Blaise Pascal · Mathematics
Pascal the physicist and engineer: the <em>Pascaline</em> calculating machine; the great Puy-de-Dôme experiment proving that the air has weight and that the vacuum can exist, against the ancient dogma that ‘nature abhors a vacuum’; and Pascal’s law of pressure in fluids.
When he was only about nineteen, Pascal set out to spare his father, a royal tax official drowning in columns of figures, the drudgery of endless arithmetic. His solution was audacious: a machine to do the sums. The Pascaline, which he designed and built in the early 1640s, used a train of geared wheels, one per digit, with an ingenious mechanism that carried the ‘tens’ automatically from each wheel to the next - the hard part of mechanical calculation. It could add and subtract directly, and it was among the first working calculating machines in history; Pascal built around twenty, several of which survive. Beyond its practical use, the Pascaline embodied a startling idea, one that would echo for centuries: that a part of human reasoning, the labour of calculation, could be handed over to a mechanism of brass and gears. Pascal had made a machine that, in a narrow but real sense, thought.
The key had been forged in Italy. In 1643 Evangelista Torricelli filled a long glass tube with mercury, sealed one end, and inverted it into a dish of mercury. The mercury did not all run out; it fell to a height of about seventy-six centimetres and stopped, leaving an empty space at the closed top. Torricelli offered a radical explanation: we live ‘submerged at the bottom of an ocean of air,’ and it is the weight of that air, pressing on the mercury in the dish, that holds the column up. The empty space at the top was, he suggested, a vacuum. Pascal seized on this and saw how to test it decisively. If the mercury is held up by the weight of the air above it, then carrying the tube to a high place - where there is less air overhead, and so less weight - should make the mercury column fall lower. The idea of nature’s ‘horror’ predicted no such thing; the idea of air pressure predicted it exactly. Here was a way to force nature to choose between the two theories.
Pascal pressed on from the atmosphere to fluids in general, and arrived at the principle that still bears his name. Pascal’s law states that pressure applied to an enclosed, incompressible fluid is transmitted, undiminished, to every part of the fluid and in all directions. Push on a confined liquid at one point, and that push is felt equally everywhere. The consequences are enormous and everyday. Because pressure is force divided by area, a small force on a small piston can be turned into a large force on a large piston connected to the same fluid: this is the hydraulic press, the principle behind car jacks, brakes, and heavy machinery, by which a person’s hand can lift many tonnes. Pascal had found a law that lets fluids multiply force. Fittingly, the international unit of pressure - the pascal - is named in his honour, so that his name is now stamped on every weather report and tyre gauge in the world.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that Pascal built the Pascaline, that the Puy-de-Dôme experiment showed the mercury column falls at altitude because the air has weight (not because nature abhors a vacuum), and that Pascal’s law states pressure in a confined fluid spreads undiminished in every direction. Explain these ideas and why they m…
Leads to Rene Descartes.
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