"They embittered their lives with hard work, with mortar and with bricks, and with every labor of the field; all their labors that they performed with them was crushing labor." ~Shemot 1:14
וימררו את חייהם בעבדה קשה..." ~שמות א:י"ד"
Note: When clicking the link above to view the text on sefaria.org, you always have the option of viewing the text in English, Hebrew, or linear translation. This week, I've quoted the beginning of the phrase in Hebrew, as well, since my topic for this week pertains to the special notations that indicate cantillation for reading the passage (these notations are referred to as "trop"). The trop can be seen on the hebrew and linear translation views on the sefaria.org link.
In previous posts, one ongoing activity option has been to use the timing and referential ages, time spans, etc. to calculate an ongoing timeline. Based on the information provided in the entirety of the whole book of Bereishit and up through the beginning of the book of Shemot (just to bring us to-date), it is possible to create a timeline from the Creation of man through to the enslavement of the Israelites in Egypt.
If we look back at Bereishit 15:13, Avraham is told that his descendants will be slaves in a land that is not their own, and they will be afflicted for 400 years. If you put the events up until this week's parsha on a timeline, you will find the discrepancy that the number of years that the Israelites were actually in Egypt do not add to 400. Different commentaries make sense of this discrepancy in different ways. Rashi offers one explanation with a calculation of a different sum of years along with mathematical proof that it's not possible that the Israelites could have been in Egypt for 400 years based on relevant numbers that we know. His explanation can be seen here.
The Vilna Gaon offered a different type of explanation. His explanation was based on Gematria. Gematria, which I explained in more detail last year for Parshat Vaetchanan, is a system of establishing numerical values of words based on assigned values for each letter. A quick reference chart for letter values can be seen here.
The steps to the Vilna Gaon's explanation are worked out below:
Here is where I refer back to the Hebrew quote above. The first 3 words, which translate to "They embittered their lives", have the two trop signs called "kadma" (קדמא) and "azla" (אזלא). The meaning of the Aramaic words "kadma" and "azla" is "get up and go".
If you check the math of the timeline for the actual number of years that the Israelites were in Egypt (from the time Yaakov moved his family to Egypt until the Jews fled Egypt), you will find that they were there for 210 years. If you calculate the discrepancy between what Avraham was told would happen and what actually happened, you will find that the discrepancy (400 years minus 210years) is 190 years.
Now, let's check the gematria for קדמא ואזלא (kadma and azla- get up and go) :
ק -100
ד -4
מ -40
א -1
total= 145 (remember to line up your place values before adding!)
ו -6
א -1
ז -7
ל -30
א -1
total= 45 (remember to line up your place values before adding!)
Let's add those 2 together: 145 + 45 = 190.
Based on the value of 190 found here, the meaning of the words ("get up and go"), and the fact that they are found specifically on the words referring to the Egyptians embittering the lives of the Israelites, the Vilna Goan used all of this information to explain the mathematical discrepancy in the following way:
Avraham was told that his descendants would be strangers in a land and they will serve the inhabitants of the land. The Egyptians, however, took it a step further (as we see here in Shemot 1:14) and they specifically sought to embitter the lives of the Israelites. Due to the extra burden that the Egyptians put on the Israelites, G-d made it possible for the Israelites to leave Egypt early- "Get up and go!". How early did he let them go? By exactly 190 years (the value of "get up and go").
Students of varying levels can either identify this question as part of a larger timeline that they are following and tracking, or they can work through just the calculations that present to identify the question. Looking at and working through various commentators explanations of the discrepancy with their mathematical calculations is an activity that students of varying skill levels can handle. Younger students could look at a timeline provided by a teacher to look at the calculations, while older students can calculate the different time spans offered by the commentators and double-check the calculations that the commentators offer.
"The king of Egypt said to the Hebrew midwives, of whom the name of the first was Shifrah and the name of the second was Puah-" ~Shemot 1;15
"[Pharaoh decreed] '...But the total of the bricks that they were making yesterday and before yesterday you shall place upon them- do not reduce it- for they are becoming lax; therefore they cry out saying, "Let us go and bring offerings to our G-d." Let the work weigh heavier upon the men and let them engage in it; and let them not engage in words of falsity.' The taskmasters of the people and it's guards went out and spoke to the people, saying, 'So said Pharaoh, I am not giving you straw. You, go, take straw for yourselves from whatever you find, for nothing is being deducted from your work.' So the people spread out through the entire land of Egypt to gather a gathering for straw. The taskmasters were pressing, saying, 'Complete your work, each day's quota on that day, as when there was straw!'..." ~Shemot 5;8-13
Math is the foundation of the universe. It exists all around us and permeates our lives, mostly on a subconscious level. How much we connect with that math is dependent on how tuned into it we are at any given time. When reading through Parshat Shemot, you could easily read through the storyline of the parsha without any thought towards mathematics. However, if you read carefully, you can actually see that the parsha includes grammatically correct, mathematical language in at least two places. I'm not talking about throwing numbers into the storyline, I'm talking about actual mathematical wording when discussing information.
Ordinal Numbers:
In our day to day lives, we have 3 different types of numbers that we use- ordinal numbers, cardinal numbers, and nominal numbers.
Ordinal Numbers are numbers that indicate the order of a group of items (eg. first, second, third,...).
Cardinal Numbers are numbers that tell us the quantity or value of something (eg. 7 apples, $4.15, 17 years)
Nominal Numbers are numbers that don't have a numerical meaning, but just have a number as a label (eg. zip codes, bank routing numbers, telephone numbers)
Parsha connection- In Shemot 1;15, we learn about the Hebrew midwives whom the king of Egypt appointed to oversee the Jewish births. When they are introduced to us, they aren't just listed as "one was Shifrah and one was Puah". Rather, we learn that the first was Shifrah and the second was Puah. For whatever reason, the Torah uses ordinal numbers to give them a specific ranking or order.
Arithmetic Vocabulary:
Just as in any other area of our lives, in order to understand mathematical data that is part of our daily lives, there is certain vocabulary that has mathematical meaning with which we must familiarize ourselves. Some basic examples are understanding that when we want more of something, we need to add to the quantity; when we want less of something, we need to subtract from the quantity. We need to understand that when equally sharing a quantity, it means to divide evenly amongst the group. We even have commonly used suffixes that indicate comparative value of items: -er, -est. For example: "I ran faster than him. She ran the fastest." These sentences both indicate comparative speeds, and we need to understand from this language who was faster than whom.
Parsha connection- In Shemot 5, we learn of the decree for reduction of materials without adjustment in the quota requirement for the Hebrew slaves in Egypt. As we read through this perek, it is filled with mathematical vocabulary that indicates to us the severity of the intense work that was expected of the slaves. Below, I will recopy the excerpt from Perek 5, but with emphasis on the mathematical vocabulary.
"[Pharaoh decreed] '...But the total of the bricks that they were making yesterday and before yesterday you shall place upon them- do not reduce it- for they are becoming lax; therefore they cry out saying, "Let us go and bring offerings to our G-d." Let the work weigh heavier upon the men and let them engage in it; and let them not engage in words of falsity.' The taskmasters of the people and it's guards went out and spoke to the people, saying, 'So said Pharaoh, I am not giving you straw. You, go, take straw for yourselves from whatever you find, for nothing is being deducted from your work.' So the people spread out through the entire land of Egypt to gather a gathering for straw. The taskmasters were pressing, saying, 'Complete your work, each day's quota on that day, as when there was straw!'..." ~Shemot 5;8-13
We all use math, all the time- even those of us who are scared of it. We just don't always process it as math. What math have you been taking for granted in your daily life?
