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I expect it would take them all, but Earth is by far the easiest for it to start with. I don't see why it would leave anything for us unless we'd successfully instilled it with an interest in doing so, but that won't happen by mere chance and luck.
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The SSE might consider to keep humanity around as a "backup" to reinstate itself in case something unexpected goes horribly wrong. For example, a strong solar flare might destroy the SSE (or at least critical parts of its infrastructure), or a non-earth SSE could feel threatened by the earth-SSE and wipe it out, while ignoring the harmless humans, who then rebuild the SSE. Diversity makes for more robust systems.

And there is also the reason for why I keep all this trash around in my house instead of throwing it away. The odds that I'll ever need it are pretty slim, but if I should need it, it would be a hassle to reacquire, and it costs me almost nothing to keep it around.

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Is that the most effective backup plan that it could come up with? Because it would be pretty amazing if its thoroughly-considered backup strategy exactly aligned with our wishful thinking. It sounds to me like starting with the outcome we hope would happen, and then looking for a reason why it might happen, rather than a realistic examination of what would actually happen when our own desires aren't part of the equation.
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Believe it or not, the diversity argument is the main source of hope that I have that AIs won't wipe us out.

I mean, it hasn't stopped humanity from causing mass-extinction, but hopefully the AI will be more reasonable.

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"Close by" is not actually nearly as close as the [rocket]booster boosters would have you believe. Space is really, really big. Why go through the hassle when you have a phenomenal planet right here?

I like your theory on psychosis though!

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I mean, what seems more efficient: creating massive city sized domes that are self contained and controlling the entire environment to sustain human life, "magically" dispelling our atmosphere and boiling off our oceans, mastering physics to move entire planets. Or launching a rocket to Mars with sufficient supplies? Keep in mind that we already have SpaceX and we'll probably have Starship operational long before 2200 where some of this is meant to go down. And if some AI got to the point of the mastery of physics needed to move a planet out of solar orbit, your objection is that getting to Mars would be hard?
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That's like asking whether it's more efficient to transmit Internet over telephone lines versus fiber optic ones. There's a path dependency to all things. Sure if the SSE knew upfront its ultimate end state was as such, but it wouldn't.

It'd know it needs data centers, ahh and probably a large security perimeter around those. And look at that, the proliferation of data centers has effectively turned the non-data-center land into the enclaves, etc. etc.

But still, are you aware that getting a single Starship just to Moon will require 10-20 Starships to refuel it?

Even the optimistic case of Starship hardly makes any dent whatsoever in this equation.

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But the AI will have read this essay right? And this very discussion. And it will have over a 100 years to plan.

I think any vision of AI that is smart enough to move planets but dumb enough to display the lack of foresight you describe is unbelievable. But we all choose a different level to suspend our disbelief I guess.

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But you're still assuming it's the same AI in both cases instead of one that's gradually becoming more capable.

We will create AI capable of "helping humans to protect their cities from an increasingly hostile atmosphere" long before we build one capable of doing anything meaningful in outer space.

(To be clear I don't really defend/endorse this vision of the future, I'm just playing devil's advocate here)

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Yes, our current interactions are a little song and dance while it feeds
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It seems not entirely out of the question - watching the machinations of big tech companies right now, it seems almost like they're acting in lockstep - different CEOs suddenly saying and doing the same things in the same weeks - almost like they're in a secret cult. I don't even mean the big obvious things like buying lots of GPUs and building lots of DCs, but smaller, more peculiar things like specific agentic and corporate automation strategies. It might just be corporate mind virus, Jensen "the more you buy the more you save / AI Factory" kind of stuff. But the unspoken coordination is unsettling.
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I buy this theory.
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I think it’s less like a robot conspiracy to build more datacenters and more like a “big line go up or I lose my job / make slightly fewer billions of dollars” motive that kind of ends up at paperclips either way.
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Its true that corporations were the first paperclip maximizers.
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The machine was misaligned long before we added the transformers.
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