Actual knowing is way bigger than just the thoughts in your head, than just the verbal thoughts in your head. Our bodies can remember things; our silence can remember things. The words that go through our head, the thing we call thoughts, is really the smallest part of our consciousness. So, nonduality is simply about allowing yourself to expand your awareness way, way, way beyond the thoughts that are in your head.
Nonduality means that if you limit your knowing to verbal thoughts, then everything you know is wrong. This is because verbal thoughts are just a definition of something. Only a fragment of the real thing. We all have a deeper knowing that we can access any time though silence.