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The Block Stacking Problem
John D. Norton Department of History and Philosophy of Science University of Pittsburgh https://sites.pitt.edu/~jdnorton/jdnorton.html February 21, 2025 In the block stacking problem, a collection of blocks are to be stacked at a table edge.
If you are impatient, here are the answers that will be developed below: Puzzle 1 and 2: Simple principles of balance, extending back to Archimedes, affirm the stability all the stacks as long as they have finitely many blocks. Each stack with a finite number of blocks n extends horizontally and farther so, the greater the value of n. The effect of taking the infinite limit is to eradicate all extensions beyond the table edge. The application of the logarithmic approximation to this inequality proceeds almost identically with the same calculation that determined which blocks m are fully past the table edge.
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