  Can an AGI create a more intelligent AGI? Under idealized assumptions, for a
certain theoretical type of intelligence, our answer is: "Not without outside
help". This is a paper on the mathematical structure of AGI populations when
parent AGIs create child AGIs. We argue that such populations satisfy a certain
biological law. Motivated by observations of sexual reproduction in
seemingly-asexual species, the Knight-Darwin Law states that it is impossible
for one organism to asexually produce another, which asexually produces
another, and so on forever: that any sequence of organisms (each one a child of
the previous) must contain occasional multi-parent organisms, or must
terminate. By proving that a certain measure (arguably an intelligence measure)
decreases when an idealized parent AGI single-handedly creates a child AGI, we
argue that a similar Law holds for AGIs.
