Meaning of inaction in action and action in inaction in Bhagavadgita 4.18
Here is a better understanding of the verse. I would like to start with an analogy.
Inaction in action: Unattachment amidst Action
Suppose a person is taking his food and we request him to listen to a story simultaneously. So, we would say "Listen to the story while eating" or an act of "listening in eating" is requested. This way, we urge him to listen without interrupting his eating. Similarly Sri Krsna preaches "Inaction in action" which means Inaction or unattachment should be fully practised right during the action. In other words, it is desirable that unattachment be practised while the cause of the attachment (action) is in progress. Working with sense of ownership and practising unattachment after the action is just not sufficient.
Action in Inaction: Action amidst Unattachment
Now let us suppose that the same person is listening to a story and we request him to take food simultaneously. So, this time an act of "eating in listening" is requested. Now, what does Lord mean here when he preaches "Action in Inaction"? He means that one should take up an action amidst this state of Inaction. In other words, one should already be in a state of unattachment when one takes up an action.
And such a man who stays unattached amidst action and performs action amidst unattachment is declared as the intelligent among men. He is well unattached although doing all sorts of activities.
And unsurprisingly, very similar ideal of Karma yoga was discussed by Swami Vivekananada when he was lecturing on Karma yoga. Here (Karma Yoga -> Karma in its Effect on Character) are his words:
The ideal man is he who, in the midst of the greatest silence and solitude, finds the intensest activity, and in the midst of the intensest activity finds the silence and solitude of the desert. He has learnt the secret of restraint, he has controlled himself. He goes through the streets of a big city with all its traffic, and his mind is as calm as if he were in a cave, where not a sound could reach him; and he is intensely working all the time. That is the ideal of Karma-Yoga, and if you have attained to that you have really learnt the secret of work.
The verse by the God and lecture by Swamiji look very similar. And it seems easy to follow what God means by "Inaction" is nothing but "greatest silence and solitude" in Swamiji's words.
Therefore, as we see that in first case Lord means that unattachment should be practised while the action is in process. And in second case, He means that action should be started amidst a state of already-in-unattachment. This way, the Lord preaches to be in state of unattachment all the time.
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