A 2000-year-old Philosophical Problem that Stumps Modern Machines

Buridan's Ass is one of the oldest insults in existence. It has been consistently used to make fun of a particular worldview — one that doesn't allow for free will. But this notion gained new relevance, when we started making little electronic Buridan's Asses, which had to come to terms with the problem on more than just a philosophical level.

Jean Buridan was a pretty smart guy. Born in the 1300s, he came up with the idea of "impetus" - what we would now call inertia. Objects, he said, are set into motion by forces and move according to the dictates of those initial forces. He differed from most other philosophers of his time by stating that impetus didn't simply vanish and cause the object to stop moving. Friction and other forces opposed the impetus and stopped the object. Today, we recognize that he was right about that. Clever.


Unfortunately, this clever guy's name was hitched to one of the more infamous philosophical burns in existence. Buridan espoused the theory that rational beings react to situations the way objects react to forces. They act, without will, under the influence of the greatest force. So if a rational person had a choice between two possibilities, that person would choose the best option. There was no other way for them to go. If, however, the person was presented with two equally good options, they would have to stop, as objects did while under the influence of equal forces, and wait until one option became better than the other.

Other philosophers ridiculed this theory, and came up with the idea of Buridan's Ass. A donkey, presented with the choice between two equally desirable and equally distant bales of hay, would not be able to make a choice between them. Presented with twice the amount of food it needed, it would starve to death. This was not the first time such an idea had been aired. Aristotle first came up with the concept, although his example was that of a man having to choose between food and water. The attachment of Buridan's name to the idea of an ass told everyone exactly what people thought of his philosophy. Biologically, this notion is incredibly tough to test, but starting in the later half of the twentieth century, we came up with our own version of Buridan's Ass — machines.

One little ass has already popped up in electrical engineering. Say you have something giving out a continuous range of voltages, and a device that tests the voltage every so often and switches the continuous range to either zero or one. At some point, it's going to test when the voltage is straddling halfway point exactly. Which should it switch the voltage to? Each option is equally correct, and if there is no way to choose between them within a certain time, there's a problem.


The most formal application of, well, ass-theory, came from Leslie Lamport. He showed that, if a sample ass has to make a decision between two absolutes, and starts at some point in a continuous range of values, there are always going to be some starting points that end in the ass starving to death. No matter how many fail safes and specifics built into the system, there is going to be a stalling point. Lamport stresses that this theory doesn't say that the ass could never decide. The problem with the ass is that it's mortal, and therefore has limited time. Computers, although they do things quickly, also have a limited time. If the ass were immortal, and the machine had an infinite amount of time before its operator got impatient and hit it with a hammer, it's possible that the paradox would resolve itself. But not within any bounded length of time. You can read the entire paper, updated in 2012, here.

Top Image: A. Davey

Via Buridan's Principle, Paradoxes.


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