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Awakening of Geometrical Thought in Early Culture, by Paulus Gerdes. Minneapolis, Minnesota: MEP Publications, 2003. $49.50. Pp. 200.
It is commonly believed that geometry started in ancient Egypt as a result of problems of field measurements and that it emerged as a deductive science in ancient Greece. However, since the post-World War II period a number of historians and mathematicians have stressed that there is ample evidence of geometrical thinking in pre-Greek cultures, going back as far as the Paleolithic Age. These findings raise the question as to how and why geometrical thought originated. There are basically three answers. The creationist answer, that God bestowed mathematical knowledge on Adam, relies on faith rather than on science and can be disregarded. A different perspective stresses human beings' capacity to observe and to abstract from observation. For example, the concept of a circle could have been derived from the observation of the sun or of the moon. Observation of the shape of objects could have been the first step and conceptualization of those forms as having geometrical properties could have been achieved subsequently through the power of abstraction. This approach may seem convincing, but it meets an objection: it sees the development of knowledge as divorced from the development of the society within which that knowledge is developed. Innumerable examples to the contrary can be provided. If this is the case in general, it must be the case also for early geometrical thought.
The third...