You should stop thinking altogether, although thinking is not the enemy. One great thing about a well developed, consistent meditation practice is that you will have no enemies. Not self does that. In order to have an enemy, you have to have a clear sense of yourself as someone who could have interests that are inimical to those of someone else, which you can’t have once not self arises in your mind.
So thinking is not an enemy, but it is a problem. Thoughts emerge from consciousness, as everything does, but thoughts are sort of the noise of consciousness. A very few thoughts may actually be useful, but the vast majority just serve to reinforce your sense of self. The more you meditate, the more you notice your repetitive, useless thoughts.
As you work on silencing your thoughts, which will just happen with time if you sustain a consistent meditation practice, you can start directing your thoughts to consciousness. Consciousness is omnipresent, but it is ephemeral and elusive. As your thoughts become quieter and fewer, you start to notice consciousness because it is the background condition for thoughts.
A useful analogy is space. You usually do not notice it and you cannot see it, but you are always surrounded by space. If you were not, you could not move. Look out a window and look through space to whatever else you can see. It’s obvious that the space is there, but you can’t see it.
Consciousness is to your mind, to your awareness, what space is to your body. It is the invisible, necessary precondition for your mind’s existence.
As you start to notice it, consciousness will gradually take over and become the default perspective from which you look at the world. This is what you want to happen. With the shift to consciousness, both wisdom and compassion arise automatically.
So keep meditating and letting your thoughts decrease in both quantity and volume.
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