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Physicists describe speech with continuous mathematics, such as Fourier analysis or the autocorrelation function. Linguists describe language instead, using a discontinuous or discrete mathematics called “linguistics.” The nature of this odd calculus is outlined and justified here. It treats speech communication as having a telegraphic structure. (Non-linguists normally fail to orient themselves in this field because they treat speech as analogous to telephony.) The telegraph-code structure of language is examined from top to bottom, and at each of its several levels of complexity (compared to the two levels of Morse code) its structure is shown to be defined by possibilities and impossibilities of combination among the units of that level. Above the highest level we find, instead of such absolute restrictions, conditional probabilities of occurrence: this is the semantic field, outside linguistics, where sociologists can work. Below the lowest level we find, instead of such absolute restrictions, conditional probabilities of phonetic quality: this is the phonetic field, outside linguistics, where physicists can work. Thus linguistics is peculiar among mathematical systems in that it abuts upon reality in two places instead of one. This statement is equivalent to defining a language as a symbolic system; that is, as a code.

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