Spinning Yarns

We learn, and we teach, through a process of analogy. Analogy is a mechanism whereby we construct a simulacrum in order to capture the essence of an idea, in some alternate framework. Typically, we think of the analogy as being something as close to identical as possible to the original idea; however, it is virtually essential that the medium in which we choose to construct the analogy be distinct from that already available in the context of the idea being imaged. It is through the differences in the analogy that we bring the essential components of the original idea into sharpest relief.

For example, consider the idea of number. What does “three” mean? More crucially, how do you — even assuming you understand the essence of three-dom — convey this idea to someone else. You might show them three apples, and three writing instruments, and three automobiles, and so forth. By providing a sequence of examples which differ both externally (vehicles vs. fruit) and internally (dump trucks vs. passenger cars), you permit the learner to eliminate non-essential components of the idea of “three”, and focus more narrowly on the idea itself.

We derive facts about the universe either inductively, or deductively. Inductive learning is what our brains are most directly constructed to do: Gathering a wide variety of disparate data, and synthesizing general patterns of experience from them. Using these patterns, we may then reason deductively, and so long as our inductive experience provided us with accurate enough data, our deductive conclusions should be fairly commensurate with reality.

When we construct an analogy, we are playing on the powerful inductive capabilities of our neural brains. To use a meta-analogy, it is like constructing a clay model of the thing we are trying to build — we make it look similar to the focal concept, and then establish a “binding” in our minds between the analog (the model) and the thing it is supposed to represent. Having made this binding, we use properties of the model to illustrate properties of the focal concept. We do not attempt to equate the model with the focal concept — any more than we would equate the clay model with the final product — but we take advantage of the parallelism between the two in order to more completely understand the final product’s essential features.

When constructing or learning from an analogy, it is worthwhile to ask questions such as, “Is the binding of this analogy to its focal concept valid?” Informally, this corresponds to asking whether the analogy is sufficiently parallel to the focal concept that reasoning about the analog can be expected to give valid information about the focal concept itself. To use another metanalogy, consider a ‘pantograph,’ a draughtsman’s tool which mimicks the motion of the pen at a different location on the page, perhaps at a different scale. An ideal analogy is like the pantograph, in that it should mirror every salient feature of the original. In practise, most analogies are valid only within a very narrow range.

Another key property of analogies is that they are typically simpler than the focal concept they are intended to reflect. It is quite uncommon to give an analogy for something which has more detail than the original — after all, the objective is to illustrate essential concepts, rather than intricate details. The ability to understand an analogy is often strongly dependent upon environmental issues such as cultural and societal background, but many good analogies exist that arguably span cultural boundaries through the foundations of human experience. For example, many analogies fall under the category of “anthropomorphization,” which is to say, using the human body and behaviour patterns as representative analogues for various phenomena in the world. We label parts of the guitar with names like “head,” “neck,” “body,” “waist,” etc., and we speak of what our computers “want” or “need” when they are not working as we might wish.

Part of the power of analogy as an instructional tool is that it enables us to use smaller, simpler, concrete ideas (which we already apprehend) to understand larger, more complex and/or abstract concepts which do not correlate directly to our sensory experience. Thus it is that we teach our children basic arithmetic with integers, before we teach them about real numbers; we teach them algebra using real numbers before we teach them about calculus; we teach them about calculus before we teach them the more general algebras of groups, rings and fields; and so forth. At each stage, the new concepts are drawn by analogy from those learned previously, and so the process of abstraction and generalization is made easier.

Analogy can also be used as a rhetorical tool — and it is in this context that the question of analogic validity is most appropriate. One possibly unfortunate property of analogy is that we may often be misled by an analogy which is attractively similar to the focal concept — but which does not have a valid binding to the focal concept. For example, we might assert that a good government is like a well-run machine; however, it is virtually never useful to apply reasoning about a mechanical device to large human bureaucracies such as a government — even though there may be some trivially satisfying parallels in the imagination.

Filed by Michael at 20:00 under Philosophical
No Comments