The unexpected fundamental influence of mathematics upon language

Abstract. The functional structure of human language networks in the brain could be revealed in an indirect way by measurements in the abstraction level of words. The result is a very large deter­ministic graph or network, respectively, which was unknown in mathematics up to now. The whole network can only be represented in a matrix. Following Shannon's theory, it displays optimum properties for information processing (maximum entropy). The structure of the network can be subdivided by introducing word classes with increasing magnitudes which could contribute to an understanding of the biological generation of networks. The hypothesis is that such facts are valid for all natural languages. Differences will exist only in the individual distribution of matrix dots. That means, speaking precisely, that every language has a distinct individual network structure of its own. Surprisingly it can be shown that the superior general type of the universal network structure can be generated by statistical experiments. The properties of these networks were compared with those of natural language networks which are definitely not statistical. Finally the enigma of the famous Zipf-diagram can be disclosed by observing networks and text paths which run inside of them along existing connections from node to node. A staircase curve emerges, which is a better description of reality than a smoothed power law. All this can be repeated by experiments, which means that eventually we found a transition from descriptive to constructive science. Therefore the new ideas could be applied immediately also in technology. Certainly the basic biological language structure arose a long time ago. Later on the typical patterns of the network connections for different language families should have evolved separately and were almost certainly accompanied by optimization processes for maximum entropy. Nowadays the details of the connection patterns for any language have to be learned anew by every child, and in this process, unusual alterations are not allowed by its language community.

Technology, ease, and entropy: a testimonial to Zipf´s Principle of Least Effort

Glottometrics ist eine unregelmäßig erscheinende Zeitschrift für die quantitative Erforschung von Sprache und Text.

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