Why does space shuttle fly up with its belly upward and its back downward (i.e., astronauts sitting upside down)?
One reason is to protect against space debris. Here on Earth, most of the space junk (small rocks and ice, etc.) that falls towards the planet burns up in the atmosphere before it can get to us. The space shuttle is outside the atmosphere, though, so it is much more exposed to debris (which may be traveling at very high speeds). The space shuttle's belly is designed to take intense heat and pressure so that it doesn't fall apart when it re-enters the atmosphere, and is therefore much better suited for taking hits from flying space junk.
Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN
Not only does the Space Shuttle fly with the windows pointed towards the Earth (upside down)... but it flies backwards as well. The tail of the spacecraft precedes the nose. The reasons for this are simple. First off, is the sun. The sun has immense amounts of radiated power in space, where there's no atmosphere to protect the humans. Putting the spacecraft with it's bottom to the Sun means that the heat-resistant tiles on the bottom are the most exposed to the full power of the Sun, thus keeping the astronauts safer and cooler than they would be otherwise. Second, the cargo bay. Again for reasons related to the sun, and more importantly, for reasons related to space junk and micrometeriods, the cargo bay is shielded as much as possible, by the body of the Shuttle. Third, propulsion. When the Shuttle prepares to depart it's position orbiting the Earth, the first thing it must do is slow down. The Shuttle is slowed by firing the two smallest of the five nozzles on the back of the craft. The deceleration provided 'flips' the Space Shuttle over by standing it on end, which puts the belly down. Having the belly face the atmosphere is important, because now those same tiles are required to shield the astronauts from the heat of re-entry. Remember - the astronauts have no concept of sitting 'upside down'. There's no gravity, and thus, no 'up' in the standard sense. The Space Shuttle can fly any way it wants to, and the astronauts don't know the difference.
Frank DiBonaventuro, B.S., Physics grad, The Citadel, Air Force officer
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'