That reasoning using language and using diagrams were different, at least in important respects, was brought home by the Pythagorean discovery of irrational numbers. ... Words, equations, and diagrams are not just a machinery to guarantee that our conclusions follow from their premises. In their everyday use, their real importance lies in the aid they give us in reaching the conclusions in the first place.
- from the Foreword by Herbert Simon of Diagrammatic Reasoning: Cognitive and Computational Perspectives. Edited by Janice Glasgow, N. Hari Narayanan, and B. Chandrasekaran. AAAI Press.
Image from "Diagrammatic representation and reasoning" by Kulpa, Z.