One who reads a book like "Gödel, Escher, Bach" sees articulated the discovery that all systems of formal thought, including mathematics and logic itself, reach points of self reference, in which their own rules cannot be applied. In other words, mathematics cannot be legitimized through mathematic principles, and logic cannot be substantiated through logical principles. All enterprises which depend on formalized, consistent principles of thought face a moment when they have to say, in effect: "I don't know how this works--but it somehow does, so I'm gonna go with it."

Human thought has recognized these pockets of irrationality we carry around in ourselves in a variety of ways. Mythology and religion have their own, diverse ways of naming and interacting with what appears to be, not only unknown, but unknowable. Physics grapples with ways to describe the paradoxes it is encountering in the interface between what is observed and observation itself. Artistic expression has expressed and celebrated the irrational through means including painting, music, dance.

It appears the most dangerous thing we can do, with regard to the irrational, is to pretend it does not exist. When we do so, it emerges unexpectedly and unpredictably, as a confrontation with our own unacknowledged shadow. We need to establish a relationship with the irrational. To do so, however, requires more than reliance on the formal systems of thought which themselves reach an impasse in the face of the irrational. We need to rely on our capacities for symbolic expression, metaphor, imagination, and feeling. In short, we need to use our whole brain—and not depend only on the disciplines emphasized within the STEM curriculum, except to the extent these disciplines themselves develop language capable of naming and acknowledging paradox and mystery.