By Gordon Rugg
Two of the most common complaints about managers and about teachers/lecturers are:
- They’re too vague
- They’re too specific
Although these complaints are opposites, the underlying problem for both of them is the same. It involves the gulf of instantiation, which is the topic of this article.
The diagram above shows the key concept. Each of the black circles represents a tangible action, tangible item, or tangible event. The key point is the tangibility; you can point to the action or item or event. You’re dealing with reality, not with opinions or abstractions. This level of reality is technically known in knowledge representation as the instance level.
The counterpart to the instance level is the abstraction level. In the diagram above, the green circles represent two levels of abstraction. The dark green circles are at a lower level; the lighter green circle is above them, on a higher level.
The abstractions may take various forms, such as classification systems, or layers of explanation, or layers of sub-tasks. For example, in a classification system the dark green circles may represent the categories of cat, rabbit and dog, and the light green circle may represent the higher-level category of animals, with the black circles being individual cats, rabbits and dogs.
Abstraction levels are by definition abstract; you can’t point at something and say it’s the class of “igneous rocks” or “major land battles” or whatever. You can point at an individual rock and say that it belongs to a particular class, but when you do this, you’re pointing at something on the instance level, among the black circles, not at the class level.
So how does this map onto education and management? It maps on like this.
Education and management
Individual items at the instance level only have very limited power. Knowing a single fact, or how to do a single action, doesn’t usually get you very far. For example, knowing how to do a single action on an assembly line, such as welding a particular connection, won’t help you if you need to weld something different, such as a different metal, or a different thickness of components. Teaching and giving instructions only at this level is usually too specific.
This is where craft skills come in. Craft skills involve joining up this sort of knowledge, working upwards from the instance level into more general principles, as in the diagram below. The diagram shows how the instance-level items have been collected into three groups. This might, for instance, represent one group of knowledge about welding, another group about soldering, and a third group about riveting.
This sort of knowledge is valuable, but is often not appreciated enough. One reason is that it usually involves low-status manual work. Another is that it is limited in its power. In the diagram below, the three classes aren’t joined to each other at a higher level. The light green circle, representing higher-level knowledge, isn’t connected to the lower-level dark green circles.
This is where “just the facts” approaches and training courses can lead to learners becoming frustrated, because they’re being taught the “what” without any “why” to make sense of it. The higher-level linkages provide the “why”.
Approaches that focus only on the higher levels can be frustrating because they don’t specify how to go from the abstraction level (e.g. “activate the flux capacitor”) to the instance level (e.g. “press this button, then that button”). This leads to complaints about being too vague or too abstract.
In an ideal world, education and training would provide a completely joined up set of knowledge, with no gaps between abstract principles and tangible instances where they cross the gulf of instantiation, as in the diagram below.
In practice, however, the amount of knowledge involved is usually so vast that joining it all together is not possible. Research into expertise has consistently found that even within a narrowly defined area of expertise, the number of pieces of information required for that expertise is in the tens or hundreds of thousands. So, choices have to be made about how to cross that gulf of instantiation, and about where to cross it.
The diagram below shows how these choices map onto an old divide in the education world between universities and polytechnics. In this idealised model, universities focus on the higher levels of abstraction, which give more understanding of the key general principles, at the expense of the instance level. Polytechnics, in this model, focus on the instance level and the lower levels of abstraction, giving more directly applicable knowledge, at the expense of understanding broader unifying principles.
In practice, as you might expect, things aren’t quite this clear-cut. University courses normally include practical classes where students learn how to cross the gulf of instantiation between abstract concepts from the lectures, and tangible actions and objects at the instance level in the real world; for example, how to translate abstract database theory into how to use this instance of a database. Case studies are another well established way of crossing the gulf of instantiation.
These two approaches help with the gulf of instantiation, but in practice they only provide partial coverage. There’s a tendency for universities to assume that the students can work out for themselves how to cross the gulf of instantiation for anything not covered in practicals or case studies. In reality, this assumption is optimistic. Typically, there’s variation in how completely the gulf is crossed within a course or module, ranging from no instantiation for some topics, through partial instantiation for others, to complete instantiation for yet others, as shown below.
