Holmes takes chapter thirteen of The Beginning of Infinity, by David Deutsch: Washington's first veto, in 1792, was over how to round seats among the states. Round to the nearest, says Watson; mark this, says Holmes: four states, ten seats, and nearest rounding gives eleven. Every fix breeds a paradox, proven impossible in 1975. Lestrade asks if two centuries were wasted. No: an impossible wish points to a better one.
The strongest case in The Beginning of Infinity is chapter thirteen's apportionment problem: Washington's first veto, in March 1792, was over how to round each state's share of House seats, and the obvious fix, rounding to the nearest whole number, can hand out eleven seats where ten were meant; every patch bred a new paradox until Balinski and Young proved in 1975 that no rule can be both proportional and paradox-free, and the author's lesson is that wishing for something logically impossible is a sign that there is something better to wish for, such as a system that removes bad rulers without violence.
On the book: The Beginning of Infinity by David Deutsch
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The Beginning of Infinity: Explanations That Transform the World
Penguin · Jan 1, 2011
