Head Explodes: Continuum Hypothesis

I am a 36 year old mother of two, attempting to finish her college degree online. My day starts at 5:30am with an IV drip of coffee. That’s bull shit, I straight funnel that shit like a beer bong! I’m a college student now, that’s how I roll! Between getting myself into a respectable I use that term very loosely state for work, hauling children out of bed by their toes, beating them with broom handles, chiming the bus departure countdown in NASA-esque fashion, flying to work in my Lesbian hockey player car Subaru, attempting to act like I know what I’m talking about in the world of non-profit fundraising, hob nobbing at the Coop while picking up Asian dipping sauces and organic fennel, flying to the afterschool program to magically whisk the kids out the door so we can go for a “family” walk the only viable time I can actively ignore them without being caught, getting super on the table by 6:30pm, tiny people showers by 7:30pm, and lights out no later than 8pm…I’ve completely forgotten where this absurdly long sentence was going…Oh, yes! That’s right, between all this bull shit responsibility nonsense and school work, it’s any wonder that I can get any sort of grade that resembles the definition of “decent.”

I am now in my second term of classes. This means I have successfully passed two, very serious, classes already. Both classes were research based, meant to educate my classmates, meant to educate myself, blah, blah, blah. With that being said, I’ve pretty much jumped onto the sarcasm bandwagon for this second term, at least with my math class. I’m so awesome at being awesome, that I decided to take an online math class…online. On-FUCKING-LINE!!!Who does that??? Aside from crazy people who actually “enjoy” math. No one. Not unless we are being held at gunpoint, our children’s lives are being threatened, or we need the credits to graduate. So, there I was…taking an online math class.

It’s any wonder my professor has not asked me to leave the class already. I come out and voice my distain of all different aspects of mathematics, and basically approach all my assignments with an air of satire. For those of you wondering what exactly I mean, may I present to you exhibit “A”. Also known as “The Continuum Hypothesis and Why Math Professor Will End Up Hating Me.” I should add, I have absolutely no idea what I am talking about mathematically.

(This is the actual “paper” I wrote for my infinity assignment) *drops dead from mathematical stress*

Truth be told, infinity and I don’t get along. Why? Many reasons. I don’t like numbers I can verbally count to represented by letters, but then again, I don’t like numbers I can’t count to. It bothers me to know there are unknown numbers swimming around in space and all around us. Numbers that are just lingering around until someone plucks it out of thin air because they turned n into 0.2345. The worst part for me is not having a definitive number of something, I don’t like that it can go on, and on, and on, and on, and on…much like my seven-year-old daughter when she’s explaining the very real concept of unicorns hidden in our every day. Couple all this together with the overall concept of the Continuum Hypothesis that is can neither be proven true or false, and my head pretty much exploded. Infinity is a unicorn.

I could end my explanation there, but I’m not sure that falls within the rubric guidelines. Therefore, I will close my eyes and jump head first into the world of unicorns…I mean the continuum hypothesis. In the late 1800’s, Georg Cantor proved that there is a one-to-one relationship between natural numbers and algebraic numbers.

For example: a1 = 2; a2 = 3; a3 = 4

In short, each number we are used to has a little algebraic buddy that is just like it. Twins separated at birth. It would have been nice if Cantor had stopped there, but he didn’t. Instead he dug a little deeper, and looked between the numbers. He not only wanted to see if there were one-to-one ratios within these fractions of numbers, but he also wanted to see how many there were. In other words, he wanted to see if there was an infinite number of one-to-one ratios. The answer? He has no idea. He could never prove if there were an infinite number of sets or not. This means that poor Cantor died in 1918 not knowing the answer.

Thankfully, David Hilbert (from the Hilbert Hotel problem) decided to support Cantor by basically saying the continuum hypothesis was “the most important unsolved problem in mathematics.” Of course, if I were running a hotel like his, I would also find this to be the most important problem in mathematics. It is because of the “unsolvable” issue that mathematicians have continued to work tirelessly on trying to prove something other than “unknown.” The closest any two have come are Curt Godel in the 1920’s when he determined the hypothesis could never be proven as false. About 50 years later, Paul J. Cohen determined that it can also not be proven true.

As I said in the beginning, my head pretty much exploded. I’m not a mathematician, I don’t play one on TV, and I didn’t stay at a Holiday Inn last night; but I did try very hard to wrap my brain around this unsolved mystery. The best I could come up with is the problem where you start out 4 feet from a wall. Your first step, you cut the distance in half to 2 feet. Your next step, you cut that distance in half to one foot. Each time you take a step, you are cutting the distance in front of you by half. With each step, you get closer. However, because you keep cutting the distance in half, you will never actually reach the wall…at least not in a way you can prove it. Each step is broken down into a smaller part. This is much like a number line.

 

You______1’_______2’_______3’_______4’_Wall

Starting 4’ away

You_____1’_____2’ Wall

You just cut the distance in half. Let’s do it again.

You____1’ Wall

Now we start cutting the distance down into fractions. Take one more step.

You_____0.5’ Wall

Again…

You_____0.25’_Wall

Each step is half of the last. It can keep getting smaller, but it can never fully stop. That is until your Fitbit tells you have reached your step goal for the day, or you’re tired of looking at the wall.

 

 

References:

TEDEducation. “How Big Is Infinity? – Dennis Wildfogel.” YouTube. YouTube, 2012. Web. 25 Apr. 2016. <https://www.youtube.com/watch?v=UPA3bwVVzGI&gt;.

 

Koellner, Peter. “The Continuum Hypothesis.” Stanford University. Stanford University, 2013. Web. 25 Apr. 2016. <http://plato.stanford.edu/entries/continuum-hypothesis/&gt;.

 

2 thoughts on “Head Explodes: Continuum Hypothesis

  1. If you ever need help on any of your Math stuff, please do let me know. That was my major in college. I would be more than happy to help you get that decent grade!

    Liked by 1 person

  2. Silly, silly mathematical conundrums — because while, in theory, you never reach the wall, you will reach the wall. Every time. Unless there is a forcefield, which may or may not be theoretically possible. I may have talked about this, at great length, with a college calculus professor over very many beers at some point of my college career.

    And worse than a math course online . . . a math course online in which you must write essays?! Ouch.

    Liked by 1 person

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