ORIGINAL QUERY:
Date: Sat, 14 Jan 2006 16:27:07 +0100
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I have a question for the Nexus readers: "Are there any relationships between architecture and higher mathematics?" By "higher" I mean, mathematics at the level of 1st master and up. The topology paper in the NNJ vol. 7 no. 2 by Jean-Michel Kantor goes in that direction, but the reason why I propose it is different: I recently wrote a paper (in Dutch) on "Africa and higher mathematics". "True, die-hard" mathematicians sometimes take architectural math as "baby math", and of course, related to Africa, there are some down-to-earth social (extremist) influences involved. Nevertheless, in the architecture case, the question could be seen as a modification of Mario Salvadori's query at the first Nexus conference for architecture and mathematics in 1996: "Are there any relationships between architecture and mathematics?"
Comments
In the second mode, mathematics is directly embodied in our work, and only later does an abstract thinker devise a symbolic description of our accomplishment. Many catenaries and funiculars were built before mathematicians had a vantage point “high” enough from which to describe them. Tesselations were treated exhaustively in practice centuries before the theory was in a podsition to concur. For millenia, boatbuilders have been bending battens and planks to arrive at complex surfaces of least local change in curvature which accord very neatly with their hydrodynamic objectives. In this respect, the bent spline on the naval architect’s drawing board is a calculator, and the bent battens enveloping a hull form under construction are computer controlled machines, and I mean this in a real, fuctional sense, not as a metaphor. In both cases, the workings of the calculator were not given abstract form until Schoenberg’s 1946 theory of mathematical splines. In this second mode, the real world is always richer and more complex than mere description, and the mathematicians’ approximation is destined to play catch-up.
The opposition between these two perspectives is ancient. Medieval philosophers kept up a heated debate between the (Platonic) “realism” of the former orientation and the “nominalism” of the latter. I suspect replies to your query will fall into one camp or the other, with a preponderance coming from the realist side, as this is the inherent tendency – I would submit – of the Nexus readership. I am reading into your query a nominalist bias more like my own and wish you all the best with your investigation. I look forward to your discoveries!
I recently wrote an endorsement for MIT at their request:
"Stiny is to 'shape' as Chomsky was to 'word' or Wolfram to 'number.' In my view, though, Stiny may well prove to be the most radical of the three. How different a place his pictorial world is from standard textual or digital worlds: with shape there is no vocabulary, no syntax, no bits, no atoms. As Stiny draws, he talks. Shapes and shape rules bear the force of argument. These drawings are to be looked at keenly, even traced and redrawn by the reader. The supportive text illustrates what can be seen and done, providing both a personal and intellectual history. Through its drawings and maxims, Shape challenges much conventional wisdom in philosophy and education, in computer science and artificial intelligence, and in design and the visual arts."
The biggest hurdle to overcome is our understanding of fractal geometry. I can't solve a logarithmic equation but I suspect I understand fractal geometry or at least its application better than most. If Fractals are the geometry of nature as Mendelbrot proposed, then fractals rarely if ever reiterate at smaller and smaller scales to infinity. Those pretty fractal computer generated pictures we are so used to seeing are artifical. In natural fractals, shaped over time by the forces of wind, water, fire, gravity, etc., reiterate 1 time or 2 or 3 times, then the molucular composition causes a new fractal to appear. The same is principle can be (and is being) applied to Architecture. Unlike the rigid and dogmatic Modern Movement, the Fractal Movement is inspired by the limitless patterns of nature in all all its aspects, infinite and ever changing.
Another source of higher mathematics in architecture is to be found in mechanics. Building collapses provide particularly good, if tragic, opportunities to study structural behaviour, into which I suspect higher mathematics often enters. Ah, but you say, that is engineering and not architecture. Well, I suppose that depends on how you view architecture: in my opinion, any aspect of the built environment is included under the umbrella of architecture, and our aim at interdisciplinarity reflects that fact.
Dirk's question is related to the query proposed by James McQuillan:
In spite of many architecture students' objections to learning mathematics, more than just a fundamental understanding of mathematical concepts and even a way of thinking is essential to the architectural education. This is why we publish papers about Didactics in the NNJ.
I hope that readers will think about and respond to these queries: this is an important part of keeping dialogue open within the NNJ community.