Aesop’s Boy who Cried Wolf

Aesop The Boy Who Cried Wolf

The Fable

Wikipedia’s summary is:

The tale concerns a shepherd boy who repeatedly tricks nearby villagers into thinking a wolf is attacking his town’s flock. When a wolf actually does appear and the boy again calls for help, the villagers believe that it is another false alarm and the sheep are eaten by the wolf.

Apparently:

Teachers have used the fable as a cautionary tale about telling the truth, but an educational experiment in the first decade of the 21st century suggested that reading “The Boy Who Cried Wolf” increased children’s likelihood of lying.

My Comments

A Variation

As commonly told the tale concerns ‘villagers’. Its seems odd that they do not find a more trusted person to watch over their flock, and so even if the boy had been lying the villagers would seem to deserve some blame for the sheep’s deaths. In the original, though, the people who respond are actually ‘labourers’, which makes more sense. So in what follows I do not suppose that the villagers were responsible for the selection and tasking of the boy to watch the flock.

Truth-telling

This is intended as a moral tale, to discourage children from lying. But there are two problems:

  1. It makes no sense, logically.
  2. It appears not to have the intended effect.

There is a puzzle here, depending on what you make of the tale. Either the teachers or their students are mistaken: why? I find this interesting as an application of mathematics that does not involve numbers.

If we try to model the situation logically, then how do we know that the boy was originally lying? Maybe he later confessed, but can we trust a confession that he may have felt was coerced? A reasonable interpretation is:

  • On many occasions:
    • The boy raised the alarm.
    • The villagers responded.
    • The villagers found no wolf.
  • Later:
    • The boy raised the alarm.
    • The villagers did not respond.
    • The wolf ate the sheep.
    • The villagers blamed the boy.

More than this, we do not know. It may be that the earlier alarms were false. From a probability theory point of view if this is the only hypothesis we consider then we should assign a probability of ‘1’, and the conventional moralist interpretation would seem justified. But what if the earlier alarms were genuine, and the response of the villagers had scared off the wolf? Once we recognize this possibility then the conventional interpretation no longer seems justified.

From a pedagogic point of view, what lesson might we expect others to take from the tale? If we suppose that the student has never been falsely accused of lying by those in authority (parents, teachers, ‘adults’) then possibly it might not occur to them that the villagers were mistaken, and hence it might be thought that they would draw the intended conclusion. But how could we ever now that someone else doesn’t think that they have been falsely accused? If they have, what lesson might they draw?

It may seem that the boy was given an unreasonable job to do. By being diligent and truthful he ended up in disgrace, seeming worse than if he had simply failed to raise the alarm. Maybe after the first time, he would have done better to ‘raised the alarm’ in such a way that the villagers would arrive too late to save the sheep. (Maybe he could rush and trip or otherwise invent a plausible excuse for delay). Surely everyone would be better off?

The boy would have been to lie (about the reason for the delay) than to act as instructed to the best of his ability.

This seems a reasonable conclusion about lying for a student to draw. (He may also draw conclusions about the insightfulness of his teachers and – once he discovers that the conventional interpretation is widely accepted – about the supposed ‘wisdom’ of those supposedly ‘in authority’.

Induction and probability

Inductive reasoning  is where a prediction is made based upon experience. In this case, the villagers have never found a wolf after many alarms, so – inductively – they may reasonably come to expect not to find a wolf if they responded to the next alarm. But this is not to say that the alarm was necessarily false.

A ‘mathematical’ interpretation is given by Bayesian inference: If at some point a villager thinks that the boy might be false alarming (with non-zero probability), and that if he were not then with some non-zero probability a wolf would be noticed, then with each failure to find a wolf the probability that the boy is falsely alarming should be increased by the ‘Bayes factor’, and so tend to 1, virtual certainty. Thus this fable provides an example of the failure of Bayesian inference. (In this case, because the alternative to the boy false-alarming is not a suitable hypothesis to which Bayesian inference can be properly applied.)

A logically minded student might suppose that the villagers were not very good at inference, and that their teachers had failed to appreciate this.

Pragmatism

From the point of view of an individual villager, if there is a strong enough majority in favour of not responding, there may seem no point in suggesting that there may be a wolf, and every incentive not to. There is not even any incentive to consider any alternatives to the majority belief that no wolf was found because there was no wolf. Once the sheep have been killed there may seem little point in defending the boy by ‘speaking truth to power‘ and some  strong incentives not to challenge the common view. Thus the story suggests a difference between saying what is actually true and going along with a common view.

Social truth

It is clearly sensible for villagers and children not to challenge a common view once sufficiently strongly held. But how do such odd views form?

If we suppose that the villagers are intolerant of psychological (as against logical) uncertainty, then in particular the recognition that there may have been a wolf is uncomfortable, and the only obvious way to remove the uncertainty is to deny it, and to suppose that there was no wolf. Thus all those with such intolerance have an incentive to suppose the alarms false. Once the sheep have been savaged there is an additional incentive to blame the boy: the alternative would be to blame the common view of the villagers, when there is no obvious way to remedy the discomfort that this would cause.

Thus the fable can be read as suggesting that the tendency to reduce ‘felt’ uncertainty and establish some ‘common-sense truth’ can not only lead to disaster (the loss of the sheep) but also to necessary ‘white lies’ and abuse.

Adaptability

The fable also speaks to a dilemma of adaptability: continuing to respond when there may be no wolf would seem maladaptive, yet the obvious adaptation leads to harm. But the story can also be read as providing a socially acceptable solution.

Suppose that the villagers differ in their tendency to form various beliefs and to consider alternatives, and do not feel obliged to have a common reaction. Then one might expect the response to decline with each alarm. Eventually the wolf might attack when there has still been some response, and even a single villager could call for reinforcements and so save some sheep.

Cohesion

There are many circumstances in which activity needs to be concerted to be effective, yet in the face of uncertainty it may, as above, be better for a minority to behave usefully than for everyone to be useless. The ability to act in concert is something that needs developing and maintaining, so having a general concern for social cohesion seems reasonable, and so a default to act in concert might seem indicated. That is, cooperation might seem a better default than collaboration. Such an attitude might well promote a tendency to deny uncertainty as far as seems reasonably possible.

The key, here, seems to be to recognize that collaboration, in which social cohesion is developed and maintained while at the same time at least tolerating any tendencies of the collaborators that aren’t certainly harmful, and even encouraging the development of reasonable differences (e.g., of viewpoint, experience, skills, affiliations). Possibly the ‘villagers’, suspecting that the child was raising false alarms, might have tried engaging with him to resolve the situation, rather than simply ignoring him or telling him off.

Overall

It seems to me that ‘the boy who cried wolf’ can be used as an example of what is, in fact, a very common problem: if one views a situation in the common way, one may well find the common interpretation plausible, even compelling. But outside of the common view, the ‘correct’ interpretation is much less clear. Sometimes, it pays to ‘think outside the box‘, even when the box is not so obvious. Mathematical modelling may help to clarify the box and challenge ‘common sense’ as well as have its more common use, of solving problems when taken ‘at face value’.

Dave Marsay

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