Some notes on the incompleteness theorem and shape grammars.

Theodoros, Dounas

Abstract

The paper presents a critique of the Shape Grammar paradigm viewed through the lens of the incompleteness theorem of Gödel. Shape Grammars have been extensively researched through many lenses. Their productive systemic nature was the focus of the first papers along with more recent treatises in the field while their use in analysis of known building styles has been extensive and a proven mechanism for style analysis. It is surprising though that use of Shape Grammars in actual design in practice however has been minimal. The architectural community has not actively used the paradigm in the design of real buildings, probably because of the rigid analytical approach to style and rules, following from the academic analysis that the paradigm has been subjected to. However I propose that there is another underlying reason, other than the rigid approach to construct a Shape Grammar. The nature of the concurrent application and creation of the rules lies close to the incompleteness theorem of Gödel, that uses a multitude of Turing Machines to prove that a from a set of True Axioms-A-we will never be able to determine if all sentences are true, without having to invent new axioms, outside the initial set-A-, thus unproven in terms of their true or false nature. Negation of this possibility drives us to the conclusion that true Design can never be feature-complete and thus can never be placed in a trusted framework that we all agree or believe it to be the complete truth. © 2013 Springer-Verlag Berlin Heidelberg.

Citation

DOUNAS, T. 2013. Some notes on the incompleteness theorem and shape grammars. In Zhang, J. and Sun, C. (eds.) Global design and local materialization: proceedings of the 15th International conference on Computer-aided architectural design features 2013 (CAAD Futures 2013), 3-5 July 2013, Shanghai, China. Communications in computer and information science, 369. Cham: Springer [online], pages 368-375. Available from: https://doi.org/10.1007/978-3-642-38974-0_35

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 15th International conference on Computer-aided architectural design features 2013 (CAAD Futures 2013)
• Start Date: Jul 3, 2013
• End Date: Jul 5, 2013
• Acceptance Date: Apr 5, 2013
• Online Publication Date: Jul 3, 2013
• Publication Date: Dec 31, 2013
• Deposit Date: Sep 19, 2024
• Publicly Available Date: Sep 19, 2024
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Pages: 368-375
• Series Title: Communications in computer and information science
• Series Number: 369
• Series ISSN: 1865-0929; 1865-0937
• Book Title: Global design and local materialization
• ISBN: 9783642389733
• DOI: https://doi.org/10.1007/978-3-642-38974-0_35
• Keywords: Incompleteness theorem; Incomputability of shape grammars
• Public URL: https://rgu-repository.worktribe.com/output/1791820