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14. Stay Where You Are:

Buridan’s Donkey

The Question:

A cowboy, very thirsty and very hungry after a trek through the desert, enters a saloon and spots a bottle of water at one end of the bar and a loaf of bread on the other. Both are equidistant from where he stands. Which will he choose first, the food or the drink?

A couple have the choice between watching a soccer game or a romantic movie on TV. How will they decide?

When approaching a traffic light, you stop if it is red, you keep going if it is green. But if it just turned yellow, do you stop or keep going?

A devoted mother buys her son two neckties. In order to please her, he wears one of them for her next visit. But even a dutiful son often finds it hard to satisfy a domineering mother: “What, you didn’t like the other one?”


The Paradox:

Sometimes it is difficult to make up one’s mind. A lady may stand in a shoe store and not be able to decide which of the two pairs that appeal to her in equal measure to buy. It may happen that after a few minutes of deliberation, she walks out of the store without making any purchase. (More likely, she buys both pairs.) The frustrated couple, unable to agree on what to watch, may turn off the TV altogether and read a book and the newspaper. And the conflicted driver may alternately hit the gas and the brake pedal until he provokes a traffic accident. The dutiful son, on the other hand, made a choice!

There is a mental condition called aboulia. Aboulic individuals show a lack of will or initiative and are unable to act or make decisions independently. But it would certainly be a stretch to imagine that a cowboy, famished and parched, would die of thirst or hunger, simply because he cannot decide which need to satisfy first.



The situation is usually illustrated with a donkey standing between two equidistant bales of hay. Unable to decide from which one to feed, the donkey eventually starves to death. The anecdote is attributed to opponents of Jean Buridan, one of the most important French philosophers of the 14th century.

One of Buridan’s areas of interest was the notion of free will. He was of the opinion that human behavior is determined rather than free and that everything happens, and is done, for a reason. But he recognized a problem in situations where there is no reason to prefer one option over another. “Should two courses be judged equal, Buridan opined, “then the will cannot break the deadlock, all it can do is to suspend judgement until the circumstances change, and the right course of action is clear.” In other words, the donkey should wait until something changes. If it dies while waiting…well, too bad.

“Buridan’s Ass”, which the poor animal became known as, was actually not invented by the French philosopher. Rather, the philosopher’s detractors came up with the donkey example in order to prove him wrong. The idea that a decision maker, spoilt for choice, remains immobilised, had been ridiculed long before Buridan held forth in Paris. Aristotle had already criticized the absurdity of a man “who, though exceedingly hungry and thirsty and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is”. A pragmatic answer to the problem was formulated by the eleventh century Persian thinker Abu Hamid Al-Ghazali: “Suppose two similar dates in front of a man, who has a strong desire for them but who is unable to take them both. Surely, he will take one of them, through a quality in him, the nature of which is to differentiate between two similar things.” The mentioned ‘quality’ is what we call free will.

Yogi Berra: when you get to the fork, take it /////



Nihil sine ratione (nothing happens without reason), as Gottfried Wilhelm Leibniz was wont to say. Hence, whenever a choice is made, there must be a reason for making it, and whenever there is a reason for making a choice, free will is unnecessary. But when there is no rational reason to choose one alternative over the other, and a choice must be made nevertheless, free will is required.

Thus, the son who chooses one necktie over the other, demonstrates free will…up to a point. Though he shows himself obedient by wearing one of the neckties, he reveals through his choice that he likes the other one less, thus proving that he possesses free will after all. (Which is exactly what his domineering mother scolds him for.) The ass, on the other hand, lacks a reason to choose one bale over the other and cannot decide. By dying it demonstrates that it does not posess free will.

Many thinkers found the idea, carried over to human beings, absurd. Nobody would fail to act simply because he cannot decide. Faced with an existential dilemma, a rational person would certainly make a choice and thereby prove that she has free will. Hence, beings who are able to make decisions in such ambiguous situations, demonstrate the existence of free will.

Technical Supplement:

The computer scientist Leslie Lampert once pondered the situation when he finds himself “unable to decide for a fraction of a second whether to stop for a traffic light that just turned yellow or to go through.” He believed that something similar might occur in electrical engineering. Say, an analog signal that can vary continuously between ten and twenty must be converted into a digital bit, either a 0 or a 1. Any signal below fifteen is converted to 0, above fifteen to 1. What if the signal is exactly fifteen? The computer, unable to decide, will stop…at least until random noise pushes the signal onto one side of the threshold. (In pure mathematics, such an occasion cannot occur, since the point 15.0 has ‘Lebesgue measure zero’, i.e., it is infinitely thin.)

Lampert came up with ‘Buridan’s Principle’, which says that “a discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time”.

But nobody took him seriously. Neither Science nor Nature, the two most influential scientific journals, were willing to publish his paper. Because no dead donkeys had ever been observed, starved between two bales of hay, the journal referees did not believe that the phenomenon existed in computer science either. The traffic light example did not convince them either. One reviewer commented that if this problem really existed in computer science it would be so important that everybody knowledgeable in the field would have to know about it. “I’m an expert,” he wrote, “and I don’t know about it, so therefore it must not exist.” The paper was eventually published in Foundations of Physics.



Comments, questions, observations: 

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