Evidence for the existence of God

[Faith No More]

I agree that QM is strongly counter-intuitive. So also are our notions about the solidity of objects and the constancy of time and space intervals. I don't see that as the same as being unintelligible. As I understand it QM is one of the most thoroughly tested and consistent theories in all of science. Its perplexing findings just show that we need a better model of causality.

Sounds more like our current physical models of some phenomena are incomplete not that the phenomena themselves are beyond the reach of inquiry.

Perhaps.  QM is thoroughly tested but not widely understood.  Much of it has do with probabilities, like how a particle has a probability of being in different places until observed.  There may even be an element of randomness to it, which would lead one to believe it may very well not be as intelligible as we'd like.  The theories put forth to explain wave function collapse seem so outrageous that it appears as if our basic understanding of the universe is flawed.  Not to mention that we have to go even further down the rabbit hole with string theory to try to explain the existence of particles.  Perhaps understanding this is all a matter of time, but one could just as easily assume that the fundamentals of the universe are beyond our reason.

How about the Uncertainty Principle?  That says that the more precisely you try to measure one trait of a particle the less you can know about another of that particle's traits.  There is a certain amount of unintelligibly built into the foundations of the universe.

Something can be intelligible without being widely understood.

I guess that depends on how you are using "intelligible."  If you mean "able to be understood," then I guess that would barely qualify, but if you mean "clear," things like QM don't qualify.

All of this is true. I would say in reply that people are able to overcome those bias. While in a particular illusion, one line may appear longer to the unaided eye, one can use a ruler to determine the actual lengths are equal. As I see it reason is self-correcting rather than inherently flawed. If two clocks show a different time, I can bring in a third, etc.

What you're describing here is empirical verifiability.  Congrats, Chad!  You are now a proponent of science!

But I mentioned that in the part of my quote you chose to edit out.  It's only self-correcting in the sense that collectively we can overcome it.  If there was only one person in the world, their ability to understand reality would be greatly limited. It would be nigh impossible for them to overcome their biases on their own because of the flaws in how the brain processes information. It's becoming increasingly demonstrated that we humans come to conclusions first and interpret the world around us to fit those beliefs as opposed to the other way around.