Every time you go to sleep you have the experience of being without a mind. You cannot deny that you exist while you are asleep and you cannot deny that your mind is not functioning while you are in dreamless sleep. This daily experience should convince you that it is possible to continue your existence without a mind. Of course, you do not have the experience of full consciousness while you are asleep, but if you think about what happens during this state you should come to understand that your existence, the continuity of your being, is in no way dependent on your mind or your identification with it. When the mind reappears every morning you instantly jump to the conclusion, ‘This is the real me.’
If you reflect on this proposition for some time you will see how absurd it is. If you really only exist when the mind is present, you have to accept that you didn’t exist while you were asleep. No one will accept such an absurd conclusion. If you analyze your alternating states you will discover that it is your direct experience that you exist whether you are awake or asleep. You will also discover that the mind only becomes active while you are waking or dreaming.
From these simple daily experiences, it should be easy to understand that the mind is something that comes and goes. Your existence is not wiped out each time the mind ceases to function. I am not telling you some abstruse philosophical theory. I am telling you something that you can validate by direct experience in any twenty-four hour period of your life.
Take these facts, which you can discover by directly experiencing them, and investigate them a little more. When the mind appears every morning, don’t jump to the usual conclusion, ‘This is me. These thoughts are mine.’ Instead, watch these thoughts come and go without identifying with them in any way. If you can resist the impulse to claim each and every thought as your own, you will come to a startling conclusion: you will discover that you are the consciousness in which the thoughts appear and disappear. You will discover that this thing called ‘mind’ only exists when thoughts are allowed to run free. Like the snake which appears to be a rope, you will discover that the mind is only an illusion which appears through ignorance or misperception.
[Ramana Maharishi] sometimes told a story about a man who wanted to bury his shadow in a pit. He dug the pit and stood in such a position that his shadow was on the bottom of it. The man then tried to bury it by covering it with earth. Each time he threw some soil in the hole, the shadow appeared on top of it. Of course, he never succeeded in burying the shadow. Many people behave like this when they meditate. They take the mind to be real, try to fight it and kill it, and always fail. These fights against the mind are all mental activities which strengthen the mind instead of weakening it. If you want to go beyond the mind, all you have to do is understand that it is ‘not me’.
Clouds come and go in the sky, but the appearance and disappearance of the clouds don’t affect the sky. Your real nature is like the sky, like space. Just remain like the sky and let thought-clouds come and go. If you cultivate this attitude of indifference towards the mind, gradually you will detach yourself from your 'little self' and awaken to your real Self.
Annamalai Swami was a direct disciple of Ramana Maharshi. Excerpt above from these talks.