Maths

            I’ve done some math during my life. It was always my favorite subject in school and I eventually ended up studying engineering in college, which was practically all math. My job doesn’t go to quite the same level, but I’m still using a calculator regularly. What I’m setting up is the possibly unexpected idea that I don’t believe math applies directly to the real world. Let me explain.

            Math to me is a conceptual tool that is useful for modeling, predicting, and simplifying real life phenomena, but only after the phenomena has been reduced to an idealized form. Generally the more math you use the less idealization, but even the most basic parts of math are based on idealizations of the real world. Take pi as an example. Pi is the ratio between a circle’s diameter and its circumference, and already we’re dealing with idealization because perfect circles don’t exist in nature. Already one step removed from the real world, pi still doesn’t fit into our math. Pi gets a lot of attention for being an irrational number, meaning that it consists of a never ending and never repeating string of digits. This might seem mysterious and unpredictable, sort of a loose cannon of the number world, but to me this is a glaring example of how our math is flawed (I keep saying “our math” because I don’t believing the math that humans use is the only possible math, but that is a whole other discussion that I don’t want to get into at the moment). Since it’s impossible to write down all the digits of pi, it can only ever be used as an approximation. The true value of pi completely escapes our grasp. Just a heads up, this fact is also true of every single measurement ever taken. That’s a pretty devastating blow to math’s ability to represent the truth of the real world, and it’s also a reason why pi isn’t all that special. Technically, there are a few measurements that define units. When you weigh the International Prototype Kilogram it’s exactly one kilogram, but that’s more a(nother) reason why the IPK is stupendous and less a triumph for mathematics.

The IPK is so great

            Leaving out all that irrational number bullshit, we’re still left with adding, subtracting, multiplying, and dividing, aka doing arithmetic to, discreet objects. For example, take four apples. Add two apples to get six. Double the number of apples to have twelve. Divide out a fourth of the apples to have three. Then subtract two apples and one apple is left. Repeated an infinite number of times, this process should always result in one apple. It’s too bad that the apples have to be completely idealized first. The reason this apple arithmetic works is that it assumes that one apple equals one apple equals one apple, just like how the number one equals the number one equals the number one. In the real world, every single apple is unique, so they can’t be used like numbers. One apple plus another apple is not equal to a different apple plus another different apple, but one plus one always equals one plus one. Numbers are also homogenous in a way the worldly objects aren’t. It is impossible to cut an apple in half and have two identical pieces the same way that the halves left after dividing one in half are identical. The only example of arithmetic that might work in the real world is if you subtract out everything to get zero, because if you have three apples and then take all three away it doesn’t really matter what kind of apples you had to begin with. Only math has to go and ruin this situation too, since if you ask any math major they’ll tell you that subtraction doesn’t exist, it’s only addition of an inverse. Inverse apples definitely aren’t a real thing, so there goes that.

An inverse apple?

            Now it might be possible to do this kind of arithmetic with quantum particles, because as far as physicists can tell all electrons are identical (as far as values for mass, charge, and spin go anyway). Assuming this isn’t just due to a lack of measurement precision; electrons start to look a lot like numbers. An electron can’t be divided into fractions and subtraction is still right out (an anti-electron is kind of like an inverse electron, but an electron plus an anti-electron results in energy, not zero) so it’s not perfect. This leaves addition and multiplication as a sort of fancy way to count. There’s also the fact that the quantum mechanics that describe the behavior of electrons are far removed from experiences of the macroscopic universe and can only be expressed using math, so I’m not ready to except quantum particles as an example of how math existing in the physical world.

            I’m not trying to say that math is bad or doesn’t have value. The measurements, predictions, and models that math can create are absolutely amazing and incredibly useful. Almost none of the aspects of modern civilization would be possible without math. Sure, the Romans build some pretty great stuff without using math as we understand it, but I think we’re doing things better now (the road I help build beat Roman roads any day). I just think it should be acknowledged that math is using abstractions and idealizations, and isn’t some great truth at the heart of the universe. Also pi really isn’t that cool.