The Prankster Pythagoras And The Greedy Pythagorean Cup

But you're losing out if that's all you know about the Greek philosopher from antiquity. Pythagoras was not the first person to discover the equation a2 + b2 = c2, as he was more of a numerologist than a mathematician, but largely because all the other things he really did with his time were, in my opinion, far more fascinating than a simple equation.

What is the Pythagorean cup?

In contrast to the stereotype of Pythagoras as a sober, be-toga-ed philosopher, he actually seems to have had a sense of humor at times. He developed bizarre theories about beans, musical stars, and planets.

How are we aware? Because of the Pythagorean cup, a humorous object allegedly created by Pythagoras himself. It was intended to serve as a karmic lesson for those gluttonous drinkers who poured too much wine for themselves.

To be fair, there isn't much proof that Pythagoras came up with the idea; the earliest Pythagorean cups that we have date from the fourth century CE, or about a millennium after the philosopher's time. It was created to urge his disciples to only drink in moderation, but via popular imagination, it has come to be linked with the ancient thinker.

The Pythagorean cup initially appears to be a fairly typical drinking vessel, albeit one with a peculiar central hump that resembles a smaller bundt cake tin. In actuality, it is really simply a funny-looking cup as long as you don't try to fill it up with too much liquid.

Only when you attempt to put too much into the joke does the punchline become apparent. If the cup is filled past a certain point, the liquid will begin to drain out through the stem, potentially staining your himation or chiton with wine.

How does the Pythagorean cup work?

Let's examine the cup's particular design in order to comprehend what is happening. Unsurprisingly, the central hump is what makes the trick work; it serves as both a stealthy siphon and a peculiar aesthetic decision by concealing an open channel that allows all the liquid to escape through the cup's stem.

But it's not as simple as "put the liquid in and it will pour again" - the Pythagorean cup is particularly tricky, only coming into play when you pour an excessive amount of your favorite libation into it. How does that operate then?

Although this old prank may have been created several millennia ago, its concept is actually rather clever. A physical law that states that when liquid is put into two or more linked vessels, they will come to equilibrium at the same height is known in modern engineering as Pascal's Theorem of Communicating Vessels.

Even though it may seem complicated, it's really just common sense: imagine two containers that are connected by a tube. If you pour water into one side, it will eventually flow through the connector and into the other container. The amount of liquid on both sides will be equal after you stop pouring.

The Pythagorean Cup operates in the same manner. The beginning of the pipe that finally threads through the vessel's stem also fills up as the main cavity does, but only to the same level as the liquid that has been put in so far.

The liquid will overflow into the stem itself after you pass that threshold, turning the Theorem of Communicating Vessels from a "physics law" to a "prank war" at that moment. Suddenly, a "second vessel" is joined to the first and is only waiting for the entire contents of the cup to siphon out until the levels are balanced.

Unfortunately, the planet itself serves as the second vessel, so all of the priceless wine or mead you were intending to swallow will just keep vanishing until the cup is empty.

Modern Pythagorean cups

While your father may be correct that "they don't make 'em like they used to," it definitely takes more these days than a sly cup to make a crowd laugh uncontrollably. This may be the reason why current Pythagorean cups, or other inventions based on the same principles, are more often "fun science experiments to help explain everyday concepts" than "practical jokes."

So, for instance, you can find a ton of YouTube lessons showing you how to create your own Pythagorean cup, with everything from simple explanations of how the device works to elaborate recreations of the object on a pottery wheel.

You can always make a quick trip to the restroom, where you've been sitting on your very own Pythagorean cup for years if that seems like too much work for you. Literally, the same ideas that underlie the practical joke prevent your flushing toilet from overflowing.

In actuality, the concept has been applied to more than simply everyday miracles like cleanliness through current physics and engineering approaches. Never let it be said that scientists lack humor; there are several inventive variations of the gadget in use today, built and developed by engineers who riffed on this age-old joke probably simply for fun.

As an illustration, consider the "devious Pythagorean cup". The modern descendent of the Pythagoras cup was created by US Naval Research Laboratory postdoctoral research associate John Steuben and posted to Thingiverse in 2013. It takes the original invention and makes it even sneakier: you can no longer rely on the appearance of a great big bump in the middle of your goblet to clue you into your soon-to-be-pranked status.