My definition of irrational includes the fact that you cannot derive everything that true in a system of math from its postulates. That's more than irrational. That is crazy.

It means that mathematics is fundamentally crazy like my schizophrenic mother. She heard voices that did not originate in her consciousness.

And so math gets truth from the outside that we cannot discover from the inside. We know that's so because if we move a few axioms from the outside to the inside, then we can derive some more of those truths from the inside that previously came from the outside. But even more extra truths have been introduced to the system from the extra axioms.

So here is my really crazy idea. Meaning that I cannot prove it from the axioms of science, but that it may be true. The way that the natural order of things and the supernatural communicate is based on the mathematics that provides that some systematic truth cannot be reduced to the system postulates.

Just as mathematical truth may came from outside the system of mathematics, communication of information can come from outside the natural system.

As shown by Goedel, a requirement is a threshold level of complexity. So when our brains got sufficiently complex, we could communicate with each other via the incompleteness mechanism. And likewise, we could communicate with supernatural intelligence, althought I suspect that the communication is mostly one way, from them to us, and we egotistically assume that we are inspired people.