Some consequences of recursion in human affairs

Abstract

Meaningful sequences of symbols in natural languages, and also in the most useful artificial computer languages, are constructed following rules whose applicability is independent of the scale of the construct. Thus, for example, a single adjective, an adjectival clause, a sentence or a complete paper can all be used in the same way as a qualifier, and similarly for other basic grammatical components. This scale-independent assembly technique has been named ‘recursive’ by linguistic theorists. The same recursive technique is used in the reproduction and growth of many living organisms and, indeed, in the growth and operation of organised human society, which can be regarded as a living organism in this general sense. The scale independence of such recursively defined organised systems creates statistical corelations at every scale; that can account for empirical statistical distributions such as Zipf's law for the use of words and Pareto's law for the distribution of income. The large-scale corelations also invalidate the ‘ergodic process’ as a model of a generator of meaningful text, so that widely used measures of information technology such as ‘cost per bit’ are of questionable value.