Why is Mathematics so Useful in Describing Reality?
Mathematics is often called the language of the universe. It’s the most vital part of any scientist’s toolkit, helping them sort the wheat from the chaff in bloated data, giving them new perspectives on old theories, and enabling them to predict phenomena in the world around. But why is it so? Why is fancy number manipulation so effective?
Before we try to answer this famous question (first posed by the physicist Eugene Wigner), we must first understand why might mathematics is useful in the first place and why we are stuck with it.
Mathematics is extremely useful in the sciences, especially in fields like physics, as it allows us to work with abstract concepts and ideas that evolution could not consider while developing our intuition. We have a wickedly powerful and accurate intuition for everyday situations like throwing a stone, visualising objects in three dimensions of space and jumping. But let’s say you were tasked with solving a problem which was posed in four dimensions of space, how would you go about doing it?
If you said mathematics, you are absolutely correct (hooray!). We might not be able to visualise anything other than the three dimensions of space (you cannot even imagine objects in lesser than three dimensions of space, try it), but that does not stop us from generalising the concepts behind what we call a dimension and extending it to any number of dimensions. All we have to do is say:
Ok so every point in a certain patch of three dimensional space is characterised by a set of 3 points, so any point of n dimensional space will be characterised by set of n points.
To perform generalisations of this sort, mathematics is indispensable. There is no other tool that (at least I know of) could perform this feat. This sort of generalisation is what allows scientists to do wizardry with mathematics.
One of the pillars of mathematics is logic. Logic is a field of study that’s a bit tricky to define, but for intents and purposes it can be defined as: the study of correct reasoning, given certain true or false statements. In logic, we’re taught about logical operators, like: AND, OR, NOT (along with XOR, NAND, NOR if you’re a lucky computer science student) that act on conditions and either give a true or a false as an answer. An AND operator only gives a true as output when both its inputs are true, whereas an OR operator spits out true when one of its inputs is true. Listing out the outputs of logical operators in the form of truth tables, is a useful way to learn about operators.
Now imagine putting in the same conditions with the same operator and getting true or false randomly. Or a statement being true one day but false the next, for no good reason. Breaks reality doesn’t it? This is exactly why I believe that mathematics is such a great tool for describing reality. One of its base assumptions is that reality makes sense, and that things don’t just randomly happen, nature does not just do things on a whim. Now in a world, where things happen randomly, mathematics will be one of, if not the poorest tool to describe reality. But why does nature make sense in the first place? Who knows.
Logic makes mathematics the powerhouse of imagination that it is today. It enables mathematics to be used as a tool to predict, model and extract information from the world. It does this under the assumption that reality makes sense, and things don’t just randomly happen. Making this assumption, seems like a no-brainer, but it really isn’t. Answering why does reality make sense in the first place is of deep interest to not only mathematicians but also philosophers. String theorists suggest that we’ve been asking the wrong question all along. They say that we should instead be asking, “Why do we find ourselves in a universe which makes sense?” Now that is something to ponder on.
Originally published at http://shortdotcircuit.wordpress.com on November 27, 2020.
