This is the thing which the LORD hath commanded: Gather ye of it every man according to his eating; an omer a head, according to the number of your persons, shall ye take it, every man for them that are in his tent.’ And the children of Israel did so, and gathered some more, some less. And when they did mete it with an omer, he that gathered much had nothing over, and he that gathered little had no lack; they gathered every man according to his eating. (Ex. 16-18)

Jews in the desert were given manna – one omer (Biblical measure) per member of the household. Biblical commentator Rashi explains:

Some gathered [too] much [manna] and some gathered [too] little, but when they came home, they measured with an omer, each one what he had gathered, and they found that the one who had gathered [too] much had not exceeded an omer for each person who was in his tent, and the one who had gathered [too] little did not find less than an omer for each person. This was a great miracle that occurred with it [the manna].

Some gathered more, some less… But when they measured, each got exactly one omer of manna. How can this be? Let’s denote one omer of manna as M. Suppose, someone first gathered the amount m1 and then, decided to work some more and gathered an additional amount m2. Normally, we would expect that the total amount gathered would be the sum of  m1 and m2m1 + m2. Yet, this is not what happened – when the gathered manna was measured, it was exactly one omer M. Similarly, if one worked less and gather an amount of m2 less than others, he didn’t bring home m1m2, but exactly one omer M. How can it be? From this fact one can easily derive the formula for the amount of manna gathered:

m’=(m1+m2)/(1+m1m2/M2),

where m’ primed is the total amount of manna collected by first gathering m1 and then gathering m2 amounts of manna. Let’s consider the following example. Someone worked twice as hard and thought he had gathered twice the amount of manna. That means that the extra portion m should be equal to an omer of manna: m1 = m2 = M. Let’s plug this in our formula and we get 2 M in the numerator and 2 in the denominator. Thus M’= M – those who gathered more still got only one omer of manna. Let’s suppose someone lazy worked only half a day presumably gathering only half an omer of manna. Let’s do the math. In this case, m2  is ½ of M and has to be taken with the minus sign. We get ½ M in the numerator and ½ in the denominator. Once again, those who gathered less still got their one omer of manna. The formula works!

Those who studied Special Theory of Relativity will immediately notice the uncanny resemblance of the formula above to the formula for addition of velocities:

v’=(v1+v2)/(1+v1v2/c2);

where v1 and v2 are the two velocities we are adding together and c is the velocity of light in the vacuum. Indeed, the analogy is clear. The velocity of light in the vacuum, c, is a universal constant. That means that if you shoot a laser beam from a rocket flying at half the speed of light, the velocity of photons will not increase by 50%. In fact, when we measure the velocity of photons in that beam of light, we will find they all moving with the same constant velocity c. Similarly, if you shoot a laser beam from a rocket flying in the opposite direction at half the speed of light, the velocity of photons will not decrease by 50%.  It will still be c.

The same is with manna. Those who worked more or worked less – when measured, everyone gathered the same amount, one omer of manna. The omer of manna is also a universal constant just as the velocity of light in the vacuum. Perhaps this is why one omer of manna was preserved for generations to come – yes, to remind us of the miracle in the Sinai desert – but also to teach us the concept of relativity.

 

The Gathering of the Manna, c. 1460-1470.

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