Most of the examples in read me first are series of instructions. If you don’t follow the step-by-step information precisely, you may end up with a result that’s different from what you have expected. I’m sure many of you share my experience of an IKEA’s BILLY shelf with one of the panels facing a wrong way! But there are also examples where you could change the order of actions or omit a step or two.
Let’s look at the child’s morning routine again. The alarm clock rings three times in this routine with the aid of a snooze button. Once you get up, put on clothes and then have breakfast, it is followed by two options: (a) walking to school if it is sunny or (b) being driven to school if it is snowing. This is an ‘either-or’ case where one cannot do both options in the same sequence and the choice leads to a significant difference in the overall length of time and the quality of experience for the child (and for the parent). The given order of events may be modified: you can have breakfast before putting on clothes. Interchanging these events may not have effect on the overall outcome as long as they have taken place; though it is also true that some actions can’t happen before some others (such as getting up cannot happen after putting on clothes or having breakfast); here the order follows traditional conventions (you go to breakfast after putting on clothes rather than before). Meanwhile, the snooze button may not be essential for some children. If we were looking for a well-disciplined child’s routine, this algorithm would be simplified not only by removing a snooze button but also by removing the option of the snowy situation – the child would be expected to walk to school whatever the weather!
What makes this algorithm interesting is the possible different options it offers by implication. Algorithms can have flexibility built in it. You can choose or change the order, repeat some steps, or omit others; you may add another step to make your morning more successful, interesting or satisfactory (such as brushing your teeth after the breakfast). Algorithms can accommodate nuances to the sequence without necessarily changing the fundamental structure.
In this way the construction of an algorithmic sequence can engage the concept of ‘affordance’ as part of its flexibility. First introduced by James Gibson in the 1960s, the concept of affordance came from psychology where the original definition included all interactions that were possible between an individual and their environment. By the structural necessity of going through any sequence step-by-step, algorithms can respond to the changing context of the environment at each step of the process. We may call it being adaptable. The environment varies from moment to moment, from person to person. This flexibility of algorithms allows affordance, that is to say interactions with the environment for the construction of a unique reality. That is what we see in the example of the child’s routine.
Affordance can be created and expanded with the minimum material and dynamic rules. Binary code in computing is one such example: it uses only two symbols (0 and 1) and, if we look at 4-digit codes there are sixteen of them (0000,0001,0010,0100,1000,0011, etc.). What makes this algorithm dynamic is the distinct, specific data-transporting connection rules set between the two symbols. This then enables 0 and 1 to be stringed together to signify an exponentially infinite number of things. As such, affordances may be discovered by setting ingenious rules.
Meanwhile, it is worth noting that affordance is not about probability. While probability deals with all possible combinations of a given set of material, affordance is context specific at each step. Listing all possible combinations of the child’s morning tasks isn’t useful, even if we make conditions as to which tasks need to precede/succeed which others to reduce the number of possibilities; without connection rules, punching out 0s and 1s in all possible combinations doesn’t give each series of symbols any data transportability. I have a few more examples from non-musical fields, which I believe serve well to get closer to the heart of the matter.
Making French fries requires three actions: wash, cut, and fry the potatoes. Frying has to happen last, but washing and cutting can be done in either order, much like the tasks of putting on clothing and having breakfast in the child’s morning routine. Do you cut the potatoes first then wash the matchstick pieces, or do you wash the whole potatoes first and then cut into matchstick pieces? Some of you repeat the washing stage: wash-cut-wash. Expert cooks know which sequence suits which kind of potatoes. They assess the condition of the vegetable at each process and react to it, in order to achieve the desired outcome. The potatoes can be fried twice too. There is much expert knowledge involved in the decision-making process at each step.
A similar subtlety is involved in baking a cake. Sugar, butter, and flour are the main ingredients for sponge cakes of most kinds, but the order in which these are mixed is different. Do you know why? The chemical affordances are key information in this process, promoting necessary chemical actions that are essential for each type of cake. (More on this in sequence section.)
