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In The Hungry Earth, where Amy, Rory and The Doctor visited a drilling site a couple on the ridge waved to them.

The Doctor says that that's them 10 years in the future. But if Rory and Amy are sent back to the 40's by the Weeping Angel, how could that have happened?

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    Timey wimey, wibbily wobbily....? – sumbuddyx Apr 14 '14 at 9:29
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    Time can be rewritten? – Mac Cooper Apr 14 '14 at 9:44
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    Its Wales, was probably their cousins who look exactly like them – Marriott81 Apr 14 '14 at 11:40
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    @sumbuddyx: I hate that quote. It just answers everything. – Voldemort Apr 14 '14 at 12:15
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    Maybe Peter Capaldi at some time missess them, figures out that he can land the TARDIS outside the city, get in a cab, and take them for one last adventure ! – Rick Sanchez Jul 10 '14 at 19:55
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It's because the arrival of the future Rory and Amy in "Hungry Earth" doesn't create a fixed point, whereas the Doctor learning about their deaths (in "Angels Take Manhattan") does.

It's the nature of 'Who' that certain interactions can create a specific event that must take place in order for the future to unravel in the correct way. This event is described as a fixed point and can never be changed without massive (and potentially catastrophic) disruption to space and time.

Given that New York already a hot spot for temporal activity, it seems that because the Doctor is unable to rescue them immediately, their presence will have such a substantial effect on the world that removing them later (for example by travelling to another point nearby and travelling in space to their location) will still have a considerable impact.

By comparison, their standing at a great distance and viewing their younger selves doesn't have enough of an effect on the timeline to qualify as a fixed point. The future can be violently altered without affecting the rest of the universe since their presence (or not) doesn't make that much of a difference to the world.

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    The fact that this isn't a fixed point is supported in episode, for those wondering: The Doctor does explicitly say the events of "Hungry Earth" are not a fixed point. – Mac Cooper Apr 14 '14 at 14:03
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    "AMY: Hey, let's go and talk to them. We can say hi to future us. How cool is that? DOCTOR: Er, no, best not. Really best not. These things get complicated very quickly, and oh look. Big mining thing. Oh, I love a big mining thing. See, way better than Rio. Rio doesn't have a big mining thing. " – Valorum Apr 14 '14 at 15:32
  • @Mac Cooper: Yes, but in that case, he was referring to the potential deal between humanity and the Silurians, not necessarily the hill sighting. Although really, the hill sighting should be a fixed point, since it's just as much witnessing their own future as reading the Melody Malone book or seeing their own gravestones is. – Amy Apr 14 '14 at 16:22
  • It's obviously not a fixed point, because events in that episode change the sighting on their way back... (and then The Big Bang changes everything again, so the original sighting could be possible) – Adeptus Mar 2 '15 at 4:06
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In "The Power of Three" (S07E04, the episode before "The Angels Take Manhattan"), Amy says that she and Rory have been travelling with the Doctor for 10 years.

We think it's been ten years. Not for you, or Earth. But for us. Ten years older, ten years of you. On and off.

(Timestamp 04:24-04:33)

This means that they could have already gone back and waved to their 10-years-younger selves.

6

Time travel.

The went back and waved to themselves sometime after this episode (probably during their anniversary trip in "The Power of Three", since Amy mentioned in that episode that she and Rory had spent a total of about ten years together in terms of time on Earth + time on the TARDIS by that point, which aligns with the Doctor's estimate of the Amy and Rory on the hill being from ten years in their future, and it fits his comment about them feeling nostalgic), but before the events of "The Angels Take Manhattan".

2

Shortly thereafter, the Eleventh Doctor arrives in Cwmtaff with Amy Pond and Rory Williams, having promised them a vacation in Rio de Janeiro, missing by several thousand miles; the TARDIS has brought them to the wrong place yet again, much to the annoyance of the companions. As they look across the valley, Amy spots two figures waving at them from the opposite hillside. It is Amy and Rory from ten years in their future, coming back to revisit past glories. Though she finds this "interaction" with her future self thrilling, Amy still wants to go to their intended destination.

The revisiting of "past glories" must have happened in between the events of two episodes. You mustn't forget that sometimes there can be a big gap in between episodes, of which we can only speculate what happened. Also, "The Hungry Earth" is the eighth episode of the fifth series, and "The Angels Take Manhattan" (in which Amy and Rory get sent back in time) is the fifth episode of the seventh series. A lot of time in between, 'ey?
Some people think that it was actually their future selves warning them for something, and not waving at them.

Well, whatever the case, I am sure it has nothing to do with and it doesn't interfere with the unlucky events in "The Angels Take Manhattan".

Besides, their future selves were standing quite far away from their present-day selves, so the distance wouldn't have been enough to create a fixed point in time. Also, they didn't talk to each other, while Amy did say farewell to the Doctor in The Angels Take Manhattan, thus creating a fixed point.

Speculation alert!!!

  • just to clarify: are you saying that perhaps /The Angels take Manhattan/ takes place more than 10 years after the mining incident? That is, that they went through the mining incident, ten years later (From their P.O.V, not the location's P.O.V [the episode takes place in 2020]) waved to themselves, and then some time after the waving they ended up back in the 40's? Not discounting the theory, of course, just asking if that's what your theory is. – Mac Cooper Apr 14 '14 at 11:32
  • @Mac No, no, I don't want to make that impression, I just mean that the two episodes have little to do with eachother in those aspects. – nidunc Apr 14 '14 at 16:29
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In The Angels Take Manhattan the Doctor had mentioned that Amy was looking older. So perhaps they were having long gaps in between adventures with the Doctor. We don't know specifically when that Amy and Rory were taken from so it could have easily have been after The Hungry Earth time.

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    Whilst this has hints at the start of an answer I'm not quite sure what your actual answer is here. Could you edit this to be clearer? – TheLethalCarrot Jan 18 at 14:26

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