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In The Restaurant at the End of the Universe, Arthur, Ford, Zaphod, Trillian, and Marvin have just stolen Hotblack Desiato's stunt ship after leaving Milliways and traveled into the past 2 million years before their own time.

”Trouble is,” said Ford, ”that the one instrument in this whole ship that is giving any reading is worrying me. If it is what I think it is, and if it’s saying what I think it’s saying, then we’ve already gone too far back into the past. Maybe as much as two million years before our own time.”

As they realize that this ship is about to crash into the sun, they discover a teleportion device (their only means of escape) and leave Marvin behind to control it so they can escape despite the fact they have no idea where they might end up. Arthur and Ford end up on the Golgafrincham ship which shortly thereafter crash landed on pre-historic Earth (i.e. roughly 2 million B.C.), and Zaphod and Trillian end up back on The Heart of Gold.

”I trust you had a pleasant meal?” said Zarniwoop to Zaphod and Trillian as they rematerialized on the bridge of the starship Heart of Gold and lay panting on the floor.

As I understand from the beginning of the book, at this point the Heart of Gold had been left with Zarniwoop alone on the ship in Arthur's "own time" (in the 1980's). There doesn't really seem to be any explanation as to why the teleportion device sent Zaphod and Trillian 2 millions years into the future as far as I can tell.

So, am I misinterpreting something to the story and the gang really left The Heart of Gold 2 million years before their own time, or did the teleportion device also act as a time machine when Zaphod and Trillian stepped into it? Or perhaps did Zarniwoop have The Heart of Gold travel back in time?

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    The odds of the Heart of Gold slipping back in time and picking up Zaphod and Trillian are extremely long. In fact, I would say almost infinitely improbable... – evilsoup Aug 3 '13 at 9:55
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    Oh dear, I hadn't thought of that (promptly vanishes in a puff of logic). – Drew Chapin Aug 3 '13 at 19:39
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It is the Improbability Drive that picked them up. As Trillian tells Zaphod when they pick up Ford and Arthur in THHGTG:

"Improbability Drive," she said patiently. "You explained it to me yourself. We pass through every point in the Universe, you know that."

So every point in the universe can be anywhere/anywhen in time-space. As evilsoup pointed out, it is just very very improbable (i.e. piece of cake for the Heart of Gold).

Also, note that in the Wikipedia entry Technology in The Hitchhiker's Guide to the Galaxy it is noted that:

Karey Kirkpatrick, who with Adams (before his death) adapted the novel for the screen in 2005, described the improbability drive as a "plot contrivance machine", allowing Adams to construct elaborate plotlines based on coincidences that would, in other narratives, be considered too improbable to be believed.

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Strictly speaking, anything that can bypass the fabric of spacetime to move from one place to another instantly should be able to move through time as well... at least according to the interpretation most commonly used when considering such things.

Examples that occur to me, off the top of my head:

  • are the H2G2 emergency teleport you mention
  • Stargate instances of wormholes hitting solar flares, used on a number of occasions
  • Pernese dragons going Between and ending up in different times as well as places
  • Star Trek was mostly good in avoiding teleporters shifting through time, but there's the time portal in The City on the Edge of Forever and a lot of instances of wormholes misbehaving in their temporal characteristics.
  • Dr Who is so full of examples that I'm not even going to pick one

I would agree that the probability of Zaphod and Trillian falling through time (which in some versions is how they got to the Restaurant in the first place) and ending up right where they started is infinitely improbable... or at least a very large finite improbability. As she said, the likelihood of such things happening is "quite probably, I'm afraid" :p

Also, as I can't comment with my present rep level, I'd like to agree with @Zottek that the Heart of Gold is literally a plot device heh.

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