Article LXXVIII: Reincarnation and Karma

Reincarnation and karma are central concepts in Hinduism and Vedanta. Since the Atman, or Self, is eternal, the death of the physical body does not affect the Atman. Instead the Atman transmigrates to a new physical body dependent on past actions, or karma. Hence, at the beginning of each life, and throughout each life, one's state is determined by past actions. However, this law of karma does not imply that one has no control over one's existence. Quite the opposite is actually true. Although our current state is determined by our past actions, our future state is determined by our current actions. Hence, we have total control over our future state because it is determined by the actions of the present.

Often spiritual aspirants question the necessity of orienting toward the path of enlightenment in the present life. However, the human life is unique, in that only from a human birth can one reach enlightenment. Also, each bit of progress toward enlightenment is not lost through reincarnation, but the spiritual growth is preserved through the process of reincarnation. Therefore, although one's spiritual efforts may not lead one to enlightenment in this life, those efforts will allow greater joy in the current life and in future births. Ultimately, those efforts and will lead one closer and closer to supreme bliss and enlightenment.

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Katha Upanishad

The context of this scripture is a dialogue between Naciketas, a spiritual aspirant, and Yama, the god of death:

IV.11: By mind alone is this to be realized, and (then) there is no difference here. From death to death he goes, who sees as if there is difference here.
IV.12: The Purusha (Atman) of the size of a thumb dwells within the body. He is the Lord of the past and the future, and thenceforward one fears no more. This is verily that.
IV.13: The Purusha (Atman) of the size of a thumb, the Lord of the past and the future, is like a light without smoke; He is verily (the same) today as tomorrow. This is verily that.
IV.14: As the rain-water fallen on a (high) peak runs down to the hill-sides variously, even so, he who sees the attributes as different, verily runs after them.
IV.15: As pure water poured into pure water becomes the same, so becomes the Self of the sage, who knows (the unity of the Atman).

Figuratively, Atman is described as the size of a thumb, which is said to be seated in the lotus of the heart. However, Atman is truly beyond limitation of space and time as alluded to by the other verses. For symbolic purposes and as an aid to meditation, the Atman is simply described to be centered within the lotus of the heart.