Yale University Press published ‘The Diagonal’ by Jay Hambidge in 1920. It was republished in 1926 as ‘The Elements of Dynamic Symmetry’. ‘Dynamic Symmetry’ documents a series of special rectangles, most with irrational proportions, that subdivide evenly and in proportion to the whole. For some reason this subject is polarizing.
Everywhere Pole: Mystics claim these proportions hold the secrets of the universe from the growth of plants and animals to the formations of hurricanes and galaxies. Historical references for this include Plato’s ‘Timaeus’ and Luca Pacioli’s ‘De Divina Proportione’ with illustrations by Leonardo Da Vinci. It is a theory of Everything that requires a fair amount of faith.
Nowhere Pole: Scientists and mathematicians point to the lack of precision in the above theory. They note that the natural variations in plants*, animals and universal forces show no proof that there is a governing proportion system. Many art historians also avoid this issue because very few artists specifically note its use. This is fair a position because scientists, mathematicians and art historians work in the domain of proofs and factual evidence.
But what if both sides are missing the point? What if all their focus on Rules ignores the usefulness of the Tools. What if we look at this from a different perspective?
Linear perspective is a form of geometry that can be made to be mathematically precise. We all know that the person off in the distance is not a Lilliputian but most of us have had to be taught a system for translating 3D information onto a 2D surface that reconciles with our shared experience. Yet, outside of academic exercises, how many of us still construct mathematically precise perspectives? Most of us use our experience with this tool to fudge things so that they look right. Sometimes we even distort the perspective to expand, contract or warp the space based on our intent.
All rectangles have a topology that subdivide the whole. There are 8 (commonly used) root rectangles whose subdivisions relate proportionally back to the whole. The potential of these rectangles has less to do with their aspect ratio being some divine truth or aesthetic short cut and more to do with the mathematical truth that their proportional decomposition permits one to construct rhythm, hierarchy and balance within the rectangle that relates back to the whole. See here.
Dynamic Symmetry is a geometric tool for organizing surface relationships (rhythm, movement and hierarchy) within a static image just as linear perspective is a geometric tool for organizing spatial relationships (depth) on a flat image.
Below is a drawing by Vincent Van Gogh. Diagram 1
Now take a look at this…
“Poetry surrounds us everywhere, but putting it on paper is, alas, not so easy as looking at it.” -Vincent Van Gogh