Sheep and Goats—A Footnote to Testing Tests

A Chinese High School math exam question has recently gone viral on YouTube.

It goes something like this:

“A ship is carrying 74 goats and 35 sheep. How old is the Captain?”

As it turns out, there is nothing new about this question. It has often been used over the past forty years or so to test the ability of students to identify ‘fake’ questions, tolerate ambiguity or develop ‘critical thinking’.

The story in fact goes back even further. The French novelist, Gustave Flaubert, posed a similar question to his sister, who was beginning the study of mathematics in school, in a letter dated 1841.

This ultimate origin story is in fact the most interesting part of the puzzle.

In France in the 1840s, universal education was still in its infancy (literally) and many, left and right of the political spectrum, questioned its utility and the motives underlying the introduction of a nationwide school curriculum.

On the right, it was viewed as an attempt to uproot people from their local culture and encourage less privileged members of society to question their lowly status and the class system as a whole.

On the left, intellectuals such as Flaubert saw it as a recruitment drive aiming to produce a mechanized bourgeois society organized exclusively around industry and finance, at the expense of poetry, mystery and genuine human relations.

It is for this reason that Flaubert jokingly poses his sister this pseudo-problem, as she is about to embark on her academic studies.

The answer Flaubert was begging was presumably that an artist (and by extension a person) should be free of the constraints of science and finance and thereby at liberty to choose certain things.

Different from Flaubert, however, in whose communication, the ironic intent is gentle and apparent, recent versions of the question are applied en masse, perhaps with benign intent, but with the clandestine purpose of ‘tricking’ candidates into providing incorrect answers in the interest of ‘scientific’ research.

Online discussions of actual responses to this problem include some very revealing examples.

One Chinese candidate recently looked up the average weight of sheep and goats and the bureaucratic requirements regarding age and experience stipulated for a ship’s captain charged with carrying cargo of this bulk within the territorial waters of the People’s Republic. This candidate concluded that the captain must be aged 28 years or older.

Flaubert would have hated this eminently unpoetic solution. But it is the best, if we assume the question to be a fair one.

Other literal-minded question solvers have not been so resourceful. One hapless French student, confronted with the question in the late 1970s, argued desperately that the number of sheep plus the number of goats is too high to be the age of a person, while the number of sheep divided by the number of the goats is too low. Therefore, the correct answer must be the difference between the two values given.

Flaubert would have hated this candidate’s unctuous but desperate efforts to please his or her masters even more.

And yet, who can blame candidates for not taking such a question seriously in the context of the ordeal of a math exam and attempting to answer it in these terms? Just as experimental subjects consistently pumped up the electric shocks administered in the Milgram experiment.

The ‘sheep and goats’ question is not really about math education, but rather, like the Milgram experiment, about obedience to authority.

People come up with ridiculous answers to this question, not because they are foolish or uncreative, but because they are conditioned to do so by the constraints of an authoritarian educational system.

The experiment is actually self-defeating in its own terms. There are many genuine math problems that have no solution. This may be because no such solution has yet been found or because (more troublingly) it is impossible to find such a solution. Evidence suggests that cases of the latter are by far more numerous.

This means not only that we all know much less than we think but, more worryingly, that there are many things we can never know—not because of our own limitations as human beings or those of our technology, but because of the essential ambiguity and inscrutability of the things themselves.

Disturbing this may be, but we would all be better served, were this fundamental uncertainty included openly in our school curricula and political discourse, rather than used divisively to test the supposed degree of intelligence or stupidity of students and tests, or politicians and voters; sorting them, by way of some kind of authoritarian trickery, into groups of sheep and goats.

So far as math and other questions are concerned, ‘Duh’ is often the best answer. Gödel, Homer Simpson and the Zen masters told you so.