Intelligence is not Restricted to Consciousness

Intelligent beings do conscious things: talk, sing, play, work, pray, etc. and they do unconscious things, like transmit visual data from the retina to the brain.

What is the unconscious? Is it a mysterious place? Not really. It is, however, inaccessible by consciousness.

Intelligent individuals process information by electrical and chemical messages. For each and every system and sub-system that exists - for example,  the cones in the retinae of the eyes - there are codes that the intelligent system uses to control the flow and processing.
Only some of the intelligent systems are conscious: language, music, maths, structured movements and behaviors, imaging, etc. These systems have high-level codes in them which eventually cause the intelligent individual to be "aware" of them, and to be considered conscious. There are a certain class of codes that bestow awareness-of-being-done. Language follows rules and codes that create the sense of "I-am-aware-that" I am talking; the processing of visual data before the brain does not.

The systems that do not do so are considered unconscious. Again, the system of structures and messages and the codes employed in moving information from the cones in the eye to the brain is not a system that has consciousness associated with it: we are "unaware" of it. However, it goes on working none the less.

Thus, we may think of intelligent individuals as systems of information processing with conscious and unconscious sub-systems of information processing.

There is nothing particularly mysterious about the unconscious at this point. There are more mysteries about consciousness and things like Chomsky's Deep Grammar of Language, one of the foremost "conscious" systems of intelligence.

The "unconscious" processing is still connected to our environment, even though we don't consider it conscious. The "unconscious" keeps on working. It works in the background. Intelligent beings parallel process by nature, and we may think of consciousness as foreground processing and unconscious as background processing.
So why are we surprised when someone springs a surprise on us, like a Joan of Arc who seems to have had a "global" intuition of the state of France - physically, morally, and spiritually - of her time? She had as good an unconscious processing system as anyone else, maybe better. Perhaps she had extra unconscious processing capacity, which could turns its resources from the autonomic maintenance of the body to a higher level knowledge
Somehow, she was able to make her unconscious; i.e., good knowledge but unexpressed in language, or math or music or images, make the transition from unconscious to conscious. She heard voices: language; she saw things: images.

It seems to me that a lot of what people call "God", or the Holy is actually deep unconscious knowledge of intelligent individuals whose intelligent processing systems are working well and have the happy ability to take the "silent" and "background" knowledge of their unconscious system and give it language, give it form and shape, shove it to the foreground of awareness, and make it a gift to the rest of us.