By helping us understand the first transition, author James Bailey hopes to provide a conceptual model for the second. At first the transition to a new vocabulary does not affect the way we understand the world itself. The epicycles of the moon's behavior, for example, were simply reexpressed with sines and cosines instead of with circles and lines. Soon, however, a change of vocabulary is accompanied by a much deeper change in understanding .
Scientists choose underlying fictions that are well-adapted to their vocabulary.
After Thought, page 80. After Thought is at its best in the first two sections, wherein Bailey takes us inside the classical mind and then through the paradigm shift that occurred with the invention of the calculus. The presentation is scholarly yet engrossing, synthesizing concepts and figures from hundreds of years of scientific and philosophical literature, Descartes side by side with Thoreau. The explosion of the Internet and the possibility of integrating the processing power now isolated on a hundred million desktops are also woven into the argument. In the end, After Thought becomes an appeal to faith.