As you will recall, I have been reading Padovan's "Proportion".  Having had a few days to digest the material now I figure it's a good time to write up the arguments as I see them for (and against) using proportional systems in design.

From a perceptual standpoint (the standpoint of our thesis), the primary question of any approach to design is the effect that the approach has upon the viewer.  The desirability or utility of any given approach is therefor predicated on the particular effect that the designer wishes to induce in the user.

"Van der Laan encouraged me to see a proportion system not as a tool or recipe that makes good design 'easier', but as something vastly more important.  The role of the system he discovered, the 'plastic number', is not to help make a better architecture, but rather, the role of architecture is to embody the plastic number."[1]

Padovan goes to great lengths describing three approaches to humanity's relation to nature, based on Worringer's 'Abstract', 'Empathic', and 'Oriental' descriptions.  He describes, in particular, the role of architecture in each case as mediating (or reflecting) our understanding of the natural world.  In the 'Abstract' forms (including 'Oriental') an order is imposed upon or set up against an unknowable external world.  In the 'Empathic' forms, order is seen as arising from the ordered and knowable external world (though Padovan argues (via Kant) that this is simply our perceptual systems subconsciously imposing order).

Much of Padovan's text is taken up with his thesis regarding the transitions between the three (or two, for him, with 'Oriental' merely being an 'Abstract' form) approaches to the external environment, and their implications for the use of proportional systems in design.  He argues, that the ancient Greek philosophers brought humanity from seeing nature as an unknowable external force to seeing it as a realm comprehensible via Numerology (Pythagoras).

In such an environment, where numbers are seen to order the world, and the secrets of the universe are just an equation away, an 'Empathic' tradition arises wrt the use of proportion in architecture.  Numeric correspondences are used to tweak the viewer's sense of underlying patterns, to suggest the emergence of a new pattern of understanding, but more, the 'truth' of the numbers is seen as itself an ideal to be embodied by the architecture.

Padovan then argues that the various scientists of the Enlightenment (Copernicus, Bruno, Kepler, Galileo, Newton, and Berkeley) while creating an ordered universe, divorced the underlying patterns of the universe from direct connection with human experience.  This culminated in Hume's philosophy suggesting that there is no absolute truth that can be based on our experiences of the world; that all is merely perception and opinion.

In such an environment, all discussion of numeric 'truth' becomes irrelevant.  If nothing can be known from the world around us, then hoping to find truth in the emergent patterns of numbers observed in the world is hopeless.

From Hume's relativism, Padovan argues that Kant provides a sort of lifeboat.  Our perceptions and our perceptual mechanisms, including our model of the universe, can be used as a foundation for knowledge.  Now, as we may recall, the human perceptual system is constantly seeking for underlying patterns and orders in our environment.  It is searching for concepts and clues that will allow us to better understand (and thereby, better cope) with our environment.  Our model of the universe is constantly being reevaluated and revised to take into account new perceptions, and to resolve inconsistencies.  We are pattern seeking creatures.

Here Padovan inserts the discussion of Van der Laan .  As we have discussed in the past, Van der Laan used perceptual experiments (in the line of Fechner, as Padovan mentions) to discover various types and orders of size which were the limits on our ability to perceive differences and relations in size.  From this he built up his proportional system, the 'plastic number', which he sees as being 'not a means, but the end, of making architecture'.[2]

As we see from the quote, Padovan and Van der Laan see the plastic number as an absolute good, though derived from perceptual experiments and itself considerably malleable.  That is, they see the plastic number as an end or goal in and of itself. The plastic number, in their understanding, should be applied in all architecture, having been discovered as something solid which is based on human perception.

You may see the problem there.  Padovan constructs a world in which an ideal, a truth, is constructed, then immediately returns to the world of the renaissance.  Having discovered one pattern in the world, that pattern is taken as absolute truth, and the search is halted.  The problem here is that Kant's lifeboat is not a stable foundation on which to build a temple.

The problem that arises in Padovan and Van der Laan's search for a proportional system is that the entire idea of proportional systems is not examined to see their effect on human perceptual systems.  Padovan does take some time to review experiments which tried to prove whether there was any effect of particular proportions on a viewer, but this doesn't address the underlying issue.

As we have mentioned, humans are pattern-finding animals.  We are constantly searching for rules and models which better describe our environment and allow us to better cope with that environment (in the largest sense of environment, including our own bodies, that immediately around us, and the world at large).  What is the effect of proportional systems embodied in architecture on a pattern-finding animal experiencing that architecture?

The first thing we need to answer the question is to look at the effect of proportional schemes on the environment in question.  We can characterise these effects along much the same lines as Padovan does.  Proportional schemes tend to have additive and multiplicative characteristics such that multiple dissimilar elements with readily comprehensible interrelations combine in such a way as to produce composite elements which are themselves related to the individual pieces.

In other words, a proportional scheme will tend to produce designs where a complex phenomena appears to resolve itself.  It will tend to produce an impression of emergent order.

Consider, in contrast to a proportional system, a grid.  A grid is, similarly, a generative/limiting mechanism in many architectural designs.  It is readily comprehended, and is highly ordered, but is comparatively not complex at all.  The grid does not read as a complex phenomena resolving itself between parts and whole, but rather as a highly ordered phenomena which remains static.

So, what is the effect of this impression of emergent order on the human perceptual system?  Well, as we understand the perceptual system, which is constantly searching for such emergent orders, the effect will tend to be mimic that of a discovered order.  If the perceptual system cannot resolve the order, it will tend to produce anxiety. If it can, it will tend to be perceived with excitement and interest.  If the order is too easily resolved, or not of sufficient complexity to engage, it will tend not to be noticed or noticed with boredom.  The nature of this effect will depend in no small part upon the individual perceiving the work involved.

Given this effect, how and when should we use proportion in design?  Padovan and Van der Laan are asserting that proportion in design (and particularly, the plastic number) should be used at all times, that it is, in effect, a moral requirement for building.  This assertion is tied up with an implicit moral argument regarding the purpose of design; that the purpose of design should be to inspire confidence and solidity while inspiring the observer with the potential to find greater depth in the universe.  It is interesting to note that the most effective designs using the plastic number are religious in programme.

Separating out the two concerns, moral and effective, proportion is a tool which allows a designer to produce an impression of a complex phenomena resolving itself.  This impression can be used to lend a certain set of associations to a design which are tied to our interest in resolving patterns and finding deeper orders in the universe.

Care must be taken when using this particular tool, as it is playing on one of the most basic human perceptual systems.  An order which is trivial or uninteresting, yet takes a great deal of investigation to resolve will tend to produce a negative reaction.  Similarly, an order which is painted on at the last moment will tend to have a poor reaction, seeming to the viewer to be an attempt more to obscure the truth or apologise for something than an approach to underlying reality. This same caution, of course, applies to all generative/limiting orders, and indeed most tools in design, if the design does not actually help the user cope, it will not likely be well received.

[1] Proportion, pp15
[2] Proportion, pp15