Part of what makes this one hard is that it’s an essential foundational step but rarely used in practice— everything that’s actually useful about Turing machine

Part of what makes this one hard is that it’s an essential foundational step but rarely used in practice— everything that’s actually useful about Turing machines is several levels removed from symbols on a tape. Probably the most visible outcomes of this work is complexity analysis of algorithms- you can’t talk about how much computational effort you need to do something until you have an agreed measure of computational effort. How many steps or tape cells a Turing machine would need is that fundamental measure, in a similar way to how the speed of light is our fundamental measure of velocity; they’re essential to our understanding of the field but not used on a day-to-day basis. Instead, we use more convenient ones that are themselves derived from the first-principles units.