Dynamic Symmetry and William Blake

This summer I read some interesting books I had acquired on Cape Cod in May. They ranged from compositional methods to philosophical writings to the alchemical relationship between paint and artist to color theory. When one reads several books simultaneously one finds oneself making analogical connections between what appears to be separate studies. These analogical insights usually come unprovoked. Somehow the unconscious is linking things in their proper substantive relationship that one would not necessarily see at first sight. Baudelaire called this acknowledgement of intuitive relationships a “correspondence”. I found such a surprising analogy or correspondence between the writing of William Blake and the compositional theory of Jay Hambidge in his book on The Elements of Dynamic Symmetry, 1919. These are the two ideas I found fascinating and strangely connected: Hambidge’s idea of the reciprocal of a rectangle and William Blake’s insight,”… nature (Blake called), is one continued (continuous) vision of imagination.” (Kathleen Raine, Blake and Antiquity, Bollingen Series,1962, p.3) Obviously, patience is needed for me to explain this analogy. So let me begin with what is a reciprocal of a rectangle.

A lesson in “The Reciprocal”:

Jay Hambidge believed that , “A process connected with the science of plan-making which was thoroughly understood by the Greeks, was that of determining the reciprocal of a rectangle. A reciprocal of a rectangle is a figure similar in shape to the rectangle but smaller in size.” (Hambidge, p.30) The ratio of the larger rectangle is the same as the smaller one (contained within the larger rectangle) with only a variance in proportion. To create a dynamic rectangle, one begins with a square,which Hambidge refers to as a unity or 1. This term is important for what I will express later. And from this unity, one adds a reciprocal, which is an addition of space that creates a rectangle that fufills a Golden Section proportion.

Example 1

So from a square or a unity one creates a rectangle that contains the unity plus a rectangle that is the same ratio as the whole or larger rectangle. Building a golden section rectangle depends, “… upon the fact that the diagonal of the reciprocal cuts the diagonal of the major shape at right angles.” (Ibid. p. 30).

Example 2

And within this rectangle, referred to by Hambidge, as the ‘whirling square’, one can create an infinite number of reciprocals that spirial around a fixed point, creating again and again an infinite number of rectangles that are of the same proportional relationship. Every rectangle within the larger rectangle is related and analogous.

Example 3

So from a unity, one creates another deep unity that is no longer a square but a rectangle that contains the unity and has within itself a rectangle that reflects its larger whole. This is the key to what I found interesting and analogous to Blake.

William Blake:

Blake states that, “… nature is one continuous vision of imagination.” Blake states elsewhere that, “every Natural effect has a spiritual cause.” Nature, itself, is analogous to the imagination. Nature is a continously unfolding, visionary product. Nature, itself, is Imagination.

But how is this product generated and by whom? Blake was heavily influenced by the Neo-platonists as well as his own Christian faith. The source, Blake seems to imply, is Divine. Divine, in the Christian sense, as well as in terms of Platonic thought, “All things exist in their ‘Eternal Forms’ in the Divine mind.” There exists an ‘Imagination’ that is beyond human comprehension, in a way. I say, in a way, because if I take the idea of the reciprocal– that the rectangle created beyond or in addition to the unity (square or 1) is proportional to the larger rectangle (the whole)- I see that they are analogous and the only real difference is size. The human element is contained within the larger Divine Element, and yet directly mirrors the larger whole in such a way that the only difference is one of proportion. The human capacity to imagine is analogous to the capacity of the Divine to Imagine. To Blake, the imagination is the very essence and material substance of Nature. It is the imagination, that is able

To see a World in a Grain of Sand

And a Heaven in a Wild Flower,

Hold Infinity in the palm of your hand

And Eternity in an hour.

(Songs of Innocence)

Gaston Bachelard states in Earth and Reveries of Repose that , “The imagination is primary and precedes any action or observation. (Precedes is the key word.)  Imagination then takes experience (One’s conscious life in the world) and enlarges upon it, searing it into our souls.” And again, “Imagination immediately turns a substance (matter) into a value (quality) and therefore material images transcend sensations.” Kathleen Raine states in Blake and Antiquity that,”Blake considered the Divine Imagination to be present in all men- indeed all creatures.” (Raine,p.88) The outward forms of nature correspond to the informing mind or life.(Ibid.90) One could take the idea of the reciprocal further and say that the rectangle of the ‘whirling square’, in which one can infinitely create a reciprocal, reflects that the Divine Imagination can be carried into every creature that lives, and the only variance is proportion.- beginning with the Divine Imagination to the human imagination to the imagination of an animal to that of an insect etc. -through all things that have life in existence.This allows Blake to pronounce that the, “Imagination is not a state; it is Human Existence itself.”

“That which is above is like that which is beneath, and that which is beneath is like that which is above, to work the miracles of one thing.” (The Marriage of Heaven and Hell)

Raine continues this thought, “the hidden thoughts of man are his share in the Divine Imagination- hidden, perhaps, as Jung has described the archetypes that determine our nature,  because inaccessible to normal consciousness; they create us, not we them.” (Ibid.90) Blake calls us to recognize phenomena as a portion of the ‘soul’ regenerating and ressurrecting nature. Imagination re-invests the world with meaning and beauty and subsequently creates a world in which art connects us, not only to nature, but to that interior soul that yearns to know itself- through the beautiful. Blake refers to the artist as one open to that ‘portion of soul’. ” I see Every thing I paint In This World,” Blake wrote, “… to the Eyes of the Man of Imagination, Nature is Imagination itself. As a man is, So he Sees.” (Ibid.,p.100)

As a man is, So he Sees.



Author: Judith Reeve

For nearly 30 years I've developed my painting practice in the studio, building on what I leaned from my student days at the Lyme Academy of Fine Art. Along with my daily journey creating images which I write about here on this blog, I am also currently writing a book on the color practice of Robert Henri.

6 thoughts on “Dynamic Symmetry and William Blake”

  1. Wow, I could spend a long time following all the implications of this with my *own* imagination. I’ve always found the idea of “Correspondences” really evocative, and have related it to Synchronicity and Manifestation and many other phenomena. I particularly like this quote: “Imagination immediately turns a substance into a value”. Might science and art find themselves brothers rather than rivals, one of these days?

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