I'll make some idle musings tangential from the main point. The instantiation of abstract concepts in computer hardware leads to complications. The access time

I'll make some idle musings tangential from the main point. The instantiation of abstract concepts in computer hardware leads to complications. The access time for x and y can vary, as can the power use, or who gets charged for measuring it. I can think of an augmented f(x) which includes some those measurables as part of the public interface, but then the result would be probabilistic, and would need to exclude functions which can measure exactly where each object is located. It might possible to encode multiple values at the same location, eg, via quantum spin states, so treat "location" as more than a position in space-time. At the end though, this says that an object's composition and location in space-time is the only "public interface". All else is artificial. Copyright law is one of these artificial distinctions. If you have a movie on your computer, and I have one on mine, my copy might be in violation of copyright law. A duplicated movie can lead to harm, even though the public interfaces for both give identical results.