Buridan's ass

thumb|Political cartoon c. 1900, showing the [[United States Congress as Buridan's ass (in the two hay piles version), hesitating between a Panama route or a Nicaragua route for an Atlantic–Pacific canal]]

Buridan's ass is an illustration of a paradox in philosophy in the conception of free will. It refers to a hypothetical situation wherein an ass (or donkey) that is equally hungry and thirsty is placed precisely midway between a stack of hay and a pail of water. Since the paradox assumes the ass will always go to whichever is closer, it dies of both hunger and thirst since it cannot make any rational decision between the hay and water. A common variant of the paradox substitutes the hay and water for two identical piles of hay; the ass, unable to choose between the two, dies of hunger.

The paradox is named after the 14th-century French philosopher Jean Buridan, whose philosophy of moral determinism it satirizes.

Although the illustration is named after Buridan, philosophers have discussed the concept before him, notably Aristotle, who put forward the example of a man equally hungry and thirsty, and Al-Ghazali, who used a man faced with the choice of equally good dates. Aristotle, in ridiculing Anaximander's idea that the Earth is stationary simply because it is spherical and any forces on it must be equal in all directions,

Andalusian philosopher Averroes (1126–1198), in commentary on Ghazali, takes the opposite view.

Later writers satirised this view in terms of an ass which, confronted by both food and water, must necessarily die of both hunger and thirst while pondering a decision.

Many later philosophers have addressed this problem of "choice without preference". In his Ethics (), Baruch de Spinoza accepts that his determinist philosophy implies that such a state of indecision could happen, but that this should be classed with other irrational behavior:

Social psychologist Kurt Lewin's field theory treated this paradox experimentally. He demonstrated that lab rats experience difficulty when choosing between two equally attractive (approach–approach) goals. The typical response to approach–approach decisions is initial ambivalence, though the decision becomes more decisive as the organism moves towards one choice and away from another.

Buridan's principle

The situation of Buridan's ass was given a mathematical basis in a 1984 paper by American computer scientist Leslie Lamport, in which Lamport presents an argument that, given certain assumptions about continuity in a simple mathematical model of the Buridan's ass problem, there is always some starting condition under which the ass starves to death, no matter what strategy it takes. He further illustrates the paradox with the example of a driver stopped at a railroad crossing trying to decide whether he has time to cross before a train arrives. He proves that regardless of how "safe" the policy the driver adopts, because indecision can cause an indefinite delay in action a small percentage of drivers will be hit by the train.

Lamport calls this result "Buridan’s principle": Specifically, the input to a digital logic gate must convert a continuous voltage value into either a 0 or a 1, which is typically sampled and then processed. If the input is changing and at an intermediate value when sampled, the input stage acts like a comparator. The voltage value can then be likened to the position of the ass, and the values 0 and 1 represent the bales of hay. As in the situation of the starving ass, there exists an input on which the converter cannot make a proper decision, and the output remains balanced in a metastable state between the two stable states for an undetermined length of time, until random noise in the circuit makes it converge to one of the stable states.

The metastability problem is a significant issue in digital circuit design, and metastable states are a possibility wherever asynchronous inputs (digital signals not synchronized to a clock signal) occur. The ultimate reason the problem is manageable is that the probability of a metastable state persisting longer than a given time interval t is an exponentially declining function of t. In electronic devices, the probability of such an "undecided" state lasting longer than a matter of nanoseconds, while always possible, can be made negligibly low.

In asynchronous system design, arbiter circuits have been developed to make such decisions. They can reduce to insignificance the probability that a metastable state occurs, at the cost of increased decision time.

Buridan's principle

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