Shelach- More Unit Conversions

"[The spies] arrived at the Valley of Eshcol and cut from there a vine with one cluster of grapes, and they carried it on a pole, by two, and of the pomegranates and of the figs." ~Bamidbar 13;23 

Rashi on 13;23 says:
And they carried it on a pole, by two: From the implication of that which has been said, "And they carried it on a pole," am I not aware that it is carried by two people? Why does the Torah say "by two"? It means that it was carried by two poles, not by two people. How was this done? Eight of the spies took a cluster; one took a fig; and one a pomegranate. Joshua and Caleb did not take anything, for with [the spies'] entire being, i.e., they had no goal in bringing the fruit other than that they intended to spread slander against the Land of Israel, by saying, "Just as its fruit is unusual in its size, so are its people unusual." And if you wish to know how much the burden of one of them was, i.e., how much one of them was able to carry, you can go and derive this from the stones which they set up in Gilgal. They lifted for themselves, each individual, one stone from the Jordan onto his shoulder, and set it up at Gilgal. Our Rabbis weighed [these stones]. The weight of each one was forty se'ah. And we learned that the load that a person can raise onto his own shoulder is nothing but a third of the load of the entire load that can be raised when they assist him to raise.

Before I begin, I want to make note that I first got this idea from 2 of my students who used this topic as the basis for their Math 'n Torah Fair project.

Back in Parshat Chayei Sarah we converted between two Biblical units to be able to compare weights that were measured with different Biblical measurements. What if we want to figure out, here, the weight of each fruit? Or what about how much weight each person was carrying? Again, we'll need to look to unit conversion to find out answer. In order to figure out these weights, we'll need to know the equivalent weight of a se'ah.

A se'ah is usually used for measuring volume. However, the reference which Rashi is using here is from Gemara Sotah (34a), where they chose to use the weight measure of se'ah. Most modern day estimates for the weight of a se'ah are between 2.25 gallons and 4 gallons. For our purposes, let's use the 2.25 gallon reference, as this will tell us the smallest possible estimate for the weight of the fruit. 1 gallon of water is just over 8 lbs, so the weight of the fruit, if we use the weight of water, would be 2.25 x 8 = 18 lbs. 

Let's think about:
1) What was the weight of each fruit?
2) How much weight was each person carrying?

To begin, let's organize the information that we have from Rashi.
*The fig was carried by one person
*The pomegranate was carried by one person
*The cluster of grapes was carried by 8 people

According to Rashi, each of the spies could carry a weight of 40 se'ah. This would mean that the spies carrying the fig and pomegranate were each carrying 40 se'ah x 18 lbs each, which is 720 lbs.

Now, for the grapes, Rashi says that the load that a person carries on his own is only 1/3 of the load that a person can carry with assistance. By this reasoning, 40 se'ah was only 1/3 of what each spy could carry; in other words, each spy carrying the grapes would be able to carry 40 x 3= 120 se'ah. This is the same as 120 x 18 = 2,160 lbs.

By this reasoning, the 8 spies carrying the grapes together should have been able to carry a total of:
120 x 8 = 960 se'ah or 
2,160 x 8 = 17,280 lbs

So, by our calculations the weights were:
pomegranate = 40 se'ah = minimum of 720 lbs
fig = 40 se'ah = minimum of 720 lbs
cluster of grapes = 960 se'ah = minimum of 17,280 lbs

The parsha does say that the fruit was big...

To give a little perspective, 
*Arnold Schwarzenegger is recorded as deadlifting 710 lbs. This would mean that each of the spies was approximately as strong as Arnold Schwarzenegger.
*A large elephant is approximately 15,000 lbs, which means that, based on the estimates here, 8 Arnold Schwarzeneggers could possibly carry 1 reasonably patient large elephant.

Everyday Connection:
Let's test the premise- The idea that each spy carrying with a group was able to carry 3x the amount that they could carry individually is an interesting one. I wonder how this would test out in everyday life. How much weight can you lift on your own? How much weight can you lift with one other person? Two other people? Is there are pattern that emerges in the ratio of [# of people] to [weight lifted]?