The saying is "Dig a hole clear to China," with the idea that China is on the opposite side of the world from us.
But as you can learn by having fun on this online "Antipodean Map" page, China is actually not directly on the other side of the world from the United States. "Antipodes" is the name for two points that are directly opposite each other on a solid object. New Zealand and Australia are called that because when they were first discovered by Europeans, they were considered to be "the other side of the world."
Someone who wanted to dig a hole through the Earth and come up in China would have to do two things:
1) Figure out how to survive the incredible heat and pressure of the Earth's core, and
2) Start in South America
Almost any straight line from the continental U.S. directly though the center of the Earth will wind up in the Indian Ocean. We have almost no antipodean land, in fact. Granada, CO, is the antipodes for the Íle Amsterdam, about halfway between Madagascar and Australia. It's home to a research station with about 30 workers who rotate on and off. Íle Saint-Paul, about 50 miles away and even smaller, is the antipodes for Cheyenne Wells, CO. Its research facility is not even permanently staffed.
Until someone fixes that whole temperature (just shy of 10,000º F) and pressure (3,600,000 atmospheres) thing, though, it'd probably make more sense to fly or take a boat.
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