Physical Interpretation
A physical interpretation of this principle comes from the heat equation. That is, since log |f(z)| is harmonic, it is thus the steady state of a heat flow on the region D. Suppose a strict maximum was attained on the interior of D, the heat at this maximum would be dispersing to the points around it, which would contradict the assumption that this represents the steady state of a system.
Read more about this topic: Maximum Modulus Principle
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“For pain is perhaps but a violent pleasure? Who could determine the point where pleasure becomes pain, where pain is still a pleasure? Is not the utmost brightness of the ideal world soothing to us, while the lightest shadows of the physical world annoy?”
—Honoré De Balzac (1799–1850)