Post date: 09-Mar-2012 06:17:03
We humans use a large number of symbols in our written languages. Often these same symbols are also used to write mathematical ideas and we each have learned how to manipulate these mathematical symbols to undertake arithmetic, trigonometry, calculus and the like. More recently computers have been developed which can store and process vast quantities of these written symbols far more rapidly than humans. However, while human brains can learn to store and manipulate symbols, the operation of a brain remains very distinctly different to that of a computer. Furthermore, Natural spoken languages are very distinctly different to mathematical languages (including computer programming languages).
Written language symbols were developed to record spoken languages that had evolved in very much earlier times. Children acquire speech in a largely automatic and effortless process, before learning to read and write, and then only with considerable effort. In each case, the recognition system is primary to the production system. For example, infant comprehension precedes speech; vocabulary for reception is generally larger than for production; multi-linguals that speak with a foreign accent do not hear with a foreign accent (Lamb 1999).
The artificial written symbols (letters, words, punctuation, sentences, paragraphs etc) are attached to natural spoken language; not the other way around. The correspondence between spoken language and written language is only broad; consider “I am going to” vs. “I'm gonna” vs. “amona”. The rhythm, stress and intonation of spoken language are not completely captured by the written symbols; consider “Jennifer put her briefcase on the dining-room table” vs. “Jennifer put her briefcase on the dining-room table” vs. “Jennifer put her briefcase on the dining-room table”. One word can represent multiple concepts, and concepts can be represented by multiple words; consider hard and difficult.
In mathematics (and in computers), each symbol has a precise, formally defined meaning, founded on a small group of axioms. Natural languages are very different. Consider the natural language word 'game' as famously explored by Wittgenstein. In seeking a definition of a game, Wittgenstein first sought that which was common to all games. He found only a complicated network of similarities, overlapping and criss-crossing: sometimes overall similarities and sometimes similarities of detail. Look for the similarities in board-games, but then extend to card-games, and then on to ball-games. There is often winning, losing and competition, but what of the card-game patience, or throwing a ball to ones-self? What of the role of skill and luck; of the difference of skill in chess and in tennis. What of a war-game? Wittgenstein found that it was not even possible to draw a natural boundary around the meaning of a word. But Wittgenstein's whole point was the astonishing realization that we do not need a definition in order to use a word successfully in natural language. What does it mean to know what a game is, and not be able to say it? (Wittgenstein 1953)
“A crucial property of a conceptual system is that none of its concepts can be described without an account of its relationships to various other concepts.”
Lamb worked up from the various characteristics of spoken language to arrive at a theory for the structure in the human brain that must exist to support it's idiosyncratic nature. Lamb's structure is a network of nodes (called nections) which can become activated to varying degrees. The activation of one node can flow on to neighbors, but weakening with distance. The activation of a nection in Lamb's structure is equivalent to a concept, and learning involves the recruitment of latent nodes which happen to have the requisite connectivity to assemble the new concept.
No-where in Lamb's network, is there a place for the storage and retrieval of symbols. “There is no such thing as the meaning of a text apart from an interpreter. And meaning is not conveyed by a text, as the usual metaphor would have us believe. Rather, elements of the text activate meanings in the minds of interpreters. ... A text cannot be interpreted except by virtue of information already present in the system before the text is received. ... There is therefore no possibility of perfect communication through language.” (Lamb 1999)
Lamb,S.M (1999), Pathways of the Brain: The Neurocognitive Basis of Language. John Benjamins Publishing Co.
Wittgenstein,L. (1953), Philosophical Investigations. Blackwell.