The definitions of ‘knowledge’ and ‘understanding’ are problematic. According to my perspective, knowledge and understanding complement each other. In order to understand something, you must acquire a certain amount of information; claiming to know something implies that there is understanding. However, to understand something is very uncertain, it depends on the reliability of knowledge on which the understanding is based. For example, if we claim to know a language, we must understand that language. “Only seeing patterns can give us knowledge, only seeing particular examples can give us understanding”; this quote implies that knowledge and understanding are to some extent, interdependent. If knowledge is gained through patterns, which are shapes, figures, or elements, then understanding must be achieved by processing knowledge through reason, language, and intuition. For real understanding to take place examples themselves are not enough nor are the patterns on which the original knowledge is based. We should be acquainted with specific examples, but we also need to understand the concepts on which the knowledge is based. Through art, and math, it can be seen that patterns and examples are indeed important for knowledge and understanding, but only seeing general patterns and particular examples alone will not give real understanding, that comes with reason, intuition as well as sense perception.
When we claim to know a person, is this knowledge dependent on the pattern of, for example, his or her face? Knowledge of a person requires more than this mere recognition, but the pattern is a starting point. Intuition has a role in moving from recognition to knowledge and eventually to understanding. The human face is made up of patterns of features, which even newborn babies can intuitively recognize. Studies have been carried out to determine the recognition by newborn babies of their mothers' faces. In a 2001 experiment carried out by I.W.R Bushnell, it was found that newborns rapidly “process sufficient information about their mother’s face ... to allow effective recognition memory.” (Bushnell 2001). This suggests that the ability to recognize patterns is innate, but does this mean the infant knows and understands that this person is his or her mother? In this case the baby does seem to have knowledge that that set of patterns belongs to a source of food, comfort and affection so to an extent knowledge has been gained through patterns. Understanding, also, has been gained though the baby experiencing examples of comforting behavior and food supplies. However, the baby can only know this person is his or her mother later through reason, experience and intuition. As human beings, we tend to identify with faces. It has been shown that individuals feel secure when they are in contact with other human faces. Faces consist of a specific pattern; the brow, the eyes, the nose in the middle, and the lips. However, we may know that the pattern is a face, but that alone does not give knowledge of the person; it may lead to recognition; we can know what our friend looks like through sense perception but real understanding of who our friend is, needs reason, intuition and experience.
Art can be defined as the expression of human creativity. According to Picasso “Are we to paint what's on the face, what's inside the face, or what's behind it?”. Art is an area of knowledge, often associated with patterns of shapes, colors and motifs. Knowledge of art can be gained through recognizing patterns especially in work by artists who have used intuition in their oeuvres. In Picasso’s artwork for example, the artist uses the aesthetic techniques of cubism to distort images, and figures. For example, in the artwork The Weeping Woman, Picasso depicts a woman crying. When we look at the artwork, we are able to discern something of a pattern of a face, despite the fact that it does not conform to the usual pattern, we know there is a face there. The distortion does not render the face unrecognizable, its skewed proportions and ambiguous perspective makes it looks rather odd, but we do see the pattern, and therefore we are not disturbed by the image. In fact, it is the distortion of the accepted pattern that provides an insight, giving us a more profound understanding of the human face itself. Our knowledge and understanding of the face have been enriched by the deformation of the familiar pattern.
Poetry is another manifestation of human creativity – patterns of words are put together to convey meaning. One approach to poetry is to identify the pattern of stressed and unstressed syllables in each line and to identify the meter – is it an iambic pentameter or perhaps tetrameter? Is it a trochee or a spondee? While such scansion can be a useful tool in order to know the poem, it is not enough for real understanding. An example is the poem, “The Canonization” by John Donne. The poem is written in the pattern of iambic pentameter and iambic tetrameter with a repeated pattern of rhymes, A B B A C C C A A. Working out this pattern is useful, in one way we can claim to know the poem. However, with reason and intuition we realize that the rhyme scheme echoes the beating of a heart or maybe the sound of funeral drums thus is understanding achieved and we know the true meaning of the poem. In fact, "The Canonization" is a complex analysis of the nature of human love – is love purely physical, is it Petrarchan, erotic, or metaphysical? Understanding of this does not come from the visual pattern of the syllables; real knowledge and understanding comes from reason, intuition and experience.
Math is an area of knowledge to which patterns are intrinsic and yet knowledge of math requires more than simply looking at patterns and understanding requires more than working some examples. Fractals are an example of apparently simple patterns but understanding of the math behind the patterns takes much more. The mathematician Cantor, working during the 1800s on set theory, was so astounded by his discoveries that he wrote, “I see but I don’t believe it” (Cantor 12). Perhaps he perceived patterns in numbers but did not understand the significance of what he saw. He showed that the set of integers has an equal number of members as the set of even numbers, cubes, squares and roots. Further, he suggested that the number of points on a line segment equals to the number of points on an infinite line. In this, Cantor was exploring the concept of infinity – previously a taboo. Many condemned Cantor for challenging the previous convention of patterns of numbers. From Cantor’s ground-breaking work on transfinite sets, the Swedish mathematician Koch developed the idea of fractals – a pattern repeating itself to infinity. Ironically, this turns the prescribed title around; knowledge has given insight into patterns and the patterns help understanding of the nature of infinity. In his fascinating research, Ron Eglash explores the patterns of fractals in African culture. He demonstrates the relevance of fractals, patterns, in African architecture, design, and even in the layout of traditional villages. Palaces in Africa consciously have been built in the form of fractals, spirals or rectangles reflecting the social hierarchy. Here, in this situation, it appears that understanding the patterns leads to a better, more in-depth, knowledge and understanding of the society in which the patterns are found. How was it that these fractals were developed before the algorithms, the mathematics itself was discovered? In this case, the patterns appeared intuitively before the knowledge and understanding but the patterns did lead to that knowledge. According to Eglash, many of the African fractals are based on random number generators. Fractals are found in nature, in architecture, even in the replication of the AIDs virus. Fractals are even found in our vegetables. Brassica oleracea, or broccoli is made up in the form of fractals – repeating patterns of shapes. And yet, we can only know what broccoli really is by tasting it. If knowledge were limited to the simple patterns, then we would not understand anything.
As humans in constant search for understanding and certainty we must be ready to see patterns, to look for examples, but we must also be aware that neither patterns nor examples alone are sufficient. In Art, real understanding can begin with identifying patterns and seeing examples, but reason and intuition arealso imperative; Picasso’s paintings and Donne’s poems reach beyond the patterns and lead us to a more intuitive understanding of what it is to be human. Similarly, in math, a subject frequently associated with patterns and examples, if our knowledge simply stays on the level of those patterns, we will not reach understanding.