Abstract
The research on the interpretation of mathematics as part of the sciences of mind, introduced as ‘Geisteswissenschaften’ in the German philosophy, reflects the relationship between mathematics and arts, including architecture. This study focuses on the early works of the philosopher Max Bense where he described the contours of an intellectual history of mathematics related to philosophy. He pointed out strong relationships between mathematics and all areas of human creation abilities. In particular, his investigations on the relationship between arts, including architecture, and mathematics in important historical phases reveal that the mathematics of an age is reflected aesthetically in the artistic styles or theories of art. His thesis posits that a high point in mathematics corresponds to a high point in art. Later on, Bense developed an aesthetic theory on the basis of mathematics, semiotics and information theory.
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References
Bacon, Roger. 1962 [1267]. Opus Majus V and VI, De Scientia perspectiva, Scientia experimentalis Opus Majus, Vol. II. In the Internet Archive, Robert Belle Burke (transl.). New York: Russell & Russell Inc. https://archive.org/details/opusmajusofroger002065mbp. Accessed 7 February 2024.
Behling, Lottlisa. 1944. Gestalt und Geschichte des Maßwerks. Halle (Saale): Max Niemeyer.
Bense, Max. 1946. Konturen einer Geistesgeschichte der Mathematik. Die Mathematik und die Wissenschaften. Hamburg Claassen & Goverts.
Bense, Max. 1949. Konturen einer Geistesgeschichte der Mathematik II. Die Mathematik in der Kunst. Hamburg: Claassen & Goverts.
Bense, Max. 1982 [1965]. Aesthetica. Baden-Baden: Agis. 2nd expanded edition.
Bense, Max. 1997 [1934]. Raum und Ich. Eine Philosophie über den Raum. In Elisabeth Walther (ed.). Max Bense. Ausgewählte Schriften in vier Bänden. Band 1. Philosophie. Stuttgart: Metzler: 5–71.
Bense, Max. 1998 [1969]. Einführung in die informationstheoretische Ästhetik. Grundlagen und Anwendung in der Texttheorie. In Elisabeth Walther (ed.). Max Bense. Ausgewählte Schriften in vier Bänden. Band 3. Ästhetik und Texttheorie. Stuttgart, Weimar: Metzler: 251–417.
Bense, Max. 2004 [1951]. Kybernetik oder die Metatechnik einer Maschine. In Barbara Büscher, Hans-Christian von Herrmann, Christoph Hoffmann (eds.). Ästhetik als Programm. Max Bense/Daten und Streuungen. Berlin: Diaphanes: 50–61.
Birkhoff, Georg David. 1933. Aesthetic measure. Cambridge, MA: Harvard University Press.
Bruck, Robert (ed.). 1905. Das Skizzenbuch von Albrecht Dürer. https://digital.slub-dresden.de/werkansicht/dlf/71653, Taf.136. Accessed 7 February 2024.
Dehio, Georg. 1922. Das Straßburger Münster. München: Piper. https://doi.org/10.11588/diglit.12157#0010
Descartes, René. 1969 [1637]. Discours de la méthode ed. and transl. by Lüder Gäbe. Hamburg: Meiner.
Herrmann, Hans-Christian von. 2018. Geist der Abstraktion. Mathematik und Ästhetik bei Max Bense. In Elke Uhl, Claus Zittel (eds.). Max Bense. Weltprogrammierung. Stuttgart: J. B. Metzler: 83–94. https://doi.org/10.1007/978-3-476-04702-1_6
Jones, Owen. 1856. The Grammar of Ornament. London: Day and Son. https://archive.org/details/gri_33125008700086. Accessed 7 February 2024.
Lambert, Johann Heinrich. 1768. Kurzgefasste Regeln zu perspektivischen Zeichnungen, vermittelst eines zu deren Ausübung, so wie auch zu geometrischen Zeichnungen eingerichteten Proportional-Zirkels. Augsburg: Eberhardt Kletts. http://www.kuttaka.org/~JHL/L1768a.pdf. Accessed 7 February 2024.
Leibniz, Gottfried Wilhelm. 1679. Zur allgemeinen Charakteristik / Zur Characterstica universalis. In Ernst Cassirer (ed.). 1966. Hauptschriften zur Grundlegung der Philosophie. Band 1. Hamburg: Felix Meiner.
