White noise and information content

So this is a little follow up to a discussion we had in the reading group chat last weekend.

So I made the statement that white noise was too random and symmetric, hence the problem I was having in the generative music project I was working on, and that got connected to information content and compressiblity.

Yaxu expressed that it feels counterintuitive to say highly random things are less compressible than things that aren’t random, since you can’t really get usable information out of something like noise.

But I was thinking it makes more sense from the perspective of subtractive synthesis: you’re taking out frequencies out of a wave form in order to shape it into something more musical, but if you’re reducing frequencies then you can think of that as reducing the information content. Maybe that helps explain why things that are super random are so useful for procedural generation: you’re taking something that has (hopefully) very high information density and then applying structure to it in order to, in a sense, unpack the dense information content into a looser but more interesting structure.

I’m trying to stay very heuristic but hopefully this is an interesting way to think of noise and randomness?


Hmm I’m happy to accept that random things are less compressible, but less happy to accept that randomness is high in information… In a way white noise contains maximum surprise, as you can’t predict what will happen next… But in practice, it’s not surprising at all - it’s formless, like silence. So when I use randomness in music, I mainly use it like silence - to bring attention to something else.

I realise this just comes down to semantics, as the definition of ‘information’ in information theory is particular and useful… But I still find this discrepancy interesting.

Somehow I find ‘compressibility’ much easier to think about, and it reminds me of Komolgorov complexity… From wikipedia:

Consider the following two strings of 32 lowercase letters and digits:

  • abababababababababababababababab , and
  • 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7

The first string has a short English-language description, namely “write ab 16 times”, which consists of 17 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, i.e., “write 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7” which has 38 characters. Hence the operation of writing the first string can be said to have “less complexity” than writing the second.

… I’d also say the first string is ‘more patterned’ than the second, and that ‘write ab 16 times’ was the pattern.

Anyway yes subtractive synthesis is an intereseting way of thinking about all this thanks… and brings to mind a sculpturer chipping away at a block of marble, rather than additively working with threads…

What’s interesting is that compressibility is always subject to some frame of reference. For example, if you generate a long series of uniformly random integers, the output sequence is optimal incompressible and so contains the maximum amount of information.

But, if you then do an FFT on your time-series and look at the frequency spectrum over time, the output is flat and invariant. So from the long-term, zoomed-out perspective, it actually contains minimal information.

So the amount of information the series seems to contain is dependent on whether you’re “zoomed-in” (e.g., hearing each number of the sequence as a note), or “zoomed-out” (e.g., hearing each number as a sample of a waveform, in which case it is heard as whitenoise). And your perception will change over time… for the first couple of bars, it might sound like an unfolding melody, before you figure out the pattern (drawing random ints from a distribution).

I do really like the notion of “surprise” that you mention here. In the musical context, it plays the same role as entropy does in information theory, but implicitly bounded to include only those patterns that we can perceive, and also encompasses the idea that our perception of a situation evolves over time.


This is just a small side note but the way you’re talking about perception of a melody reminded me that this is one of the canonical examples Husserl used to talk about experiencing things “in retention”. The phenomenon, even though it’s experienced over time, is still in your “present” in such a way that it can be experienced as a single thing that is evolving as the perception interplays between expectation/horizon and the thing itself.

I feel like there’s probably connections to be made between Husserl/Merleau-Ponty and the experience of hearing/performing algorithmic music.


Thanks @ideoforms, that helps a lot. So if you compress 5 minutes of white noise as “play 5 minutes of white noise”, that’s very low kolmogorov complexity… If you ‘zoom in’ and try to compress individual samples, then you’ll find very high kolmogorov complexity. Is one more ‘lossy’ than the other?

I just picked up “fearful symmetry” by Ian Stewart and Martin Golubitsky (I think it was mentioned in the chapter of the self-made tapestry that we read), and they say “Mathematically, a uniform, featureless plane has a vast amount of symmetry, but nobody ever looks at a wall painted in a single colour and enthuses over the wonderful patterns.” (I guess they didn’t misspend their youth then, eh…) This seems related - mathematically, a uniform plane is more symmetrical even than a circle, but in all practicality it has no symmetry at all.

I am going to use a Hollywood film from the popular media to talk about film techniques and film languages that emerged in Se7en. directed by David Fincher. That’s a way I look at information content in the Interpreter(Live Code computing) has possibility with random function in Mathematics. I understand random function from a perspective of Mandelbrot set fractal. And chaos belong to set of rules base system, when code processing is like a Single Coding theory instead of thought process is a Dual Coding theory [McLean, Alex. “Artist-Programmers and Programming Languages for the Arts” London, 2011, P.25]

Sound designer usually work with the Foyle artists’ to capture noise but not whitenoise. The sound designer’s role is to understand and breakdown sequences in a filmmaker’s visual information structure. There’s a very strange kind of sound pattern if visual medium is omitted.

I am using the film Se7en, a crime thriller with Mills(Brad Pitt) and Somerset(Morgan Freeman) as the investigator detectives who are to capture the serial killer John Doe(Kevin Spacey). At the end (Pitt) shot John Doe in the head 6x times. To draw these examples that the interpreter is lacking in Live Code environment.

The video link leads to the ending scene that "We don’t know why the evidence of the murdered is omitted. But it’s explain below:

Object permanence is the understanding that objects continue to exist even when they cannot be seen, heard, or otherwise sensed. This is a fundamental concept studied in the field of developmental psychology, the subfield of psychology that addresses the development of young children’s social and mental capacities. There is not yet scientific consensus on when the understanding of object permanence emerges in human development.

How is a montage setup in a film? Montage is setup Through Continuity editing of single shot and mixing shots of similar sequence in cinemaphotography. And the contrasting editing is a montage but do not get confused with jump cuts.

a montage was used to create symbolism.

Eisenstein, Sergei. English transl, Jay Leyda. “Montage of Attractions” in The Film Sense. New York and London: Harvest/HBJ, 1947.

Sound also have montage::

Sound Montage
K. J. Donnelly
Montage theory remains at the heart of filmmaking and film studies, although many of its original concerns and insights have perhaps receded from view. Sound montage, theorized with the arrival of recorded synchronized sound in films, was the first theory of sound, as well as image, and sometimes explicitly derives ideas and inspiration from music-based theory. Its most influential theorist was Sergei Eisenstein, who also tested and experimented with his ideas in feature films. Montage theory often focused on asynchrony as potentially progressive in aesthetic (and to a degree, political) terms. The crucial notion of sound/music parallel and counterpoint, while perhaps not generating a tremendously robust analytical method, has nevertheless remained an important analytical lens for filmmakers and film criticism. Using this concept, the chapter argues that there has been an unacknowledged persistence of the modes of silent and early sound film in contemporary cinema.

“what makes you so special that people should listen?!” Seven - Scene - Creating expectation for the climax
The major types of film sound
These five sound elements are: dialogue, foley, sound effects, background and music.

180-degree rule in the scene is break by the position of John Doe’s Center

Montage in both visual and sound is a systematic way to editing, whitenoise/foyle/music can be a subtraction in a narrative that visual pattern in the film are symbolically edited

The symbolic meaning I am referring is in the theory of omission:

Note: Sound Montage is new to me also. But I think has relevancy in sound & image. In live coding we are consistently editing but we cannot just wanna to do it without a composition or story. Montage is a short coming to achieve greater goals in sound composition. Even with Live Code.