Penrose argues that the underlying nature of human understanding is non-computable. There is no algorithmic approach that can mimic or reproduce exactly what we call ‘understanding’. He provides some examples, especially our understanding of what the ‘integers’ mean.
Biologists will tell you that all human thought occurs in the frontal lobe. Anything ‘computable’ (i.e. any thought that can be reproduced computationally), has to be frontal lobe thought.
Buddhism clearly distinguishes between frontal lobe thought (chatter) and non-thought. There is a concept of a separate stream of thought in Buddhism, which has little to do with the frontal lobe. In fact, quieting all frontal lobe activity, through meditation, is a first step to stepping into this second stream of thought.
This second stream is called non-thought. Non-Thought does not mean no thought.
A good analogy is – think of regular thought as your motion as you swim against a river current. You are still moving, although not necessarily making much progress.
Think of non-thought as, stopping all struggle against the current and going along with the river. It does not mean you stopped moving. In fact, you are moving, though in accordance with nature (the Universe). And therein is the beauty of non-thought, it does not deprive you of actions, it only lets you act in ways the Universe considers constructive.