Monday, 7 October 2013

Mysterious mathematics 3


Don't read this if you are sick of rants.

I wanted to do a follow-up of my previous posts on architecture and mathematics.  What better way to start than googling the two terms.  Bad mistake.  It can give you indigestion.  Not the number of hits, but the knotting stomach induced by the sheer inanity of some amateur design journalist grappling with the subject.  If you are masochistic, go to 10 Amazing Examples of Architecture Inspired by Mathematics on Flavorwire. The bloopers make you cringe.

First up, an innocent enough project for a building for an undefined Buddhist program, incorporating a mobius strip surface.  To justify it, the author manages to describe the lumpen stasis of a traditional stupa and its circumambulatory path as a 'twisty space'.  She should visit one sometime.

This introductory example of the mathematical marvels in architecture is also conspicuously a project, not an actual, built building.  I wish they would stop doing that, especially when there is a perfectly good, prize winning built example of a Klein Bottle House (the proper 3D version of the mobius strip) near Melbourne, Australia.

At least Walter Netsch's US Air Force Academy’s Cadet Chapel in Colorado Springs, Colorado has the merit of having been built.This piece of full sized origami is described as shaped like a tetrahedron,which it clearly isn't.But what can you expect from an author who first quotes the definition of a tetrahedron as a four sided object with triangular sides, and then promptly confuses it with pyramids, which have five sides including a square base.

I can afford to gloss over the geodesic domes of the Eden Project because it doesn't have anything offensively wrong.  But I am offended by the breathy, guileless description of Foster's office tower in London known as The Gherkin.  According to the author: "the modern tower was carefully constructed with the help of parametric modeling amongst other math-savvy formulas so the architects could predict how to minimize whirlwinds around its base."  Give me a break!

Yes, parametric modelling is a key feature of the practice's characteristic approach to generating apparently complex shapes.  Which are surprisingly buildable, because of the way the parts can be scheduled for automated manufacture and reliable logistics in assembly.  This use of bespoke software is lucidly explained in Chris Abel's admirable book Architecture, Technology and Process,  and incidentally, compared at length to the way Gerhy uses the CATIA software suite to solve his complex building geometries.

OK.  I am actually grateful for the reminder of the Philips Pavilion at the 1958 World’s Fair. And this time, the author commits no bloopers, probably because she simply names the dominant geometry as the use of hyperbolic paraboloids employing steel tension cables.  Why do I miss mention of Felix Candela and his much earlier experiments with the same form in concrete?  Or the factoid that these curved forms can be generated from repeated straight lines, which made them buildable by conventional building materials.  Therein lay the fascination with their mathematics for architects like Candela, trying to build his formwork out of timber, before casting it in plastic concrete.


Mathematical allusion is getting pretty desperate when the owner of this Toronto home, named the Integral House is "a calculus professor who wrote textbooks and wanted to incorporate the mathematical sign into the home’s name and design. Undulating glass and wood walls also echo the shape of a violin."  Might be delightful, but the maths is in the room acoustics and the material choices and assemblies of the 200 seater performance venue, not in the trite simile.

 I've previously pointed out that any undergraduate architecture student could generate Barcelona’s Endesa Pavilion by trial and error in ten minutes, with the free SketchUp modelling software.  The "mathematical wizardry" is entirely that of the people who make the program run fast enough to use, not in translating the solar geometry algorithms.



I'll gloss over Cube Village, built by Dutch architect Piet Blom, because the author doesn't attempt a mathematical description of it.

And then, joy of joys, a truly worthy project.  Gaudi's Sagrada Familia cathedral in Barcelona.

The author enthuses over the virtuoso exercise in numerology, itself unremarkable in the tradition of mystical religion.  She does mention the hyperbolic paraboloids of surfaces, and even the "catenary arches".  She obviously has no idea of the true magic of Gaudi's insight, that the optimum shapes of the compressive structure in masonry could be empirically developed, by modelling them as pure tension, upside down as catenary chains, loaded with intuitive estimates of the superimposed loads.

And so we end with a mathematical whimper, a fractal gas station makeover in Los Angeles.  This might seem a bit unfair.  There is something serious about fractal geometry, and there is definitely something important about how the form generation potential of meshed surfaces has lately influenced architecture everywhere.  My angst is two-fold.

On the one hand, I refer back to the insight that hyperbolic paraboloids can be generated from straight sticks or cables to employ conventional building materials.  Employing a software package like 3D Studio Max automatically creates 'mesh' substitutes for the complex curved surfaces, and thereby turns them into forms that can be clad by combinations of flat sheets cut or folded into triangles, the joints typically filled with generous beads of mastic.  This is the main reason why we can now build all the rendered fantasies that so dominate the architectural magazines.  But it is also the reason why so many of these tortured forms end up with all those slivered triangles all over their surfaces, as they do in the example used.

My second reason for despair?  The author clearly doesn't understand any of this.
Read the original here.

1 comment:

Alyce said...

Having quite an interest in mathematics and architecture, this post has sparked my attention to the fact that the buildings critiqued have really only been based of the idea of visual connotations of geometrical shapes rather than the principles and possibilities in which mathematics can really produce. After reading your post and the '10 Amazing examples of Architecture inspired by Mathematics,' it is evident where the main problem lies; in the author's attempt to portray a mathematical description of the building without having a full understanding of how complex the subject really is. I believe that it is not enough just to pick and choose these select few buildings and claim how amazing they are due to their 'mathematics' when really they have been based on a parabolic, hyperbolic of 'integral' shapes without further discovering their possibilities. Unless the building started with a particular formula in mind with a clear concept, I highly doubt that these so called 'mathematical buildings' like the Mobius Strip Temple and Barcelona’s Endesa Pavilion would have been based on the pure idea of a 'twist' or 'geometric shapes' without it being by an accident to begin with.

It appears to me that before authors should praise the mathematical abilities of the architect's intent, they should start at the beginning and refer to the older architecture and how man relates to it. Gaudi's Sagrada Familia cathedral is a good example at how carefully considered each element of the building was designed particular through the mathematical side. Again, after the reading it does appear that the author only glazed over its main features without focusing on some of its most delicate and technical ones. Perhaps the architecture would look more thoughtfully designed rather than it appearing like it had been made on sketchup in ten minutes. Another issue with this is the parametric modelling. As I only have a basic understanding of some of the programs including Rhino and Grasshopper, it is easy to get lost in the 3D modelling software and fall upon new designs that the one originally intended.

In terms of the Integral House, this one really annoys me for the reason that it was designed from a pretentious musical mathematician who thought he could just combine the two together just because they a violin and an integral sign may look similar. This building could be taken purely as just a house designed to represent the musical side with the curves representing the violin and the glass and wood paneling to represent a vertical stave! It's almost as though the 'mathematics' of the integral came as an afterthought once he realised the two might actually go together.

Apart from this, my argument seems more to lie in the question as to why these buildings in particular are recognised as the top 10 rather than the many other ones such as the Mercedes Benz Museum, the Guggenheim or even the basic triangular pyramid at the Louvre!