In the film of The Hitchhiker's Guide to the Galaxy, Arthur saves Ford from being run over, and later Ford saves Arthur from the Earth being demolished.
But in the original radio series and books, we don't seem to be told how the two met, and why Ford would select Arthur (of all Earth's inhabitants) to save.
Putting the film aside, did Douglas Adams ever describe anywhere the circumstances of their meeting, and why Ford chose to save Arthur?
Arthur was Ford's only real friend during the fifteen years he spent on Earth, which implies that Ford partially felt like he owed it to Arthur.
Arthur, your whole planet has been destroyed.
Arthur: Couldn't you have done something?
Ford: I saved your life.
[from the 2005 movie]
However, ultimately, it is made clear in the original radio production that Ford saves Arthur because he wants to. In fact, he is almost desperate to:
Ford: Arthur! Will you please just listen to me, I'm not fooling. I have got to tell you the most important thing you've ever heard, I've got to tell you now, and I've got to tell you in that pub there.
Arthur: Why?
Ford: Because you're going to need a very stiff drink. Now, just trust me.
[The Hitchhikers Guide To The Galaxy Original Radio Scripts, Fit The First]
Not only does Ford take the time to explain everything to Arthur, he even buys him a packet of peanuts. Ford saves Arthur from imminent death, because that's what good friends do; even when they're from Betelgeuse.
In the Infocom text adventure (which was written by Adams and Steve Meretzky, and which Adams described as representing yet another version of the Hitchhiker's canon), it is clear that Ford is originally planning to leave Arthur behind. (Over the course of the game, you are able, thanks to infinite improbability, to play out their departure first as Arthur and then as Ford.) However, when Arthur is lying in the mud in front of the bulldozer poised by his house, he sees Ford and cries out to him, "What about my home?" Ford initially thinks that Arthur is talking about the immanent destruction of the Earth, and that Arthur has found out Ford's secret. Ford quickly realizes that Arthur is actually concerned about having his house bulldozed, but he feels sufficiently chagrined that he decides he really ought to take his best Earthly friend along with him when he escapes the doomed planet.
The book is consistent with Mikasa Pinata’s answer: Ford, on his own initiative, chooses to save Arthur. If he explicitly states a reason, I skimmed over it, but here’s an excerpt from the key conversation. It occurs in front of Arthur’s house, with Arthur lying in the mud to block the bulldozers, and Ford seems to have deliberately made a special trip.
FP: Hello, Arthur.
AD: Ford! Hello, how are you?
FP: Fine, look, are you busy?
AD: Am I busy? Well, I’ve just got these bulldozers and things to lie in front of because they’ll knock my house down if I don’t, but other than that, …, well, no, not especially, why?
FP: Good, is there anywhere we can talk?
AD: What?
FP: We’ve got to talk.
AD: Fine, talk.
FP: And drink. It’s vitally important that we talk and drink. We’ll go to the pub in the village.
︙ (more discussion about the bulldozers)
FP: Listen to me—I’ve got to tell you the most important thing you’ve ever heard. I’ve got to tell you now, and I’ve got to tell you in the saloon bar of the Horse and Groom.
AD: But why?
FP: Because you are going to need a very stiff drink.
︙ (more discussion about the bulldozers)
— The Hitchhiker’s Guide to the Galaxy, Chapter 1
The back story is equally sketchy, but this is relevant:
… “None at all” is exactly how much suspicion the ape-descendant Arthur Dent had that one of his closest friends was not descended from an ape, but was in fact from a small planet somewhere in the vicinity of Betelgeuse and not from Guildford as he usually claimed.1 [Emphasis added]
Arthur Dent had never, ever suspected this.
This friend of his had first arrived on the planet Earth some fifteen Earth years previously, and he had worked hard to blend himself into Earth society—with, it must be said, some success. …
— The Hitchhiker’s Guide to the Galaxy, Chapter 1 (from before the above excerpt)
Subsequent paragraphs indicate that he (Ford) spent a lot of time drinking. Which brings us to Chapter 2, in the pub:
FP: … How long have we known each other?
AD: How long? Er, about five years, maybe six. Most of it seemed to make some kind of sense at the time.
FP: All right. How would you react if I said that I’m not from Guildford after all, but from a small planet somewhere in the vicinity of Betelgeuse?
AD: I don’t know. Why, do you think it’s the sort of thing you’re likely to say?
FP: Drink up.
The world’s about to end.— The Hitchhiker’s Guide to the Galaxy, Chapter 2
____________
1 Already quoted by Valorum.
I’ve probably thought about the ethics of Ford’s actions more than is strictly healthy, but here’s my take, supplemental to the several good answers already posted.
Ford is a genuinely good guy in an extremely difficult position. He knows that Earth is about to be destroyed, killing everyone on it. He doesn’t like that but can’t possibly stop it. Nor can really do much that’s even remotely helpful, as much as he might like to. He could tell people, but they, reasonably, would not believe him. He could persist, except that there’s very little time.
However, there’s a single person in the world to whom this doesn’t matter. If Ford tells Arthur to come along for a drink and tells him some apparent nonsense, Arthur will go along with it. Not forever, but long enough. Saving Arthur is probably the only thing Ford is capable of doing to make the situation less awful. Save one person, who happens to be his friend, because only his friend will listen to him. Arthur is probably the person Ford would most like to save, but he’s also probably the only one he can save, so he does.
For the left field answer:
Because of the infinite improbability drive.
The odds of Ford and Arthur being picked up while in space were the same as the phone number of the flat where Arthur had previously met Trillian and Zaphod. All things ultimately being ruled by phone numbers after all.
“The Hitchhiker’s Guide to the Galaxy says that if you hold a lungful of air you can survive in the total vacuum of space for about thirty seconds. However, it does go on to say that what with space being the mind-boggling size it is the chances of getting picked up by another ship within those thirty seconds are two to the power of two hundred and seventy-six thousand, seven hundred and nine to one against. By a totally staggering coincidence, that is also the telephone number of an Islington flat where Arthur once went to a very good party and met a very nice girl whom he totally failed to get off with—she went off with a gate-crasher. Though the planet Earth, the Islington flat and the telephone have all now been demolished, it is comforting to reflect that they are all in some small way commemorated by the fact that twenty-nine seconds later Ford and Arthur were rescued.”
Ford was always going to rescue Arthur because they were already caught up in the infinite improbability field created by the drive. Any other reasons he might have had were simply justifications to himself. Free will is an illusion. Lunch time doubly so.
"Trillian, is this sort of thing going to happen every time we use the infinite improbability drive?"
"Very probably, I'm afraid."
Ford never meant to be stranded on Earth for 15 years, and Arthur was probably the only one who acted like a friend to him instead of thinking him a madman for his ramblings about looking for green flying saucers. He owed him.
Or maybe Ford just wanted to save him because yes.
