Two, 4, 6, 8 … What comes next?
Once you recognize this as a sequence of even numbers, counted by twos, then you know that the numbers 10 and 12 come next.
Two, 3, 5, 7, 11 … What comes next?
This sequence of prime numbers (numbers divisible only by themselves and 1) continues with 13 and 17.
There is elegance in number sequences. Patterns discovered reveal a logical underpinning to the world in which we live. As a former physics major (who spent two-thirds of my college years deeply ensconced in the intricacies of the laws of our universe), I am energized by the patterns that define our world.
British philosopher-mathematician Bertrand Russell (1872-1970) expressed it this way:
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere … yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”
Even Torah contains mathematics that illumine the beauty of the existence in which we live. While the numbers within Torah may not unlock hidden biblical codes that prophesy the future, they do reveal the elegance that is God’s Creation.
So when a discerning bar mitzvah student pointed out that his Torah portion, Naso, contained two amazing numerical sequences, I was fascinated.
Parashat Naso contains Birkat Kohanim, the Priestly Benediction, a blessing first recited by the Israelite priests on God’s instruction as they blessed the people. It has maintained a central place in Jewish prayer, being recited in the ancient Jerusalem Temples, during Shabbat morning services, in Jewish homes on Friday night and at almost every Jewish life-cycle ceremony.
Birkat Kohanim is a simple yet complex three-line prayer:
Yivarechecha Adonai v’yishm’recha.
Ya’er Adonai panav elecha veechuneka.
Yeesa Adonai panav elecha v’yasem l’cha shalom.
May Adonai bless you and watch over you. May God’s countenance shine upon you and be gracious unto you. May God’s countenance be lifted up to you, and grant you peace.
Three lines of Hebrew, 15 words and 60 letters in total. Look closely and beautiful patterns emerge.
Count the Hebrew words in each line: 3, 5 … What comes next?
The number 7, completing two patterns — odd numbers counted by twos, and the next prime number. Both answers capture sophisticated arithmetic construction.
Different rabbis tried to assign meaning to this pattern. The Spanish rabbi Bachya taught that this pattern reminds us of the foundation for all blessings: the three patriarchs, the five books of the Torah and the seven heavens of mystical meaning. To him, our ancestry, our sacred book and our spiritual universe are all aligned in each moment of blessing.
Count the letters in each line: 15, 20… What comes next?
The number 25, the next when counting by fives. What a wonderful progression in our modern decimal system — 15, 20, 25. Or, if you add the number of letters together, you get 60, recognized by Italian biblical scholar Moshe David Cassuto (1883-1951) as the basis of the ancient Babylonian sexagesimal (base 60) system.
And it gets better.
Next week, at the inauguration of the mishkan (the movable wilderness sanctuary), each tribal head brings identical sets of sacrifices. The greatest offerings, in quantity and, apparently, in prominence, were the korbanot shelamim (peace offerings). Each leader brings 15 animals: five each of rams, goats and sheep. Together, 12 tribes brought 60 of each animal.
The Midrash (Bamidbar Rabba 14:18) connects these offerings with Birkat Kohanim. Birkat Kohanim — containing 60 letters — concludes with the hope for peace (shalom), while the peace offerings (shelamim) contains 60 gifts to the Divine. Montreal scholar Shai Peretz notes:
“Given the strong correspondence between the two adjacent Torah sections, the question is of the chicken and the egg. Which element impacts on the other? Do our offerings to God yield blessings, or do God’s blessings lead us to make offerings to God?”
These fascinating questions hint at a deeper reality. As my bar mitzvah student Quinn Chambers suggested,
“It is interesting to find these patterns in the Torah, since Torah is filled with so many laws and religious ideas. Perhaps these mathematical patterns show that the Torah is not just a bunch of pretty ideas, but rather that it is also connected to the laws like mathematics and logic that govern life.”
Once you recognize these patterns in the text, it becomes more difficult to consider math/science and religion to be completely separate arenas of existence.
May the mathematical beauty of Birkat Kohanim open your eyes to the religious elegance in our world.