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I can build a smaller brain.

f(x) = 0.

That's great, now make it learn something :)
It's the simplest AI nihilist!
I take your brain, add a couple more rules, and presto! It can perform any computation.

    Ix = x
    Kxy = x
    Sxyz = xz(yz)
This brain is interesting. Basically you get a no for everything you ask, right?
Yeah, this is small brain time.