Significance of Conway's Game of Life || What is Conway's Game of Life?
On another fresh morning in march of 1970, while preparing the mathematical games’ column Martin Gardner opened a letter from John Horton Conway, (then) mathematician at the University of Cambridge. The letter contained 12 pages of a very new and interesting game, page 9 of that bunch of ideas started with the heading “The Game of Life”.
Yup, it didn’t even take half of the total pages to make a game that left a scar on the computational mathematics of all time.
What is this “Game of Life”?
Another of those computer games which were being developed those days, but, unlike the majority of the games, it was not there to entertain the user, but to mesh up the wires of the brain (which was a kind of entertainment for those mad geniuses).
In more technical terms it was a cellular automaton, that is in terms of Wikipedia “is a discrete model of computation”.
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| Bill Gosper's Glider Gun in Game of Life and The creator of the Game of Life J H Conway |
To visualize, a cellular automaton consists of a grid and each cell in that grid can exist in a finite number of states, like on and off. With the states, each cell also has a set of cells from its surrounding, which make up the neighboring cells with their respective states. And the state of each cell at t = 0, i.e. initially is predefined or can be defined. And then with incrementing the ‘t’ with +1 marks a new generation is obtained from the initial generation i.e. at t = 0 according to some set rules (generally mathematical functions). The rules apply to all cells in that grid simultaneously and with each increment in time generates a new generation where the state of the cell is defined by the state of the cell in the previous generation and the set of rules.
So, it is clear from this, that once you put the initial configuration of the cell and allow incrementation on time it will automatically spawn the next generation and the next, and so on.
From this cellular automaton thing, it was clear to Conway that this game needs only one input, i.e. the initial generation or the generation at t = 0, and the further generations will be determined by the previous generation and thus will require no other inputs, only implementation of rules with incrementation with time.
And that’s why Conway called it a ‘zero player game’.
The Game:
As mentioned earlier, this game requires no other input than the initial generation, and then after this will continue even if there is no player around to keep its name’s meaning and I mean it.
So yes, being a cellular automaton, the only player here is the rule or better the set of rules.
And Conway chooses the players very carefully so that :
There should be no explosive growth.
There should exist small initial patterns with chaotic, unpredictable outcomes.
There should be potential for von Neumann universal constructors (As per J. V. Neumann life could be defined by any creation which can self-replicate and simulate a Turing Machine, and he was thinking of ‘making life’ by satisfying these conditions using electromagnetic components floating randomly in a fluid).
The rules should be as simple as possible, whilst adhering to the above constraints.
And after assessing all these conditions for rules, he came up with a set of rules that are:
Birth Rule: An empty, or “dead,” cell with precisely three “live” neighbors becomes live.
Death Rule: A live cell with zero or one neighbor dies of isolation; a live cell with four or more neighbors dies of overcrowding.
Survival Rule: A live cell with two or three neighbors remains alive.
In accordance with the rules with each generation, some cells live, some die and “Life-forms” evolve, one generation to the next.
So yes, this was the whole game, The game of life, the game of rules.
Significance of “Game of Life” in understanding the universe:
It is one of the simplest algorithms that can show self-organization and emergence. Besides being that simple, it can show an extremely varied behavior just based on a slightly different initial state (or generation at t = 0) of the grid. Thus, the system became one of the simplest chaotic systems ever built by human beings.
And being chaotic, and easily programmable, it is one of the major points of interest in studying the chaos, and in trying to find a pattern in chaotic systems. Because it needed no fancy equipment like a slow-mo camera and other innovative methods to study each generation, the only thing you need can even be a pen and paper (yes, Conway and others created some patterns manually with pen and paper and it is also worth noting that it was released in the games section of a mathematical magazine), but seeing the randomness and huge amount of data coming out of that randomness and advent of the computer caused them to switch over the computer.
Then again there is this unsure question of whether we live in an advanced simulation of some super intelligent and advanced beings? Right, this is yet an unanswered question. But, that doesn’t stop us from assuming the answers and their consequences.
It is obvious that if the answer is a straight “No”, there will be far less race of imagination than in the case of a “Yes”, and you can just feel it.
Some people just went beyond this question assuming that the answer is a “Yes”, then they tried to assume what type of simulation would it be? Would be something fancy and predictable like modern computer games or stupid and unpredictable like Conway’s game of life.
Conclusion:
John Horton Conway, a brilliant mathematician in search of defining an interesting and unpredictable cellular automaton, created a game, initially in a pen-and-paper mode (published in a magazine) called the “Game of Life”, which not only satisfied his goals but also satisfied other’s search for a subject to study randomness and unpredictability.
Thus, this stupid-looking unpredictable game of life opened a new door to the easy and affordable study of chaotic systems, one of the famous mysteries of the known universe.
After a half-century of this blazing creation, the creator finally went on to rest forever in 2020 due to the pandemic. But, that surely doesn’t mean putting the legacy of Conway to rest. The legendary of the Game of Life will continue to thrive for centuries coming.
