Mathematics and the Real World Read Online Free PDF Page B

shape to the adult eye is highly dependent on familiarity and education. For example, the attitude toward modern art initially was almost hostile, and it moderated over the years as the general public became more and more familiar with it. Babies have not had time to become familiar with any particular shape or form. What, then, is the origin of their preference for the golden ratio? The answer is simple: Evolution. An examination of the dimensions of the human head reveals that they are close to the golden ratio. Likewise, the proportions of sections of the human face, such as the ratio of the width and height of the eyes, the height and the width of the ears, and so on, are also close to the golden ratio. The evolutionary advantage to an infant who can recognize and is happy to discover a figure with those proportions is clear. Babies who are calm when they see their mother approaching, in contrast to exhibiting discomfort or even crying for help when they see a bird of prey nearby, havea greater chance of surviving. Hence the feeling of greater comfort when confronted with rectangular forms that have proportions similar to those of the human face rather than other forms is etched into the human genes. This has nothing to do with the golden ratio itself. In fact, research shows that babies also feel at ease with the shape of a hand, and the evolutionary reason for that is self-evident. Evolution rewards a baby who reacts with discomfort if held by a predator compared to its reaction when held by a human being. I would hazard a guess that if it were possible to perform similar experiments with birds, we would find that of all geometric forms, the most pleasing to a young chick would be an acute-angled triangle.
    At this stage we may still wonder whether babies may have learned to feel comfortable with ratios similar to the golden ratio in the first weeks after their birth. The answer lies in the signs of discomfort and fear when they are faced with certain forms. Psychologists claim that about one-tenth of all children experience a primeval fear of clowns. Recently an occupation known as medical clowning has become widespread. It involves clowning activities meant to relax and help children requiring hospitalization. But cases have also been reported in which the activities of the medical clown only harmed the child, and the condition of the terrified children deteriorated when they saw the clown. This too is related to geometry and its evolutionary roots. The sight of a clown, with all his bright colors and the nonhuman proportion of his limbs and head, calls into play the same genes that make infants cry for their parents’ help when they see a multicolored bird of prey or a tiger approaching. It is unreasonable to think that in the modern world children would “learn” to be afraid of clowns. These innate features are the inception of geometric recognition. (We will often refer below to the simple but illustrative metaphor of confrontation with a tiger.)
    Another basic mathematical ability that almost certainly played a role in the evolutionary struggle is the ability to identify patterns. I am not familiar with controlled experiments that show that the tendency and ability to recognize patterns is ingrained in the genes, but imagine early man with a tiger stealthily creeping up on him in the grass, leaving a trail of flattened grass. The ability to identify the trail as a source of danger could be life-saving.Ability to recognize patterns is not restricted to visual patterns. Consider for instance patterns of sound. For most of us, hearing very few notes is enough to recognize a pattern and sometimes to identify an entire tune or melody. As recognizing patterns is an attribute that is helpful in the evolutionary struggle, those who had this ability had more offspring than those that lacked it. It is thus almost certain that the tendency to recognize patterns is passed on genetically. Less harm is caused by seeing a