Who Chooses the Best Answer? — From Shortest Paths to AI
Optimization is older—and more political—than a technique for ‘finding the most efficient answer.’ Travel from reflected paths in Alexandria and the brachistochrone in Groningen through calculus of variations, least squares, gradient descent, constrained and linear programming, stochastic and dynamic methods, computational hardness, interior points, and neural-network training. The journey keeps objectives, constraints, algorithms, computational cost, and value judgments on separate layers.
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Alexandria
Seeing a Shortest Route in a Broken Path of Light — the Catoptrica
Unfold a reflected path at a plane mirror and the equal-angle route becomes the shortest broken line. This geometric argument is an important shoulder for later variational principles. Yet the work survives only in a medieval Latin translation, was misattributed to Ptolemy, and is only doubtfully assigned to Heron. It does not say that light minimizes geometric distance in every medium and setting.
Replay on the map from scene 1Scene index