Geographical models are worth teaching, and the reason is not that they describe the
world accurately, because mostly they do not. The warrant is that the purpose of a model
in this subject is to generate a prediction precise enough to be wrong in an informative
way. On that criterion a model earns its place by how much you learn when reality departs
from it, which means the failures are the product rather than a defect.
Von Thunen's rings are the clearest case. The model says perishable, heavy goods are
grown near the market and light, durable goods far from it, because transport cost rises
with distance at different rates for different products. Modern dairy is produced
hundreds of kilometers from the cities that consume it, which looks like a refutation.
Work out why, and the model hands you the answer. The assumption that failed is uniform
transport cost rising steeply for perishables; refrigerated transport cut that rate
sharply, which flattens dairy's profit line, and a flatter line crosses the others much
further out. The model predicts exactly the change once the new parameter is supplied.
More usefully, it also predicts where the old pattern should survive, and it does:
goods limited by bruising or by hours of freshness rather than by temperature, such as
soft fruit and cut flowers, still cluster close to their markets. A student who works
through that has learned something about transport economics that no amount of
describing real land use would have taught.
The demographic transition model works the same way. Its account of the sequence is
robust, since death rates fall before birth rates in every case, for a reason that
generalizes: mortality responds to infrastructure imposed from outside people's
decisions, while fertility responds to slower changes in belief and in the position of
women. Its timing is drawn from one region's history and is now badly wrong, because
later transitions import ready-made medicine and compress stage 2 into decades. Noticing
which half travels and which does not is the lesson.
The strongest objection is not that models are inaccurate. It is that teaching them
installs a default expectation that students then apply where it does not belong. The
concentric zone model was drawn from American industrial cities, and a student who
carries it to a city where the elite occupy a central historic core and the poorest
occupy peripheral settlements will read that city as deviant rather than as differently
organized. The model supplies not just a prediction but a norm, and the norm is
parochial. Worse, models are compact and memorable while their caveats are neither, so
what survives an examination is usually the diagram.
This objection is substantially correct and should be conceded without softening. The
concentric model has been used to make other cities' arrangements look like failures to
develop properly, and that is a real intellectual harm rather than a hypothetical one.
But it is an argument about how models are taught rather than whether. The harm comes
from teaching a model as a description and then adding limitations as an appendix, which
reliably produces students who remember the diagram. Teaching the assumptions first, and
treating any departure as a question about which assumption failed, produces the opposite
habit. The test is whether a student presented with an unfamiliar city asks which
assumption does not hold here, and that is a teachable disposition.
There is a limit worth stating, because the position should not be pushed past what it
holds. A model is only worth teaching if its assumptions are explicit enough to be
checked. Von Thunen names four; the demographic transition's assumptions about
industrialization are buried in its framing rather than stated, which is why it is more
often misapplied. Where a model's assumptions cannot be recovered, it cannot fail
informatively, and then the objection wins.
Within that limit, the case holds. A model that predicts nothing cannot be checked
against anything, and a discipline that only described what it observed would have no way
to be surprised. The rings are wrong about dairy, and finding out why teaches
more than the correct answer would have.