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The breathing is imperceptible, that is all, because there must be movement of the breathing for it to be perceived. However, obviously the body continues to have breath flowing through it.
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As i understand it,
That which is thought & spoken about as breath is an object of perception and is tied to the body.
In the fourth jhana the object of perception is not thought & spoken about as the breath.
In general the object there is a kasina, there are various types of kasina, ie light & colors associated with absorbtion 'visions'.
An interesting circumstance about the passage:
When one has attained the fourth jhāna, in-and-out breathing has been totally stilled.
Is in the case where the fourth jhana is sustained in dependence on the air element as the air kasina because the in & out breaths are the air element.
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It would seem physiologically impossible, and it is so, to the mind, until one experiences it. This is why it is taught that true knowledge comes from direct experiencing (through practice), and not from what one has read, or is told, even by one's teacher/guru (read: guide).
But then consider that deep sea divers, or certain tribes that live by oceans/seas free dive for prolonged periods of time on a single breath. The official Guineas book of record is > 20 minutes... The average swimmer can hold their for 2-3 minutes without breathing.
In my own subjective personal meditations the deeper I go, the shallower I realize I'm breathing. In fact, one of my methods of going in deep, fast, is to still my breath as much as possible, and prolong the holding periods in-between to close to a minute (or more). At a certain point, i consciously let go, and my body subconsciously continues it on its own. Kinda like a subtle hand-over. If I follow my breath, I've gone up to a single breath every 2/3 minutes before I lost sense of my body. And on an occasion or two, I have snapped out of deep meditation to instantaneously realize that I wasn't breathing. And I had no idea how long I was under. It could have been two minutes, it could have been 10.
Thus to me, Science has proof it is possible, but my own personal experiences remove all doubt (for me).