From the polytechnic perspective, a lot of research breakthroughs came from problems at the level of craft skills and instantiation, often when industry couldn’t get any further by trial and error, and couldn’t see how to get further forward.
The concepts above map neatly onto management. Some classic forms of bad management are:
Giving orders only at the instance level. This is usually perceived as micromanagement, which is very unpopular. It also means that if something unexpected happens, the person involved has no idea of the broader context and of how to respond appropriately.
Giving abstract orders which can’t be fully instantiated. Sometimes the orders can’t be instantiated because the person involved doesn’t know how. Sometimes, the orders can’t be instantiated because they’re physically impossible.
So, crossing the gulf of instantiation is an inherently hard problem. However, the concept of the gulf of instantiation is a useful conceptual tool that makes it easier to work out ways of crossing the gulf, rather than just complaining about people being too vague or being too specific. Which raises the question of just how to cross the gulf more efficiently…
Crossing the gulf
The gulf of instantiation is a significant problem in computing, though it’s usually referred to by other terms, such as instantiation. There are numerous types of formalised diagrams, such as flowcharts and ERDs, whose purpose is to force designers to instantiate just what happens where and how. None of these formalisms is perfect for all purposes; even within a single purpose, any given formalism still has its limitations, so there has been a continuous churn in terms of which formalisms are popular at a given time. Still, despite being imperfect, they’re a lot better than nothing.
In brief, any systematic representation will help reduce problems with the gulf of instantiation. Systematic representations are particularly likely to help with semi-tacit knowledge such as Taken For Granted (TFG) and Not Worth Mentioning (NWM) points; by definition, these are not normally mentioned explicitly, and are a rich source of miscommunication problems. The “wh” questions in English are a simple example of how to instantiate, by reminding the user to think about who, what, where, when, why, and how.
Although bridging the gulf completely isn’t feasible for something as large as a taught degree course, it becomes a lot more feasible when dealing with smaller problems. Bridging the gap reduces the likelihood of failure, which is important for safety-critical systems in which failure may be catastrophic. It’s also important in everyday systems for reducing failure demand (i.e. having to fix problems caused by not doing something right the first time round).
There’s a lot about representations elsewhere on this blog. They’re typically cheap, quick, and simple to use once you learn them, but they’re not as widely used as they should be. They’re well worth exploring.
Research, theory and the world
If you’re into theory of knowledge and the scientific method, you can apply the gulf of instantiation to research and ideology as well as to teaching and management. There’s a long tradition of people generating hugely elaborate abstract models, and either ignoring the gulf of instantiation completely or only mentioning the points where their model does manage to cross the gulf, while ignoring the points where it fails dismally to cross the gulf. As usual, Plato has a lot to answer for on this score, but there are also plenty of more modern individuals to share the blame.
There’s widespread agreement that good theories are elegant and powerful, but there’s widespread disagreement about how to define elegance and power. One way of defining them is via graph theory, using the concepts of the instance level and levels of abstraction to measure descriptive power, predictive power, and elegance.
We can define the descriptive power of a theory in terms of how many instances that theory links to. For example, a theory which says that an invisible black cat created the observable universe has very high descriptive power, because it links to every instance that exists. It’s a powerful theory in terms of descriptive power, but it has obvious limitations.
The predictive power of a theory can be very different from the descriptive power. Predictive power is about predicting where new instances will be found; the more new places, the more powerful the theory. The invisible black cat theory fails badly in terms of predictive power. A classic example of a theory with high predictive power is the periodic table, which not only correctly predicted the existence of elements not yet discovered, but also correctly predicted the properties of those elements. You can further refine this by looking at the proportion of correct predictions to wrong predictions, to weed out predictions so broad that they’re useless in practice.
The elegance of a theory can be defined in terms of how many links it contains at the abstraction levels; the fewer the links, the more elegant the theory. Typically, scientific theories aim to be highly elegant, with high predictive power and high descriptive power.
Much could be said about how these concepts map onto philosophy, theology and conspiracy theories, and much doubtless will be said, but that’s another topic…
Notes and links
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