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Pythagoras' Cup

Sometime around 570 BC, Pythagoras of Samos[1] was born. Famous as an ancient Greek philosopher, mathematician, and founder of the Pythagorean brotherhood. The latter, although religious in nature, formulated principles that influenced the thoughts of Plato and Aristotle, and contributed to the development of mathematics and Western rational philosophy.

Pythagoras is also credited with making a cup (a modern replica is shown right) that, by applying the laws of physics, teaches us to drink wine in moderation. It is also called "the Cup of Justice"[2] because it reflects one of the basic principles of ancient Greek law, that of "hubris"[3] and "Nemesis"[4]. When the limit is exceeded (hubris), not only what has exceeded the limit is lost, but also everything previously acquired (Nemesis).

How it works A Pythagorean cup looks like a normal drinking cup, but within the one shown right you can just make out the domed top of a column set at the cup's centre. This is actually a hollow tube, positioned directly over the stem of the cup and over a hole at the bottom of the stem. As shown in "A" below, this tube runs almost to the top of the central column, where there is an open chamber. The chamber is connected by a second pipe to the bottom of the central column to create a U-bend, the sort of thing you find in a modern toilet.

When the cup is filled, its liquid content can enter the second tube and rise up it to the chamber at the top of the central column[5]. As long as the level of the liquid does not rise beyond the level of the chamber, the cup functions as normal ("B"). If someone greedily pours a liquid (of uniform density) to above the height of the column, as shown in "C" above, then gravity creates a siphon through the central column, causing the entire contents of the cup to be emptied through the hole at the bottom of the stem ("D").

With a single application of hydraulics, Pythagoras teaches us to accept moderation. Enjoy the wine you already have in your cup and, by not being greedy, derive the maximum benefit from it.


1. Samos is a Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, which was called Ionia by the ancient Greeks.

2. Also known as a Pythagoras cup, Tantalus cup, Greedy Cup, or Cup of Justice.

3. For the ancient Greeks, hubris came to be defined as the overconfident, self-important presumption that leads a person to disregard the divinely fixed limits on human action in an ordered cosmos.

4. In ancient Greek religion, Nemesis is the goddess who enacts retribution against those who succumb to hubris (arrogance before the gods).

5. Following Pascal's principle of communicating vessels.


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