In the beginning of the parsha we are immediately informed that Sarah Imeinu was 127 years old upon her passing. There are numerous midrashic statements that focus on the fact that all of her years were lived to the fullest. Sarah maximized her time in this world and Chazal teach that these 127 years are an expression of completion. Similarly, we find that Achashveirosh ruled over 127 countries and we are taught that this is a way to express his dominion over the entire world. In fact, there are even midrashim that compare Sarah to Queen Esther based on this number.
What about the number 127 connotes the idea of a completed unit? Perhaps the answer to this question lies in the night sky. There are 12 mazalos, constellations, that each are considered to rule over one month. Most people are somewhat familiar with this concept, even if they do not understand the dynamic by which each month is designated to its mazal. Additionally, Chazal discuss the fact that there are seven objects in the sky that move independent of the stars. These objects are: the sun, moon, Mercury, Venus, Mars, Jupiter, and Saturn. Every hour is considered to be under the rule of one of these planets and each of the seven days of the week is also designated as under the influence of one of these seven objects. Besides the hourly dominance, these objects can always be found in one of the 12 mazalos and the combination of mazal and object project an influence to this world.
Chazal express all of nature somehow being showered upon us from the metaphysical heavens through these 12 mazalos and 7 objects. As such, all of nature and all the happenings of this world come through these items. Thus, it is clear how the number 127 shows completion. 127 is the number 12 and 7 put together (not added, but written side by side). 127 shows the epitome of a complete existence. Sarah was able to live such a full life that her years are able to be expressed by this very symbolic number.
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