In algebra right now I’m being tickled with the study of imaginary numbers. It’s funny, normally when people think about imaginary numbers, we think, “Well, what good will that do? They’re not real! What purpose could they possibly serve?” Au contraire, imaginary numbers are all around us. For why did we decide that some numbers are imaginary and some are “real,” anyway? What is reality, after all? Is it everything we have decided we can wrap our subjective brains around? Meh, I don’t like the way the square root of this negative number looks – it doesn’t make any sense to me. It doesn’t follow the rules and logic we’ve established for mathematics. Must not be real. But then some of our stubbornly curious ones realized that all real numbers can be lumped together with imaginary numbers in a new category called complex numbers, and in fact many mathematical relationships can be represented with an imaginary and a real part. In fact, when you get really deep into the study of complex numbers, you’ll find that even things like simple trigonometry are “an illusion.”
It’s interesting that the author of all things mad, Lewis Carroll himself, was actually very disturbed by the concept of imaginary numbers, and so wrote Alice in Wonderland as a sort of criticism of the insanity of it all. He believed mathematics had to be logical, and by logical, of course, it had to be real – to be tangible. But as it turns out, all tangible relationships can be represented by complex numbers! What a rabbit hole we’ve stumbled into!
Imaginary numbers are a reminder to me that our logic, our grasp on reality, can be hugely flawed – yes, even that of people who have decided to become comfortable with imaginary numbers. You can make analogies to explain how these numbers work, how to manipulate them, how they can be applied, how you can relate them back to the “real” world, but I’m not sure I will ever not be amazed that the square root of negative one can actually be meaningful, that it is something that can be felt and realized in “reality.”
Every time we think we understand something, often times Someone just pulls the rug out under us. Whoops! Sorry, you just don’t really know anything after all. It’s an amusing thing that I can only attribute to a Creator, a Divine Engineer Who likes to tease us with strange concepts like the creation of an entire universe ex nihilo, from nothing, or the idea that “empty” space can actually bend and have a shape to it, or that stars can disappear in tears in the fabric of this space, or that we can only really know where an electron is in one instant but not in the next or where it’s going or how fast it’s going.
I believe God delights in us when we ponder over His creation. You don’t even need a fancy degree to do it, you can just take a nature walk and marvel at all the little details of the forest, like the contours of the trees’ bark or the countless ripples on a pond. But if you do take a fancy degree to figure out what the bare bones of that forest are, it’s even more unimaginable to me as to how you could lose sight of the magnificence of it all, or could even conceive that such beauty could be an accident. You see that beneath the surface everything is actually nearly incomprehensible chaos, and yet the end result is a beautifully crafted universe with at least one lovely planet full of intricately ordered life (admittedly less ordered with the presence of flawed human beings, but, still).
“Trust in the Lord with all your heart
and lean not on your own understanding;
in all your ways submit to him,
and he will make your paths straight.” – Proverbs 3:5-6