While normal people have sex-lives and hobbies, I’m over here thinking about pi. It’s not that I’m a super-nerd, I’m actually not all that smart, but I’m curious. Einstein said that’s a good thing and I believe him.
So I was thinking about pi and my question was this: In year 7 maths we find out that the diameter of a circle multiplied by pi equals the circle’s circumference, right? But how can an infinite number give a finite answer?
I asked the guy who did a really cool Tedtalk about maths, Roger Antonsen, and he was kind enough to answer. He explained that pi isn’t infinite, it is a finite number, and “do you mean how the numbers continue on without repeating themselves?”
I dunno. I dunno if that’s what I mean.
I just confirmed with my son who said, “It’s not an infinite number. It’s just a very, very accurate number. You think of it as infinite because the numbers beyond the decimal point are infinite, but pi itself is not infinite.
Ok I get it now, nerd-boy.
Speaking of nerd-boys, Roger also quickly translated one of his blogposts about pi into English for me, too, which did provide more insight. (Crazy smart people who can “quickly translate” things…). You can find it here.
What I found really helpful is that he explained it is just a ratio. That’s when I had a little lightbulb moment. Of course it’s just a ratio! I told you I’m not overly smart, and also I went to a terribly crappy high school, and this is completely obvious when you think about it.
The reason why Pi can go on forever and yet give a complete number as answer lies in the maths itself. Circumference/Diameter = Pi.
It’s not that a never-ending number is giving us a whole number, rather that whole numbers as a ratio (circumference and diameter) are always giving us that same never ending number. It is because of this that the opposite can be true. I’m not sure if this makes sense, but this is how my brain finally gets it.
It also makes me think that when we use pi to calculate a circumference, the answer would never be 100% accurate (but close enough) since pi – as stored in the calculator – could never be complete. On the other hand, whenever we use the circumference/diameter to get pi, pi is always accurate but our calculators would not be capable of showing it.
Pi is cool, when you think about it. Not because it goes on forever but the fact that every single circle, whether it’s big or small, adheres to the ratio.
Of course, it’s dumb to say that circles “adhere” to anything. They’re just doing their own thing, being circles. And if you think about it even further, numbers aren’t really “real”, but a language we have created to describe what simply just is.
The language of numbers is oddly flawed, too, as evidenced by things like Zeno’s paradox which I wrote about the other day. Zeno’s paradox shows how mathematically, movement can be seen as impossible since there are an infinite number of points we need to move through to get anywhere. If I want to move my arm 10cm, first I need to move it 5cm, 2.5cm, 1.25cm, etc etc, and as you know, I will never get to zero.
If I never get through all the points I must move through, how could I ever possibly move?
Surely it all this means is that maths is not a perfect language. It makes me like maths more, somehow. It’s imperfect just like me. *winks at maths*
The universe is amazing and maths is an example of how we are sitting here within it thinking we could completely figure it all out. It’s like trying to understand the colour purple when you’re actually living inside the colour red – you know nothing but red your whole life, you’ve never seen anything but red.
The way you have to describe purple, when you live in red, is going to be long and convoluted. If you could just step outside the red, you’d understand. But we can’t. This is why we ask weird questions like “where did the big bang start?” which of course makes no sense. You’d have to be outside it not within it – we are the big bang; it didn’t start anywhere within itself.
This is such a small piece of the puzzle (or pie), there is too much to learn and I don’t have enough time.
But today, I finally made peace with pi.