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I'm actually fairly new to meditation myself (I've always done quiet time and reflective time, but not "shut down the mind" time until recently), and have found it immensely helpful right off the bat. I'm already taking new action in my work life that I've been putting off for years, that I feel has a direct correlation to becoming just a bit more in tune with my brain.
I find taking 10 or so minutes after doing TRE exercises, to try to actively NOT think at all, is a very natural slot for meditation. The body is already in a fully relaxed state, so you can very easily become mindful with little physical/external distraction.
What was unexpected to me is what a tough mental exercise "no thought" can be. Its very easy to go down long thoughtful quiet mental paths where you're exploring an idea. . . but to actively try to stop thought from happening entirely is a very unique experience. Different thought processes keep firing at you from different directions, and in the process of shutting down one three more fire off. You think your mind is finally quiet for like 2 seconds then you realize you're thinking about how your mind is finally quiet and the dam breaks loose and the brain starts firing off again.
At this point in my meditation experience, its all still a random haphazard assault of unwanted mental activity, but apparently these thought processes can be identified over time as you get more familiar with them (sometimes being traced back to certain events in your life that created the thought process) and thus you can gain significantly more control of your mind. I'm finding just at step 1 - making the attempt to quite my mind - I'm already gaining noticeable mental control.
The thing is, even though meditation feels like an assault of unwanted uncontrollable mental activity to me right now, that I inevitably surrender to in full defeat within 15 minutes, I feel great afterwards.
Really interesting stuff to me. The brain is a very interesting creature.