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Some Controversies Around Formalization in Architecture

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Part of the Digital Innovations in Architecture, Engineering and Construction book series (DIAEC)


Formal Methods is a designation that has its origin in the computer sciences, where it is widely used. Due to the increasing importance of computer systems, and their growth in scope and complexity, formal methods are expanding within these disciplines.

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  1. 1.

    Yes, architects can become gods!

  2. 2.

    Since we’ve talked about music, let’s take a small example there. Someone has noticed that there are 11 repetitions of “Herr, bin ich’s” in the area where Jesus announces “Einer unter euch wird mich verraten”, in St. Matthew Passion by the divine Johann Sebastian. It seems credible that Bach chose the number judiciously: it is the number of apostles who are surprised, since the other was the traitor. But many other semiological observations by scholars about other numbers appearing in the Passion, 3, 7, various multiples, 22 and its sacred and esoteric derivations seem far-fetched.

  3. 3.

    That this is a common and current assumption can be seen, for example, on the “mathematics and architecture” page of a widely used digital encyclopedia (, where mathematics appears to be reduced almost exclusively to the use of eye-catching geometric shapes.

  4. 4.

    Alberti, which is the object of one of the exhibitions in our 6FMA (“Alberti Digital—tradition and innovation in the theory and practice of architecture”), was one of the first that extended the formal methods to design automation. For example, he invented the premises of what we now call shape grammars.

  5. 5.

    Of course, we have to add yet another strong paradigm—the informal or irrational approach, gaining force in the eighteenth century and having many worshipers in the present time, with the war cry “between poetry and reason, I choose poetry”. But that’s a topic for another time.

  6. 6.

    Which seems to contradict the aforementioned thesis of the non-human scale of Egyptian architecture.

  7. 7.

    This caricatured example carries some irony in trying to apply to this very text some of the principles that we have been enunciating. We leave it to the reader to discover.

  8. 8.

    To be more accurate we should say that generalization of languages is only rarely carried out in major scientific, especially mathematical, advances. In most cases, our ideas or their materialization in actions are always carried out in restricted languages. In particular, all artistic objects or events are produced in a context of linguistic restriction. Popular culture even speaks of the artist’s style. This is not to say that art does not do linguistic research. Some even say that this is the very griffe of art. What is meant is that the introduction of restrictive rules to language constitutes an inevitability of development.

  9. 9.

    What qualifies the architect, in this age of intense division of labor, as one of the last professionals who must be a polymath renaissance man.

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Correspondence to Franklim Morais .

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Mora, P.L., Ruivo, C., Viana, D.L., Morais, F., Vieira Vaz, J., López-Chao, V. (2023). Some Controversies Around Formalization in Architecture. In: Mora, P.L., Viana, D.L., Morais, F., Vieira Vaz, J. (eds) Formal Methods in Architecture. FMA 2022. Digital Innovations in Architecture, Engineering and Construction. Springer, Singapore.

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  • Print ISBN: 978-981-99-2216-1

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