STEVEN WOLFRAM'S NEW SCIENCE

although the pace of human intellectual achievement quickened dramatically in the 20th century, few generations of mankind can claim to have been alive for, much less to have understood, a paradigm-shifting advance in understanding when it occurred

van gogh, one of the most important artists in the western canon, never sold a single painting in his lifetime. few, certainly fewer of the larger public, understood the general theory of relativity when it was published by an obscure swiss patent office bureaucrat.

steven wolfram's "new kind of science" is an advance of that magnitude and his discovery is easy for the general public to comprehend. as a friend said, it is a real "page turner," which makes it unique in the serious scientific literature.

to understand how astounding wolfram's discovery is, consider the state of theoretical physics today. it still operates in the einsteinian paradigm and has struggled for years to develop a mathematical formula that would serve as a grand unified theory of the five fundamental forces of nature. it is no closer now than it was a generation ago and exotic modifications like "string theory," and "membrane theory" hve been advanced to shoehorn the workings of the universe into a mathematical model.

now, just as newton did to the copernican paradigm and einstein did to the newtonian paradigm wolfram says the einsteinian paradigm is insufficient as a means of moving physics forward and that he intends another revolution . never one for false modesty, wolfram states this explicitly in the first senence of the book: "three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. my purpose in this book is to initate another such transformation and to introduce a new kind of science..."

as theoretical physicists and mathematicians have labored producing blackboard-long formulae of daunting complexity to explain less and less, some have thought that when a comprehensive formula was discovered it would be simple and "elegant." they were right that it would be simple and elegant but they were wrong that it would be a mathematical model.

wolfram's discovery is the "cellular automata" and it's astonishing ability to show how even notoriously complex physical phenomena like the common snowflake can be produced by the repeated application of simple rules.

in the chapter titled "the crucial experiment" wolfram describes what led to his discovery. starting with a single black square or "cell" on a computer grid wolfram devised a simple "rule" that would dictate the generation of additional cells in succeeding steps. so, for example, if the cells to the right and left of the starting cell were black, the newly-produced cell was to be white, if the adjoining cells were white, the new cell would be black, and so on. in this simple program there were only eight different possibilities of color combinations. wolfram then ran the program and as he puts it, what he saw "i did not believe...could possibly be correct."

this simple cellular automation produced patterns of staggering complexity that, as a theoretical physicist, wolfram recognized only the most intricate mathematical formulae could produce. as he continued to run the program, for 50 steps, then 500, then 1500, the pattern became more complex, or dissolved into randomness, or repeated itself endlessly, or died out, depending on the rule.

in the end there were 256 different patterns that could be produced by variations on that initial eight-component rule and the resulting patterns ranged from pure white grids to pure black grids to grids with diagonals to fractal "nested" structures. the implications, even to the non-scientist are clear. on one level this is the language of evolution itself. starting with a single cell and the simplest cosmic code, immensely varied life forms can be produced. looking at these patterns one's sense is that a look behind the curtain of creation itself is obtained.

wolfram's second, equally important, discovery was that making the rule more complex did not make the output more complex. he used mobile automata, turing machines substitution systems, tag systems, and others whose workings are unimportant because their output was not more important than that produced by rules of child-like simplicitly.

and so it goes for over 1200 pages. the only criticism one can make of "a new kind of science" is that wolfram badly needed an editor. that is tribute to the simplicity and "elegance" of his discovery and for the general reader repetition of the basic theme at least reinforces learning.

both in the beginning of the book and then in succeeding chapters wolfram considers the implications of his work for: "mathematics," "physics," "biology," "social sciences," "computer science," "philosophy," "art," and "technology," in other words, every aspect of human comprehension.

over 30 years thomas kuhn revolutionized the understanding of scientific epistemology with "the structure of scientific revolutions." in that book he showed how the conventional wisdom that scientific advances were made as the product of incremental steps each piled on top of the other was false and that instead scientific history was characterized by periods of quiescent "normal" science interrupted by occasional "revolutions" that resulted in the creation of a new scientific "paradigm," indeed, a "new science." copernicus fashioned one such revolution, newton another, einstein a third. with "a new kind of science," steven wolfram has made another.

-benjamin harris