- Large-Size Message Construction for ETI:Music in Lingua Cosmica
Recent research, as well as older work, indicates that messages for extraterrestrial intelligence (ETI) written in a terrestrial language must necessarily be supplied with extra-linguistic information. Without such information, recipients will find messages nearly impossible to interpret, even if the messages were of considerable size. I have proposed in a number of papers to juxtapose messages with annotations on their logic contents, using a suitable lingua cosmica (LINCOS). The formalism of the calculus of constructions with induction (CCI) provides the foundation for the cosmic language used in this paper, LINCOS-CCI, which is still under development. Presumably the recipients, knowing the concepts of CCI, would recognize that LINCOS-CCI expressions employ constructive logic and would be able to translate from the form used by us to their own particular notation.
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Perhaps, however, recipients of a message sent with associated annotations in LINCOS-CCI might not recognize that concepts of constructive logic are involved. A solution to this problem is redundancy—messages should be large, and most of the various logic constructions should appear repeatedly in the LINCOS-CCI annotations. Even then, however, recipients may not immediately fully appreciate the formalism employed, because it may deviate too far from those to which the recipients are accustomed. In that case, messages would be difficult, if not impossible, to interpret.
The latter consideration points to the need to instruct recipients of our messages on our notational conventions in LINCOS-CCI, rather than using LINCOS-CCI to annotate conceptual aspects of the messages. Of the many conceivable ways of attaining this objective, I propose here to associate certain musical concepts with their expressions in logic. In short, I propose an interstellar message for ETI that consists of a recording of some piece of music, augmented with descriptions of the score using expressions in LINCOS-CCI. An extraterrestrial recipient having at its disposal the music itself, the score in some easily understood notation, and the LINCOS-CCI annotations [End Page 38] would have powerful means at hand for solving the interpretation problem. Rather than expecting LINCOS-CCI to explain the structure of music, examples of music help the recipient to identify concepts and formalizations of the cosmic language.
For this paper, Indonesian gamelan music was selected for several reasons (Fig. 5). First, its scores are relatively simple and are written in an easily understood notation. For example, the two scales in Indonesian gamelan music are composed of notes that can be written using only a small set of integers, and thus are easily represented in LINCOS-CCI. Second, the rules of well-formed gamelan music are elegant and simple; they match nicely with the sound of the music, and can be formulated in LINCOS-CCI. Third, gamelan music is abundantly repetitive: sets of four to eight lines are played over and over again, in various tempi. Finally, listeners can recognize fairly easily the tones and their representations in the score, allowing for an association between the music itself, the musical notation, and the LINCOS-CCI annotation. If the project succeeds, any extraterrestrial recipients would gain a better understanding of the formalism of LINCOS-CCI.