Making Things Strange: An Inverse Problem in Teaching

It is common to explain the unfamiliar by reference to the familiar, but when teaching a quotidian science (of the everyday) this explanatory mode is inverted.

Strange Ideas#

Many are mystified and threatened by the algorithm. This word is most typically invoked in discussions about the black boxes that digest our data and spit out personalised feeds, advertisements and recommendations. The inner workings of the black box are complex and often proprietary, maintaining their distance and strangeness.

$$input \xrightarrow{black \ box} output$$

The algorithm is a more general tool than the discourse suggests, with applications that extend far beyond e-commerce and social media. Students of programming usually take a course in algorithms. Here they learn how to write code that prints sequences of characters to the screen or calculates statistics for a dataset. Later they encounter more complex algorithms that can help simulate enemy movement in video games or — indeed — generate personalised recommendations for a vast social network.

The generality of a tool like the algorithm lies in its abstractness. Conceptual and underspecified, its implementations apply to a broad class of particular cases. Mathematical operations like sum are similarly abstract. We can conceive of summing a collection of physical objects, summing a set of integers or summing millilitres of liquid. In a computer program, a simple algorithm would be employed to implement the concept of asum.

When teaching there is tendency to appeal first to concrete instances rather than directly engaging with an abstract concept. The first model of the algorithm that many encounter is the recipe. To develop an understanding we direct knowledge from a familiar, concrete source (recipes) to an unfamiliar, abstract target (algorithms) through the invocation of metaphor (or analogy):

$$source \xrightarrow{metaphor} target$$

Appealing to the Familiar#

In The Art of Computer Programming the computer scientist Donald Knuth (1968) explained how an algorithm is analogous to a recipe. Just like a recipe, it takes a finite amount of inputs and produces a specific output. This transformation requires that a sequence of steps be first defined and then carried out in a particular order. It can be expected that Knuth's analogy (like all analogies) will crumble at some point; for now, it is enough for us to "grasp" at the abstract concept in a useful way.

Just as a cook follows a recipe to produce a meal, a computer processes code to produce a desired output, which could be a successful calculation or a graphical representation. For some computer scientists, the salient distinction between these two kinds of procedures is the degree to which the instructions can be said to have precision. A recipe — they assume — is prone to ambiguity and may yield different results depending on who interprets its steps. The education of a programmer then places a strong emphasis on achieving precision when defining the goals of a program, articulating clearly the structure of the requisite code and testing effectively the reliability of its performance. As a teacher I am fascinated by this bait-and-switch as pedagogical rhetoric. Coding is like cooking. This is a model of cooking and how it maps to our concept of programming. You are programmers not cooks. Here is why our programs must never be merely like recipes.

Most programs are composed of functions, small self-contained procedures that transform a set of inputs into an output. A calculator is a program that can perform different kinds of mathematical operations, each defined by an appropriate function (sum, multiply, divide). "Pure" functions in programming are essentially the same as mathematical functions. They map a set of inputs from a source domain to a target codomain. In a pure function, like sum_two_numbers, given multiple inputs (2, 3) there is only one output (5). The function sum_two_numbers should achieve the same transformation in all contexts. It will always map the same two numbers in the source domain to one number in the codomain.

$$domain \xrightarrow{function} codomain$$

The process of cooking a meal can also be understood as being composed of smaller procedures. A meal consists a combination of materials, each of which has been transformed by an appropriate procedure (peeling, mixing, heating). However, a cooking procedure may yield different outputs dependent on context. For example, two people may have varying degrees of skill and/or may interpret the instructions differently. On this limited account, a cooking procedure is further from the Platonic ideal of a mathematical function than a computer program, assuming that such programs consist strictly of pure functions (and most — in fact — do not).

$$recipe \xrightarrow{interpret \ \& \ act} meal$$

As an aside, it should be noted that the distinction between technical (computational) and nontechnical (culinary) procedures that privileges the former as more effective has been challenged by some theoretical computer scientists (see Cleland, 2001). In addition, practitioners in fields like molecular gastronomy assert that great precision can be achieved when cooking, if certain rules and principles are followed, perhaps resulting in a more algorithmic cookery. As Dan Cox suggests in a blog in Digital Ephemera, understanding through metaphor might operate in a bidirectional manner, rather than the strictly unidirectional $source \to target$ scheme:

Across the bridge of metaphor, recipe and algorithm might have more to offer each other in comparison than appears at first glance.