Algorithms of this kind are plenty in music. Rule-based composition or improvisation makes full use of affordances in a playful way. In composition, canon may be the most representative of all. In order to illustrate how affordances are utilized in music, let us look at a fugue. Fugue is a type of canon construction with specific transposition rules. In composing a fugue, the question of what makes an interesting fugue rests on two premises: first the thematic material is interesting, and second the fugal treatment is interesting. With an interesting thematic material, we can make an interesting fugue relatively easily. Making an interesting canon out of a less interesting thematic material is difficult but not impossible. Here is an excellent example:
You can listen to it here
The art of making a fugue is to think creatively about how to combine the given material. A musically significant challenge (for the composer and for the performer too) is to recognize within the theme some characteristics which can be elaborated for development through fugal repetitions in the course of the piece. In other words, the observation of musically pertinent affordance in the theme is precisely what makes a fugue interesting. The assumption that, as long as themes and generative rules are decided, the rest takes care of themselves through some probability rules is plain wrong: what divides good and less good compositions, rests on the creative strategies employed in the combinatorial processing of themes and rules as a piece of music. Bach in the above example does not have the most inspiring theme (no attractive gesture nor interval in sight). But he uses its harmonic stability maximally to guide the music to gain tonal variety through imaginative transpositions. Perhaps unusual for a fugue, the performance of this piece may put more emphasis on the harmonic pathway than the theme itself.
The practice of improvisation on a given theme fllows a similar guideline. You play between the temporal/textual development and the thematic character, creating tension and resolution from the potential of the theme. Some experimental music (where basic material and rules are outlined) and what I have called elsewhere as 'prescriptive notation' (notation that gives instructions such as tablature) operate on similar principles in performance in that the tasks of 'sense-making' as music are very much in the domain of the performer.
These observations lead me to posit a hypothesis: understanding affordances in a given situation requires experience and expertise in the field. Knowing all the possibilities in a given situation is one thing, but understanding their affordances is another. This understanding can be gained through detailed analysis, knowledge, experience, intuition, feeling of their presence, or just by trial-and-error. Knowledge and expert skills are equally important in this process.
The ‘unique reality’ found through making most of the affordance in an algorithmic process is real and not abstract. It is mutant, and changes every time the sequence is carried out. But something of the expertise remains throughout like a fingerprint.
Perhaps one of the most telling cases of 'affordance management' as expert skill is conducting. Conductors do more than conducting in a sense that they plan both the content and method of a concert preparation as well as 'conducting' in the concert. Planning of sectionals, that is to rehearse a musical work in separate instrumental groups, is an example of affordance management. This affects not only how efficiently the conductor can work with the individual instrumentalists/groups, but also how the musicians listen to each other and liaise with each other in the live performance.1
Another example of affordance management as expert skill may be observed in musical instrument pedangogy. In a one-to-one music lesson, a music teacher sometimes says ‘I have told you everything I know about how to play this music. Now forget everything I’ve said, and just play.’ I don’t think the teacher is behaving irresponsibly by saying this. The pupil has understood from the teacher which interpretive possibilities are present in a musical work, and how one might navigate through them as performance, much like learning how to cook. What is being asked, to forget everything the teacher has said so far, is that the pupil pays attention to the temporal context of a performance as it unfolds. In doing so, the performer directs a performance, setting the interpretive possibilities in motion, and mobilising them as affordances. A moving performance always has something surprising, yet that something feels so inevitable. Knowing something and doing it is not just a matter of translation. It is an art.
The concept of affordance links directly with the ideas of context and expertise and can be seen as one of the ways in which the achievable quality of this art can be assessed. It is also a way of identifying the technical and mental expertise of an algorithmic nature that musicians have embedded as performance skills. It is perhaps the most invisible and slimey subject dealt in this exposition; yet it is perhaps the most critical concept for the performing arts.
