You will need: a single von Neumann machine
Method: A von Neumann machine is any device that is capable of creating an exact copy of itself given nothing but the necessary raw materials. Create one of these that subsists almost entirely on iron, magnesium, aluminum and silicon, the major elements found in Earth's mantle and core. It doesn't matter how big it is as long as it can reproduce itself exactly in any period of time. Release it into the ground under the Earth's crust and allow it to fend for itself. Watch and wait as it creates a second von Neumann machine, then they create two more, then they create four more. As the population of machines doubles repeatedly, the planet Earth will, terrifyingly soon, be entirely eaten up and turned into a swarm of potentially sextillions of machines. Technically your objective would now be complete - no more Earth - but if you want to be thorough then you can command your VNMs to hurl themselves, along with any remaining trace elements, into the Sun. This hurling would have to be achieved using rocket propulsion of some sort, so be sure to include this in your design.
So crazy it might just work.
Earth's final resting place: the bodies of the VNMs themselves, then a small lump of iron sinking into the Sun.
Earliest feasible completion date: Potentially 2045-2050, or even earlier.
Source: "2010: Odyssey Two," by Arthur C. Clarke
Notice the source. The great Arthur C. Clarke, who passed away yesterday, perhaps out to begin another Odessey.
So VNMs are machines that are capable of producing another VNM. Can a human being be one VNM ? Perhaps no. The VNM is not supposed to die. Then, the virus? Doesn't die but is capable of reproducing. ( Well, that's also a debate). How about amoeba? It reproduces in a very interesting way - binary fission. At some point of time, (when it feels like) the single cell organism just divides into two cells, two independent organisms. So as long as it gets its food, it can continue this process, and some day consume the entire raw material source - the earth. But all the silicon and magnesium and iron may not be edible. So as long as they don't get adapted to this kind of diet, the earth seems to be safe from them.
But lets cross-examine that assumption of death. Why is the VNM not supposed to die? It can very well die and be the Frankenstein it is supposed to be as long as the rate of creation is greater than the rate of death. And that can be assured in the design phase itself. Or maybe the version 2 of such machines can be made adaptable to their limiting factors - lack of raw materials etc. They can be made to have a science of themselves.
Just like us the human beings. We are fast working towards ensuring that our rate of survival is greater than the rate of death, that we can make best exploitation of the resources. We sure will win one day discovering newer ways of using all the silicon-iron-magnesium that there is in a process that outputs more of our kind.We will win against disease, death and war, and will become the VNMs ourselves.
All this even if we put no efforts in building the VNM.
(Also look at the time-line Clarke suggested.)
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