Monthly Archives: July 2013

This is a concept we learn pretty quickly but not all of us learn exactly why. The most I was told was that it just doesn’t work because you’re dividing by nothing, and that kind of wording made it sound complicated enough that I simply took it as all I would ever understand. Recently my calculus professor explained it to us in an incredibly simple way that made me question, yet again, why we aren’t taught these kinds of things back in elementary school.

So to start: Multiplication is basically a whole bunch of addition.

Say you have 2×5.
It’s basically 5+5 or 2+2+2+2+2

6+6+6+6+6+6+6 or 7+7+7+7+7+7
6 added seven times or 7 added six times.
That’s why we read it “six times seven.”

Division, of course, is just the opposite.
Division is just a whole bunch of subtraction.

12/4 is

What you’re doing is subtracting that number until you get 0. In this case you subtracted 4 3 times. Therefore, 12/4 = 3.

SO where does the zero issue come in?

12/0 is basically

… Wait let’s try that again.
Hmm maybe again.
Nope. Not getting anywhere.

THAT is why you can’t divide by zero. You can subtract 0 again and again and again but you just can’t get anywhere. It’s as simple as that.

So when people say “Oh crap that thing exploded, someone must have divided by zero!” they’re actually highly overestimating the complexity of that operation. All they’re really implicating is that some foolish person was busy trying to subtract nothing instead of monitoring the dangerous chemicals they were put in charge of.

Also the whole “In Soviet Russia, zero divides by you” thing – that’s perfectly fine. Zero can divide by you or anyone else it wants to.
0/you is basically

NOPE done it’s already 0 it took 0 times to get it to 0. That’s the answer. 0.

And that’s how zero and division work.

So to sum it all up: No internet, dividing by zero is not the destroyer of worlds or the creator of black holes. It’s just silly.

I know that many people find it impossible to be a person of faith and a person of science.
A person of prophets and of professors.
I manage it. How? Because I can say that I know that I know nothing.

I’ve met some who don’t bother with school because “my reward for faith in the next life is all that matters.”
I’ve met some who don’t bother with church because “what I learn in this life is all that matters.”
I bother with both because when I die, I want to know what questions to ask.
I want to know how to go about pulling back the rest of the curtain and knowing how He did it all.
Because I will never be satisfied.
Because I know that no matter how much I read and no matter how much I think I know, I don’t.

Every time I believe I understand the contents of a room a door is opened in the back that I hadn’t even seen before.
A door that leads to other rooms and other hallways filled with other doors.
A new way to understand this Earth.
A new way to understand why we’re on it.
A new way to see everything, and a new way to question it all again and again.

This isn’t the hard part, though, the questioning.
The hard part comes in between philosophy and practicality.

I know that chairs are for sitting on and that if I sit on one, one that is sturdy, it will be solid and it will hold me.
But I also know now that if I were to sit there infinitely that, eventually, the atoms that make up that chair will arrange in such a way, that I will fall through it.
I should fear chairs.
Logically I should fear that at the moment I sit on one it just might be that moment when those atoms are going to let me fall.

Ignorance is not bliss, ignorance is sanity.

Apples come from apple trees, the biological purpose of an apple is, like many fruit, to provide nutrition for the seed, give it a way to grow and change and eventually become like its parent.
Apples are placentas.
I know that don’t want to eat a placenta.
But as I bite into an apple I don’t consider what I know comparatively about apples, I remember that I know that they’re healthy and that I’m hungry.

Sometimes I don’t give myself enough credit, because I do know things.
Sometimes I wish I didn’t because sometimes it’s nice to eat artificial raspberry candy without knowing that it might have been flavored by beaver gonad secretions.
Sometimes I wish I did because it’s hard to learn a new program when I keep clicking some unknown button that ruins the display.

No matter the case though, neither frustration or cringing can warrant a stop to discovery.

I recognize that knowing things is hard.
The effort to get there and the consequences of arrival; both can bring headaches but both bring progress.

Maybe I’m greedy, because, like a hoarder, I am never satisfied with what I have.
I always want more.
Maybe I’m a philanthropist, because I want to share what I’ve got.
Even if it isn’t much.
Even if it’s a weird fact you didn’t actually want to have on your mind.

There’s a fear in having your mind blown, in glimpsing the depth of your own ignorance.
You can take that fear in a couple different directions, but I often take it in both.
There’s sadness in realizing that, for all of your work and effort, there’s concepts and ideas that you haven’t even scraped at and perhaps never will.
A feeling of inadequacy and small insignificance.
But there’s another feeling.
A feeling of happiness because there is so much room for growth because you understand further just how magnificent and big you really are.

You’re a child of God with a unique spirit and the potential far beyond human understanding, a potential that stretches far beyond this life.
You’re a conglomerate of atoms and materials from countless galaxies and stars that blended together to create the miracle that is life.

Regardless of what anyone does or does not believe I know that we as humans are magnificent and capable of doing and knowing so much.
Good and bad
Big and small.

