"Then [Joseph's brothers] took [Joseph], and cast him into the pit; and the pit was empty, no water was in it" ~Bereishit 37;24
This week we learn that Joseph was 17 when his brothers had enough of his reporting on their behavior and they decided to throw him into a pit before, eventually, pulling him out and selling him off to a passing caravan. So our question is, what would be a reasonable estimated minimum size for a pit from which a 17 year old man would be unable to get out?
Volume: the amount of space, measured in cubic units, that an object or substance occupies (ref dictionary.com)
For our purposes, when we think about volume, it's going to be the amount of empty space (technically, air filled space; this happened in Canaan, not in the vacuum of Space) inside the dug out pit. Volume, being a measurement of amount of space that is occupied or contained in an area, is calculated by multiplying the length x width x height (Let's keep it to simple shapes, for right now). This calculation works nicely with a space that is a box or a cube, but not, say, a cylinder. A more general calculation rule, which will also work for cylinders and some other shapes, is to calculate the area of the bottom shape and then multiply the bottom area times the height of the object. For a cylinder, this bottom shape would be the circle. Area of a circle = (radius)2 x π
**radius is the distance from the center of the circle to any point along the edge or circumference of the circle. From the exact center, this distance will be the same for any point along the circumference.
**π- read pi- is a constant number that, for our purposes, can be rounded to 3.14)
Since we don't have records of Joseph's size and no Biblical growth charts remain intact for us to be able to determine the size of the average Biblical 17 year old male, we will make our calculations using the assumption that they were the same size as we are today. Any variations from this assumption will cause the answer to be scaled proportionally.
Height- If we use a growth chart, we can see that, nowadays, an average 17 year old man would be approximately 70 inches tall (about 5 ft 10 in).
Width- Shoulder to shoulder would be the widest part of the body. I'm having trouble finding a shoulder to shoulder measurement from a reliable source, but an average men's suit is approximately 18.25 inches across at the shoulders. Let's assume, given that Joseph was out working as a shepherd, that he was broader than that- let's say 20 inches.
Length- Just to establish an easier set of numbers, let's just say that, whether circular or square, he would have fit into the pit in any direction in which he was put, so the length would also need to be more than 20 inches for him to fit inside.
Okay, so if we assume that this pit was a square at the bottom, and he had to fit deep inside the pit in order to be stuck and not pull himself out, and it had to be wide enough for him to actually fit in when they threw him down, we could estimate the dimensions to be:
Height- 120 inches. Human arm span is typically equivalent to a person's height, which is 70 for Joseph. We already assumed his shoulder span to be 20 inches. If we subtract his shoulder span from his arm span we will get the distance from his shoulders to his fingertips (70 - 20 = 50). Divide that by 2 and we get the distance from each shoulder to fingertips. (50/2 = 25). The average man's fingers are approximately 4 inches, and if we subtract that from his shoulder to fingertip length, we get the distance from his shoulders to knuckles - just enough for him to grab on the the edge of the pit and pull himself up, assuming sufficient upper body strength. That number is 25 - 4 = 21 inches. Most online sources of head size only give dimensions for head circumference, which is relevant for hat sizes but not the distance from shoulder to head. Based upon observation we can assume that when a person's arms are outstretched above their head, the head reaches halfway up the arms. This would reach 10.5 inches on Josephs arms, let's make it 11 to simplify the numbers. 21 inches of shoulder to knuckle length - 11 inches of shoulder to top of head height = 10 inches that his arms reach above his head. Add that to his height: 70 + 10 = 80 inches is the height of his knuckles with his arms outstretched. The average vertical leap for an NBA player is 28 inches. Adding this to his outstretched knuckle height and we get 80 + 28 = 108 inches, or 9 feet. That means that if Joseph had explosive jumping power and a cliff hanger's upper body strength, he could hoist himself out of a pit 9 feet deep. There are records of NBA players with vertical jumps ranging from 40 inches to 60 inches, but we're going to stick with the average for this and say that a 10 foot pit (120 inches) is sufficiently deep enough for Joseph to be unable to rescue himself.
Width and length- 40 inches in each direction (that would give him a little less than an extra foot on either side of him to move around inside the pit)
Now for the calculation:
in inches: 40 x 40 x 120 = 192,000 cubic inches
in feet: 3 1/3 x 3 1/3 x 10= approximately 111 cubic feet
If we wanted to make it more challenging, we could try the calculation assuming that the pit was a cylinder. In that case, we could still use the 120 in or 10 ft for the height, and we would use 20 in or 1 2/3 ft for the radius (if we assume that it's 40 inches all the way across, then 20 inches would be from the center to the side of the pit).
The calculation:
in inches: (20)2 x 3.14 x 120 = 150,720 cubic inches
in feet: (1 2/3)2 x 3.14 x 10 = approximately 87 cubic feet
If you compare the volume of the square pit to the volume of the cylindrical pit, you can see how much extra space is cut out when you have a comparable sized circle cut into a square. That extra corner space really adds up!
So, how big would your pit be?
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