Why do we tend to use 8.5-inch by 11-inch paper? How did a dollar bill come to exist in its present size? What determined the choice of musical notes that created a chord? Why are the logarithms in the growth stages of a peacock’s tail the same as those in a daisy? What makes some spaces inviting and other stressful? Why are some things just plain easier to learn than others?
We are surrounded by the above phenomena daily, yet it’s usually children that stop to ask such questions. Why? Perhaps the answer lies in the fact that these phenomena feel so natural, so organic to us that they become transparent. What is it about a thing that allows it to become more transparent than another? Attempting answers to many of these questions is the subject of György Doczi’s book, The Power of Limits: Proportional Harmonies in Nature, Art and Architecture.
Doczi asserts that humans gravitate towards things that express proportional harmonies. Sometimes this harmony is quite visible and mathematically demonstrable, but frequently it is discovered only with intense examination. The book endeavors to reveal many of these harmonies along with their ability to generate patterns in nature, art, and architecture. His work was surely a landmark for botanists in 1981; now one finds titles like The Algorithmic Beauty of Plants. It appears that High Renaissance artists like DaVinci and Albrecht Dürer also observed and documented many of the same harmonies and algorithms and these are also explored within this body of work.
One of the fundamental harmonies examined is contained in the Pythagorean rule of the Golden Section. One does not need to be a mathematician to appreciate this rule. Whether examining a successful graphic design or the relationship of cities to states, the rule states that the small part stands in the same proportion to the large part as the large part stands to the whole. Pythagorus expressed the rule mathematically A:B=B:(A+B). To paraphrase Doczi, where this rule is observed, there usually exists a generative quality that goes beyond the mere energy created by the action of polar opposites.
Evidence of this rule can be found to exist in things and events as varied as the Biblical version of the Golden Rule to the Constitution of the United States of America. Perhaps the secret of lasting endurance of the Constitution of the United States of America lies in the framers’ intuitions and observations of the necessity of a harmonious balance of power in the construction of anything, organic or inorganic, in order for it to remain a living and viable thing.
When the rule of the golden section is applied to training, it would indicate to this writer that creating opportunities for every participant to build upon already familiar harmonies during the training process is not only efficient but has the potential to empower each participant’s learning process. In the same way that light, color and sound waves all share vibrations, so do content, context, and language—the building blocks of knowledge. Content, context, and the process by which they are imparted, form either a harmonious, whole body of knowledge or are perceived as confusing and anxiety producing. Some spaces simply make us comfortable; though we may not be able to pinpoint why. In the meantime, we are too easily distracted from the content at hand by all the noise of disharmonious elements.
A marriage of art and science in the training process becomes a necessity for there exists a reciprocal, harmonious relationship between content, context, and the remainder of the learning environment. An underlying whole, harmonious body of work employing these building blocks of knowledge aids comprehension. A participant’s sense of an underlying harmonious whole allows the utilization of her intuition, making for an efficient, satisfying learning experience. If one is to increase the potential for ease of learning, the reciprocity of the golden section can hold the key to a learning experience that also becomes generative in its ability to aid greater pattern recognition (and to garner future participants).
The rule of the golden section when applied to computer screen real-estate would find the golden point at which navigation tools would separate from other content in order to deliver a harmonious experience for the eye—which is still simultaneously and subliminally “hearing” the language exhibited on the remainder of the screen. There is less real separation of the experiences of the eyes and ears than is generally recognized and accounts for above average hearing acuity of a blind individual.
Content will ideally reflect the same harmonious relationships found in nature. Language, like music, has a rhythm and flow that makes for ease of retention when harmonious. The design harmonies among content, context, and language determines whether the experience offered by a website is of a quality that is disposed to unite with the greater body of knowledge that each participant already possesses. Learning is a natural high that, when exploited, also tends to be generative in nature, creating a demand for more. To the degree that the website experience is a rewarding one for the participant, can determine whether or not the generative power created within a harmonious union of diverse parts will have the chance to make itself heard amidst all the noise.
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