In the end, what do I know?
I know that layers in Photoshop are essential to using the program.
I know that it took me a long time to master them, and I know that I can still master them further.
I know that there are some things that I probably shouldn’t talk about while people are eating, especially if it’s a raspberry Jolly Rancher. Or an apple. Or an oyster from the Rockies.
I know that I want to be as open minded as I can both about religion and about school, but I know that no one is perfect.

Despite it all, I know that I will never stop exploring.

I will never stop asking.

I know that I know nothing and I know that I know some things.

And I want to know even more.

So you have a number line, from 0 to 1.


Now say you have a ruler, you hold it up to these, and measure. The length from 0 to 1 is one unit. Right? Right.
So now. What is the length of 0? Not 0 to 1 just 0. Well, it’s 0 of course. What’s the length of 1? 0.

Okay what if we split it up?
What’s the length of 1/4? 0. 1/2? 0. 3/4? 0.
All of these, these rational numbers and integers, each of them have a length of 0. So where does the one unit measurement from 0 to 1 come from? Irrational numbers.

Between 0 and 1 there are more than infinite irrational numbers. More than infinite.
Say for instance you have these irrational numbers.
Sure it looks like with this you could count them all, but the thing is you can have
0.A21A11A13… You can have infinite combinations of numbers with infinite length.
They are by definition uncountable. And that’s where you get 1 unit. Each number in and of itself is of 0 length but you have so many more than infinite irrational numbers crammed between there that you get a length.

To put it into perspective if you had a box filled with all of the Real numbers, meaning all integers and rational numbers and irrational numbers, you would have 100% chance of pulling out an irrational number. Not 99.99999%, 100%.

It’s all so interesting, and such a fundamental concept of numbers. So why have I not learned until now, until I reached college and happened to have a mathematician for a teacher who cared about going and filling the gaps in my education? As he wrote all of this and more up on the board he told us that it really wouldn’t be that long before this kind of knowledge simply disappeared. Until it was gone, until no one knew about it anymore. Because no one would teach it. Concepts like this should be introduced in elementary school. Mathematical concepts like this are so fascinating. It depresses me to imagine that I was told I was getting a “superior” education with the International Baccalaureate program in high school. It didn’t even scrape the kinds of concepts I’m learning now.

I don’t know about other countries. But public education in the US is suffering. You shouldn’t have to be going into more directly mathematical fields to learn these kinds of things. You would think they’d be more fundamental.

Not to mention the things that are being taught are being taught so poorly. At the University of Utah one of the most consistently failed classes is College Algebra. Algebra. We shouldn’t even need this class! But no, not even that is getting the concepts in most people’s heads correctly. The first few weeks of my calculus class is, unavoidably, being spent learning simple algebra concepts that we’ve never heard of or hardly absorbed because we just can’t go onto these more complicated things without that foundational knowledge.

If ever I was to leave my ambitions in computers, it would be to become a teacher for this exact reason. To teach the things that aren’t on the simplified, dumbed down curriculum. What sucks too though is that I have had teachers that tried to do this, that went out of their way to teach us the cool things we should have been learning but weren’t. 2 were punished for it and ended up leaving to entirely other school districts because of the crap they were putting up with from administrators. Another got complaints from students and parents because the kids didn’t want to learn. They were so used to the simple packets, “read this textbook and regurgitate it then get the grade, forget everything, and move on” method of learning that they didn’t want to try. They didn’t want to explore and discover new topics, they didn’t want to expand their thinking and philosophy, they didn’t want to use their brains and think critically. They wanted to be told step by step how to get the grade and leave the class, gaining nothing from it but a GPA.

In the end of everything my GPA was crap in high school. My grades were crap. Why? I didn’t want to waste my time throwing up memorized crap onto the packets that were used in place of teaching and interaction. I didn’t want to write papers on studies and works that other people wrote while I could have been learning and discovering the things they wrote about and truly explore them for myself.

If college weren’t so expensive, if I wasn’t already drowning in student loans, I would never want to graduate. I would stay in school and keep learning everything I could because for the first time I have the chance to learn the things my teachers didn’t know or didn’t care to take the time to teach us. If i had (or as I like to think, once I do have) the money, I’d go back and get as many degrees as I can learning about as many subjects and areas as I can.

The thought that I could end up doing one thing, working in one field, for the rest of my life, terrifies me, no matter how interesting or how well paid that field is. Because there is so much out there. So many things I’m missing, so many things I want to see and at least begin to understand. That was the one question I could never answer: what do you want to do when you grow up? Because they want one answer. They want that one career you want to do for the rest of forever. I refuse to limit myself. Yes I want to make a living because you can’t get anywhere without being able to support yourself in something. But I don’t want to know everything there is to know about that one thing, that’s not me. “Narrow your scope” “narrow it down” “pick something” that’s what I was told growing up. Heck. No.