Wednesday, November 5, 2014

Mathematicians: the original texters?

"p(A|B) = p(B|A) p(A) / p(B)"
 - Bayes' Theorem

"LOL!! UR RLY 2 S2PID!"
 - Mental excretion which passes for conversation these days

1. Math Formulas Suck

One of the big problems I always had with math classes as a kid was memorizing formulas. 

Aside from being the only thing a well-hidden calculator can't do for you (they even have online calculators now that can "show your work"...man, kids have it good these days!) formulas seemed so...abstract.

As a kid, I totally got what was going on when we divided 190,393 by 3482. We were seeing how many times we could shove the number 3482 into the number 190,393 without breaking it. I may have hated doing it (especially when we were forbidden from using our dear old friend " with a remainder of" and had to start hanging out with the much more tedious "decimal point") but I got the concept.

With formulas, I didn't know what the hell was going on. 

It's like printing out directions from Mapquest: I know the steps I'm supposed to follow because someone told me, but I can't tell you why I took this particular street or if there was a better way to do it. For all I know, Mapquest is intentionally sending me on a crazy-ass loop-di-loop, turning a five minute drive into a twenty minute merry-go-round. 

Similarly, for all I knew, any math formula they gave me might have involved multiplying in an unnecessary number only to divide it back out later or other time wasters.

In both cases, what's missing is any sense of context.

Now, just like my blind reliance on Mapquest is due to my own ignorance of a given territory, my mindless plugging numbers into a formula was (is) based on my ignorance of the logic behind what the formula is accomplishing.

2. Math Formulas Are Actually Awesome

Turns out, mathematical formulas are just abbreviations of well-thought-out logical sequences. 

Take the above-quoted case of Bayes' Theorem: p(A|B) = p(B|A) p(A) / p(B). Looks intimidating, right? It even looks somewhat suspicious with the repetition of the variables "A" and "B" so many times. Surely those things are cancelling themselves out somewhere, right?

Wrong. Turns out, Bayes' theorem is just an abbreviated way of listing all the factors you should consider when determining what the odds are that the presence of one variable will be accompanied by the presence of a different variable. It's just making sure you don't take a small piece of information and assume it provides you with a bigger piece of information. 

For a stolen example: if 90% of computers that malfunction are overheated, what are the odds that your overheated computer is malfunctioning? The impulse is to say, "oh, that's easy, 90%," but the impulse is wrong. Knowing only the above facts, we don't have enough information to know whether your overheated computer is malfunctioning. For all we know, 99% of all computers are overheated anyway, even if they're working perfectly. We need more information. 

Bayes' Theorem is essentially a list of all the information we need and how to apply it logically to find out the new information. But instead of writing it out longhand ("To find out what the odds are of factor A occurring given the presence of factor B, you must first determine the odds of factor B occurring given the presence of factor A, and multiply it by the probability of A over the probability of B, this is because the odds of factor A are directly related to blah blah blah...") Bayes came up with a shorthand version so that our tiny brains can see it all at once and keep track of it (see this same link for a better explanation of how exactly Bayes' Theorem works then I could ever hope to provide...especially since I don't fully understand it myself yet).

Now, the trick is this: in order to avoid mindlessly plugging numbers into any formula, you have to eventually buckle down and understand the long-hand version. Just like the trick to being able to give good directions is to understand the whole layout of the area in question.

That's why school-aged me didn't know what fractions were about. I was too lazy or dumb to learn what they were doing and why (I still am, for the most part, but at least I now understand my lack of understanding...if I fall asleep during an algebra class, I'm less like Jeff Spicoli and more like Socrates).

3. Are Texting Abbreviations Awesome?

Which brings us to texting. Texting uses abbreviations too. You're and your become "ur." Laugh out loud becomes "LOL." 

Just like with math formulas, using these abbreviations saves space. But this is true only on the condition that you can, upon demand, provide the longhand versions of what those abbreviations mean. If not, you're wasting your time and making a fool of yourself (I cite as an example: people who write LOL when they are nowhere close to laughing out loud, or even chuckling, for that matter).

So, are texters in fact part of a rich tradition of distilling complex information into more manageable, bite-sized nuggets, just as the mathematicians before them?

4. No, Texting Abbreviations Actually Suck

No, texting abbreviations actually suck. They suck because the concepts they are abbreviating are usually bite-sized to begin with, so making them more so is annoying and pointless and makes you look like a lazy ass. 

The word "your" is only four letters long, folks. And the word "you're," while five letters long, is actually already an abbreviated form of "you are." 

Because of this "ur" should not be considered the useful distillation of the words "your" and "you're," it should be considered the bile that emerges from our cultural throat after we've finished vomiting up literary clarity and sense of style.

"E=MC²" may look suspiciously like "U+Me=BFFs" but one would take several pages to fully explain, while the other one simply means that you and I will probably drift apart during high school.