Wednesday, May 17, 2006

The trouble with models

Models are central to science. A scientific model is a kind of representation of physical reality, an analogy if you like. For example, the image on the left is of the "planetary model" of a nitrogen atom.

The power of analogy is that it lets us think about one thing in terms of something else—often something simpler or more familiar. An example of this is metaphor: when we say, for example, that "life is a journey", we are using the relatively simple model of a journey (with a starting point, a period of travel, a destination, etc.) to understand the more nebulous concept of life. The importance of metaphor was first revealed to me by the marvelous book Metaphors We Live By, now available in a second edition. (About 15 years ago, I picked up a copy at a used bookstore more or less by chance. It had a tremendous impact on my thinking; it was some time later that I learned that it's actually rather a famous book.) The authors, Lakoff and Johnson, argue not only that metaphors are ubiquitous, but that they in fact structure the way we think. Using what strikes me as a more general version of the same argument, Douglas Hofstadter suggests (in a very entertaining essay) that analogy may be the "core of cognition".

Analogies are indeed wonderful. But it is well to remember that no analogy is perfect, and sometimes an analogy can actually be an obstacle to understanding. The notion that "life is a journey" can be helpful, but it may lead us to overlook aspects of life that don't resemble a journey. For example it may cause us to unduly focus on trying to "get somewhere" in life. An alternative to the title Metaphors We Live By might be Metaphors We're Trapped By. Notwithstanding the fact that a metaphor can be very informative, strictly speaking, it is always a lie. Or as statistician George E. P. Box put it:
"All models are wrong; some are useful."
The trouble is, we often confuse models with reality. (Incidentally, that applies to fashion models too!) What is true about a model may not be true about what it represents. Sound familiar? It's very much like the objection I quoted in my recent post about definitions: it may not be valid "to draw conclusions about what is true about the world based on what is true about a word". (And what is language but a type of model? I believe this links rather directly to the field of semiotics, but unfortunately I don't know much about that!)

More things in heaven and earth ... than are dreamt of in your philosophy

It seems there has been an increasing recognition that models lie at the heart of science (rather than "laws"). And models are necessarily imperfect. The planetary model of the atom was soon superceded by the Bohr model, which was followed in turn by even better models. At its best, science progresses by recognizing the shortcomings of models and substituting more appropriate ones. But the process by which this is achieved remains controversial. The interplay of deductive and inductive reasoning is part of it, but it may be far more complex than that, as Thomas Kuhn argued in The Structure of Scientific Revolutions.

Whether we like it or not, we're stuck with models, not only in science but in language and indeed in the core of thought itself. In an essay on "The Fall and Rise of Development Economics", Paul Krugman has a fascinating section on "Metaphors and Models" in which he writes:
"The problem is that there is no alternative to models. We all think in simplified models, all the time. The sophisticated thing to do is not to pretend to stop, but to be self-conscious -- to be aware that your models are maps rather than reality."
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Anonymous Mohammed_TA said...

And history attests to this. Many a sage have taught by parables. No doubt, models are powerful tools of learning.

11:27 PM, May 20, 2006  
Blogger Nick Barrowman said...

There's a discussion of science and modeling over at Adventures in Ethics and Science. (And I just left a comment.)

10:14 PM, May 31, 2006  

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