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| Pascal's Law |
 Title text: Reductio ad absurdum fails when reality is absurd. |
Explanation
Pascal's law states that when a change in pressure occurs in confined incompressible fluid, it is transmitted throughout the fluid and the same change occurs everywhere. It was discovered by mathematician Blaise Pascal in 1653. This is the principle underlying hydraulics, and the diagram shows a hydraulic lift that allows a heavy weight to be lifted (on the right) by pressing with much less weight on a small amount of fluid (on the left).
Ruina montium ("wrecking of mountains" in Latin) was an ancient Roman mining technique in which small tunnels were dug into the side of a mountain. When the tunnels were filled with high-pressure water, the rock adjacent to the tunnels would fracture, making it significantly easier to remove. Thus, Randall's attempted disproof of Pascal's Law by reducing it to an absurd statement failed to work, because that absurd statement was entirely true.
Reductio ad absurdum ("reduction to absurdity" in Latin) in the title text is a form of argument in which something is assumed to be true and then this is shown to lead on to absurdity or falsehood, such that the original premise can't be true after all. In mathematics it's called proof by contradiction. In the title text, however, it is pointed out that some truly real things already are absurd, so it would be wrong to rely upon this method to conclude that they don't occur.
Transcript
- [At the left, a teacher is holding a pointer, pointing at a picture on the screen.]
- [The picture shows a hydraulic lift, with a small fluid vessel on the left connected to a tube at the bottom, which connects to a large vessel on the right. On top of the large vessel is a weight labeled 1000 and a Cueball. The fluid in the large vessel is labeled with an upward arrow. Megan's hand is over the small vessel, with a downward arrow indicating that she's pressing on it.]
- [Cueball, Hairbun, and Blondie are sitting at school desks going left to right.]
- Cueball: No, that can't be right.
- Cueball: If hydrostatic pressure worked that way, then you could use it to make machines that exert near-infinite force.
- Cueball: And ancient people could have demolished entire mountains just by drilling small tunnels and filling them with water.
- [Caption below comic:]
- When I first learned about Pascal's law, I tried to disprove it by showing that it would lead to absurd consequences, but it turns out hydraulic presses and ruina montium are both real things.
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