This morning, the wildly popular Facebook blog, I Fucking Love Science, posted the above image. The blog, probably one of the most popular on Facebook, is getting a lot of attention recently due to the (somehow shocking?) revelation that it is run by a young woman. It’s a wonderful blog that uses little-known scientific facts to blow people’s minds on a daily basis. And though usually I enjoy their posts, I woke up to this one, and felt a little disappointed. The image explains the nature of the irrational number Pi, and goes on to describe its magical wonder at having an infinite, non-repeating series of integers. Though most of the information she gives is theoretically true, it really has more to do with the nature of infinity than the magic of the number pi, which really isn’t all that special.
To see why, let’s think about what pi actually is. Pi is simply a number. It’s the ratio of any circle’s circumference to its diameter. And while it is somewhat fascinating that every circle ever has this same ratio, it is more a result of the definition of a circle, than a miraculous coincidence. As discussed in my post, The Limits of Language, science and mathematics are simply the languages we use to understand the universe. If we forget to think about them that way, then when these coincidences and patterns crop up, we assume they are miracles of the universe and attribute special meaning to them, when they are simply anomalies in our language system. Take pi for example. There is a constant number that exists that defines the ratio of any circle’s circumference to its diameter, but because that number doesn’t fit nicely into our number system, we have to make up a symbol for it. If we try to define that number using our numerical language, it yields the irrational number that the Facebook blog considers so magical, when it is really just a problem of translation. And, yes, it is true that in an infinite, non-repeating, random series of integers, theoretically every combination of integers will exist, but this is more a result of the series being infinite, than anything that has to do with pi specifically.
Another reason that pi is not special (sorry bud) is that there are literally an infinite amount of irrational numbers. In fact, as Georg Cantor proved, and as can easily be seen, there are actually more irrational numbers than rational ones. Once again, this goes back to how we define our numbers. Numbers exist on a scale, much like wavelengths of light. This scale can be, for lack of a better term, ‘zoomed in’ on to the nth degree (meaning infinitely). So between any two integers, 3 and 4 for example, there are an infinite amount of numbers that we cannot fully represent using the number system that we’ve created, and each one of them translates into an infinite, non-repeating decimal that has the same characteristics of pi.
So yes, infinity as a concept is really something special, but it is simply that: a concept. Though we can represent it and theorize about it and try to define its characteristics, it merely exists in our own minds.