Why 3 is the Best Number
The place beyond two is filled with possibility
In the land of numbers things can get pretty competitive. Zero is often touted as the ultimate number invention even though it means nothing. Without the zero much of modern math wouldn’t be possible. It’s also a part of another favorite, the 10 which forms the global base ten system. Zero also makes up the dynamic duo of binary. Which brings us to number one. By definition it should be the best. It also represents the boundary between nothing and something, between fractions and a whole, and is the easiest part when learning multiplication and division. It also forms a key part of the definition of prime numbers, another set of special digits that’s given the spotlight often in our digital age. Within the primes there is the lucky 7 and the unlucky 13. There’s also number 2, the scrappy sibling of 1. With two it enters into the plural range and forms the basis for even numbers, which are neat and clean unlike those odd ones. The number 5 gets some special treatment as the half of 10. Likely a scheme between 10 and 2. This finally brings me to number 3.
As a base number it doesn’t really produce anything elegant like the 1, 2, and 5s do. The set of multiples form an irregular pattern of {3, 6, 9, 12 ,15, 18, 21…} where it can’t seem to decide if it’s odd, even, prime, or anything really. When we take a ratio of 1/3 it is by definition irrational with its awful repeating decimals. If we move into logs, that realm is dominated by 10s and 2s. A base 3 doesn’t really play very nice. It almost seems like three is there simply to make every calculation more complicated and messy. But it has special characteristics that makes it the best number.
With zero we get none. With one the singular. Two serves up the pair. With three, however, we get a group, we get parts. Lining them up side by side, there becomes a beginning, middle, and an end. Without the 3 there would be no story arcs, no three act plays, no rating scales, and even no sense of time. There is only a past, present, and future when thinking in threes. Same with negatives, zero, and positives. By having three points it introduces the middle and it’s relative sides above and below. It provides an anchor point to compare relative values, at least on a one-dimensional line.
If we move into two dimensions, the number 3 provides the start of geometry. Three points introduces the triangle and along with that the basis for much of geometric shapes. All polygons can be reduced to a series of triangles. The only shape that avoids this fate is the circle, but even then three points are needed for most of the interesting properties of circles. Like the arc for example requires the center point and two edge points to make up both the radians and the inner angle for the wedge it forms. In fact, there would be no angles without three points at all!
The real magic comes when we move into the third dimension. Suddenly the flat Cartesian plane becomes a space where prisms and spheres come to life. They have volume. The plain movements of translation and rotation are now coupled with roll, tilt, and yaw exponentially expanding the ways shapes can move. There is this wide array of planes and curvatures that can render more complex peaks and troughs beyond the typical two-dimensional waves. Only when reaching the third dimension are we able to start modelling and understanding the real physical space around us, and it starts to feel less like a odd abstraction we have little relation to even if all math and numbers always feel a little strange.
Of all the digits in our little number family, the number 3 often gets treated like the odd one in the bunch. It’s not clean, it’s not neat, it doesn’t make the math life easy, but it holds a special place it my heart. It is a magical little number that makes so many things possible.
