The Impact of Notation Systems

The Impact of Notation Systems: From the Practical Knowledge of Surveyors to Babylonian Geometry

Peter Damerow

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Pre-Euclidean geometry in Mesopotamia.<br>
Calculation of an area of trapezoid in geometrical school text, ca. 17th century B.C.

Mesopotamian proto-cuneiform and cuneiform clay tablets written in the time period from the invention of writing (around 3200 B. C.) to the development of Babylonian mathematics in the Old Babylonian period (around 1900–1600 B. C.) document the development from elementary spatial knowledge to an esoteric art of formulating complex geometrical problems and solving them using sophisticated arithmetical tools applied to geometrical intuition. It is evident that the spatial cognition under these circumstances differs considerably from what has been identified in non-literate cultures. The representation of this new form in the documents of surveyors, school texts, and the problem-texts of Babylonian mathematics have been studied. It turned out that the emergence of the new kind of spatial cognition documented in these sources was primarily based on the growing knowledge of surveyors and the scholarly reflection on their means and practices.The resulting mental constructions remained implicit but can be partly reconstructed from the arithmetical operations of Babylonian mathematics.They turn out to show “non-Euclidian” peculiarities such as the neglect of the role of angles, resulting from the practices of surveyors which they reflect.