March 7, 2010

• Pi and Spirituality

   

  From Kabbalah made easy

   

   

  Pi and Spirituality

  If there is a God, then everything is interconnected, so we shouldn’t be surprised when we find the famous math enigma Pi π hinted to in the Torah, and in Kabbalah. Sure, the Greeks, Babylonians, and Egyptians may have had the kabbalists beat in the general field of ancient mathematics, but while science and math have evolved in amazing ways over the millennium from abacus to supercomputer; spirituality, the mystic's forte, hasn’t.
  They had it back then and they still have it. We’re still waiting for the world to catch on to ideas like Love Your Fellow Man, and we’ll continue teaching and talking about it until it does. We can find Pi hinted to if we look a little deeper into the words of scripture, so too the meaning of life and the important ideas are still there. We need to continue to mine the depths of Jewish wisdom. It’s not out of date.
  Despite the fact that Jews were involved in advanced mathematics in Egypt, Babylon, Greece and all throughout the ages, some historians are quick to dismiss their understanding of math, based on a cursory glance of Jewish literature. We may not have had the first textbook for algebra, but numbers and calculations are of primary concern in every corner of Judaism; from the song Who Knows One? sung on Passover, to the complicated systems of Gematria (math coded in the letters of the Torah). Indeed the early sages were often called Sofrim, which means “scribes” but can also mean “counters” as the sages were often involved in counting days, months, years, as well as letters, words, and verses in Tanach.

  Mysterious and profound

  On a deeper level, the kabbalists delve into the concept of holy emanations or divine traits called Sefirot which comes from the same grammatical root as Sofrim and refers, among other things, to the divisions the Almighty created that are inherent in the transition from an infinite being to the finite world we live in. So counting or enumeration is not just a practical way of measuring lima beans to be sold in the market, but an esoteric path to the heavens as well.
  Sages in the Talmud also took numbers as symbols that traverse huge gaps, tying together discordant themes. For example, the number of judges needed in concluding a court’s ruling on the new moon is seven, which the sages compare and relate to the seven words in the last sentence of the Priestly Blessing, and the seven officials that served King Achashverosh in the Book of Esther. In other words, numbers can serve as bridges that unite disparate divine texts. Put that in Newton’s pipe and smoke it.

  A little bit of infinity

  Fascination with Pi, the ratio of a circle’s circumference to its diameter, has occupied mathematicians for a long time, and math history buffs are familiar with a verses from the Book of Kings I Chapter 7 that describe a pool that King Solomon had built which state the ratio of 3:1, a very rough estimate of Pi which is partially calculated as 3.14159. (The digits keep going forever without any known pattern.) It’s a given that the ancients did not use the number symbols we use, called Hindu-Arabic numerals; these symbols didn’t become popular until the 10th Century. But the Hebrews had words for numbers and used the letters of the Aleph-Bet in place of numbers. And of course they were no strangers to the concept of infinity. Certainly mathematical infinity is not exactly the same as philosophical infinity, but they are cousins. What many people who don’t know Hebrew miss out on is the basic understanding of the primary four-letter name of God, -spelled yud, hey, vav, and hey, it is a construct of three words: he was, he is, he will be, i.e. infinity in time. The English word God is an accurate word but it’s like instant coffee; just doesn’t quite hit the spot. Compounded with a weak word, English speakers are also Godophobic. Unless they are Bible thumpers people tend to avoid talking about God in any real way. But the Psalms and other parts of our tradition are filled with interesting nuances about the Creator. There is infinity in time, space, love, omniscience, and much more; maybe infinitely more. We cannot limit the concept of the Creator, but He gave us a variety of influences or qualities of His, so to speak, to focus our attention on.
  If a circle and a line that cuts through it are a type of miniature infinity in our world, or the world of mathematics, then maybe the ancients knew more about it than we think. Math historians say one ancient manuscript Mishnat HaMiddot by a second century Rabbi Nechemia apparently adjusts the math of King Solomon’s pool by pointing out that it had a lip, which would add a bit to the 3, not quite one seventh which is needed but nonetheless intriguing.

  They did know a thing or two

  Another overlooked source is in the Babylonian Talmud Tractate Eruvin 14a. The statement is made that for every circle the ratio of the circumference to the diameter is 3:1, to which the Talmud asks, “From where?” and the answer is the verses from Kings regarding the pool. This Talmudic passage is odd since the Talmud generally asks “From where?” when it wants to know the Biblical source for Jewish Law. The question doesn’t make sense in this context when we’re asking for the source of an easily demonstrated geometrical measurement. Take a string or rope and measure any circle’s diameter and circumference and you’ll get a fairly accurate answer. A commentary on the Talmud therefore states that the real question of the Talmud is the following: We know 3:1 is inexact. We want to know for purposes of Jewish Law can we round it off this ratio to 3:1. Since the Book of Kings uses an inexact measurement we understand God to be teaching us that it’s ok to use that inexactness in questions of Jewish Law like the proper dimensions of a round sukkah.
  And if you aren’t asleep yet, I’ll tell you something even more fascinating. What makes Pi unique is that it can’t be described in a fraction, i.e. it is irrational. 22/7 is approximate. Through Gematria, we find a more exact version of Pi based on a fraction. Gematria is the numerical system of the Hebrew letters. In the verses of the pool the word for diameter is kav- spelled kuf vav, which would have the numerical value of 106. But instead, in this passage it is spelled with an extra hey, kuf vav hey which makes it 111. An 18th C. sage and math expert, called the Vilna Gaon, noticed that if the value of 111/106 for the diameter is multiplied by 3 for the circumference the result is 3.1415, a closer approximation to Pi. Maybe the ancients knew more than we think?

  A kabbalistic metaphor

  With the world of technology and science advancing at a dizzying pace, we often put the past into a box labeled “Primitivo”. Whatever is older is less intelligent. Less sophisticated. In math the concept of infinity has evolved and advanced over the years. Our understanding of galaxies and light years has broadened our minds. Yet some fundamental truths like peace, love and harmony still struggle like a clinically depressed turtle to move forward for humanity. The Torah is still relevant after thousands of years. And what whets our collective appetite from the paths of spirituality outlined in the Torah all come back to the infinite Creator and His creation. All lines lead back to the circle. What a surprise to find the kabbalists articulating that creation in geometric terms.
  They meant it as a metaphor, not a visual account but an esoteric description. They described the divine act of creation as a circle cut through. Is it a coincidence that the kabbalists use a metaphor that is one of the paradigms of mathematical enigma, the Pi that fascinates mathematicians and has a cult following of people trying to memorize its endless amount of numbers? Contained infinity. That’s a description of Pi, and a description of the creation itself. Once upon a time we were a little closer to the truth.

  • 7:29 pm
  • 1 Comment