I'm confused about why the existence of algae and humans doesn't already resolve this YES the way it's defined. We're nanomachinery too.

The goal of this market is to asertain whether something like the "self-replicating nanobots" of science fiction are possible. The sort of robots that could easily wipe out humanity, terraform planets, and act as the ultimate manufacturing system for whoever controls them.

Algae can't build any physical object in less time than it would take our current human civilization to build it, and humans aren't less than 1mm in length.

@IsaacKing Are eukaryotic cells not allowed to build a human or aggregate into one?

@EliezerYudkowsky 4 billion years is quite a bit longer than it would take our current human civilization to build any given object.

@EliezerYudkowsky Points for effort though

What counts as an "arbitrary schematic"? Would it have to be able to e.g. forge a 1 mm Tungsten sphere from unrefined Tungsten ore? Ore contaminated with Plutonium? Is there an information limit to the size of the schematic?

Those both seem like perfectly reasonable and achievable tasks, so yes.

No information limit, but of course the entire schematic doesn't need to be stored in a single bot; there can be an external computer coordinating them, or distributed computation across the swarm.

@IsaacKing How many steps removed is the final product allowed to be from the bots? With arbitrarily many steps, it seems trivially possible to manufacture anything humans can make (though not necessarily faster), since you could just implement a Turing machine and run an AGI on it.

@adele Yeah that's fine. If the nanobots can build a functional computer, I think it's a safe assumption that they can build anything else.

@IsaacKing You've suddenly made this question a lot less interesting. A functional computer can be made with a wide variety of materials and processes. And the most basic tools for macromanipulation are even more flexible.

At this point being faster than humans really depends on the tools the humans and nanobots start with and the optimization power behind them both to be able to design the process to build the object.

@Imuli I don't really see how this makes things less interesting? If the nanobots impliment an AGI, how does the AGI begin building the thing unless it's directing the nanobots to begin construction?

The market resolves once our knowledge of physics and engineering is sufficent to have a definitive answer to the question.

A formal existence proof would make this resolve YES, without demonstration or even a concrete blueprint?

@ScottLawrence If the scientists are confident that the proof is correct, yes. I'd even accept a non-formal proof, in the form of a strong scientific consensus that it's possible. (Similar to how everyone agrees that sending a human to Mars is possible in theory, despite it never having happened yet.)