The Arizal explains that when Adam and Chava ate from the Eitz Hadaas, they caused damage in two names of Hashem. That is, in the names ש-די and אדנ-י where the letter dalet was removed in each name. The name ש-די without the ד spells שי (or יש) while the name אדנ-י without the ד spells אני.
We know that the sin of the Eitz Hadaas was sourced in gaavah, haughtiness, as they should have submitted themselves to the command of Hashem not to eat from the Eitz Hadaas. Instead, they violated Hashem’s word and transgressed. Fascinatingly, the words אני (“I”) and יש (“there is”), which are the words that remain from ש-די and אדנ-י when the dalet is removed, are both expressions of haughtiness.
After eating from the tree, Chava said the nachash שיאניה, deceived me and I ate. This is a unique word as this is the only time it is found in the Torah. Remarkably, the word השיאני is comprised of the words אני and שי!
As a result of this sin, death was introduced to the world. Torah is the antidote as it gives life. Learning Torah restores the dalet to these two Holy Names of Hashem. This is what is meant in אשרי אדם שומע לי לשקוד על דלתותי יום יום, praiseworthy is the person who listens to me, to hasten to my doors everyday. The word דלתותי refers to the two dalets (the letter ד spelled out spells דלת, so דלתותי refers to two dalets), which serve as the rectification through learning Torah, as לשקוד refers to learning Torah as in הוי שקוד ללמוד תורה, be diligent in the study of Torah.
When the sin of Adam is rectified, then we merit arichas yamim like it says אורך ימים בימינה, length of days is at its right.
