SOME HISTORICAL NOTES From: Stephen Wolfram, A New Kind of Science Notes for Chapter 12: The Principle of Computational Equivalence Section: Intelligence in the Universe Page 1181 Theories of communication. Over the course of time the question of what the essential features of communication are has been discussed from many different angles. It appears to have always been a common view that communication somehow involves transferring thoughts from one mind to another. Even in antiquity it was nevertheless recognized that all sorts of aspects of language are purely matters of convention, so that shared conventions are necessary for verbal communication to be possible. In the 1600s the philosophical idea that the only way to get information with certainty is from the senses led to emphasis on observable aspects of communication, and to the conclusion that there is no way to tell whether an accurate transfer of abstract thoughts has occurred between one mind and another. In the late 1600s Gottfried Leibniz nevertheless suggested that perhaps a universal language - modelled on mathematics - could be created that would represent all truths in an objective way accessible to any mind (compare page 1156). But by the late 1800s philosophers like Charles Peirce had developed the idea that communication must be understood purely in terms of its observable features and effects. Three levels of so-called semiotics were then discussed. The first was syntax: the grammatical or other structure of a sequence of verbal or other elements. The second was semantics: the standardized meaning or meanings of the sequence of elements. And the third was pragmatics: the observable effect on those involved in the communication. In the early 1900s, the logical positivism movement suggested that perhaps a universal language or formalism based on logic could be developed that would allow at least scientific truths to be communicated in an unambiguous way not affected by issues of pragmatics - and that anything that could not be communicated like this was somehow meaningless. But by the 1940s it came to be believed - notably by Ludwig Wittgenstein - that ordinary language, with its pragmatic context, could in the end communicate fundamentally more than any formalized logical system, albeit more ambiguously. Ever since antiquity work has been done to formalize grammatical and other rules of individual human languages. In the early 1900s - notably with the work of Ferdinand de Saussure - there began to be more emphasis on the general question of how languages really operate, and the point was made that the verbal elements or signs in a language should be viewed as somehow intermediate between tangible entities like sounds and abstract thoughts and concepts. The properties of any given sign were recognized as arbitrary, but what was then thought to be essential about a language is the structure of the network of relations between signs - with the ultimate meaning of any given sign inevitably depending on the meanings of signs related to it (as later emphasized in deconstructionism). By the 1950s anthropological studies of various languages - notably by Benjamin Whorf - had encouraged the idea that concepts that did not appear to fit in certain languages simply could not enter the thinking of users of those languages. Evidence to the contrary (notably about past and future among Hopi speakers) eroded this strong form of the so-called Sapir-Whorf hypothesis, so that by the 1970s it was generally believed just that language can have an influence on thinking - a phenomenon definitely seen with mathematical notation and computer languages. Starting in the 1950s, especially with the work of Noam Chomsky, there were claims of universal features in human languages - independent of historical or cultural context (see page 1108). But at least among linguists these are generally assumed just to reflect common aspects of verbal processing in the human brain, not features that must necessarily appear in any conceivable language. (And it remains unclear, for example, to what extent non-verbal forms of communication such as music, gestures and visual ornament show the same grammatical features as ordinary languages.) The rise of communications technology in the early 1900s led to work on quantitative theories of communication, and for example in 1928 Ralph Hartley suggested that an objective measure of the information content of a message with n possible forms is Log[n]. (Similar ideas arose around the same time in statistics, and in fact there had already been work on probabilistic models of written language by Andrei Markov in the 1910s.) In 1948 Claude Shannon suggested using a measure of information based on p Log[p], and there quickly developed the notion that this could be used to find the fundamental redundancy of any sequence of data, independent of its possible meaning (compare page 1075). Human languages were found on this basis to have substantial redundancy (see page 1090), and it has some× been suggested that this is important to their operation - allowing errors to be corrected and details of different users to be ignored. (There are also obvious features which reduce redundancy - for example that in most languages common words tend to be short. One can also imagine models of the historical development of languages which will tend to lead to redundancy at the level of Shannon information.) Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002), page 1181. © 2002, Stephen Wolfram, LLC