Waves have a curious kind of being, even water waves. A wave in deep water, moving in a certain direction along the surface, is composed of water that itself never actually moves in that direction. Instead, the water molecules only go up and down, as a buoy will reveal, while the wave appears to move horizontally. Even though it appears to be as solid and substantial as any material object, a wave is a moving form, not simply a single body. At each successive instant, a wave is an ever-new assemblage of water, whose changing individuality is subsumed under the outward form of the whole wave. In this sense, a wave is a process, not a substance, as Maxwell noted. Waves interfere with each other because they are interchangeable and thus not distinguishable; two processes can coincide in space and time, but two substances cannot. Thus the wave reveals a whole new possibility of identity, for one identifies waves by their amplitude (that is, height) and by their wavelength or frequency, rather than by the ever-changing bits of water that make up the wave at any time. Even if one distinguishes one wave from another as they approach from a distance, when they pass through each other, one can no longer sustain that distinction, which makes sense only in the context of ordinary bodies.
-- Peter Pesic Seeing Double: Shared Identities in Physics, Philosophy, and Literature
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