Toldot- A Timeline Through Deductive Reasoning

Deductive reasoning: a logical process in which a conclusion drawn from a set of premises contains no more information than the premises taken collectively (ref. dictionary.com)

When trying to problem solve, deductive reasoning helps us logically move from one step to the next. Deductive reasoning allows us to look at the information that we are provided with and state, with certainty, that the next logical step can also be relied on, because the original information proves the next step. Each step that is proven through deductive reasoning can then be relied on as a fact to support our logical thinking towards a final solution to the problem at hand.

As we've been reading through the parsha each week, we have followed storylines which offer some concrete sense of time. However, taken together, how much time is actually passing between each phase of each story? If we take the individual pieces of information that we are provided with from the text and Rashi's commentaries, we can use deductive reasoning to calculate some of the missing pieces of information in order to put together a fuller picture for ourselves. Is the story between the parshiot a straight timeline, or is it broken into parts dealing with each "main character"? With some deduction, we can find out. (My completed storyline for the primary Toldot "characters" with some added information appears at the bottom of this post. Check your calculations and timeline against mine and see how they match-up. Can you fill in the extra information that I calculated?)

Whenever sorting information for problem solving, the first step is to map out the information that you have.

• From Lech Lecha 17;17 and Vayeira 21;2 we know that when Isaac was born, Sarah was 90 years old and Abraham was 100 years old
• From Chayei Sarah 23;1 we know that Sarah lived to be 127 years old
• From Rashi's commentary on Sarah's death, we know that she died upon hearing the news that Isaac was to be sacrificed at the akedah
• From Rashi on Toldot 25;20, we know that Rebecca was born in the year of the akedah
• From Chayei Sarah 25;7, we know that Abraham lived to be 175 years old
• From Toldot 25;20, we know that Isaac was 40 years old when he married Rebecca
• From Toldot 25;26, we know that Isaac was 60 years old when Esau and Jacob were born
• From Rashi's commentary on Toldot 25;27, we know that Jacob bought Esau's birthright when they were 13 years old
• From Rashi's commentary on Toldot 27;2, we know that Jacob took Esau's blessing from Isaac when Isaac was 123 years old
• From Toldot 26;34, we know that Esau was 40 years old when he married Judith and Basemath

The second step to problem solving is to identify the questions that you are trying to answer.
--How old was Isaac at the akedah (and Sarah's death)?
--How old was Isaac at Abraham's death?
--How old was Rebecca when she married Isaac?
--How old was Rebecca when Esau and Jacob were born?
--How old were Isaac and Rebecca when Esau sold his birthright?
--How old were Jacob, Esau, and Rebecca when Isaac gave Jacob Esau's blessing?
--How old were Rebecca and Isaac when Esau was married?
--How old is Jacob (and Esau) at the end of Toldot?

Now let's see what information we can use to answer these questions:
--How old was Isaac at the akedah (and Sarah's death)?

• Sarah was 90 when Isaac was born, and she was 127 when she heard of the akedah. 
• 127-90=37, so Isaac was 37 at the akedah and when Sarah died

--How old was Isaac at Abraham's death?

• Abraham was 100 when Isaac was born, and Abraham lived to be 175.
• 175-100=75, so Isaac was 75 when Abraham died

--How old was Rebecca when she married Isaac?

• Isaac was 37 at the akedah, which was the same year that Rebecca was born.
• Isaac was 40 when he married Rebecca.
• 40-37=3, so Rebecca was 3 when they were married (keeping strictly to math here, no societal norms commentaries)

--How old was Rebecca when Esau and Jacob were born?

• Isaac was 60 when they were born
• Isaac was 37 years older than Rebecca
• 60-37=23, so Rebecca was 23 when they were born

--How old were Isaac and Rebecca when Esau sold his birthright?

• Isaac was 60 when they were born; Rebecca was 23 when they were born
• Esau and Jacob were 13 when the birthright was sold
• 60+13=73, so Isaac was 73; 23+13=36, so Rebecca was 36

--How old were Jacob, Esau, and Rebecca when Isaac gave Jacob Esau's blessing?

• Isaac was 60 when they were born; Rebecca was 23 when they were born
• Isaac was 123 when he gave Jacob Esau's blessing
• 123-60=63, so Jacob and Esau were 63; 23+63=86, so Rebecca was 86

--How old were Rebecca and Isaac when Esau was married?

• Isaac was 60 when they were born; Rebecca was 23 when they were born
• Esau was 40 when he was married
• 60+40=100, so Isaac was 100; 23+40=63, so Rebecca was 63

(click on the picture for a larger view of the timeline)

From this timeline, we can see that, although most of the storylines in these few parshiot are in order, there are some pieces of information that are placed out of order, seemingly to keep them together with the sections that discuss the particular "character" in more depth.

Chayei Sarah - Unit Conversion

"And it was, when the camels had finished drinking, the man took a golden nose ring, its weight a beka, and two bracelets on her arms, ten gold shekels their weight." ~Bereishit 24;22

Unit Conversion:

Unit (or Unit of Measure): a standard amount of a physical quantity (ref. dictionary.com)

In Math and Science, units are a critical aspect of calculation. Units, in simple terms, are the base quantity that we choose to use to measure physical properties- a length, a weight, a volume, etc. You can measure with standard units- units that are already established by society and have specific value assigned to them (e.g inch, cm, pound, gram, gallon, liter, etc.); You can also measure with non-standard units- units that you choose for you convenience, but are not standardized to all places and situations (e.g. the paperclips that I have in a box on my desk, or the length of my right foot).

In order to compare measurements of different items, we need to measure them using the same units. This is where unit conversion comes in. If we have items measured in different units, then we need to convert them all to the same units of measure in order to be able to say how they compare to each other. We need to know how many cm are in an inch, and then make sure that all items we're comparing are measured in either cm or inches. In general, it doesn't matter which measure you choose to use, you just need to pick one and make sure that everything that you're comparing is measured with the same measure. If I want to compare my height over the past 5 years, I can measure myself consistently in ft, or I can have some measurements in ft and some in meters, but in order to compare, I need to convert all the measures to either ft or meters to know how my height has changed. Note that in order to calculate the conversion from ft to meters or vice versa, I need to know that 1 meter is approximately 3.28 ft.

So, how does this connect to the parsha?

In Chayei Sarah (Bereishit 24), Avraham's servant, Eliezer, is sent to find a wife for Yitzchak. When Rivkah meets him at the well in Nahor and she offers water to both him and his camels, he realizes that she is the right woman for Yitzchak. He then, in Bereishit 24:22, gives a gift to her-- and here is where we find units of measure. Eliezer gives her "...a golden nose ring, its weight a beka, and two bracelets on her arms, ten gold shekels their weight."

So, what if we want to know how much the weight of her jewelry was altogether? Or, how big was the nose ring compared to the bracelets? How can we compare the weight of a beka and the weight of ten shekels? Rashi helps us out here and tells us that a beka is the weight of a half-shekel (see Rashi on this Pasuk to see how he knows this). So, we now we know that the nose ring was the weight of a half-shekel and the two bracelets were the weight of 10 shekels. So, the weight of all of Rivkah's jewelry from Eliezer was 10.5 shekels. The weight of the two bracelets together was 20 times the weight of the nose ring. Or, if we assume that the bracelets were equal in weight, then each bracelet was 10 times the weight of the nose ring.