Cellular automata could describe quantum physics, the universe and biological evolution
First of two parts
To Shakespeare, all the world was a stage. To natural philosophers of Newton’s era, it was a mechanical clock. Physicists of the 19th century viewed reality more like a steam engine. Today a fair number of scientists regard nature as a computer.
You can’t blame scientists for conceiving of the universe in terms familiar from their everyday life. That’s just the way that thinking works, whether it’s about the laws of nature or anything else. And you have to admit that nowadays computers have invaded everyday life so thoroughly that it’s only natural for scientists to think about nature in a computational way.
Fortunately, describing the universe as a computer does make a certain amount of sense. Laws governing how the universe works are expressed in mathematical formulas. You use those formulas to compute what nature will do, such as when the moon will position itself for the next solar eclipse. Just as you do a digital computation to figure out where the moon will be, nature simply conducts a real-time analog computation of its own that puts the moon where it is supposed to be.
Traditionally, the math used for computing physical laws, like Newton’s laws of motion, use calculus, designed for tasks like quantifying change by infinitesimal amounts over infinitesimal increments of time. Modern computers can help do the calculating, but they don’t work the way nature supposedly does. Today’s computers are digital. They process bits and bytes, discrete units of information, not the continuous variables typically involved in calculus.
From time to time in recent decades, scientists have explored the notion that the universe is also digital. Nobel laureate Gerard ’t Hooft, for instance, thinks that some sort of information processing on a submicroscopic level is responsible for the quantum features that describe detectable reality. He calls this version of quantum physics the cellular automaton interpretation.
Cellular automata are like simplified computers, implementing algorithms, sets of step-by-step instructions as in computer programs. ’t Hooft is not the first to suggest that the universe is in some way like such computers. Cellular automata’s origins go back to work by Stanislaw Ulam and John von Neumann in the 1940s and ’50s. But their potential for science most deeply was explored in the 1980s by the mathematician Stephen Wolfram. Wolfram left science to become an entrepreneur, but in 2002 he compiled his cellular automaton research into a self-published book called A New Kind of Science.
As described in depth in Wolfram’s book, the simplest cellular automata are just rows of squares, like pixels on a computer screen (each pixel is a “cell”). A pixel can be either white or black, corresponding to 0 or 1 as in the binary math used by digital computers.
Suppose that you start out with one black square on the top row of the screen, smack in the middle. All the other pixels are white. A cellular automaton specifies rules for how the colors of the squares should change in each subsequent row. (Technically, we’re talking about “time steps,” with each step forward in time progressing down one row.)
Usually, a cellular automaton’s rules specify color changes based only on the current color of the square and the color of its immediate neighbors. So for instance, if you start with one black square on the first row, its two neighbors are both white. The rule might be to switch colors if your neighbors are both white, otherwise stay the same. So the center square would switch to white in the second row. Or it might be to switch colors if you are the same color as both your neighbors. Or to switch colors only if both neighbors are the same color as you are.
These examples could go on and on. In fact, there are 256 possible rules for how to change colors for a given starting cell and its two neighbors. (Each of the three can begin either in black or white, giving eight possible starting configurations; a cell can change in two ways for each configuration; and 2 to the 8th power is 256.) Wolfram’s book catalogs the properties of all 256 possible cellular automata rules.
Many of the rules produce nothing interesting — after a while, the screen turns all black or all white, for instance. Or a line just runs straight down the center of the screen. Some rules produce interesting patterns, like nested triangles. A few produce enormously complex patterns, and even the impression of motion, such as blocks of black squares moving about the screen and colliding, like billiard balls.
Wolfram’s studies led him to conclude that all the complexities of the natural world could evolve from cellular automata–like processes — simple rules applied to simple starting conditions. Like ’t Hooft, Wolfram suspected that quantum phenomena could be derived from cellular automata rules, along with the rest of particle physics, relativity and other aspects of physics. Wolfram even contended that biology, including evolution, was the output of cellular automata in action. He suggested that evolution did not require Darwinian natural selection, because all biocomplexity could be produced just by the operation of simple cellular automaton rules.
Wolfram’s approach to science has not exactly seized command of the scientific enterprise. But from time to time new papers do appear applying cellular automata to various research fields, including evolution and even the origin of life. In one recent paper, for instance, Theodore Pavlic and colleagues at Arizona State University describe a way that natural selection and cellular automata processes can collaborate in evolution.
While a cellular automaton can evolve into complex patterns, Pavlic and colleagues write, it does not encounter the feedback that occurs in an evolving biological system. With the evolution of life, the natural selection “rules” for survival are imposed by the environment — your best strategy for surviving depends on features of the environment you find yourself in. But as members of a species interact with an environment, they change that environment (by eating prey, for example, or polluting the water, or fertilizing the land). When the environment changes, the rules for surviving may change as well. Life’s activity generates feedback that influences the rules of life.
“Each new generation of a population leaves an indelible mark on its environment and thus affects the selective pressures that shape future generations of that population,” Pavlic and colleagues write in their paper.
In cellular automata, the rules are ordinarily specified at the outset, remaining the same for all subsequent time steps. No feedback.
Pavlic and collaborators, though, have developed cellular automata simulations in which the rules do change. At each time step, the cellular automaton assesses its configuration and then chooses a rule based on that configuration. As the configuration changes, the rule changes also.
This approach adds feedback to cellular automata based on their own evolution, like the self-referential feedback in naturally evolving systems. Simulations show that such cellular phenomena develop disconnected regions with complex patterns, sort of like sub-automata operating within the main automaton structure. Conceivably, Pavlic and colleagues suggest, those processes cold be a model for processes like the differentiation of real biological cells within the body to perform specialized functions.
On a deeper level, the idea of self-referential feedback may be crucial not only in the evolution of life, but for its origin as well. It may even be that the algorithmic nature of cellular automata could be the key to removing a major barrier to explaining life’s origin — defining what life is to begin with. It’s pretty hard to explain the origin of something if you don’t know what it is. Two of Pavlic’s coauthors explored that notion in sufficient depth to warrant further blogging, in Part 2.
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