Maths sucks.
It’s a very general statement, but I believe most people have said it more than once in their lives. When I was a wee lad in primary school and most of high school, I fell in to this category. Maths was something I could do, but it was tedious and I approached it like I approached Afrikaans- as long as I could pass and say “I don’t speak this language, try English” I was happy. Another similarity between my maths and my Afrikaans is that I share my lowest marks with those subjects. 49% for term 1 maths in grade 8 and for term 1 Afrikaans in matric.
I learned to love maths. Unfortunately, it took me longer to realise that Afrikaans aint all that bad (listening to some solid, respectable and passionate Afrikaans profanity at a Sharks-Bulls game may have contributed to this realisation), and that’s where the similarities end.
I had managed to get into ad-maths in grade 8 even though I never really enjoyed it. The first recollection of enjoying maths was at Bush School in grade 9 where we were taught word problems, and I loved the struggle of figuring out how all the little details would fit together. In grade 10 I went to America where I did matric level maths. They gave us graphing calculators which did all the work for you, so I managed to top the class with a lazy 97%, but I did at least learn a lot more about the graphs of functions and how to use them to avoid calculations- basically cheat- a skill I am grateful for in university. Then came grade 11 back in SA, where, being in ad-maths and all, I was dumped with grade 11 and matric maths at once. Real matric maths. Once again, maths sucked. It was so much work. But I slogged on, and hit matric, where we started to do basic university-level maths in our ad-maths class. That’s when things got real. For the first time I was exposed to the thought processes and logic that happen behind the scenes of all those symbols and equations. It was incredible. When it was time to apply for university I had to choose between maths, music and history.
I signed up for BSc. Applied Mathematics. Since then, God has blown my mind through maths. Mostly through the numbers which have been dubbed “The Maths Big 5”. Even if you have no idea what I’m talking about (because I am not the best explainer in the world), just nod your head, act smart and give God some glory for my ramblings.
1: We all know what 1 is. A whole- singular and complete.
0: Zero means “empty”, and the concept of nothing being represented as a number by itself took surprisingly long to be implemented. The first time 0 was used as a number (as opposed to simply an origin, a starting point or for separation between giving and taking) was by the Indians in the 9th century AD.
Pi: This is a well-known non-rational number. It has no exact value, because it just keeps going. It is, to our knowledge, infinite. Eternal. It is defined as the circumference of ANY circle divided by the diameter. What are the chances that pi, which is derived from something as simple as a circle’s circumference and its width, has infinitely many decimal places without any repetitions or patterns. Stop, right now, and actually think about what that means.
Here is a web site that has pi up to 200 million digits: http://www.angio.net/pi/piquery . That’s 200MB of number. A whole lot of pi (mmm, delicious) and in those 200 000 000 digits, it hasn’t started repeating itself and does not follow any known pattern. That’s crazy talk!
e: The number e is called the natural number. This is because the logarithm and exponents of e appear repeatedly in nature, specifically growth and decay of natural entities like bacteria or humans. One of the fascinating things about e is the number of ways it can be defined. The most common way is
e=lim (1+1/n)^n as n->infinity
Alternatively, also taking the limit of the sequence as n->infinity
e=1/1 + 1/(1*1) + 1/(1*1*2) + 1/(1*1*2*3) + 1/(1*1*2*3*4) + 1/(1*1*2*3*4*5) + … + 1/n!
=1/0! + 1/1! + 1/2! + 1/3! + 1/4! + … + 1/n!
Alternatively, again taking the limit
e=2 + 1/(1+1/(2+2/(3+3/(4+..))))
Since all the definitions are limits e is not an exact number (just like with pi). The longer you calculate the more accurate you will be, but never exact. It is also infinite, eternal. So why does it show up in all these different definitions (and there are other ways)? Because it really is an entirely natural number. It is core to the structure of numbers, of nature, of everything. When God spoke the universe into being he may well have started with e. The infinity of e and pi are one of God’s many ways of reminding us that he is far bigger than we could dare hope or imagine, even in something like maths.
i: It is loosely defined as the square root of (-1). In high school you would’ve been told that the square root of a negative number gives no solution, or, if you had a correct teacher, that it has no real solution. Well, they were right about the no real solution part, but it does have a non-real or complex solution(s), involving i in some way. i is called the imaginary number. It was imagined because mathematics required it to exist. You can’t see it, picture it, point at i somethings- it is entirely imaginary, non-real. Perhaps it is spiritual. We know that all the real numbers that me and you see in our day-to-day, non-imaginary lives exist on one line in an entire plane, called the complex plane, where all numbers (real and non-real) exist. All numbers each have a real part and an imaginary part, but we can only see the numbers whose imaginary parts are equal to zero. I like to believe that while our mathematics requires us to invent the number i, spirits who live in the spiritual realm treat i like any other number. That they can see and understand what i somethings look like. That while our senses are restricted to the real axis that spirits have access to the whole plane.
And then BAM! KAPOWEE! The maths Big 5 unite like the Power Rangers into one super duper equation.
e^(i*Pi)+1=0
[insert loud gasp of disbelief]
e (the natural number) to the power of i (an imaginary number) multiplied by pi (circumference/diameter) and plus one is equal to zero.
[insert another gasp, followed by applause and a smart looking elderly gentleman with spectacles nodding wisely]
The two most simple, understood and important numbers known to man. Two infinite numbers who’s exact values are unknown- one that comes from any circle, and one from any number of limits which also happens to appear everywhere in nature. An imaginary number that you can’t possibly quantify, and this little equation brings these seemingly unrelated numbers (certainly derived in separate ways) all together. With an equal sign!!! Are you freaking kidding me!?! Look how excited I’m getting, I’m using triple exclamations!!! If this isn’t God’s way of showing His perfect and mind-meltingly magnificent design, control and sense of humour in belittling us then I don’t know what is.
Maths rocks, and you can call me a dork-nerd or whatever for saying so.
Miraculous indeed.