During a recent trip to the bookstore, I picked up a copy of A Brief History of Time by Stephen Hawking. One passege I read confused me a bit...

Another prediction of General relativity is that time should appear to run slower near a massive body like the Earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher the frequency. As light travels upward in the Earth's gravitational field, it loses energy, and so its frequency goes down. This means that to someone high up, it would appear that everything down below was taking longer to happen. This prediction was tested in 1962, using a pair of very accurate clocks mounted at the top and bottom of a water tower. The clock near the bottom was found to run slower, in exact agreement with general relativity. Consider a pair of twins. Suppose that one twin goes to live at the top of a mountain, and the other stays at sea level. The first twin would age faster than the second. Thus, if they met again, the first one would be older than the other. In this case, the differance in ages would be small, but it would be much larger of one twin went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be much younger than the one on Earth.

At first, he says that the clock at the top of the tower, (Furhter from Earth's gravity), is moving faster than the one nearer the bottom (Closer to Earth's gravity), and the twin in the mountains ages faster than the one at sea level. But then he says that If a twin went into space (Further from Earth's gravity), he would be younger than the one on Earth (Nearer Earth's gravity). Why doesn't the one who goes into space age faster? is there something here I missed? Any help would be appreciated...
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"The first Human who hurled an insult instead of a stone was the founder of civilization." -Sigmund Freud