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The way i understand the way you define AGI is, that the lower bound of the Spiky profile is at least on Par with the best of humanity. This way no human can say "But it cant do X as well as Mr./Mrs. Y"

The way that many other here see it is that the fact that it has lots of spikes in many different directions and some lower bounds above the level of a 10 year old, is indeed enough generality.

Probably the G in AGI is a spectrum, and it it is now a maturing process to lift the lower bounds of the spiky profile of to the best of humanity. If this will ever work with an alien intelligence is debatable. Even in the "Culture Series" the ASI had lower bounds of some skill sets that were below the best of Humanity, and thus the "Contact" department was formed, to use these humans to cover the shortcomings the ASI could not. It might indeed be our chance for a symbiosis to make up for some of these lower spike bounds.

In the end who is to say that our intelligence is not spikey, and me are just normalizing it to a circle..

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