Weekly Words by Rabbi Adam
Although we find ourselves in the awkward period between Purim and Pesach, there was actually quite a significant holiday this week: Pi Day. 3/14 (which is how Americans write 14 March) is of course reminiscent of the start of Pi as a constant expressed in decimals (3.14). For those who can’t quite recall their maths from school, Pi is such a significant number for a few reasons: 1) it expresses the ratio of a circle’s circumference to its diameter, 2) it is completely irrational, and the digits which follow the decimal place continue unto infinity in a pattern that defies all patterns and appears completely random.
What we now call Pi was known to the ancients as well. Egyptian, Babylonian and Greek civilisations had all puzzled out at least the basics of Pi millennia ago. Yet what about that other ancient civilisation that still survives, our own? The rabbis actually did have a knowledge of Pi and they certainly had inherited many geometrical sensibilities from the ancient societies in which our ancestors had lived. Yet they also gave it a distinctly spiritual meaning.
Notable among those who tried to explain Pi from a Jewish point of view was R’ Moshe ben Maimon (Maimonides): ‘You need to know that the ratio of the circle’s diameter to its circumference is not known and it is never possible to express it precisely. This is not due to a lack in our knowledge […] but it is in its nature that it is unknown, and there is no way [to know it], but it is known approximately.’
In this way, Maimonides justified the rabbis thinking of Pi as ‘three and one-seventh’, even while acknowledging that it was far more complicated than that! Yet the approximations we make for the sake of ease aren’t down to laziness – ideally they’re a recognition of the fact that we can never really know the true number that Pi represents.
In that, Maimonides is right. We can’t ever know. We can calculate Pi to a million digits and still be no closer to ‘the truth’. On a day on which we celebrate science, on which Albert Einstein was born and which will be the ‘yahrzeit’ of Stephen Hawking, we could do with the dose of humility that the rabbis brought to Pi. Yes, this irrational number is one of the most important in the universe, but like many of the most important things, we can never know it completely, we can only make an approximation. Happy Pi Day!
For more on the rabbis and their calculation of Pi, look here.