Giving pleasure to the eye is infinitely more difficult than to the hand or mind. There are no rules and no excuses. Most architects are silent on the matter. We seem tacitly to have accepted that aesthetics is a subjective discipline and if it pleases the mind we no longer need heed the eye.

And yet, for millennia, giving pleasure to the eye has been our predominant concern, and the quest for aesthetic perfection has been central to the philosophical debate. We face now an overwhelming global urgency to build more beautiful environments: our minds are active, but our eyes are closed.

Perhaps, in our search for a philosophy with which to explain everything, we have made it too difficult. If we contend instead that architecture is, for our public if not for ourselves, pre-eminently a visual discipline and, in the sense of non-monumental shaping of habitable space, it is principally conditioned by the pragmatic need to provide flat floors and more-or-less vertical walls, then, at the elemental level and before ever we introduce into it our accumulated cultural complexities, our art is essentially that of a geometer.

Given the all-pervasiveness of the horizontal and vertical in our work, both in the actuality of the experienced built space and, more significantly perhaps, in the visualisation of that space on paper or on screen, it should be our task to encourage the geometer in us to give meaning to these relationships and, ultimately, to make them pleasing.

Architects have long sought to understand what makes one shape more pleasing to the eye than another. The square, the double square and the golden rectangle have stubbornly re-surfaced in treatises of aesthetics since the time of Plato.

Perhaps this interest may be less surprising when we consider that the eye through which the ancients experienced the world was all but identical to the eye we use today. Indeed, it probably has not changed significantly since the dawn of man. It has a deep socket to shade and protect it, and a very wide visual field, un-focused and only in monochrome in the peripheral areas, but extraordinarily sensitive to movement and light. Our tribal ancestors would have been acutely aware of this visual field, for out of it would have come both predator and prey.

To focus, however, the eye has only a surprisingly small area wherein the image is sharp. This is the ‘foveal area’ and it is directed almost instantaneously at everything that triggers its interest. The eye’s tiny muscles are thus kept constantly in motion, adjusting and re-adjusting to stimuli, each eye passing information to the brain which measures the minuscule differences of angle between them in order to triangulate and calculate distance. The eye, then, is a geometer, and one of considerable accomplishment. With them, we can focus two foveal areas on the trajectory of a falling ball, giving the brain updated differential angles every millisecond of its passage, and then plot its projected angle and distance so that the hand may intercept it.

Small wonder then that with the need for such accurate triangulations, the eye has concentrated its movement to within a very small zone. This is the ‘easy eye movement’ zone, and it coincides with the area of maximum acuity wherein the image is sharpest. The foveal area can be directed here faster than elsewhere, for outside it the muscles have to work harder and take longer to adjust, and beyond the ‘maximum eye movement’ zone the whole head has to be turned. Not unnaturally, what gives the eye most pleasure is not to move at all. Only then can the eye and mind be at rest.

Now, understanding that the eye is so structured and that it is so highly sensitive to angular relationships, it will be a little less surprising to learn that when the various zones are plotted graphically, some curious facts emerge.

Consider diagrams A and B shown on the opposite page. These show the multi-ethnic, north American, statistical standards for the viewing angles of the eye in plan and elevation. If these same angular relationships are plotted on to a flat surface for clarity, visualised as if viewed from inside the eye looking out, they appear as in diagram C. This illustrates the left eye; the right eye is the same, but handed.

We are not so concerned here with the elliptical shape given by the cut-off from the eyebrows, nose and cheeks, more with the vertical and horizontal extents. These reflect the alignment of the two eyes horizontally and symmetrically about the vertical axis of the body, a key component of vision and of architecture too.

The intriguing result of this is that, when we look out on the world, our view is framed by the overall limits of our peripheral vision, and the centre-line of the eye in its vertical axis is set almost exactly on its ‘golden mean’.

Moreover, the horizontal axis cuts the maximum eye movement zone again on its golden mean (if we take the horizontal axis to be the centre-line between the upper and lower limits of our peripheral vision, that is, the centre-line of our overall field of view which, coincidentally, is the normal declination of the fovea when sitting ‘attentive’). Furthermore, not only is the easy eye movement zone similarly disposed, but so too is the declination of the fovea when sitting attentive. All cut the centre-line at the golden mean.

The golden mean, or the golden section, is the point at which a line may be cut so that the smaller part is to the greater as the greater is to the whole. The ratio is 1:0.618 and the golden rectangle, so fascinating to the ancients, is a rectangle with the same ratio between its two sides.

Of course, all of this could just be coincidence, but there does appear to be a geometrical relationship within the very structure of the eye, much deserving of our attention. It is not that we necessarily ‘see’ these relationships, it is more likely that the eye finds them the easiest to accommodate and the mind, therefore, recognises them as familiar.

If we then go one stage further and plot the angular relationship of both eyes, as in binocular vision, and project them to infinity as in diagrams D and E – ignoring for the moment that the two eyes are set very slightly apart – then the overall field of vision, which is the context within which our view of the world is framed, is itself a golden rectangle, and the maximum and easy eye movement zones are both very close to being circles inscribing squares which are again set in relationship to the horizontal centre-line by the golden mean.

Of course, not all of the relationships are exact to the millimetre, nor could one expect it from the averaged angular data deriving from ergonomic studies, but they are all so extraordinarily close – well within the perceptual tolerances identified by Christopher Alexander and others – that it is very difficult to ignore them.

The evidence does not stop here. If, as in diagrams F and G, we then introduce the distance apart of the eyes – which at, say, 65mm appears so small as to be negligible except for very close visual tasks – and plot the effect at an average reading distance of 500mm, our overall view of the world is still framed by the proportion of the golden rectangle. Also, the maximum eye movement zone comes closer still to a circle inscribing a square. The easy eye movement zone, however, or more accurately that part of it within which both eyes can be brought to a binocular focus, is changed from a square to a portrait format with an overall proportion of 4:3.

It may again be coincidence, but this is the proportion of the elderly window I am at present looking through and it is very close to the proportion of the inside pages of a typical magazine or book. Is this perhaps why they are so pleasing to the eye?

I have put forward these observations out of curiosity and they are all easy to verify. It will be apparent that I have purposefully not tried to extrapolate too much from the angular relationships within the eye itself to the projected effect of these upon the composition of works of art or architecture, for that would be a considerable undertaking. However, I believe if this were done we might well discover some interesting new facts about ourselves and why, if we were to try through the geometry of our structures to give pleasure to the eye, we might quite literally be doing just that. Beauty may indeed be in the eye of the beholder.

© 2008 Avery Associates Architects
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