Bo- Finding the midpoint

"And Moshe said, 'So said Hashem, 'At midnight I shall go out in the midst of Egypt. Every firstborn in the land of Egypt shall die, from the firstborn of Pharaoh who sits on his throne to the firstborn of the slave-woman who is behind the millstone and all the firstborn of the animal." ~Shemot 11;4-5
"It was at midnight, and Hashem smote every firstborn in the land of Egypt, from the firstborn of Pharaoh sitting on his throne to the firsborn of the captive who was in the dungeon, and every firstborn animal." ~Shemot 12;29

In his commentary on 11;4 above, Rashi explains that "[Midnight] means when the night is divided". This is understood to mean when the night is divided exactly in half, into two equal portions. In other words, the exact time in the middle of the night when the nighttime that has passed and the nighttime that remains is exactly the same.

Midpoint:
In math, the midpoint is the exact point at which half is before the point and half is after the point. There are different areas of math where midpoint is needed.
*In Geometry, we can measure the midpoint of lines or sides of shapes (exactly halfway along a line or side).
*In Statistics, given a set of data, there is often a need to calculate the midpoint between two numbers.

Calculating to find a midpoint is the same as trying to find the mean or arithmetic average of two numbers. We can find the midpoint by adding the two numbers together and dividing the sum by 2.
*So, if you want to locate the midpoint of a 10 ft wall, think about the measuring tape along the side of the wall: the measuring tape starts at 0 (the beginning of the wall) and ends at 10 ft (where the wall ends). You would add 0 + 10 = 10, then divide 10 ÷ 2 = 5. So, the 5 ft mark would be the midpoint of the wall. 
*If you want to find the midpoint between any two numbers, say 10 and 70, you would add 10 + 70 = 80, then divide 80 ÷ 2 = 40. So, the midpoint between 10 and 70 is 40.

Connection to the parsha:
In this week's parsha, we learn that Hashem promises that he will kill the non-Jewish firstborns (humans and animals) at the exact midpoint of the night- the exact midpoint between sunset and sunrise. This is actually a calculation that we still use nowadays when calculating times according to Jewish law. Let's go through a sample calculation for finding "midnight", according to the Torah understanding of the term (ie. the midpoint of the night).

Let's take some data for sunset 1/2/2014 and sunrise 1/3/2014 in Boston, MA. The midpoint between these two times, should be exact midnight. 
--sunset 1/2/2014 is 4:23 pm
--sunrise 1/3/2014 is 7:14 am
*First, we need to calculate how many hours there are between sunset and sunrise (ie how many hours of darkness). This time difference is 14 hrs and 51 min. 
*Next, we divide this time in half. 14 hrs and 51 min divided in half is 7 hrs and 25.5 min.
*Finally, we can either add the 7 hrs and 25.5 min to 4:23 am or subtract it from 7:14 pm (get it? because it's exactly halfway between the two times, you can get to it either way). Since it's usually more intuitive to add rather than subtract, especially when working with time, let's add 7 hrs and 25.5 min onto 4:23. This give us 11:48:30 pm (that's hrs:min:sec)

For fun, let's make a connection directly to the parsha; let's calculate midnight in Egypt in the month of April, to get an idea for what time the parsha is referring to. 
This year Pesach begins on April 10, so let's take data for sunset on 4/10/2014 and sunrise 4/11/2014 in Cairo, Egypt.
--sunset 4/10/2014 is 6:19 pm
--sunrise 4/11/2014 is 5:33 am
* First, we calculate how many hours between sunset and sunrise. This time difference is 11 hrs and 14 min.
*Next, we divide this time in half. 11 hrs and 14 min divided in half is 5.5 hrs and 7 min, in other words, 5 hrs and 37 min.
*Finally, we add 5 hrs and 37 min to 6:19 pm. This gives us 11:56 pm.

Whatever date and time you choose- any season, any region- it should always approximate midnight as we know it (12 am). Test it out and see what you find!