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.