Silence, or having a quiet mind can be understood in different ways. It is not about having no thoughts. This is a phenomenon of deep meditation that should only be undertaken when there is access to a competent and experienced teacher. It is not even a goal, just a point on the way.

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Having a quiet mind can be a product of formal meditation. Mindfulness is currently a popular form but not the only one.

Going for a walk in nature can also allow the mind to quieten down.

When the mind quietens down, for what ever reason, two thins happen. 

The first is that we soften fixated attention and thoughts/feelings which we may have been ruminating on are released - which meas new thoughts can restart flowing naturally.

The second is that there is now space for new insights and 'ah ha' moments to come through. These can be minor or life changing  but always apropriate to the individual.

I would also suggest that it is the lack of a quiet mind, or the ability to access that wellspring' which is at the heart of most of our contemporary troubles as we see the people we put in to political power run wild with corruption and lack of wisdom.

This might suggest a few lifestyle directions to give more opportunities for having less on our minds!