Gifts of Yaakov

Parashat Vayishlach contains a very intriguing detail of the gifts that Yaakov presented to his brother Esav. What could be thought of as one of those unremarkable numbers that seem to intrude into our narrative turns out to be a fascinating detail that only mathematicians could have taken notice. The following excerpt would briefly explain to us the concept of "amicable pairs" which the author calls the "friendly pairs". The mystery lies whether Yaakov actually knows the mathematical properties of the number of flocks in each set of gifts he presented to his brother. But what is clear is the mathematical evidence of God's fingerprint in a very ancient text that Moses compiled for us.

In what unexpectedly turns out to be a successful effort to regain Esau's friendship, Jacob sends Esau a gift of 220 goats. Of all conceivable numbers, this is the most symbolically important he could have given. This quantity is the smaller half of what mathematicians call a "friendly pair" of numbers, the larger part is 284. The properties of friendly and perfect numbers are almost identical. If the sum of the divisors of one quantity equals another, and vice versa, then the two are called a friendly pair.

1, 2, 4, 5,10, 11, 20, 22, 44, 55, 110 all divide 220
1+2+4+5+10+11+20+22+44+55+110 equals 284

1, 2, 4, 71, 142 all divide 284
1+2+4+71+142 equals 220

THE FIRST GIFT: 220 GOATS

Now let's realize this is approximately 2000 B.C.E. and Jacob is a semi-nomadic herdsman. Such traveling flock-keepers lived a life of severe hardship, carrying with them everything they owned. There was only enough time to learn what was necessary for survival. For these reasons, it is totally impossible for Jacob could have known the properties of friendly numbers without help. So the angels of God must have told him.

In the early centuries, it was a common practice for two people to each wear one of these number (1.e. 220 or 284), signifying their friendship. Outside the bible these quantities were first mentioned by the Greek mathematician Pythagoras around 550 BC -- 1500 years after Jacob.

The scripture pointedly emphasize this quantity by a second gift of 220 sheep (Genesis 32:14). Still, Esau probably never counted any of these animals. Even if he had the exact numbers would have meant nothing to him. God alone knows the past and the future; therefore, the numbers are for our benefit not Esau's. This implies the Lord must have softened the heart of Jacob's brother. And the Holy Spirit depicted that softening by using what would be called friendly numbers. ..

Jacob's peace offerings hold still more surprises! In the verse following 14, a third gift is prepared consisting of 140 animals. This quantity is the smaller half of what mathematicians call a semi-friendly pair of numbers, the larger part is 195. These quantities differ very slightly from the former by not including 1 in the sum of their divisors. As before, 140 and 195 are the smallest possible such pair.

2, 4, 5, 7, 10, 14, 20, 28, 35, 70 all divide 140
2+4+5+7+10+14+20+28+35+70 equals 195

3, 5, 13, 15, 39, 65, all divide 195
3+5+13+15+39+65 equals 140

THE THIRD GIFT: 140 ANIMALS

James Harrison. The Pattern & The Prophecy. 1994. (pp 27- 30)