Algorithms have become ubiquitous. They optimize our commutes, process payments, and coordinate the flow of internet traffic. It seems that for every problem that can be articulated in precise mathematical terms, there’s an algorithm that can solve it, at least in principle. But that’s not the case—some seemingly simple problems can never be solved algorithmically.
Turing, in search of unsolvable problems, turned this logic on its head—he imagined an infinite list of all possible algorithms and used diagonalization to construct an obstinate problem that would thwart every algorithm on the list. Imagine a rigged game of 20 questions, where rather than starting with a particular object in mind, the answerer invents an excuse to say no to each question. By the end of the game, they’ve described an object defined entirely by the qualities it lacks.
Source: The AI Report (theaireport.net)
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