do you guys use any kind of quirky/unusual/atypical notation in your notes? I love to use ∃? to signalize that I’m trying to prove existence of something while not knowing if the object I’m searching for exists a priori (saw somebody doing it, so I took it from them)
the advent of the mass-produced graphite pencil in the second half of the 19th century coincided with profound changes in the way a performer engaged with a musical text. The generation of musicians who benefited from the new tool — capable of making durable, but erasable, markings that didn’t harm paper — were, he wrote, “the first where practice was aimed at perfection of execution, and not developing the skills for real-time extemporization on the material in front of them, or improvisation ‘off book.’” What changes does the new digital technology reflect or enable? Conversations with some of classical music’s most passionate advocates of the gadgets and with developers like forScore and Tonara that write applications for them reveal a number of developments. The traditional top-down structure of teaching has been shaken loose. The line between scholarly and practical spheres of influence is becoming blurred. And the very notion of a definitive text is quickly losing traction — and with it, the ideal of that “perfection of execution.”
Mathematical notation provides perhaps the best-known and best-developed example of language used consciously as a tool of thought. Recognition of the important role of notation in mathematics is clear from the quotations from mathematicians given in Cajori’s A History of Mathematical Notations [2, pp.332,331]. Nevertheless, mathematical notation has serious deficiencies. In particular, it lacks universality, and must be interpreted differently according to the topic, according to the author, and even according to the immediate context. Programming languages, because they were designed for the purpose of directing computers, offer important advantages as tools of thought. Not only are they universal (general-purpose), but they are also executable and unambiguous. Executability makes it possible to use computers to perform extensive experiments on ideas expressed in a programming language, and the lack of ambiguity makes possible precise thought experiments. In other respects, however, most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.
Sound Choreography Body Code is a performance collaboration between choreographer and performer Kate Sicchio, and researcher and live coder Alex McLean. The work creates a feedback loop through code, music, choreography, dance and back through code. We spoke with Kate and Alex to ask them about the work, and the thinking behind such a multimedia, multi-disciplinary piece.
This post is a crash course on the notation used in programming language theory (“PL theory” for short). For a much more thorough introduction, I recommend Types and Programming Languages by Benjamin C. Pierce and Semantic Engineering with PLT Redex by Felleisen, Findler, and Flatt. I’ll assume the reader is an experienced programmer but not an experienced mathematician or PL theorist. I’ll start with the most basic definitions and try to build up quickly.
