> No, this is a circular definition. We define an "algorithm" as something that can be performed by a Turing machine. So the Church-Turing thesis is a trivial t

> No, this is a circular definition. We define an "algorithm" as something that can be performed by a Turing machine. So the Church-Turing thesis is a trivial tautology. (Though of course a useless one.) No, that's a terrible definition, and it isn't what computer scientists typically use, though it might be what one says if they're not careful. If someone says that "algorithm" means "what a Turing machine can compute", it's because they believe the Church-Turing thesis, which says that they're the same. If they're the same, then you can talk about them interchangeably, and "Turing machine computations" have a cleaner definition than "pen and paper algorithms", so it's convenient to talk about "Turing machine computations" as if that's the ground truth. But if the Church-Turing thesis is false, then they're not the same, and you should be very careful not to mix them up. And we need a word for "the sorts of things you can compute by hand by a set of well-defined steps", and that's what "algorithm" has always meant. EDIT: Note that I'm making a prediction. If a person told you that "algorithm" means "what a Turing machine can compute", ask them what "algorithm" means if the Church-Turing thesis is false. My prediction is that they'll use a different defintion, based on what you can effectively compute by hand, like the "Effective Method" wikipedia article that my sibling posted.