Tag Archives: Architectural Geometry

Idealization and Abstraction

Let me start by saying thanks to everybody who came out and participated in last week’s event – it was an extremely interesting session led by Dr. Anjan Chakravartty who focused on what it means to represent things. 

Looking back, there are couple points that resonated with me the most.  In his talk, Anjan emphasized the difference between “abstraction” and “idealization”. For him, abstraction is (and I hope I don’t get this wrong…!) the process of extracting certain aspects of the object in question and dealing with them in isolation, a method that is effective when studying things that have a strong underlying structure which dictates the fundamental behaviour of the object, but that also have a large amount of detail that can potentially confuse the issue. Of course, this also sets the scene perfectly for drawing incorrect conclusions due to having simplified the system beyond any degree of realism. In contrast, the notion of  “idealization” is the process of transforming the object or how the object is perceived so as to bring forward certain important aspects of the system.

Despite the somewhat abstract setting, these two concepts seem come up all the time in parametric modelling.  In in any parametric model, the overall output is controlled and generated by a collection of parameters:  does it follow then that parameters are an abstraction of the model but are chosen by how well they “idealize” it?

In any case, the result of the most lively discussion following the presentation was that the abstract notion of representation is of fundamental importance to the modelling and design community as a whole.

Thanks for coming!


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Filed under Architecture, Architecture in Combination, Discussion Series, Geometry

Architecture in Combination with Representation, April 8th. @ 5:30pm

Dr. Chakravartty has kindly provided some words on the upcoming session:
Architecture in Combination with Representation
Picasso’s mural Guernica represents the aftermath of the bombing of a Basque town during the Spanish Civil War. Watson and Crick’s cardboard cut-out model of DNA represents the double-helical structure of the molecule. The Gothic arch represents the spiritual aspiration of reaching towards the heavens. Examples such as these are ubiquitous, and my aim is to step back from them so as to ask a philosophical question about representing: what *is* a representation, precisely, such that all of these examples count as instances of it? Are there conditions that are necessary or sufficient to make one thing a representation of something else, and are these conditions shared across different domains of human endeavour such as art, science, and architecture? I will review some proposals for how representation should be understood, with the goal of shedding light on these questions. Some of the issues raised concern whether intuitive relations such as similarity or mathematical ones such as isomorphism are required, whether the emphasis should rather be on the cognitive activities we perform in connection with representations as they relate to the things they represent, such as interpretation and inference, and how matters are complicated by the ways in which representations abstract from and idealize their subject matter.

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Musical Sequences

Does anyone know why they’re called that? The name is so suggestive and the theory is so nice, that I can’t help but hope there’s some underlying connection, but so far, I can’t find one.

To explain, a musical sequence is an infinite list of two symbols, usually L and S (denoting “long” and “short”). In addition, this list has the property that no section of it can be copied in a regular way so as to create the full list. Another way to say the same thing is musical sequences are non-periodic. They can be generated by repeatedly sending S to L, and L to LS. So, for instance:


The incredible thing is that they seem to pop up everywhere in the world of non-periodic and aperiodic patterns (Grunbaum and Sheppard). In fact, once 3d versions of aperiodic tilings were discovered, sure enough, 3d versions of musical sequences were also found. I also haven’t found a good explanation as to why this is the case, but it seems that musical sequences create a kind of underlying organization for less organized, aperiodic, patterns.


Their role as organizers is actually what is so useful to design. Frequently, the design intent requires a facade or plan layout to be “random”. The problem is, true randomness is a pretty ugly and unwieldly thing, so more often than not, a pattern that gives the appearance of randomness is used instead. In fact, if such a pattern were to be guided by musical sequences, all sorts of pragmatic issues, like whether or not the nodes of the glazing have any relation to the nodes of the structure that holds it up, get resolved. My personal favorite 3d aperiodic tiling, developed by L. Danzer, is currently on display in a Cecil Balmond exhibition.

The point is, here is a very nice mathematical principle that will improve the constructability of certain kinds of projects while maintaining a certain aesthetic and seems to imply some connection with music. It would be perfect, except that the connection to music is still a mystery to me.

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Filed under Architecture, Exhibitions, Geometry, Tilings