Complexity_ A Guided Tour - Melanie Mitchell [67]
Along the same lines, a 1994 article by three prominent brain researchers asked, “Is the brain a computer?” and answered, “If we embrace a broader concept of computation, then the answer is a definite Yes.” Like ant colonies, it is clear that the way the brain computes—with billions of neurons working in parallel without central control—is very different from the way current-day digital computers work.
In the previous two chapters we explored the notion of life and evolution occurring in computers. In this part of the book, we look at the opposite notion; the extent to which computation itself occurs in nature. In what sense do natural systems “compute”? At a very general level, one might say that computation is what a complex system does with information in order to succeed or adapt in its environment. But can we make this statement more precise? Where is the information, and what exactly does the complex system do with it?
In order to make questions like this more amenable to study, scientists generally will idealize the problem—that is, simplify it as much as possible while still retaining the features that make the problem interesting.
In this spirit of simplification, many people have studied computation in nature via an idealized model of a complex system called a cellular automaton.
Cellular Automata
Recall from chapter 4 that Turing machines provide a way of formalizing the notion of “definite procedure”—that is, computation. A computation is the transformation of the input initially on a Turing machine’s tape, via the machine’s set of rules, to the output on its tape after the halt state is reached. This abstract machine inspired the design of all subsequent digital computers. Because of John von Neumann’s contribution to this design, our current-day computers are called “von-Neumann-style architectures.”
The von-Neumann-style architecture consists of a random access memory (RAM) that stores both program instructions and data, and a central processing unit (CPU) that fetches instructions and data from memory and executes the instructions on the data. As you probably know, although programmers write instructions in high-level programming languages, instructions and data are actually stored in the computer as strings of 1s and 0s. Instructions are executed by translating such bit strings into simple logic operations applied to the data, which are then computed by the CPU. Only a few types of simple logic operators are needed to perform any computation, and today’s CPUs can compute billions of these logic operations per second.
A cellular automaton, being an idealized version of a complex system, has a very different kind of architecture. Imagine a grid of battery-powered lightbulbs, as shown in figure 10.1. Each lightbulb is connected to all of its neighboring lightbulbs in the north, south, east, west, and diagonal directions. In the figure, these connections are shown for only one of the lightbulbs, but imagine that all the other ones have corresponding connections.
FIGURE 10.1. An array of lightbulbs, each of which is connected to its neighbors in the north, south, east, west, and diagonal directions, as is illustrated for one of the lightbulbs. Each lightbulb can either be in state on or state off. Imagine that all four edges wrap around in a circular fashion—for example, the upper left bulb has the upper right bulb as its western neighbor and the lower left bulb as its northern neighbor.
In figure 10.2 (left box), some of the lightbulbs have been turned on (to make the figure simpler, I didn’t draw the connections). After this initial configuration of on and off lightbulbs has been set up, each lightbulb will run a clock that