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Houshalter comments on Open Thread June 2010, Part 3 - Less Wrong
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If your argument is based on information capacity alone, it can be knocked down pretty easily. An AI can understand some small part of its design and improve that, then pick another part and improve that, etc. For example, if the AI is a computer program, it has a sure-fire way of improving itself without completely understanding its own design: build faster processors. Alternatively you could imagine a population of a million identical AIs working together on the problem of improving their common design. After all, humans can build aircraft carriers that are too complex to be understood by any single human. Actually I think today's humanity is pretty close to understanding the human mind well enough to improve it.
I don't think the number of AIs actually matters. If multiple AI's can do a job, then a single AI should be able to simulate them as though it was multiple AI's (or better yet just figure out how to do it on it's own) and then do it as well. Another thing to note is that if the AI makes a copy of its program and puts it in external storage, it doesn't add any extra complexity to itself. It can then run it's optimization process on it, although I do agree that it would be more practical if it only improved parts of itself at a time.
You're right, I used the million AIs as an intuition pump, imitating Eliezer's That Alien Message.