When I lecture on the Singularity, I often draw a graph of the "scale of intelligence" as it appears in everyday life:

But this is a rather parochial view of intelligence. Sure, in everyday life, we only deal socially with other humans—only other humans are partners in the great game—and so we only meet the minds of intelligences ranging from village idiot to Einstein. But what we really need to talk about Artificial Intelligence or theoretical optima of rationality, is this intelligence scale:

For us humans, it seems that the scale of intelligence runs from "village idiot" at the bottom to "Einstein" at the top. Yet the distance from "village idiot" to "Einstein" is tiny, in the space of brain designs. Einstein and the village idiot both have a prefrontal cortex, a hippocampus, a cerebellum...

Maybe Einstein has some minor genetic differences from the village idiot, engine tweaks. But the brain-design-distance between Einstein and the village idiot is nothing remotely like the brain-design-distance between the village idiot and a chimpanzee. A chimp couldn't tell the difference between Einstein and the village idiot, and our descendants may not see much of a difference either.

Carl Shulman has observed that some academics who talk about transhumanism, seem to use the following scale of intelligence:

Douglas Hofstadter actually said something like this, at the 2006 Singularity Summit. He looked at my diagram showing the "village idiot" next to "Einstein", and said, "That seems wrong to me; I think Einstein should be way off on the right."

I was speechless. Especially because this was Douglas Hofstadter, one of my childhood heroes. It revealed a cultural gap that I had never imagined existed.

See, for me, what you would find toward the right side of the scale, was a Jupiter Brain. Einstein did not literally have a brain the size of a planet.

On the right side of the scale, you would find Deep Thought—Douglas Adams's original version, thank you, not the chessplayer. The computer so intelligent that even before its stupendous data banks were connected, when it was switched on for the first time, it started from I think therefore I am and got as far as deducing the existence of rice pudding and income tax before anyone managed to shut it off.

Toward the right side of the scale, you would ...