Friday, February 05, 2010

Areas and Dimensions

I've been talking to a lot of students in the last few days, and it strikes me that many of them are telling me the same thing. Essentially, they are telling me that a lot of their teachers have never actually discussed what areas of knowledge are, and how they might be different from dimensions of knowledge. Apparently, this is especially a problem for teachers of English literature.

Why is this so? What exactly is the problem?

Let's begin with defining that difference. A dimension of knowledge is something a bit like a physical dimension. It is an approach to a body of knowledge that is essential to that body of knowledge but is 'orthogonal' in the sense that it does not overlap with other such approaches. An area of knowledge, on the other hand, can overlap with other areas of knowledge, and is quite often carved up and distributed around; it can also evolve into several related (and also overlapping) areas of knowledge.

Sometimes, a dimension in an area may be the part of another area that overlaps or coincides with that area. A mathematical example of this is the square of a triangle's hypotenuse. Both shapes share a common edge which helps to define each shape, but they are not the same shape; that common edge is a dimension of each area, but is not itself one.

Another example of this is the human rights dimension of ethics. While 'human rights' may plausibly be considered as an area of knowledge that overlaps ethics, the biological (or religious, or legal) basis of those rights comes from other areas outside ethics. In thinking about what human communities ought to establish as a common moral basis (i.e. 'ethics'), human rights are only one dimension to be considered. This becomes clearer when one realises that ethical standards are not necessarily anything to do with human rights — for example, cheating at cards or using elements of desire to enhance advertising might be considered unethical, but they don't necessarily have anything to do with human rights. At the same time, you can't remove that dimension without crippling the whole idea of ethics.

This is not the case with areas of knowledge such as biology, chemistry or physics, considered as sciences. These are not dimensions of science because it is quite clear that you can't completely define any of them in such a way that they have nothing to do with any of the others. At the same time, it's quite clear that these entire areas of knowledge fall completely within 'science'; if any part of them was 'not science', it would be a logical contradiction.

This brings us to one of the key problems with mathematics and language. Mathematics and language are essential tools in many other areas of knowledge, but it is obvious that they are also considered to be areas of knowledge in their own right. At the same time, it's also pretty obvious that most universities issue degrees in science or the arts, but not specifically in mathematics or language. It's very common to find a BSc in Mathematical Sciences or in Mathematics, or even a BA in Mathematics, but far less common to find a BMath. The same is true for language; it's very common to find a BA in English or a BSc in Linguistics, but you don't often find a BLit or a BLing. Mathematics is a key component of engineering, but graduates get a BEng. Mathematics and language have therefore been subsumed by other disciplines.

After a while, it becomes clear that some areas of knowledge are axiomatic; they generate their own stuff independent of other areas. These include language, mathematics, and aesthetics. At the same time, some areas of knowledge are more derivative than others — science for example cannot exist without drawing on history, mathematics and philosophy; literature must have language to survive.

The difficulties are now more obvious, but why is this a problem for some teachers? I suspect it has to do not with the nature of their primary discipline(s) but more with the breadth of their exposure to other disciplines. Disciplines with internal conflicts about what other disciplines they are part of (or not part of), such as geography, force their exponents to know something about the humanities as well as the sciences, statistics as well as physics and sociology. Disciplines with internal conflicts about subjective experience, such as literature and visual arts, tend to separate themselves from other disciplines because their exponents become ever more specialised and less knowledgeable about other disciplines.

These are of course generalisations, tendencies but not necessities. Your choice of discipline may tend to limit you, but you can always choose to transcend those limits. If a statistician were to confine herself to mathematical descriptions of statistical distributions, that would be one thing; it would be quite another (and perhaps more exciting) if that statistician were to seek further knowledge in all the other domains in which her area of knowledge is used. Unfortunately for teachers of English literature, it isn't a subject used much in (or with) other disciplines.

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