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Hadrash Ve-Haiyun
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Hadrash Ve-Haiyun
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Chayei Sarah
5763
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Sarah’s lifetime was one hundred years, and twenty years and seven years; the years of Sarah’s life (Bereishis 23:1).
The posuk tells us that Sara lived for 127 years. Rashi comments that they were all equal for goodness. Rashi further explains the significance of the Torah breaking up her years into three parts. When Sarah was one hundred she was like twenty with regard to sin. Just as a twenty year old is considered free from sin because he is not liable for punishment, likewise Sarah was free from sin at the age of 100. Furthermore, at the age of twenty she was beautiful as if she were seven years old.
It is noteworthy that the number 127 is found in beginning of the Megillah. The posuk there says that Achashuerosh ruled from Hodu to Cush over 127 provinces (Esther 1:1). Indeed chazal link the two. The Gemara records that when Rebbi Akivah attempted to awake his students during his lecture he explained that Esther merited to become the Queen of 127 provinces only due to the fact that Sarah lived a full life of 127 years. We may ask, what is the symbolic significance of the number 127 both in regard to the life of Sarah and the number of provinces that were ruled by Achashuerosh and Esther?
To answer this question let us briefly discuss some elementary mathematics. In the decimal system there are exactly ten symbols. They are 0 through 9. There is no single symbol that represent the number that comes after 9. In practice we start again by returning to 0 and carry a 1 to the left of the 0. This produces two symbols, ‘10.’ We refer to this as ‘ten.’
In the binary system there are only two symbols, they are 1 and 0. If we wish to represent the number two we also return to 0 and carry a 1 to the left. Thus, ‘10’ represent the value two in binary just as ‘10’ represents the value ten in decimal. As the value increases we keep adding digits to the left. For example if we wish to represent the number sixty-six in binary we would write the following: 1000010. Here the ‘1’ in the second position from the right represents the value two and the ‘1’ in the leftmost position represents the value sixty-four. 64 + 2 = 66. The leftmost one represents sixty four in binary just as it would represent one million in decimal.
If we would wish to represent the number 127 in binary we would write seven consecutive 1’s. i.e., 1111111. It is noteworthy that all computers use the binary system. The smallest element in a computer is a “bit” which can either be a 0 or a 1. If we combine seven bits there are a total of 127 combinations. They range form 0000000 to 1111111. Indeed every character has a mathematical representation called an ASCI code. The ASCI code has 127 possible values due to the fact that every character is stored in seven bits. (In truth it is stored in a “byte” which have eight bits but the eighth bit is used for the sign, i.e., + or -.)
In summary, if we have seven digits that are arranged in order and can only be 0 or 1, then there are a total of 127 possible combinations.
The Torah tells us that this world was created in seven day. Had Hashem wished He could have created it in one day, yet Hashem chose to divide creation in seven distinct parts. Every aspect of this physical world is rooted in one of the seven parts of creation. The number seven throughout chazal consistently represents the physical world that was created in seven parts. One example in the menorah that has seven branches. Some of the commentators explain that this alluded to the seven parts of creation.
In the physical world we live in we find that different people are blessed with different combinations of blessings. For example some may be blessed with wisdom but not wealth, some the opposite. Some may be blessed with wonderful children but lack perfect health, and so on. We find many combinations of blessings but rarely do we find a person who is blessed with everything. Assuming every physical blessing is rooted in one of the seven parts of creation we may suggest that in general there are 127 combinations of blessing in this physical world. They range from nothing to everything. Although the binary system is a relatively modern invention the concept it represents is ancient.
The Torah tells us that Sarah lived for 127 years. Rashi comments that they were all equally good. Perhaps the significance of 127 is that Sarah was blessed with the full combination of what life has to offer. All seven element of creation were positive for her. This stands in contrast to the other 126 general combinations of blessing that are found among people in the world. The significance of living a life of 127 years is symbolic of being granted the totality of blessing.
Likewise we may now understand the symbolic significance of the 127 provinces that were ruled by Achashuerosh. The Megillah introduces this fact by first telling us that Achashuerosh ruled from Hodu to Cush which is interpreted by the commentaries to mean the entire world. The posuk continues to emphasis that this included 127 provinces. This symbolic number indicates that his sovereignty over the physical world was as complete as possible.
