When Apollo 11 touched down in the Sea of Tranquility on July 20, 1969, it was more than a triumph of the human spirit, it was also the story of a cybernetic wonder called the Apollo Guidance Computer (AGC), which helped the Apollo astronauts safely navigate to the Moon and back. It was a computer so advanced for its time that the engineers who created it said they probably wouldn't have tried to do so if they'd known what they were getting themselves into.
The reason why all the Apollo missions carried at least one of these computers is that the Moon missions involved navigation problems that would have made Captain Cook go bug eyed. On Earth, navigation is, at its simplest, about finding one's way from one fixed point on the globe to another. For a trip to the Moon, it's like standing with a rifle on a turntable that's spinning at the centre of a much larger turntable on which is a third turntable sitting on the rim, with all the tables spinning at different and varying speeds, and trying to hit the target by aiming at where it will be three days from now.
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