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Last August, as a team at the North Pole prepared to plunge more than two miles to the bottom of the Arctic Ocean, some of the dozens of specialists who staged the dive engaged in a time-honored ritual: drawing on foam cups, decorating more than 100 of them.

The cups were then gingerly sent into the deep. During the historic dive, led by Russian scientists, the pressure of the surrounding water crushed the cups to the size of thimbles, also squeezing their whimsies of writing and drawing.

Afterward, the tiny cups became instant mementoes of the polar dive, offering striking proof of the descent into an unfamiliar zone and silent testimony to the crushing power of plain old water.

“The real North Pole,” read one cup’s shrunken writing. “Explore the abyss,” another urged.

Deep explorers have made thousands of such keepsakes over the decades, and more recently, schools have joined the fun as a way to drive home some of the peculiarities of a planet where very deep water covers some 65 percent of the surface.

For example, in 2001, a third-grade class at Harding Elementary School in Corvallis, Ore., decorated 28 foam cups with bright fish, happy faces and American flags. The scientist father of one of the students then sent the cups into the depths of the Indian Ocean, shrinking them into small trophies for a lesson on the crushing weight of deep water.

A comparison to air pressure helps. At sea level, atmospheric pressure is 14.7 pounds per square inch. The deeper the dive, the greater the water pressure. At the resting place of the Titanic, more than two miles down, the pressure is 2.8 tons per square inch. That constantly bears down and tries to obliterate any void.

The pressure on any object in the deep sea, as at sea level, is uniform. It presses from above, below and the sides. That is because the molecules making up fluids (which in physics include both gases and liquids) are free to move about and transmit force in all directions.

Sea creatures are made primarily of water, which is virtually incompressible. So they escape destruction in the abyss.

But the high pressure causes most cavities and hollows, like human lungs, to collapse. So, too, with foam cups. They are almost all void since the foam is 95 percent air, according to the American Chemistry Council. As pressures build during descent, the air slowly compresses and the cups shrink.

Explorers of the deep escape slow torture by descending in small craft known as submersibles. A super-strong personnel sphere protects a pilot and two observers, who peer out through tiny portholes made with extraordinarily thick windows. The air pressure inside is the same as at sea level.

In its early days, Alvin, a pioneering American submersible, often carried outside its crew sphere compressible items like cork bricks and foam balls, cups and wig holders (to make shrunken heads), according to “Water Baby,” a profile of the craft.

“It’s an old trick,” the author, Victoria A. Kaharl, wrote, adding that the pressure of the deep makes “perfect miniatures.”

But the experimentally minded on such expeditions were also tempted to see what might withstand the pressure, and in at least one instance sent down a raw egg.

Filled with incompressible fluid, Ms. Kaharl wrote, the egg returned to the surface “perfectly intact and edible, but salty.”

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