First Order Isomorphism and Proto Isomorphism

In this chapter, I have tried to show that many of the illusions used in art and architecture are based on some fundamental laws of visual perception. The incongruity between images "out there" and the perceptions "in here" is used to illustrate the way the brain processes illusionary information and how the visual-cognitive systems handle such inconsistencies. From another point of view, the relationship between internal representations of visual information and the physical stimuli that provoke them reflects a type of cerebral efficiency that is truly wondrous.

For the sake of argument, consider the type of brain required for an exact iso-morphic correspondence between physical stimuli and mental representations of those events—a condition called first-order isomorphism.6 The idea suggests a one-to-one match between the physical energy in the universe and the psychological representations in the mind. Casually speaking, such a creature would be a kind of knee-jerk being—energy in, energy out. Very simple organisms operate like this.

A complicated organism of that design, such as a consciously AWARE man, would require a huge number of cognitive templates in order to understand even simple signals, such as the letters on this page. To comprehend the world of art, an isomorphic brain would be required to have countless millions of patterns to match to the diverse number of art types, colors, shapes, and the like. Even with the billions and billions of neurons in the brain, each with numerous synaptic connections, a system of isomorphism is neither practical nor attainable.

A more parsimonious model of the mind is one that is constructed on an ancestral platform of intelligent neurons that are highly efficient in making adaptations to environmental conditions. It is simply wrong to believe that we are born into this world with a totally unprogrammed mind resembling a tabula rasa upon which all experiences are written and encoded. While life experiences and our adaptation to an ever-changing world shape our perception of art (and the whole of our sensory experiences), these environmental episodes are always understood in the context of a sensory and cognitive system that evolved over millennia. Because of the physical limitations of brain size and the need for an efficient ambulatory computational brain, the extent to which incoming information can be perceived and processed is necessarily limited.

We do not perceive the world isomorphically but proto-isomorphically, by which I mean that prototypic impressions of the world are built on a preestablished platform of neurons and processing programs. One of the most salient (and frequently overlooked) characteristics of the human mind is its proclivity to establish categories, especially when it comes to visual images. We see a four-legged furry animal, and then another, and then another, all slightly different, and learn to categorize them all under the superordinate "dog." We do not have a template for each dog we have seen in the past or will see in the future, but have a prototype of dogness that is capacious enough to recognize a cocker spaniel, golden retriever, Chihuahua, poodle, shih tzu, beagle, dachshund, dalmatian, German shepherd, Yorkshire terrier, and Great Dane. That remarkable taxonomic predilection gives tremendous computational power to the brain by economically reducing redundant "dog slots." Brain neurons are efficiently organized by such a system, and access to information is likewise optimized. The human brain simply cannot process all it beholds, but it can process diverse information effectively if it is conceptualized.

Art and science (e.g., chemistry, physics, botany) are prime examples of didactic subjects that have undergone extensive systemization, especially during the Renaissance and age of Enlightenment. Much of the erudition of the scientific-technological revolution has been preoccupied with "carving nature at its joints." Less metaphorically stated, it is because of our limited processing capacity that we need the world sorted into units the brain can understand. By forming prototypes of dogs, art types, elements, plants, and the like, we function effectively, while at the same time we are able to recognize a dachshund from a golden retriever; impressionism from abstract expressionism; carbon from mercury; and a rose from a dandelion. More on this topic in chapter 8. Illusions are the intellectual appendixes of such a metamorphosis. We see, really see, illusions because our brain evolved to see the fiction better than the fact.

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