Error: Yes, it should be 310^80. I think my brain was half-writing the dimension and half-writing the more useful view of (R^3)^10^80. Thanks for catching that.

Error: Yes, it should be 310^80. I think my brain was half-writing the dimension and half-writing the more useful view of (R^3)^10^80. Thanks for catching that. As for your analogy, I don't quite follow. The actual physical model is that of the oscillators, more or less. The wave is the mathematical abstraction that does allow us to replace it with a function. In terms of information, the wave has more detail, but it is abstracted into a nice form. I think we agree on this. But the quantum wave function is serving a different role. The water wave is something that varies over the 2d space. As we look at different values, we change the x and y coordinates to see the new values. In that sense, it is 2d. For the quantum wave function, if we keep all but one of the 10^80 particles in the same exact position, but we vary the position of that one particle, we do get different values of the wave function and it does matter to all the particles as it will affect the gradient vector defining the velocity vector of each of the particles. The change is not localized to just the one particle that is changing, but impacts all particles. Of course, most of the time, practically speaking, changes by one particle will not make a difference, but situations such as present in Bell's Theorem and quantum computing are exceptions to this. Fundamentally, the current state of all the particles is needed to be known in order to know what part of the wave function is needed. That is the sense in which the dimension is not 3, but 310^80.