This is an attempt to describe how ‘adults’ learn new concepts in a formal setting, such as a college course. I’m mostly thinking about ’scientific’ subjects like maths physics and computing. I’m using learning Java as the source of examples.

It uses some other ideas. Two crucial ones are frames and mental spaces . Read that link if you are interested in this and want to make sense of this blog.  It also uses the idea of a compression.

Psychologists have usually treated concepts as categories, delineated by a definition. Work by people like Rosch showed this was simplistic, with ‘real’ concepts being more complex than this. This led to the idea of concept being based on an ‘ideal’ instance (prototype theory), a set of remembered examples (exemplars), and degree of possession of typical features (typicality).

Moving beyond concept as category, Neisser and others developed the idea of concept as implicit theory – which is very relevant to ‘understanding’ an idea. To understand what a Java object is, we need a lot more than simply to be able to decide if something is an object or not.

Typical college teaching shows all of the aspects of concepts. Often definitions are given, examples, descriptions (usually of typical instances) and so on. In addition, students will usually work through ‘exercises’ in which they are obliged to engage actively with some examples.

There is a particular problem if there is no definition of a concept. For example, the Java class/object concept has no semantic definition ( the syntax of a class definition is available, but it is no use to a student trying to understand what a class is). In this situation there is usually some teaching discourse (in a textbook or lecture) which tries to deliver an understanding of the idea through prose – but this is extremely difficult. For example one standard Java student text says that ‘objects belong to classes’. But this strongly suggests that a class is a set, and an object is an element in the set, which supports the partonomy/taxonomy confusion.

In these situations we have general concepts (class/object, or type) and examples ( JButtons, JFrames, classes developed by the student in lab sessions, or for type, ints, chars, doubles, booleans and so on).

A student coming to understand these general concepts does so by taking the examples (a multiplicity of mental spaces which include the examples), and compressing them into a frame. That’s it.

Students are individuals, and there are individual differences. For example one student may be slow to do this – he may be very fluent handling ints and doubles, while denying any recognition of the idea of type. Other students may actually do this too fast – rather as infants over-generalize terms. For example one student had absorbed the idea of inheritance, and had then assumed that ActionListener, WindowListener, MouseMotionListener and so on were sub-classes of a common base class ( semantically correct but syntactically wrong, since these are interfaces and not classes).

How do we really understand ideas? How do we make sense of things beyond the purely concrete? Like time, or jokes, or freedom, or software? That’s my question.

And I think at least part of the answer is as conceptual blends. Not my idea – it comes largely from Gilles Fauconnier. Let me outline one of his examples.

The idea of a ‘computer virus’. An irritating idea, but also creative and imaginative.

Blends have (usually) 2 input spaces. In this case, one is a computer program. This space has several ’slots’
Made by a human (programmer)
Useful
Needs computer hardware to run on

The other input space is a biological virus
Made by evolution
Harmful
Needs host living cell
Reproduces

Then we do a selective projection of these slots. In other words, we pick some from one input and some from the other. This is very precise – its not a blend as in food blender – we don’t get mush. In the output space we have

Made by a programmer
Harmful
Needs host hardware
Reproduces

And there you have a new idea.

But this is not at a conscious explicit level – the first people to write viruses did not work it out like this, in the sense that they were aware of what they were doing in this way. The hypothesis is that the human central nervous system holds, uses and transforms concepts in a way somehow related to the process described here.