The argument from the small size of the genome is more plausible, especially if Eliezer is thinking in terms of Kolmogorov complexity, which is based on the size of the smallest computer program needed to build something. However, it does not follow that if the genome is not very complex, the brain must not be very complex, because the brain may be built not just based on the genome, but also based on information from the outside environment.

I think the question in the original debate could be formulated as something like: How big a solution, in the amount of program code we need to write, do we need to find to be able to implement a self-improving artificial intelligence that will, given an amount of sensory input and opportunities to interact with its environment comparable to that of a human growing up, grow up to human-level cognition.

I don't see how the other sources of information needed for brain development is a counterargument here. Once you have a machine learning system that will bootstrap itself to sentience given a few years of video feed, you've done pretty well indeed.

I don't also see how the compressibility argument is supposed to work without further qualifiers. You might drop the size of Windows Vista to a third or less if you compressed aggressively at every possible opportunity, but would you get out of the order-of-magnitude ballpark which is about the level of detail the argument operates on?

(I wanted to say here that you'd never get Vista to fit on a 360 kB floppy disk, but on second thought that would also require something like "with any kind of sane human engineering effort you could only spend a millennium or so with". If you have an arbitrary amount of cleverness for composing the program and an arbitrary amount of time running it, you get into Busy Beaver Land, and a floppy disk suddenly has the potential to be an extremely scary artifact. On the other hand, compared to eldritch computational horrors from Busy Beaver Land the human genome has had a very limited amount of evolutionary design going in it, and has a very limited time to execute itself.

(Well you would probably run into the pigeonhole principle if you wanted to get the actual Vista Vista out of the ultra-compressed thing, but for the purposes of the argument, it's enough to get a something that does all the sort of things Windows Vista does, no matter what the exact bit pattern.))