Saturday, 16 September 2017

Notation, Constraint and Logic

I’ve been doing some experiments with notation in music and video. I’ve got a great music writing app on my tablet called “StaffPad” which does handwriting recognition (so I can handwrite squiggly notes and the software converts them into proper typeset notes) – which is great, if a little bit fiddly. However, it also has a facility for simply drawing on the score. When the score plays back, it scrolls the music, so both drawing and notes appear.

To write a note on a score is to give an instruction. There is a question about whether the instruction is about exactly “what to do” or it is in fact “what not to do”. In other words, does the symbol on the score denote the sound, or does it contribute to the conditions of freedom within which a performer might act freely?

I squiggled some shapes on the score, and then I attempted to “play” it. I should have made my squiggles a bit easier to play! I did this a couple of times. The sound that I produce can be considered as “alternative descriptions” of something. The symbols/squiggles on the score are also descriptions of the same thing. If there is any similarity between these different descriptions it is in the fact that both the graphical description and the sound descriptions have similar entropy: in other words, what counts a surprise in one, counts as a surprise in the other.

Notation is obviously different from a recording. A recording is a faithful description of exactly what is done. Notation is an invitation to create multiple descriptions. The parameters as to what is permissible and what isn’t is contained in the way the notation conveys the flow of entropy over time.

So what about other kinds of marks or notations which we use?

In logic, I can represent the statement “All humans are mortal” as ∀x:human(x) → mortal(x). What’s the difference between these? The variable x is an invitation to generate possibilities – alternative instantiations of the formula. They produce constraints on the imagination bounded by the ways in which the symbols might be manipulated. The meaning is not in the phrase “all humans are mortal”, or even in ∀x:human(x)→mortal(x), the meaning lies in the interplay between the different descriptions which are made in the light of the notation.

We misunderstand formal logic as a denotation of reason. Really it’s an invitation to generate multiple descriptions from which reason is connoted. This mistake is why attempts to prove computer software in formal systems has failed. If we understand the relationship between logic, notation and meaning differently, then we can find new applications for logic. Education is one of these.

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