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Well just bigger might not cut it, the biggest brain we know about already has about almost 10 kg of weight (belongs to a whale). We want better, not bigger.

You say it yourself, there was no intelligent hand involved in the creation of brains (but another process called evolution). This just supports my point that a GI system creating a better GI system to our knowledge has not yet happened.

I agree there's no mystical barrier, but maybe a conceptual: is there a limit to our cognitive capabilities that prevents us from designing something better than us? I don't know, but it hasn't been disproved yet either.