Starting your introduction with
A few million years ago, something very strange happened.
seems likely to turn away roughly 40% of the US population, along with any leaders who need the goodwill of that 40% to keep their positions.
The point I understand you to be making (tripling the brain size of a chimp gives more than triple the impact) could be easily made without this sentence to introduce it. Given the importance of the US in addressing the existential threat of AI, and assuming one of the goals of this article is to be a general call to action, potentially alienating nearly half the target audience seems counterproductive.
Thingspace is a set of points, in the example
(Sunny, Cool, Weekday)is a point.Conceptspace is a set of sets of points from Thingspace, so
{ (Sunny, Cool, Weekday), (Sunny, Cool, Weekend) }is a concept.In general, if your Thingspace has
npoints, the corresponding Conceptspace will have2^nconcepts. To keep things a little simpler, let’s use a smaller Thingspace with only four points, which we’ll just label with numbers:{1, 2, 3, 4}. So{1}would be a concept, as would{1,2}and{2, 4}.Some concepts include others:
{1}is a subset of{1, 2}, capturing the idea of one concept being an abstraction (superset) of another.This makes Conceptspace a partially ordered set, which means it has a Hasse diagram:(from Wolfram Demonstrations Project)
Every time you move up the diagram (e.g. from
{1}to{1, 2}) you move from more concrete to more abstract in Conceptspace, or from more specific to less specific. This up-and-down ordering is what gives you the order part. The fact that not all concepts are related by moving in one direction up or down the diagram is why it’s only a partial order, and why lattice is a better description than ladder (although technically lattice in the lattice theory sense requires the poset to have extra features, but a poset that is a powerset ordered by inclusion is always a lattice.)Hopefully the visual diagram helps make the way order (up-and-down the lattice) and concept specificity (subset/superset relation) more clear.