Truths [...] which are complex beyond the human ability to manipulate ideas.

Interesting.

As a limit on ideas this implies truth (structures) which show no observable effect (otherwise the effect would allow to at least name the truth even if it cannot be understood fully).

As a limit on understanding of truth (structures) this implies irreducibility not only in the horizontal dimension (the number of parallel items cognitively manageable - those can be offloaded to computer) but at least also in the vertical dimension (the number of reduction steps required).

Examples of the latter might be structures which

• change so little with each reduction step as to make the reduction undetectable in itself and build an unmanageable number of these on each other. Or

• Contain reductions which feed back on lower reductions thus creating cycles. Something like humans which on a high reduction level (social) but feed back on effects observed under the microscope (an effect that probably (note: 'probably' is a catch-word) cancels out on the social level).

My intuition on these structures is that they are indistinguisable from noise. If they were there they couldn't have an effect at all (except being there).

Theological note: Some beliefs in god imply exactly such irreducible undetectable truth.