The Analytic L-Matrix

In the 1970s, one of the most popular approaches for seeking an understanding of fundamental sub-atomic particles was to use something called the Analytic S-Matrix. Noting that earlier efforts to provide an explicit description of how things like protons, neutrons and mesons interacted had failed signally, some researchers proposed treating the whole system like a black box with a certain hidden but consistent structure.  By noting what came out when various other particles were thrown into that box it was hoped that certain fundamental and fixed properties of the system could be deduced, and a kind of table, or matrix, could be drawn up expressing that knowledge.

Much research data was gathered and processed, but in the end it proved impossible to synthesise it into any schema or grand statements, rather like the tale of the three blind men feeling an elephant: one touched the ear and described a heavy carpet, another the leg which he said was like a tree trunk, while the third felt the tail and pronounced it a rope. All the views were in their limited way correct, but they gave no idea of the true nature of an elephant. And so it proved with the Analytic S-Matrix, which was soon superseded by other fashions in theoretical physics like quantum chromodynamics, strings and instantons.

The idea of treating a complex entity like a black box is an attractive one, if only as a short-term approach until something better comes along. For example, given our extremely poor understanding of how the brain works at a cognitive rather than physical level, perhaps something similar could be applied there. The basic particles that we would throw in and measure as they came out - words - are cheap and plentiful, so experimental difficulties are slight, even if interpreting the data is difficult. 

In one area, the search for patterns in this way is already well-established. Chomsky's theory of 'deep structures' in the brain which lie behind all language systems have been sought assiduously, though with little agreed success. Perhaps the project was too narrow in its aims. Instead, we could look more generally at how the mind processes words and concepts not with the aim of completely explaining language, but rather to see if there are any underlying patterns or trends to thought itself.

For example, it would be interesting to compare those black holes that occur in every language - things that seem oddly difficult to say. In English, it might be the brain-twisting 'Didn't you use to not use it?' where the evolved structure of the phrase is obviously not expressing the thought clearly. There are examples in other languages; the question is, are there any in common? And what about the actual concepts we choose to describe our world; just how culturally specific are they? 

What is needed is a coordinated global project to compare and contrast linguistic usages in every sphere of human activity. This investigation of the Analytic L-Matrix may prove as bootless as that of its sibling S-Matrix.  But at the very least the world will start talking together, and will find the commonalities which bind us together as part of a family and the subtle differences that mark us out as individuals within it.

(15.3.92)

See also Moody Sonnets - Mind Your Language

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