[mxkopy]

I think there is some sort of threshold analogous to Turing-completeness (it probably is just Turing-completeness) when it comes to intelligence, in that information is eventually accessible to any system that passes it.

If there is a species that thinks in terms of things that humans never could understand, then I would argue that species isn't part of our physical reality. If their expression of concepts is at all rooted in physical reality, then we, as physical beings, would have access to it. Maybe not the first person that sees it, nor the second, nor their great-great-great-grandchildren, but at some point their children could build things/begin to appreciate what was being communicated.

[JackFr]

> If there is a species that thinks in terms of things that humans never could understand, then I would argue that species isn't part of our physical reality.

What if they think can think in our terms AND they can think thoughts we are physically unable to, thoughts that are literally inconceivable?

[mxkopy]

If the thoughts have any interaction at all between each other, we would be able to leverage that to understand those higher-level thoughts to the degree that they affect the ones on our level. As an analogy, we can project an N dimensional object onto N! planes and get a complete, but not intuitive, description of what it is.

Maybe they know the exact value of Chaitin's constant, but at least we know its properties.