##### 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 *m _{1}* and then, decided to work some more and gathered an additional amount

*m*. Normally, we would expect that the total amount gathered would be the sum of

_{2}*m*and

_{1}*m*:

_{2}*m*+

_{1}*m*Yet, this is not what happened – when the gathered manna was measured, it was exactly one

_{2}.*omer*

*M*. Similarly, if one worked less and gather an amount of

*m*less than others, he didn’t bring home

_{2}*m*–

_{1}*m*, but exactly one

_{2}*omer*

*M*. How can it be? From this fact one can easily derive the formula for the amount of manna gathered:

m’=(*m _{1}*+

*m*)/(1+

_{2}*m*

_{1}*m*/

_{2}*M*),

^{2}where *m*’ primed is the total amount of manna collected by first gathering *m _{1}* and then gathering

*m*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

_{2}*omer*of manna:

*m*=

_{1}*m*=

_{2}*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,

*m*is ½ of

_{2}*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’=(v* _{1}*+v

*)/(1+v*

_{2}

_{1}*v*/

_{2}*c*);

^{2}where *v _{1}* and

*v*are the two velocities we are adding together and

_{2}*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.

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