The bridge here is an apt (meta)metaphor itself, in that we may return from a destination via the same route that we have travelled there. Thinking of algorithms as recipes prompts us to consider recipes as algorithms. Laying a metaphor between two domains implies the formation of a loop of interpretation through which there is the possibility of better understanding both.

Making Things Weird#

The challenge for the teacher of abstract concepts is the translation of the strange to the familiar (at least initially). Food, ingredients and recipes are common sources of analogy and metaphor in these cases, and not only with algorithms as the target (Crowley, 2022). An everyday concept is leveraged to transform the strange or abstract new idea into something more familiar.

$$strange \xrightarrow{pedagogy} familiar$$

I think that this transformation is often inverted when teaching a quotidian science. By "quotidian science" I mean a science that has an everyday object as its focus. My specialisation — food science — is such a quotidian science. The inverse problem involves transforming the familiar objects of daily life into something strange and new. Achieving this transformation may coincide with the overcoming of significant resistance, due to these familiar ideas being so baked in.

A novice student of food science has a high degree of familiarity with the material that they intend to study. Eating, cooking and dieting are mundane concepts. When learning the science of food they experience the familiar becoming strange, which can be a disturbing process. While explaining the strange in terms of the familiar is a common pedagogical tool, a disturbing rendering of the familiar as strange has more often been associated with artistic work. On one interpretation (Shklovsky, 1917), this is the fundamental goal of art: to show us the objects of reality in an altered form, such that we return to the world with a more enriched sense of the objects as they are.

Shklovsky's idea — known as defamiliarisation — is an arcane concept borrowed from art criticism, yet I think it is close in spirit to how many scientific educators and communicators conceive of their role. Scientists can be sensitive to the claim (scientism) that they are iconoclasts, who destroy everyday symbols that comfort and enthrall us. Richard Feynman famously rejected the idea that his scientific worldview ruined the beauty of a flower, suggesting instead that science only served to enrich his appreciation of that beauty. This is a useful reminder that new theoretical knowledge can enrich — rather than displace — everyday intuition. A two-step process (or loop) can be imagined, in which the familiar is made strange (conceptually) before we return to the familiar (in reality) and appreciate it in a new aspect.

$$1. \ familiar \xrightarrow{defamiliarisation} strange$$

$$2. \ familiar \xleftarrow{enrichment} strange$$

The scientific and the everyday coexist and interact productively.

Defamiliarisers#

Scientists, like artists, can alter how we perceive the world. As communicators, they often play the role of defamiliarisers. Their lessons can enrich our experience and intellect, or they can damage our sense of how we relate to reality, leading to a rejection of science or even a descent into conspiracy theories. The outcome may depend on how effectively the scientist communicates and how their audience understands their motives.

Tools that move us between the familiar and the strange — like metaphor and analogy — are central to explanation, whether through artistic epiphany or scientific discovery. Understanding art as a force for defamiliarisation does not necessarily mean that artists destroy everyday conceptions of the world. Instead, through art (and science) such intuitions can be retained while being enriched. It is possible to know the pain of bureaucracy without reading Kafka, but reading The Trial will certainly make you experience that same pain in new and interesting ways!

In science communication, there is perhaps a greater rhetorical emphasis on actively changing minds and correcting falsities. Sometimes this clarity of focus is demanded in the context of a live crisis. In more normal times, it might be wise to use our scientific truths to enrich the everyday and mundane and not seek to displace them.

References#

Cleland, C. (2001). Recipes, algorithms, and programs. Minds and Machines, 11, 219-237.

Crowley, S. V. (2022). Alchemical and cyborgian imaginings in technoscientific discourse relating to holistic turns in food processing and personalised nutrition. In Metaphor, Sustainability, Transformation. I. Hughes, E. Byrne, G. Mullaly., & C. Sage (Eds.). Routledge. 65-97.

Knuth, D. E. (1997/1968). The Art of Computer Programming (3rd ed). Addison-Wesley.

Shklovsky, V. (1988/1917). Art as Device. In Modern Criticism and Theory: A Reader. L. T. Lemon and M. J. Reis (Trans.), David Lodge (Ed.). Longmans. 16-30.