Eckhart Tolle describes how presence changes your relationship to thought. Thoughts keep happening, but they stop causing unhappiness once you stop identifying with them. The mind stops arguing against what is actually happening right now.
Chapters
You continue to think, of course, thoughts still, but something, an important change then happens or is happening to the way in which you think. Most importantly, thoughts lose the capacity to make you unhappy. That's important. Next, of course, is that thinking still happens, but your sense of self Or your identity, you no longer look for it in the movement of thought. So thought still happens, not as frantic as before, but thought is no longer imbued with a sense of self. Whereas before, before presence arose, before awareness arose, you looked for yourself in every thought. That is the identification. And then thought still happens, but there's no self in it anymore. And it— no thought makes you unhappy anymore. You don't believe when you thought, what a terrible situation, I can't stand this anymore. It's just a thought. You no longer argue with the is-ness of things, which is the present moment, because continuously, internally or externally, Arguing with the is-ness of the present moment is, to use a simple term, crazy.