This little gem of 58 pages from the ‘Small Books, Big Ideas’ series was much more pleasurable and informative than I had expected. Originally purchased due to its charming format, it is literally a small size book with a page of text and a page of illustrations to pictorially explain the principles. The author is simply stated as a designer, living in Wales. Not that it mattered strongly to me for these types of small reference books, but I like the perspective from a non (pure) scientific view.

Of course, given its small size, I never expected the book to go in any deep details. But I was surprised by its concise explanations from multiple perspectives – science, math, physics, art, history, design, nature, cultures, biology, etc. In short, symmetry, and its extended principle of proportions are found everywhere around us; symmetry is visually pleasing to us – rather we are explicitly aware or not aware of this.

Quotes, Food for Thought, or “Hmm, how about that?”:

The opening quote of the book: By Leonardo da Vinci –
“Let proportions be found not only in numbers and measures, but also in sounds, weights, times and positions, and whatever force there is”.

From Intro: Both these statements spoke volumes to me as a person who appreciates (and seeks) balance.
“Any notion of symmetry is completely entangled with that of asymmetry, we can scarcely conceive of the former without invoking thoughts of the latter (as with the related concepts of order and disorder) --- and there are other dualities.”
“In addition, symmetry principles are characterized by a quietude, a stillness that is somehow beyond the bustling world; yet, in one way or another, they are almost always involved with transformation, or disturbance, or movement.”

Dorsiventrality: The symmetry of moving creatures
While this is visually obvious, it’s not something that is at the top of my mind nor would I find the words to state it as a design principle, by nature and by humans.
Animals, or any moving creature, “will be made of left and right sides that are roughly mirror versions of each other. Since they also have a front and a back (and usually a distinct top and bottom) they are not merely bilateral, but dorsiventral. This is the best arrangement to have if you need to move in a directed way. It is not only animals that express this symmetry; forward-moving vehicles, such as automobiles, boats, airplanes, etc., are by necessity, symmetrically disposed along similar lines.”
“Fins and limbs are best place laterally, in symmetrically balanced positions.”

Enantiomorphy: Left and Right Handedness
I just might be intrigued enough to research this more – the source of the dominance of right handedness.
“Amongst other things, our dorsiventral body-form gives us a pair of hands that are similar in most respects, except that they are mirror-reversed.”
This mirror symmetry, left-hand vs. right-handed, is repeated in the form of clockwise or anti-clockwise in spirals (animal horns), climbing tree vines, and even mollusk shells.
“In chemistry, this phenomenon is known as chirality, which is of particular importance in organic chemistry, since many biological molecules are homochiral, that is to say, are of the same handedness, including amino acids, and DNA. This, in effect, means that the entire chemical basis of life itself is chiral. At some early stage in the origins of life on Earth, the earliest molecules to master the art of self-replication opted for a particular stereo-chemical profiles, and in so doing determined the entire, right-handed, course of evolution.”

Fibonacci Series: Where each number is the sum of the preceding two numbers, i.e. 1, 1, 2, 3, 5, 8, 13, 21, etc.
Named by a 12th century young Italian customs officer, Leonardo Fibonacci.
“The Fibonacci numbers are frequently involved in plant growth patterns, notably in petal and seed arrangements. Flower petals are almost invariably fibonaccian in number; fir cones use series of 3 and 5 (or 5 and 8) intertwined spirals; pineapples have 8 rows of scales winding one way, 13 the other way.”
“Fibonacci patterns are not restricted to organic formations; they have been observed in many aspects of the physical world, from nanoparticles to black holes.”

Asymmetry: The Paradox of Inconstancy
That the world is a balance of symmetry and asymmetry. In what appears to be symmetry, that there is asymmetry. This tells me to accept the world as it is – all its supposed imperfections are in fact by natural design.
“One of the most important discoveries in recent science is that the notion of ‘broken’ symmetry has deep cosmological implications... The fact is that wherever one looks there are many kinds, as well as degrees, of deviation from symmetry. The human body, for example is bilateral (or dorsiventral) in its general form and some internal organs, like the lungs and kidneys follow this symmetry, but others, such as alimentary canal, heart, and liver do not. And even the overall symmetry is only approximate. Most of us have a dominant hand and eye, and there are subtle differences in the respective left and right sides of faces.”

Self-Organizing Symmetries: Regularities in Non-Linear Systems
This made me think of order within chaos – not unlike work on some days. :)
“The simple ripple patterns on a seashore, for instance, are created by a multiplicity of contributory factors, including tides, currents and winds – not to mention the more general effects of gravity and warmth from the sun. All of these are drawn into a self-organizing, self-limiting order whose charm lies precisely in the fact that it is repetitive, yet infinitely variable.”

Symmetry in Art: Constraint and Creative Potentiality
The words that humans are ‘pattern-seekers’ rang true in so many aspects of life. Again, not top of my mind, but very accurate nonetheless.
“Where symmetries of any kind are present in art they will be intimately involved with the particulars of a style, since symmetry, in art as elsewhere, is an organizing principle. It would seem that humans are symmetry-conscious creatures; we are pattern-seekers by nature, so symmetry principles are never entirely absent as a consideration in art generally.”

A Passion for Pattern: The Perennial Appeal of Repeating Designs
Creation vs. Detection. And the last phrase about science is largely accurate.
“The unconscious, but systematic exploration of symmetry groups in this way would seem to blur the distinction between the artistic activity of pattern creation and that of science, whose entire enterprise could be characterized as pattern detection.”

Experiential Symmetries: Percepts and Precepts
I’m not sure if this is now stretching the application of symmetry, but I still agreed with the words in principle.
“Symmetry is an essential component of the basic social norms of reciprocity. We expect fair dealings in social exchanges… By extension, any system of justice is bound to reflect these notions of proportionality; this is symbolized by the image of the balance-scale, that most graphic representation of symmetry.” ( )