time and frequency: the longer a musical note is sustained, the more precise we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, so we can't know very accurately its frequency.
position and momentum
doppler and range: the more we know about how far away a radar target is, the less we can know about the exact velocity of approach or retreat, and vice versa. In this case, the two dimensional function of doppler and range is known as a radar ambiguity function or radar ambiguity diagram.
The function of this collection of various"canons" is somewhat analogous to the precedents established in common law by case law.
Various functions in mathematics are also canonical, like the canonical homomorphism of a group onto any of its quotient groups, or the canonical isomorphism between a finite-dimensional vector space and its double dual.
Canonicalvariables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics.
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