And so he began to develop an Alife
game using the framework of cellular automata, a quadratic grid of binary
information recalculated in consistent, timed intervals — in other
words, a big, moving checkerboard.
THE STUDY
OF CELLULAR AUTOMATA (CA) itself came about near the end of World War
II, when the first electronic computers — till then used exclusively
by the military — found themselves without a job. Stan Ulam and
John von Neumann, brilliant minds both, had access to these massive,
pre-transistor calculators, and when they weren’t laying the groundwork
for the first hydrogen bomb, they were codifying CA. Their purpose:
to simulate biological systems on a computer.
___Twenty years later, that was pretty
much Conway’s goal, too. His new parameters for CA were simple.
Cells should not tend to replicate quickly or without limits, nor should
they tend to die too easily. A delicate balance; ask God. It took him
(Conway, that is) several years to perfect these deceptively simple
rules:
- A square,
or cell is either on (alive) or off (dead).
-In distinct, simultaneous generations, each cell reacts to its eight
adjacent cells by remaining constant or switching.
- If a living cell is touching two or three other living cells, it remains
alive in the next generation.
- If a dead cell is touching three living cells it switches on in the
next generation. (Happy birthday!)
- In all other cases a cell dies or remains dead.
___When
applied to a grid, these rules created the conditions for gliders, guns,
ships and rabbits — descriptive names used by enthusiasts for some
of the infinite patterns and behaviors of Alife. Complex, unpredictable,
beautiful, these designs. Choose your metaphor: paramecia, battlefield,
electrons, supernova, cell division, cancer. They all work if you use
a little imagination.
___Satisfied that he’d struck a balance
suitable for Alife, Conway presented his creation, now called the Game
of Life, to Martin Gardner, who wrote the Mathematical Games column
for Scientific American. Gardner was so fascinated by the possibilities
of Life that he devoted an entire column to it in the October 1970 issue,
ã and again in the February 1971 issue.
___As Life players (150 of them, no less)
responded to the articles, it became evident that the pages of Scientific
American would not satisfy this rapidly growing community. Robert T.
Wainwright began publishing a newsletter (’cause that’s how
they did things back then) to pose questions and share new discoveries.
Lifeline was issued quarterly from March ’71 to September ’73,
and in that time chronicled the developments of patterns and movements
in Life.
___Try to consider for a second the mathematics
behind combinations even as small as six cells. Then realize that the
first Life players did these calculations manually. Much of the first
newsletter was devoted to discussing the remaining undiscovered heptominoes
(seven-cell patterns); one writer questioned the possible frontiers
for manual Alifers. Using computers, the folks at MIT were already pushing
the envelope, creating “glider guns” and documenting the behaviors
of patterns far too dense to plot manually. To realize its full potential,
it seemed, Life belonged on a computer. Three decades later that’s
where it resides.
___An application of Conway’s Game
of Life now exists for most modern platforms, including Unix, Macs,
Windows and Java. There’s even one to run on a Palm PC. There are
libraries of tested patterns — organisms, if you will, that have
accumulated from the many students of Life. Each time you play, however,
it’s like lifting a big, flat rock and not knowing what’ll
come crawling out.
___All this said, Conway’s Life hasn’t
really produced anything significant save for itself. Late-20th-century
Alife experiments, such as Dr. Thomas Ray’s Tierra, owe little
to Life’s rules. Some “Theory of Everything” positors
claim a relationship, shaky at best, between Life’s simplest glider
shape and the prequark model of a proton. So what are we players left
with but Life for Life’s sake? Which is maybe what it’s all
about anyway.
Resources
& further info:
Achim’s
Game of Life Page
Alan Hensel’s Page, a
terrific Java applett
On
Numbers and Games, by John Conway, 1976, Academic Press, Inc.
Life32 application
(great Windows port of Game of Life), by Johan Bontes
BBC's
A-life page
