Mathematical Shiny Objects

Day 154: Pi Day has come and gone. I acknowledged it with cookies because I am a non-believer. We're going to be paddling in the deep end today, so be sure to wear your bathing/thinking cap. Let's begin with a circle. Draw it on your computer, paint it on your floor, put pen to paper, just draw a circle and then fill it in with colour. When you finished the job, you should have been able to calculate exactly how much colour you'd used. But you can't. Because pi. Pi is an irrational number. To date, it has been calculated out to some billions of places and its fractional sequence still cannot be determined exactly; therefore, you cannot calculate how much colour you used to fill your circle. I don't care if you weigh the paint can or count the grains of graphite left in your pencil. You cannot know the exact amount of colour you used to fill your circle. Period. Well, that's a hell of a thing, ain't it? Science just did a whopping belly-flop in our mental swimming pool.

All my senses tell me that something is wrong here. Obviously, we have used finite amounts of colour to fill a well-defined area, and yet we cannot quantify it. The trouble originates with pi, or rather with an artificial construct without a precise value, as demanded by our system of mathematics. Aha! There, dear readers, is the elephant in the room which no one wants to talk about: our system of mathematics. Heaven forbid we should have to admit we've been wrong all along in how we calculate things.

I have said repeatedly that the human mind is still in a very early stage of evolution. One example of the primitiveness of our mental capacity would be that fiction as a form of entertainment was an unknown concept a mere thousand years ago. Oh, there were a few examples of it earlier (I could point out a major one, but would be risking the displeasure of the religious among you), but the mind of the average human could not grasp the "un-factualness" of a tale. Lying was understood, but using non-fact as an amusement was not. Likewise, the idea of geocentrism was eventually discarded when humans realized that the starry field above them was far more distant and moved in a manner which could not be explained by being centered upon the Earth.

Even today, we revert to beliefs when no other explanations afford themselves in a manner we can understand. Our mental incapacity hobbles us when trying to solve the cosmological constant problem, but we lean on it because we don't know how to look in another direction. We don't even know that another direction exists. Nor do we know how to look for the stability another system of mathematics might give to pi, one which allows us to know precisely how much colour fills our circle. In fact, we have been so distracted by the mathematical shiny object of calculating pi to its last decimal place that we aren't even bothering to look for a way to make the irrational rational.