Frustration over mathematics can be overcome by yelling out, “Ewystl!” Not too
much unlike the secret password into the tree house that is undoubtedly in
pieces behind your house (you’re “working on it”), this is much like an
equivalent password to understanding the entirety of mathematics. All that you
have to do is translate each and every sentence into your own personal language,
the one that you know in your head and that you may stumble with to explain to
others (like when you try to explain something to somebody and you pause
occasionally).
Just what does “ewystl” mean? Take your guess … yeah, you’re right,
it’s completely meaningless beside the abbreviation. So is the majority of
mathematics when you don’t know the meaning of the symbols or when you haven’t
worked with the concepts. Mathematics is not unlike eating: you have to chew it
up, then you can swallow as if you are dieing of thirst. And in order to start
chewing, you have to know where to start, like where to pick up the food and
where to stab the fork.
So, over the years I have figured out my own approach to mathematics
and how to learn each of the individual subjects that make up the massive field,
and many are going to find this pretty weird and questionable since it’s not
entirely traditional – but that’s fine, you see mathematics isn’t just academic
and instead it can be applied anywhere. Recently I have found the neat
mathematics subject classification system and that’s what will be used to
outline some interesting/odd ways to approach math below.
#15 (Algebra): the gist of algebra is that you know some things, and
you don’t know some other things, so your job is to figure out how to figure out
those other things by looking at lots of numbers and so on. The way to figure
out what you know and what you don’t know is to just move around numbers and
symbols or letters from one side to another side and act like you’re dong tons
of work. But the real way to understand algebra is to go get some computer
program and then graph all of the equations that you can find (where you have
one or two unknowns) and then start to figure out how the calculator can know it
when you don’t with your equation. Computer programming is the key here; you can
make computers solve the problems for you—if you know how. Use some easy
languages at first, like BASIC. If you have an old, old computer you probably
have QBASIC installed, this small Microsoft language.
#34 (Calculus): … and once you figure out basic algebra, you’re ready
for calculus whether you want to believe this or not. The reason why you can
jump straight to calculus is because algebra is about number manipulation, and
all that calculus is about is figuring out distances. The trick is figuring out
which distances you have to find and what you know when you know those distances
or what you don’t know. All that you have to do is figure out the distance
between two points (further point minus the closer point), and then just keep on
making that further point even more close and until finally it’s so impossibly
close to the first point that you see that it doesn’t change much of anything
anymore. That’s the basis of differentiation, and if you didn’t catch that then
look at the following diagram:
http://evolution.mitprospectives.org/images/01x01.gif
That’s the entire first half of calculus right there: you have some symbols
there, and then you see some more symbols that are slightly different because
they have a plus-something, and that plus something is actually called plus
“delta x” or in your own language that would be change in “x”, which is just one
of the counting numbers that you work with so that you can keep track of where
you are in the mathematical situation. So as that change in your counting number
gets so incredibly small, you start to see that the other number (the range, or
the output, kind of like when your printer spits out some paper with ink) can be
subtracted from the “range” given no change in your counting number, divide that
by the change that you’re using and you find that it’s the exact same thing as
asking for slope, or in other words the ratio of the difference from one point
to another (some people call this ?y/ ?x – see more on the ? symbol).
Anyway, that is just the preliminary explanation of all that is going
on, and it’s much easier to get into your head when you’re doing the
interpretation of what you see on the computer screen rather than what other
people see. There’s lots of old, old math notation out there that will not make
sense to you: it is important that you translate it into your own notation. Make
up your own symbols.
The easiest way to learn mathematics, believe it or not, is to make it
up. Here’s an example. The other day I was wondering about just how long it
would take to search the entire Internet for each of the words in the English
language. What I did first was I looked up through my favorite search engine
(Google, of course) and found some text files that had tens of thousands of
words and compared them side by side (one was 2.86 megabytes in length), and
then I used “wc” to count the number of words in the file and it happened to be
roughly 300,000 words. That’s a lot. So if you look up the average response time
from Google, you will find that it takes about one second for a query to be
executed, so at minimum it is going to take 300,000 words each one second to
execute the search—but then you have to count in how long it would take to read
some of the results for each of the word, maybe you’ll find something
interesting (you will most likely not, we do not recommend you try this). So
then you have to figure out how quickly you can read, and you can count in how
many hours per day you spend, and so on, and I figured out that it would take me
33 years to finish the entire list of words at something like eight hours per
day. So now I know that I don’t want to do that, that’s a huge chunk of my life
that I want to be able to play with, right? That’s because of math, just playing
around with some numbers and making some relations here and there, that’s the
true secret to learning mathematics. Maybe somebody will want to throw in some
calculus there, to figure out the rate at which the number of words left to
search changes etc. etc.
Look around and find something that interests you, whether sports,
programming, chatting with friends, and start to make up numbers to represent
what you see, start playing around with the numbers and you’ll find that you can
make up some pretty crazy stuff, but the more crazy and the more distances and
changes you involve and the more weirdness, the more likely you’re exploring
mathematics without even needing teachers, textbooks, or the Internet. Neat.
Just remember to scream out Ewystl!
