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The principle of indifference states that, without any evidence, all potential outcomes should be considered equally probable. For example, if there’s a 10-horse race then, without any additional information, one should assume that each horse has a 1-in-10 chance of winning. It’s an important epistemological principle at the foundation of probability that might seem as safe and sound as it is obvious. But, as this video from Wireless Philosophy (Wi-Phi) lays out, a paradox first described by the French mathematician Joseph Bertrand in 1889 can make starting from a position of true indifference impossible. And, because probability is at the core of almost every scientific field, this paradox has rippled through science for more than a century, leaving in its wake disagreements, workarounds and, so far, no clear solution.
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