Logarithms and Architecture

What role do logarithms have in building our future?

The Museum of the Future pictured above, recently came to completion in Dubai, having been designed using logarithms. 

As a building, it is entirely self referential. So with its shiny continuous surface, is appears more like a Henry Moore sculpture than a building. The result is that the contorted structure cries out to be looked at. It is as if it was the only thing of any importance in the city. 

If not logarithms, then numbers have always played a part in setting the parameters of good design.

For example, geometry like the golden ratio, has has been the basis for creating harmonic proportions. From the Greeks onwards, such techniques have informed the design of buildings. Looking back at previous era’s, we generally agree that more often than not, the buildings are more satisfying to the eye. In architecture at least we can see that maths has played an important part in establishing the rules for ‘beauty’.

There becomes a point when mathematics start to take over, with dubious results.

Take Rene Descartes for example. The philosopher and mathematician (1596-1650) created a system of thought that still dominates much of how we think. Furthermore, he gave his name to the ‘cartesian’ co-ordinate system.

During the 20th Century, cartesian geometry became the basis of much of the planning of our built environment. This is why much of it is rectilinear in form. A strict grid system was the basis for the planning of post war new towns. It was on a scale to suit the motor car, not the pedestrian. These plans by and large ignore ecology. They also ignore the organic geometry of the medieval street patterns that went before. The relationship between rationalist and organic planning regimes, is often jarring. The clash between the two create alien places with little legibility. Much development in recent time has had the effect of devaluing otherwise great places.

Cartesian geometry is indeterminate, being repetitive in a way that does not admit easily to termination or deflection of any kind. It is abstract. Occasionally a happy accident occurs, relieving the monotony of the grid. An example would be Broadway in Manhattan, New York City. The original natives of the land used this diagonal route. The route was incorporated by colonialists who arrived later and gridded out the rest of the island. This street provides much of the connecting vibrancy that characterises New York. 

Pre-war planning theory developed in Europe became the predominant practice in the UK post war.

Le Corbusier had railed against the apparent higgledy piggly randomness of the ‘pack donkeys way’. He used these terms to denigrate the medieval street patterns of European towns.

His ‘Plan de Voisin’, for central Paris was his vision for transforming Parisienne streets. He wanted to turn these intricately walkable neighbourhoods into a cartesian diagram worthy of a George Orwell nightmare. What mattered was how the new geometry would work for planes trains and automobiles! Confronted with this super-plan, Paris stood its ground. Consequently the ‘Plan’ was rejected, while many cities in Europe including the UK, did not escape so lightly. 

Deflecting the grid can seem rather a quirky or random thing to do to a rationalist. What can be forgotten is that the rectilinear grid is, like mathematics, pure abstraction and not reality. True rationality takes place when physical constraints are brought to bear on the gird system which is then deflected.

So if you dig down into the ‘DNA’ of place, it soon reveals multiple reasons for deflecting the abstract grid. The more physical constraints can include;

  • topography,
  • ecology,
  • biodiversity,
  • water courses
  • arboriculture,
  • landscape,
  • drainage and water,
  • heritage,
  • utility services,
  • energy sources and distribution,
  • existing roads and transport systems.

In addition to the above constraints are the following;  

  • community,
  • desire lines,
  • existing settlement patterns,
  • walkability,
  • social networks,
  • local economy,
  • local intelligence,
  • the spiritual armature,
  • engagement and empowerment,
  • hidden history and culture of the neighbourhood.

So then, these constraints listed above become the paradigm for truly rational city or town building. They are not the top down geometries of an abstract grid. 

Start with the right premise in mind before committing too much to paper, let alone bricks and mortar.

When preparing plans, it is important to start with the right premise in mind. This applies either for individual buildings, clusters of buildings or urban extensions of any kind. 

Fractal geometry is closer to the sophisticated relationships that should inform the growth of a neighbourhood or city. This is based on natural patterns. This for example is closer to the forms of leaves and trees than abstract diagrams composed of squares and rectangles. 

Make the most out of your project, by understanding the multiple levels of information that require attention at the outset. Before pre-empting the direction of a project, take on board all the constraints that will inform the emerging design. This will pay dividends. This process is akin to assembling the ingredients for baking a cake. The ingredients must be selected in exactly the right proportion and introduced into the mix in the right sequence.

This methodology will ensure that natural systems are respected, resulting in well balanced, functional and humane environments. At the same time a rich texture will be introduced into the design. This will preserve it from the banalities of a cartesian grid.

‘Commodity, Firmness, and Delight’

The qualities inherent in a well baked cake should be those described by the Roman architect Vitruvius for architectural perfection; ‘Commodity, Firmness, and Delight’  –  (Utilitas, Firmitas and Venustas)



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