Leopold, Cornelie. 2013. Precise Experiments: Relations between Mathematics, Philosophy and Design at Ulm School of Design. Nexus Network Journal 15: 363–380. https://doi.org/10.1007/s00004-013-0148-6
Leopold, Cornelie. 2019a. The Development of the Geometric Concept of Relief Perspective. Nexus Network Journal 21: 227–252. https://doi.org/10.1007/s00004-019-00448-1
Leopold, Cornelie. 2019b. Geometric and Aesthetic Concepts Based on Pentagonal Structures. In Bharath Sriraman (ed). Handbook of the Mathematics of the Arts and Sciences. Cham: Springer: 1–26. https://doi.org/10.1007/978-3-319-70658-0_20-1
Leopold, Cornelie. 2022a. Geometry of Structures and its Philosophical Aesthetic Background. In Werner van Hoeydonck, Christian Kern, Eva Sommeregger (eds). Space Tessellations. Experimenting with Parquet Deformations Basel: Birkhäuser: 91–106. https://doi.org/10.1515/9783035625189-006
Leopold, Cornelie. 2022b. On the relationships between philosophy of technology, cybernetics, and aesthetics with their impacts on Latin America. AI & SOCIETY. Journal of Knowledge, Culture and Communication 37: 1027–1044. Special issue on Cybernetics in Latin America: Contexts Developments, Perceptions and Impacts. https://doi.org/10.1007/s00146-021-01338-2
Meier, Erwin. 2015. Basilica Vierzehnheiligen, Balthasar Neumann, 1743–1772. CC BY-SA 3.0, https://upload.wikimedia.org/wikipedia/commons/f/f6/Innenraum-Panorama_der_Basilika_Vierzehnheiligen.jpg. Accessed 7 February 2024.
Moles, Abraham André.1966. Information theory and esthetic perception. Urbana: University of Illinois Press. French original 1958.
Monet, Claude. 2013 [1872]. Public domain, https://commons.wikimedia.org/wiki/File:Monet_-_Impression,_Sunrise.jpg. Accessed 14 February 2024.
Nake, Frieder. 2012. Information Aesthetics: An heroic experiment. Journal of Mathematics and the Arts 6, 2–3: 65–75. https://doi.org/10.1080/17513472.2012.679458
Pascal, Blaise. 1658. De l’esprit géometrique Éditions eBooks France. https://www.ebooksgratuits.com/ebooksfrance/pascal_de_l_esprit_geometrique.pdf. Accessed 14 February 2024.
Riegl, Alois. 1893. Stilfragen: Grundlegungen zu einer Geschichte der Ornamentik. Berlin: Siemens. https://doi.org/10.11588/diglit.8075#0330
Riemann, Bernhard.1867. Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. Göttingen: Dieterichsche Buchhandlung. https://www.deutsche-digitale-bibliothek.de/item/DFHLJHW4XQVEUO7EX57TTI4MRX5WGVZM. Accessed 14 February 2024.
Shannon, Claude Elwood. 1948. A mathematical theory of communications. Bell System Technical Journal 27: 379–423; 623–656.
Valéry, Paul. 1895. Introduction à la méthode de Léonard de Vinci. Paris: La Nouvelle Revue Française.
Walther, Elisabeth (ed.). 1998. Max Bense. Ausgewählte Schriften in vier Bänden. Band 4. Poetische Texte. Stuttgart, Weimar: Metzler.
Walther, Elisabeth. 2003. Our Years in Ulm: 1953 to 1958, 1965, and 1966. In: Ulmer Museum/HfG-Archiv (ed.): ulmer modelle—modelle nach ulm. hochschule für gestaltung ulm / ulm school of design 1953–1968. Ostfildern-Ruit: Hatje Cantz: 90–93.
Wiener, Norbert. 1948. Cybernetics: Or Control and Communication in the Animal and the Machine. Paris: Hermann & Cie; Cambridge, MA: MIT Press.
Wölfflin, Heinrich. 1915. Kunstgeschichtliche Grundbegriffe: das Problem der Stilentwickelung in der neueren Kunst. München: Bruckmann. https://doi.org/10.11588/diglit.27250
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Leopold, C. Relationships between Mathematics and Art in Their Intellectual History - Reflections According to Max Bense. Nexus Netw J (2024). https://doi.org/10.1007/s00004-024-00768-x
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DOI: https://doi.org/10.1007/s00004-024-00768-x