HarperCollins

New York, N.Y.

1996

REVIEWED BY: Jeff A. Steely

August 1998

Scientists study the world through the vocabulary of a particular mathematical "language." According to Bailey, each mathematical language creates a new set of discoveries in the "Book of Nature." (e.g., p. 24). After Thought is structured around the three units in this "Book" – "Place," "Pace," and "Pattern." Each unit consists of a mathematical language and supporting technologies that work in concert to answer the questions of that part of the "Book." The language, in turn, influences the thinking of the entire culture. The Greeks invented and used geometry to solve astronomical problems and achieve a sense of "Place." The "Pace" unit began when Renaissance Europe moved toward equational thinking, adopting calculus and algebra to explain the universe in terms of laws of physics.

Geometry, calculus, and algebra have all been tremendous tools for understanding the world around us. Bailey argues, however, that the complex biological and cultural problems that we are trying to solve today defy the equational thinking that we have inherited from Newton and Descartes. The time has come, therefore, to move into the third unit of the Book of Nature – "Pattern." If we move beyond the use of computers as mere extensions of human, sequential thinking and allow them to undergo "bit evolution" (p.4), they can solve these complex scientific and social problems for us.

Bailey points to two changes that make the shift to "Pattern" conceivable. Parallel computing architectures, for one, provide the "brain" power for the complex, artificial intelligence applications the author believes can answer our questions through "adaptive computation" (p.51). The second factor is the vast quantity of "training data" available today. Only in the last few years has the "chronic shortage of facts about the world turned into a glut" (p. 69). We are drowning in the data we produce. Bailey states that "the culture of thought, developed to survive on a trickle of data, is being asked to deal with a flood" (p. 69). It is, therefore, time to move into the era after thought.

In the world of artificial intelligence (AI) there are two major orientations – "strong" AI and "weak" AI. Strong AI adherents seek to mimic the processes of the human brain. Weak AI proponents are, in contrast, satisfied to utilize the strengths of the computer to complete tasks associated with human intelligence. Bailey is hard to categorize. While he certainly is not trying to imitate the human brain, his goals are no less ambitious. Bailey’s weak AI approach is to "better" the human brain, by creating computers that can evolve their programming to exceed human capacity.

Part III, Bailey’s presentation of the promise of parallel computing, is not as well organized, nor as convincing, as the earlier chapters. The author does provide some interesting, easily understood examples of how these new "intermaths" might work. The topics of genetic/evolutionary algorithms, simulated annealing and cellular automata are all handled well, with very understandable examples. Bailey makes a good case for the limitations of equations for predicting the economy or understanding how proteins fold. Even his argument for teaching our children in the new maths is credible. His suggestion, however, that high school kids may create the new, evolving parallel computer network by leaving their computers working overnight is pure fantasy. The most troubling aspect of Bailey’s work, however, is his willingness to accept the "’passing of humankind from center stage’" (p. 218). The author believes that we must accept the conclusions of the evolved computers, as we will not be able to comprehend the processes by which they have arrived at these conclusions. How will humankind occupy its collective consciousness, after thought is no longer necessary?

After Thought is a well-written history of the interaction between mathematics and human thinking. The book is stimulating and thought provoking. I would recommend this work to any well-educated reader. Bailey has written for a diverse audience. Computer scientists, historians, mathematicians, social scientists, biologist, and many others will enjoy this book. Any academic library and medium to large public libraries should have a copy.

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