posted 14 April 2004 18:58            

"Mathematician Laura Tedeschini-Lalli (who refers to Kyma as "my experimental apparatus from Urbana-Champaign") was interviewed on national Italian radio where she was asked: "What have mathematics and music had in common throughout history?"  Her answer:
Well, I'll tell you what mathematics and music have in common in the hearts of those who do both. We all stand outside of that area defined by 'the pale of words', as English poet Alexander Pope describes it. The area where the minds of our students are confined. Music and math stand beyond the pale of words, looking out, exploring new territory. Musicians and mathematicians look for patterns; and when we don't find them, we invent them".

The implication here seems to be that music and mathematics are "beyond" not merely words, but beyond language itself. Mathematics and music are certainly different from verbal language, but they are not "beyond" it. Mathematics and music are non-verbal languages, but they are languages, nonetheless, with as many conceptual blinders and limitations (as well as possibilities) as verbal language.

posted 05 May 2004 14:46            

It almost seems like the paradigm shift that occurs when going from one to the next expands the horizons of one's mental models. Studying either music or mathematics generally impacts how a person perceives, understands, and interacts with the world around them. The same may be true of studying more than one spoken/written language, though perhaps to a lesser extent. Even studying Kyma itself, which, like mathematics, is essentially a spatially oriented graphical notation not directly connected with spoken words, provides new mental modeling tools. Musical notation, of necessity, models events in time that are related in space by pitch. Kyma models sounds and their elements freely as they are related in space, and then provides a timeline for arranging them in time.

Just some thoughts...

posted 06 May 2004 08:56            

A book I recently read about the UML (Unified Modeling Language) pointed out that one language may be said to be more "expressive" than another if it allows us to "more easily" express a wider range of concepts and relationships. Clearly there is a very subjective aspect to language expressiveness, but the author makes the argument that, generally, for example, the language of arithmetic is more expressive than the language of counting. That is said to be so because the language of arithmetic expresses the concept of 1000 with 4 digits, while the language of counting would need 1000 objects, which would take both more space, and a lot more effort to comprehend. Similarly, arithmetic may express the quantity 2.125, while putting together exactly two and one eighths objects may be impractical, and, again, may be difficult to precisely comprehend.

Taking that definition of "expressiveness" (expressivity?), it seems clear that certain languages can be objectively classified qualitatively as more expressive than others. For example, there is enough formality of concept definition in mathematical notation to express succinctly concepts that would require thousands of words of English. And, for the person who understands the notation fluently, comprehending the mathematical statements is far easier than comprehending the same concepts described in English.

But mathematics is more expressive only of a certain class of ideas. Musical notation is more expressive of certain musical ideas. And so forth. Consider Kyma itself. As a sound design language, Kyma is very expressive. Open a sound in the sound editor and you can quickly comprehend its parts and how they are related. Double click on one of its inner objects and you can see the parameters and how they are related. And so forth. Explaining exactly what sequences of digital synthesis and processing should be combined, and in what ways to make up a given sound would take far more English, and be far more work to comprehend, than than the same idea modeled with Kyma.

In each case, though, the underlying assumption is that the user of the language has invested significant time and mental energy into becoming fluent in the language. The question of whether that energy is well spent or not is a very personal, individual one.

It's one thing to say a language like Kyma is useful for sound design, or a language like mathematics is useful for science and engineering. It's a different thing altogether to suggest that learning such a language is enlightening to the individual that does so. We do know, however, that some individuals have found that to be the case, while others have not.

posted 06 May 2004 14:09            

Difficulties arise when, in an area such as electronic. electroacoustic, or computer music, someone (such as I) who is not fluent in the dominant language (mathematics) attempts to enter the field. Even then, however, resources are not lacking. Witness Curtis Roads's very non-quantitative Computer Music Tutorial, or Trevor Wishart's Audible Design. These works prove that verbal language is neither handicapped nor inefficient when it comes to expressing essential concepts in the area of computer music, which is my area of concern.

posted 07 May 2004 15:47            

Languages build increasingly detailed and complex models by defining concepts, and then by combining those concepts to create more elaborate concepts, and so forth. Because spoken languages are our "first" languages, they are learned "by osmosis", and are therefore very difficult to separate from cultural biases in practical use. That's not a limitation of the languages, but of how they are learned and used in practice.

Any communication that requires the "receiver" to comprehend an extremely limited set of common definitions is very limited in terms of the complexity of *ideas* that it can express. (I imagine trying to communicate to someone who doesn't speak English, and I don't speak their language).

It almost seems like the "direct path" would be on the most primal level, based purely on intuition (since it cannot rely on agreed-upon definitions of concepts). It would seem to me that it would be more error prone than the others, in terms of communicating ideas.

On the other hand, when we move outside of communicating ideas with language into shared experiences, then we have something very direct. Rather than telling you about an experience, if I can share it with you, it becomes both something I have shared, as well as something new to me because you have shared it with me.

But that doesn't seem to be communication any more. It seems to be experience.

Personally, I like art that is "about" the inner experiences of the performer (some forms of dance, for example). It does not try to communicate what those inner experiences are, and I know that I cannot share them, but I enter into the awareness that they exist--that there is an entire unique universe within each individual that only they will ever know.

For some reason, when art can show the inherent uniqueness of individuals, it seems to lead right up to the edge of that "direct path". It almost seems like art must make virutally no direct attempt at communication in order to get there. When it is trying to say something, we are in a mode of trying to comprehend it. When it isn't trying to say something (at least not trying to communicate *ideas* anyway), we may simply experience it along with the performers. It is less of a "presentation" and more of a "designed shared experience".

The best of such experiences provoke a lot of ideas on the part of the audience participants, but not because those ideas are communicated; rather because certain experiences lead intuitively to thoughts and ideas and emotions and such.