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In the Rings of Akhaten, Clara saves everybody by giving the parasite her leaf. It represented the days that her mother had, and therefore was infinitely more than normal memories, feelings etc. According to Ten

...in the present they consume the energy of all the days you might have had. All your stolen moments. They're creatures of the abstract. They live off potential energy.

So how come the Weeping Angels aren't overloaded by this kind of infinity?

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    They didn't take Clara or her leaf. Sep 22, 2015 at 1:57
  • Possibly due to the weeping angels allowing their victims to live out their normal lifespans in the past. Perhaps they are not feeding off the potential energy all at once. Sep 22, 2015 at 3:52
  • Didn't the leaf represent all the days Clara had, not her mother? Without the leaf her mother (and father) would still have existed, but she might not have. Sep 22, 2015 at 7:10

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I think the only real answer that can be given is that they are different creatures who have evolved to feed on different things. The "Old God" in "The Rings of Akhaten" is said to feed on "stories", from the transcript here:

DOCTOR: No, we didn't wake him. And you didn't wake him, either. He's waking because it's his time to wake, and feed. On you, apparently. On your stories.

CLARA: She didn't say stories. She said souls.

DOCTOR: Same thing. The soul's made of stories, not atoms. Everything that ever happened to us. People we love, people we lost. People we found again against all the odds. He threatens to wake, they offer him a pure soul. The soul of the Queen of Years.

And Clara's leaf is too much for it, because it has an infinity of potential stories, which is something the Old God wasn't expecting:

CLARA: Well, I brought something for you. This. The most important leaf in human history. The most important leaf in human history.

(The sun smiles.)

CLARA: It's full of stories, full of history. And full of a future that never got lived. Days that should have been that never were. Passed on to me.

(An energy tendril reaches for the leaf.)

CLARA: This leaf isn't just the past, it's a whole future that never happened. There are billions and millions of unlived days for every day we live. An infinity. All the days that never came. And these are all my mum's.

DOCTOR: Well, come on then. Eat up. Are you full? I expect so, because there's quite a difference, isn't there, between what was and what should have been. There's an awful lot of one, but there's an infinity of the other.

(The leaf turns into energy.)

DOCTOR: And infinity's too much, even for your appetite.

The Angels, on the other hand, are not said to feed on stories in the quote from "Blink" you provided, but on some more nebulous "energy" of the days you might have lived. And even if we do interpret that in terms of potential stories as well, the Angels are accustomed to feeding on this, the Old God is not. There is also the possibility that the Angels are only feeding on the potential of the specific span of time that was stolen, whereas the Old God would have to feed on all the infinite potential futures associated with the leaf.

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Weeping angels feed off of the energy created from sending you through time and not off of your future life. The letting you live out your life is just a bonus to not dying. David Tennant explains this in the episode "Blink". Hope I helped.

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  • The quote in AJL's question comes directly from "Blink" (full transcript here), it seems to contradict your account of what they are feeding on.
    – Hypnosifl
    Sep 22, 2015 at 5:54

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