Paradox

PASCAL’S IMPROBABLE CALCULATIONS 221The right answer is that the four-gear assembly can turn.In general, an even number of interlocked gears can turn butan odd number cannot. This principle dictates gridlock forthe nineteen-gear circuit that is depicted on the silver-gold,two pounds coin introduced by the Royal Mint on June 15,1998. Brute inspection cannot overturn the impression thatthis large assembly of gears can all spin. The gridlock is toosensitive to the small difference of whether the large numberof gears are odd or even. We need theory to overrule imagination’sverdict. Similarly, the functionalist can insist thattheory is needed to correct the impression that a functionalequivalent of you can be free of consciousness.EXPERIMENTS ON NOTHINGDuring Descartes’s visit, Pascal tried to convince him thatvacuums exist. Descartes believed that reality had to be aplenum. He wrote Christian Huygens that Pascal “had toomuch vacuum in his head.”Pascal began thinking about vacuums in 1646 when helearned of Evangelista Torricelli’s experiment with abarometer. This involved placing a tube of mercury upsidedown in a bowl of mercury. Everybody wondered what keptthe mercury suspended in the tube. The received view wasthat the “empty space” in the tube was filled with rarefiedand invisible matter. Following Aristotle, they believedthat nature abhors a vacuum. Pascal regarded the issue asempirical rather than conceptual. He conducted a series ofexperiments that dramatically supported the vacuumhypothesis. His conclusion was that there really was nothingholding up the mercury. Nor is there anything pulling