REPRINTED HERE as an epilogue is my first discussion, written a few years ago, of an idea that developed into a central theme of this book: My rejection of the dichotomy opposing a stereotypically "disembodied" mathematics to activities engaging a full range of human sensitivities.* In the book I discuss this theme in the context of Turtle geometry. In the following pages the reader will find this theme embedded in reflections on the sources of mathematical pleasure.
It is deeply embeded in our culture that the appreciation of mathematical beauty and the experience of mathematical pleasure are accessible only to a minority, perhaps a very small minority, of the human race. This belief is given the status of a theoretical principle by Henri Poincaré, who has to be respected not only as one of the seminal mathematical thinkers of the century but also as one of the most thoughtful writers on the epistemology of the mathematical sciences. Poincaré differs sharply from prevalent trends in cognitive and educational psychology in his view of what makes a mathematician. For Poincaré the distinguishing feature of the mathematical mind is not logical but aesthetic. He also believes,____________________