disc 1. The unreasonable effectiveness of mathematics ; Seeing higher dimensions and symmetry ; Understanding Ptolemy's enduring achievement ; Kepler's 3 laws of planetary motion ; Newton's powerful law of gravitation ; Is Newton's law precisely correct? -- disc 2. Expansion and recurrence--Newtonian chaos! ; Stable motion and central configurations ; The evolution of the expanding universe ; The winner is--determined by voting rules ; Why do voting paradoxes occur? ; The order matters in paired comparisons -- disc 3. No fair election rule? Arrow's theorem ; Multiple scales--when divide and conquer fails ; Sen's theorem--individual versus societal needs ; How majority improvements go wrong ; Elections with more than three candidates ; Donuts in decisions, emotions, color vision -- disc 4. Apportionment problems of the U.S. Congress ; The current U.S. apportionment method ; The mathematics of Adam Smith's invisible hand ; The unexpected chaos of price dynamics ; Using local information for global insights ; Toward a general picture of what can occur.
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