language, “2 + 2 = 4” is a sentence, where “2”, “+”, “=“, “4” are words. In fact, this is read as “Two plus two equals four,” which we see maps very well with its natural language equivalent.

Another formal language is that of computers. “If x = 2 then stop” is a sentence, where “If”, “x”, “=“, “2”, “then”, “stop” are words. This reads, “If the variable x equals 2 then stop,” again a natural sentence. Now, the main difference of formal languages compared to natural languages is that whereas the latter map to the entire sensori-motor experience of humans, the former maps to a much more restricted domain, reflected in part by the restricted vocabulary, and in part by the restricted set of rules applied when assembling sentences together, that is, the grammar of the language. However, this restricted nature doesn’t make formal languages easier to understand than natural ones. Remember, as we’ve seen, formal languages can actually be made into equivalent subsets of natural language. If the sentence “The integral of x is half the square of x plus a constant” sounds complex to you, it won’t make the statement simpler to understand if it is written in a formal way. However, when formal languages are used by computers, instead of humans, the story is different. To a computer, the sensori-motor mapping of the formal language, limited as it is in vocabulary and rules, is, in fact, natural to it, just as our primary sensations are natural to us as humans. For us, those primary sensations don’t need explanation since they are just what we are. So what’s formal to us, referring to a particular metaphoric mapping of our sensori-motor experience, is, in fact, natural to the computer, referring directly to the computer’s sensori-motor capability. Conversely, natural language, which refers to our basic sensori-motor experience, is foreign to computers as long as they have not evolved a sensori-motor apparatus, or a simulation thereof, comparable to ours. But then, that is what this book is all about.

The precursor species to modern man could communicate long before the ability of speech as we know it today evolved. The brain of the archaic Homo erectus may be considered, based on cranial capacity, as possessing the semantic capabilities to support language, but the vocal facilities of this particular species may not have been advanced enough mechanically to allow for the nuances of natural language. Perhaps, not until some time before the emergence of Neanderthals did the mechanical configuration of larynx, tongue and throat evolve to support the full range of sounds that allowed natural languages to be spoken. In fact, three distinct systems are required for humans to realize the vocal facilities they currently possess.

First is the mechanism for compressing air and expelling it in a manner capable of vibrating a membrane that can produce sound. Second is the vibrating membrane itself; that is the larynx, a mechanism that sits in the throat of a person in a manner so as to allow air expelled from the lungs to pass over a membrane, the vocal cords, so as to produce a sound. Finally, a throat, mouth and tongue mechanism that can modulate the sounds emitted from the larynx. These mechanisms, in concert, allow the production of sounds that can express the structure of natural languages.

The culmination of natural language came with the advent of writing, the facility to express language through symbols which could be imprinted on material and subsequently read back from that material. This brings us to the earliest forms of recorded history of the species, a facility that separates humans from all other species. That is, mankind appears to be the only species that has prepared a permanent visual image of complex thought that can be passed to other members of the species over long distances or over long periods of time.

Finally, we draw your attention to the communication facilities provided through art. In our first chapter, we alluded to the use of art as an efficient means of context sensitive communication. Please note that in referring to art, we’re referring to the full variety of art forms. Indeed, there are various types that impact on all of the human senses, both individually and collectively. Consider

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