People tend to engage in a form of primitive thinking known as "like causes like," psychologists have shown.
For example, doctors once believed that the lungs of a fox cured asthma and other lung ailments. People assumed that fowl droppings eliminated the similar-appearing ringworm. Freudians asserted that fixation at the oral stage led to preoccupation with smoking, eating, and kissing.
It is perhaps not surprising, therefore, that people have long thought the complexity of computer outputs was a result of complex programs.
It's been known for a while, however, that this is not necessarily the case. Computer scientists and mathematicians, notably John von Neumann in the 1950s and John Conway in the 1970s, have studied simple rules and algorithms and have observed that their consequences sometimes appear inordinately complex.
Nevertheless, it's safe to say that no one has treated this idea with anything like the intensity and thoroughness of Stephen Wolfram in his fascinating, ambitious and controversial new book, A New Kind of Science.
Simple Rule, Complex Consequences
The book is a mammoth 1,200 pages, so let me in this 800-word column focus on Wolfram's rule 110, one of a number of very simple algorithms capable of generating an amazing degree of intricacy and, in theory at least, of computing anything any state-of-the-art computer can compute.
Imagine a grid (or, if you like, a colossal checkerboard), the top row of which has some white squares and some black ones. The coloring of the squares in the first row determines the coloring of the squares in the second row as follows:
Pick a square in the second row and check the colors of the three squares above it in the first row (the one behind it to the left, the one immediately behind it, and the one behind it to the right). If the colors of these three squares are, respectively, WWB, WBW, WBB, BWB, or BBW, then color the square in the second row black. Otherwise, color it white. Do this for every square in the second row.
Via the same rule the coloring of the squares in the second row determines the coloring of the squares in the third row and, in general, the coloring of the squares in any row determines the coloring of the squares in the next row. That's it, and yet, Wolfram argues convincingly, the patterns of black and white squares that result are astonishingly similar to patterns that arise in biology, chemistry, physics, psychology, economics, and a host of other sciences. These patterns do not look random nor do they appear to be regular or repetitive. They are, however, (in some senses) exceedingly complex.
Moreover, if the first row is considered the input, and black squares are considered to be 1's and white ones 0's, then each succeeding row can be considered the output of a computation that transforms one binary number into another.
Not only can this simple so-called "one-dimensional cellular automaton" perform the particular calculation just described, but, as Wolfram proves, it is capable of performing all possible calculations! It is a "universal" computer that, via appropriate codings, can emulate the actions of any other special-purpose computer, including, for example, the word-processor on which I am now writing.