The Parable of Pi
It may have been a long time since you forgot the number pi, or maybe you have just met it. Fear not, a difficult math lesson is not waiting for you. Let’s say you want to calculate the area of a circle, you start from the first data you notice about the width of the circle. A circle with a large diameter is wider than a circle with a small diameter. So, in order to calculate the area of a circle that you draw by spreading one leg of your compass as you wish and moving it around the fixed leg, you must have a formula proportional to the length of the diameter. Because the size of the circle you draw is determined by how far you spread the compass leg, that is, how much diameter you assign to the circle.
It is as simple as that and mathematicians have done the same, they have formulated the area of a circle as pi x r². In this formula, “r” represents the length of the radius, and when the length of the radius is multiplied by itself, the square of the radius, r², is calculated. r² is the area of a square with four straight sides and four corners. What we want to calculate here, however, is the area of a circle with no corners and no straight edge. The problem here is to adapt the area of a square with four corners to the area of a circle without corners and with curved sides.
In other words, every calculation of the area of a circle based on the radius is an attempt to equate the area of a circle to the area of a square.
Can you fit a circle into a square in such a way that nothing is left out and there are no gaps anywhere? This is the problem that pi solves. Mathematicians invented pi in order to fit a square area onto the area of a circle. However, to date, no circle, no matter what its size, has ever been exactly equal to the area of a square. There has always been a little bit of space inside the square or a little bit of excess outside. If you remember, they made us memorize pi with only three digits: 3.14 This means that inside a circle you can fit 3 of the squares that you can form with the sides of the radius of the circle, but there is a gap less than a tenth of that square, that is, 14 percent of the square. When you close this gap, the circle is roughly “squared”, that is, divided into square areas. Thus, we are meant to know that within a circle there are 3.14 squares with sides equal to the radius. This is how we learned…
But the work does not end there. The calculation that there can be 3.14 squares inside a circle is still a crude calculation. And when we multiply the square of the radius by 3.14, we may be slightly overflowing the circle or leaving gaps in the circle. Let’s say you are doing a very strict engineering job, you need to calculate the area of a circle as precisely as possible, and when you calculate the area of the circle using pi, which you know to be 3.14, the space you leave out becomes very important, then you have to multiply the digits following 3 even more, make them even finer, get a pi that is even more precise. Just as rounding pi, which is 3.14, roughly to 3 increases your margin of error, rounding pi, which you can write as 3.14159, to 3.14 increases your margin of error. However, the number 3.14159 is also not enough to make the square exactly match the circle; there will still be gaps inside or outside. Now hold on tight, with the calculations made with the help of very special computers, we have reached the 51 billionth digit of pi after the dot. However, even the 51 billion digit pi number is not enough to fit the square into a circle; it is quite crude compared to the 97 billion digit one that is likely to be calculated very soon, and it leads to calculation errors. (If you find it hard to believe me, go to www.joyofpi.com or try reading the book The Joy of Pi, where pi is written up to the one millionth digit!)
The number pi, as a symbol of the discrepancy between the square and the circle, grows longer, more detailed, sharper, thinner, but it never reaches a point of finality. Pi is not less than 3, not greater than 4, but it oscillates back and forth between the two, constantly vibrating. So, no matter how many digits after 3, it is not possible to calculate a circle in square terms with certainty; you always have to accept a margin of error. It is not possible to equate an area with curved sides and no corners to an area with corners and straight sides. Although you can see the area of a circle with your eyes as a finite space with definite edges, when it comes time to put the same area into numbers, you constantly stammer, hesitate, and cannot give the exact amount. Because the number pi, even though it has been calculated up to the 51 billionth digit, is still not exact and will never be exact. Moreover, there is no order and pattern among the numbers following 3. Pi oscillates and oscillates with an unpredictable order, with the arrival of a surprise digit at each digit, never calming down; it gets thinner and thinner, never breaking off.
Let’s talk about our part in the parable of pi. Aren’t we always trying to predetermine our relationships and keep them at predictable rates? Who is adventurous enough to set out on a road whose rules they don’t know, whose route they can’t fully determine? Wouldn’t it be nice if we could mold our interactions with our spouses and friends into smooth-edged, angular and easily identifiable patterns? It doesn’t work, it doesn’t work, it doesn’t work. Day after day, you find a new surprise. You see that what you thought “I get it now!” brings you to the brink of a new unknown.
Let’s talk about our part in the parable of pi. Aren’t we always trying to predetermine our relationships and keep them at predictable rates? Who is adventurous enough to set out on a road whose rules they don’t know, whose route they can’t fully determine? Wouldn’t it be nice if we could mold our interactions with our spouses and friends into smooth-edged, angular and easily identifiable patterns? It doesn’t work, it doesn’t work, it doesn’t work. Day after day, you find a new surprise. You see that what you thought “I get it now!” brings you to the brink of a new unknown.
Don’t think that your relationship will settle down, that your hesitations will end. You are in an interaction as shaky as pi, as hesitant as pi, as chaotic as pi. You cannot overlap the circle of your soul with the edges of this mortal world. You cannot fit the curves of your love into the narrow corners of this life.
If you intend to mold something that can be bent/skewed at every point, that has no corners, that lacks straight edges, that cannot be ruled, measured or weighed, into molds with corners and straight edges, you have a long way to go until the 51 billionth step. Our hearts are always wavering, our emotions are always tossing in a whirlpool of indecision. As Yusuf (as), the epitome of chastity, who was described as “his heart almost slipped”, said, “My soul always desires evil, except if my Lord has mercy.” We are always hesitating, we are far from making up our minds; unless our Lord “rolls” our hesitations and indecisions into loyalty and love!
