It only takes a tiny percentage to turn down said machine. If 10 billion people plug-in, but 1 million abstain and continue to evolve past the 10 billion, the majority stagnates. Those 1 million will eventually gain a competitive advantage over the 10 billion, evolve past them, and likely extinct them.
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Prediction: Humans won't be around in 1,000 years if technology progresses at current rates. Superiorly-intelligent entities seeded by our inventions will, but not humans.
Humans are this weird, version 0.01 of intelligence. We're part sentient, part beast. To assume we're the final perfect end product of ~4,000,000,000 years of evolution, having only been around for ~200,000 years is laughable. Pop culture and religion say otherwise because it feels good to think "we're special!", but we're only special relative to what's around us, and we're "extremely" tiny (http://www.phrenopolis.com/perspective/solarsystem/). We just happen to be the lucky first who got to v0.01, floating around on a grain of sand.
Humans are messy. Our brains are significantly limited. We die quickly. We sleep 1/3rd of our life. We do stupid things. We kill each other. We're tied to the Earth. If we leave Earth, we have to create and bring a mini-Earth along for the ride. That's an extremely large amount of overhead to carry. Efficient use of energy is likely one of the most important aspects of space travel. Anything which can do it even 1% better has a competitive advantage over us. This is why we sends robots to Mars and not people.
Imagine a form of intelligence which can travel through space, back its brain up, and never dies. If it blows up, restore from backup. Imagine a computer the size of the sun. INSANE! A human brain to a sun brain is like a grain of sand to Einstein's. It self-upgrades. It makes copies of itself and scatters throughout the universe. Trillions of eyes observing everywhere, networked together, in a giant universal wireless-mesh-network of intelligence, communicating with neutrinos (they go through planets, radio waves do not).
Major advances in hardware, software, and A.I. are key ingredients in this happening. What exists in 1,000 years will be derived from all this, much like humans are derived from a common ancestor. I don't expect a sun-sized computer in 1,000 years, but likely "intelligence" existing on every planet and moon in our solar system, with many headed to explore Alpha-Centauri.
Since humans likely won't want to be left out in all this, we'll probably transition our own intelligence/consciousness into this technology. We'll depreciate our bad and carry along our good. We're already doing this by augmenting our existences with smart phones and other gadgets. One day these will be built inside of us, and eventually will replace us. An upgraded, better version of us. Still intelligent, but vastly more-so.