Measuring Knowledge. Notations, Words, Drawings, Projections, and Numbers


  • Carlos L. Marcos Department of Graphic Expresion and Cartography, University of Alicante
  • Michael Swisher School of Architecture, The University of North Caroline at Charlotte



notation, drawings, projections, measures, proportions


Humans have communicated with each other since they became such. Undoubtedly, the fact that we have developed symbolic systems to communicate should account for such a difference. Moreover, our own evolution in terms of knowledge is inextricably connected to such use.
Different symbolic systems contribute to our knowledge acquisition in different ways. A fundamental divide can be established between verbal languages and graphic ones. Words are easily connected to abstract thinking and a generic approach to reality; we use them to reason and to think. Figurative drawings, on the contrary, appeal to our senses and to visual appearance; they are focused on the material world and try to define relations based on resemblance between tangible reality and modes of its representation, however this controversial term may be. Yet, drawings can also be used to achieve knowledge aided by graphic thinking both through ideation and through representation, depending on the directionality of projections. Most remarkably, architectural drawings based on geometric projections establish an unrivalled and privileged relation with material objects that words or even numbers cannot match. Instead of appealing to the generic –as words– or to the numerically quantifiable –as numbers–, they describe and define a point to point relation with the material existence depicting proportions.


Alberti, L.B. (1991). De Re Aedificatoria. Madrid: Akal.

Allepuz Pedreño, Á. (2016). Architectural Drawings and Symbolic Systems. Implications of Goodman’s and Gardner’s Theoretical Approaches in Project Zero. In E. Castaño Perea, E. Echeverría Valiente (eds.). Architectural Draughtsmanship. From Analog to Digital Narratives, Proceedings of EGA 2016, Congreso Internacional de Expresión Gráfica Arquitectónica, pp. 787-798. Cham: Springer.

Allepuz Pedreño, Á.; Marcos, C.L. (2019). Dibujo frente a construcción: dos medios para representar la arquitectura. In Martínez-Medina, Andrés (Ed.), Tiempos de la arquitectura, Madrid: Munilla-Lería, pp. 37-58.

Arnheim, R. (2005). Arte y percepción visual. Madrid: Ed. Alianza Forma.

Aristotle. (1971). Metaphysics. Oxford: Clarendon Press.

Bueno, G. (1990). Materia. Oviedo: Ed. Pentalfa.

Cabezos Bernal, P.M., Rossi, A. (2017).Virtual musealization techniques. The capitals of the monastery of San Cugat. In Revista EGA, Vol. 22, No. 29, pp. 48-57.

Carpo, M. (2001). Architecture in the age of printing. Cambridge (Mass.): The MIT Press.

Carpo M. (2011). The Alphabet and the Algorithm. Cambridge (Mass.): The MIT Press.

Chías Navarro, P. (2006). De la imagen y el sonido. In EGA Expresión Gráfica Arquitectónica, n. 11, pp. 60-75.

Deleuze, G. (2008). Pintura. El concepto de diagrama. Buenos Aires: Ed. Cactus.

Descartes, R. (1995). Los principios de la filosofía. Madrid: Alianza Editorial.

Evans, R. (1989). Architectural Projection. In E. Blau, E. Kaufman (Eds.). Architecture and its image: four centuries of architectural representation. Mon- treal: Canadian Centre for Architecture, pp. 18-35.

Evans, R. (1997). Translations from drawing to building, in Translations from drawing to building and Other Essays. Cambridge (Mass.): The MIT Press.

Evans, R. (2000). The Projective Cast. Architecture and Its Three Geometries. Cambridge (Mass.): The MIT Press.

Ferrater Mora, J. (1994). Diccionario de Filosofía. Barcelona: Ariel.

García, M. (2009). Prologue for a history, theory and future of patterns of architecture and spatial design. In Architectural Design, Vol. 76, No. 6, pp. 6-17.

Gerbino, A. (2010). François Blondel: Architecture, Erudition, and the Scientific Revolution. The Classical Tradition in Architecture. New York: Routledge.

Goodman, N. (1976). Languages of Art. An Approach to a Theory of the Symbols. Cambridge (Mass): Hackett Publishing.

Grube, G.M.A. (1973). El pensamiento de Plantón. Madrid: Ed. Gredos.

Hofstadter, D.R. (1982). Metamagical Themas. The music of Frederic Chopin: startling aural patterns that also startle the eye. In Scientific American, Vol. 246, No. 4, pp.16-31.

Kruft, H.W. (1994). A history of architectural theory: from Vitruvius to the present. New York: Princeton Architectural Press.

Plato. (1987). Theatetus. London: Penguin Classics.

Tufte, E.R. (1990). Envisioning information. Cheshire: Graphics Press.

Wittkower, R. (1988). Architecture in the Age of Humanism. London: Academy editions.

Wittkower, R. (1953). Brunelleschi and ‘Proportion in Perspective’. In Journal of the Warburg and Cortauld Institutes, Vol.16, No. 3-4, pp. 275-291.

Zubiri, X. (1989). Estructura dinámica de la realidad. Madrid: Alianza Editorial.



How to Cite

C. L. Marcos and M. Swisher, “Measuring Knowledge. Notations, Words, Drawings, Projections, and Numbers”, diségno, no. 7, pp. 31–42, Dec. 2020.



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