Today is March 14. Pi Day. Pi is a constant, the ratio of the circumference of a circle to its diameter–any circle. It’s 3.14 something, something, something, and on and on. The numbers to the right of the decimal point never end and never repeat. I believe there’s even a mathematical proof that proves this. Pi is called an irrational number because it cannot be represented by the ratio of two other numbers, such as 2 also being represented by 10/5. And guess what? It’s my birthday! I think it’s cool that I share my birthday with Albert Einstein and a celebration of pi. I’ve had a few thoughts about pi over the years, so I’m taking this opportunity to talk about them.
What fascinates me about pi … is that the number is non-ending, non-repeating. But first, let’s realize that the world of math is different from the real world. More on that later, but a perfect circle does not exist in nature, although it certainly exists in mathematics. We can describe it with a single number, it’s diameter. The problem is, when we start talking about the real world, we have to consider the world of quantum physics.
In quantum physics (Niehls Bohr and Albert Einstein pictured), there’s a distance called the Planck’s length. It’s very, very tiny, at the subatomic level. And the thing is, at these short distances, there’s uncertainty built into the fabric of the universe. A man named Heisenberg theorized about it, and now it’s called the Heisenberg Uncertainty Principle. At distances smaller than the Planck length, the precise position of a particle (which at this scale, becomes more of a probability function with respect to location) is impossible (if you know it’s momentum). Anyway, you get the idea. Things get fuzzy at distances that small, and they get fuzzy in a very mathematical way. It’s baked in (i.e., formed shortly after the Big Bang).
And so what does pi have to do with quantum physics or Albert Einstein or Neils Bohr or anything else in the real world? Isn’t it a number that doesn’t exist in reality? That in reality, we always end up doing an approximation when it comes to calculations using the ratio pi? I mean, because the number is neverending, a computer could never complete the calculation using the full range of decimal places (because it never ends).
On the other hand, there are equations which do not use the term “pi”. And perhaps somewhat poignantly, it is Albert Einstein’s equation (his birthday is 3.14). E = M*C(squared). Wow. No approximation! I think there needs to be a distinction between the estimated (rounded off) results (that come into play whenever pi is in the equation) and the results that come from Einstein’s equations. Also, I think the difference is related somehow to Heisenberg’s Uncertainty Principle. Energy (E) and Mass (M) are conserved. There are laws of physics that say so. But in the quantum world (Planck’s length and smaller), imprecision enters reality. We round off.
Rounding Off. And here’s the other odd thing. According to the rules of quantum physics, unless those wave forms (wave functions) that represent particles, the stuff the universe is made of, are measured, they retain their waveform properties. In other words, it’s our conscious minds, our constant interacting with the universe by “observing” it that collapses those probability wave forms and thereby creates the physical “stuff” that constitute this universe.
And so, here’s the logical conclusion from all of this. Maybe I’ll do a Boolean algebra proof. That’d be kinda fun. Anyway, because we as conscious human beings can grasp the concept of pi, because we “observe” and thereby collapse probability wave functions, Pi is the physical manifestation of the Heisenberg Uncertainty Principle. I don’t think there is a precise way to define this relationship, but then, that’s what new branches of mathematics are all about.