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Grey goo is a fun idea but doesn’t really work.
Radiation would cause replication errors in the nanobots, eventually leading to speciation. Before you know it you just have an ecosystem again, with a whole food chain of butt eradicators and paperclip maximizers.
I don’t think this is necessarily true. The reason DNA is so affected by radiation is because it’s malleable. It’s built out of chemical building blocks that fit like Lego. Gray goo would likely be similar to extremely complex proteins which replicate like a physical version of a quine.
Flipping an individual bit through radiation is extremely easy, which is why we need error corrections, but despite that, we still get errors… Even if the probability of an error bypassing the ECC is extremely low, over a long enough timescale it will happen often enough to evolve. Especially in space where there is no atmosphere or magnetic field to reduce it.
