Challenging the ubiquity of mathematics
How much of human knowledge and understanding does math encompass, and where does it fall short in doing so?
A major goal of education right now is to show students, and even the general public, how mathematics is all around us and how one can appreciate its beauty and elegance. Numerous curricula focus on engaging and connecting students with the subject. This includes moving from more abstract theories to also showing their concretes application in our lives. Another aspect of this is also making math more fun for people. Research has shown how students better appreciate theorems and theories through being exposed to the patterns that result to or because of them. Not only does this approach make math more enjoyable, but also allows students to better apply these concepts.
Personally, I have always loved math for its pure and elegant form. I love how abstract patterns like the Fibonacci sequence appear in various parts of nature. Hence, I also believe that math is not only enjoyable, but that everything in the universe all boils down to math. Mathematics connects everything in our world, and even our world with others. If there was some alien civilization that visited our planet, it is likely that they would not understand our language nor our customs. Fortunately, the fundamental concepts of math are not bound by light-years nor galaxies, and these are probably things that our societies would have in common.
Where it may fall short (?)
But mathematicians are also scientists, and scientists work not by proving, but disproving: challenging certain things we hold true. And for better or worse, that includes the universality of mathematics. In fact, the very meaning of ubiquity and universality can still procure some confusion and debate. In spite of its vast applications, there are still some areas of knowledge that math may not be able to concretely explain. In addition, math may not even be as pure as we revere it to be. And lastly, it is this purity, and our very understanding of math that may limit its universality.
Is the ubiquity of mathematics the obsolescence of other fields?
First of all, what does it mean for a concept to be “ubiquitous” or “universal.” I would like to argue that this does not simply mean being applicable to a wide range of subjects, or that other fields simply cannot exist without it. Instead, I contend that, technical differences and definitions aside, that to be ubiquitous or universal is to make all others obsolete. At first, this may seem outrageous. How then can mathematics be universal? Is that to say that biology, psychology, and all other concepts are to be held obsolete? In an attempt to answer that, let us look at the hierarchy of the academic fields:
To some extent, this can indeed show that other subjects simply take a portion of mathematics and apply it to more concrete areas. But this is still rather hard to grasp. How can psychology, for example, be even to a certain degree, applied math. Psychological concepts and phenomena seem to be devoid of any form of math. But this is simply because the math lays to far behind the inner workings of the subject, and has simply be condensed and manipulated to meet its needs. A possible analogy for this is a computer. At its very essence, computers are essentially transistors and electrical currents, but of course we don’t directly see that when interacting with it. But its definitely still there behind the software and other levels of abstraction, in the same way math may behind the framework of other academic subjects.
Beyond the academic
Unfortunately, the hierarchy of academic fields is precisely that: academic. For something to be held as universal it must not only encompass the academic but also (dare I say) the existential. If the renaissance has shown us anything, it is the nature of human existence. Part of which are the arts: poetry, painting, and music and others. Although numerous correlations can be seen between all three and math (I once wrote an article on the mathematics in zentangles), as I mentioned, application will not suffice. One other point of inquiry is how the beauty of art and literature can be appreciated by so many, and yet the factors that contribute to such are seemingly subjective and abstract. Furthermore, the interpretations of art can vary greatly, and unlike math, there is no defined way of assessing such. Yet despite that, we have classical works considered to be timeless by almost all. These aspects of our humanity can be difficult to reconcile with mathematics. I can try to argue that, like everything else, our brains are also inherently mathematical. In the same way our brains can extrapolate the trajectory of a football, perhaps we also see certain mathematical consistencies in art and literature. A great example would be the golden ratio. Pictures or images in exhibiting the golden ratio are deemed to be “naturally appealing or beautiful.” And maybe our brains don’t consciously seek out such property, perhaps we ‘see’ it the same way we see that football heading toward our face.
But of course, what’s the existential, without the crisis
Life itself, whatever it’s definition, is definitely a significant aspect of the greater scheme of things. Yet when we ask “why do I live” or “what’s the meaning of life,” mathematics doesn’t exactly come to mind. Math doesn’t seem to play a role in the philosophical inquiry of man. Even going back to the academic hierarchy, philosophy is sometimes considered to be more pure than mathematics. One reason may be that philosophy focuses solely on the truth and logic of its arguments. In some way it can, in itself, be considered to be more universal than math. (Perhaps this article should have challenged the ubiquity of philosophy instead… yet here we are.)
Side note: It should also be noted that math is not as pure as we may have assumed. We think and do math through a base-ten number system, one that is not universal or possibly even exclusive to us. Certain principles of number theory would crumble if we tried to apply them to other number systems. For instance, the divisibility rule for three would not work, as it relies on the fact that powers of 10 always have a remainder of 1 when divided by 3. The number 10 which just so happens to be our number system.
Nihilism: there is no why
A possible solution, might actually be nihilism. Nihilists would simply postulate that life has no meaning nor purpose. Life, if it can even be called that, is nothing more than an aggregation of atoms that make molecules that make cells and so on. All of which is made possible through math. The entire universe started with the Big Bang, and through inflation and evolution, things came to be: three phenomena, and other events, which can academically be boiled down to math. We may be wrong about all of that, but whatever alternative we eventually come up with, even whatever actually started this entire thing, will have happened because all the math worked out perfectly. Ergo, all in all, math answers (or will answer) the how, the what, the when, and the where of existence. And there is no why.
Let’s not take the easy way out
The argument I gave definitely has its flaws, and is built on the pessimistic nihilism that many may not agree with. And frankly, even if the argument from there seems sound, it may very much be a lot more complex than that.
Addressing the elephant in the room
Of course, let us not forget that in pondering our own existence, we haven’t even factored in the existence of a higher being. With Him in the picture, math may be overshadowed. Theism and religion is something that math can’t explain. Whatever religion you believe in it is more likely than not math may not be able to account for the miracles and divine works it involves, let alone faith itself.
Well, this is as far as the journey goes
I don’t know about you, but I’m tired. I have taken the challenge far up the mountain as I could, and we definitely did not have an easy climb. We navigated through rough, bumpy, and very much dangerous slopes. Claims were precariously perched on disputable premises. We went from the technical to the academic to the existential, in which the last one we merely hung on with the hook of nihilism. But who knows? We may not be hanging on the edge but merely a ledge. Yes, we have climbed to the divine realms of religion and faith, where we could go no further. Or maybe we didn’t make the climb at all, and everything just collapses. But maybe that’s exactly what we need: just a bit of faith. To have faith in the future advancement of our understanding of math and the universe. To have faith in whatever we believe in, to stay strong in the face of doubt but also in that of change and realization. And of course, have faith that the math will eventually work out.
