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Cases of Discontinuous Technological Progress

We know of two technologies which underwent a discontinuous jump in improvement equivalent to more than several decades at previous rates. These are explosives and superconductors. We know of two more cases of smaller discontinuities, and several promising cases to investigate

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Discontinuity from Nuclear Weapons

Nuclear weapons were a radical improvement over previous weapons in terms of energy released per weight of explosive (relative effectiveness). They do not appear to represent a substantial discontinuity in terms of cost-effectiveness of explosives, though the evidence there is weak.