We operate in cycles. Here's one that you might have not been aware of - a 2-hr cycle/shift between right and left hemispheric dominance: "The right nostril activates the left brain (and vice versa), and it turns out that all these two-hour cycles move in concert with the breath, as it shifts form one nostril to the other. As your breath changes from one side to the other, your mindset shifts from linear to intuitive. [The Tantric text] Shivagama gives explicit information on how the flow of breath reconfigures energy patterns within so that you will know how and when to coordinate your actions with it. [...] For example - 'in climbing a high place, in athletic sports or in battle... in harsh and hot deeds,' the right nostril should be open. This is called the 'sun' or active breath, and as it brings into play the left brain, it gears you to act assertively in the world." (R. Ballentine, Radical Healing).
As you see, there's breathing right, there's breathing left, and you thought breathing was built-in and not a thing to worry about!
Ballentine continues: "Breathing through the left nostril, by contrast, is traditionally associated with the moon (and the right brain), and creates an open and intuitive state, appropriate... in marraige' [i.e. for getting along - p.s.], but also for artistic pursuits, singing, or playing upon instruments. The theme is receptivity; it is best to breathe through the left nostril when 'establishing relations with one's people.'"