Prime Factor Decomposition

The white painted walls of the maths room looked very tall and were bare from head height to the windows by the ceiling. It was a perfect cube. Mark had found that out during a lesson when they measured everything. It seemed appropriate for the room to be a regular geometric shape, although they said it was just the way it had ended up when they turned the old gym into four classrooms after the accident.

“Prime factor decomposition,” said Miss Anderson. “We know what prime numbers are – yes we do Jack, don’t make that face – and factors are numbers that divide exactly into another number. Decomposition means to break down, so what we’re doing is breaking numbers down into the prime numbers that make them up.”

“Miss, why are we doing this?”

“You mean other than that it’ll be in your GCSE exam?” Every time she was sarcastic, her Australian accent got harsher. Mark wondered if she knew that. His mind drifted away from the room for a moment.

“... every integer – that’s whole number Billie – is made up of prime numbers. It’s axiomatic. Which means it has to be the case for maths to make sense.”

“Maths doesn’t make sense,” said Jenny in what she thought was a mutter.

“Making sense is the very thing that mathematicians have been working on for hundreds of years. If I have one pen and another pen then I have two pens. We can see that. But if we take the pens away, and just write 1 + 1 = 2, does that actually mean anything? Can we prove it logically, or is it just an improvisation, a coincidental observation? If I can’t prove it then one day I might take one pen, add another pen and end up with three pens. Then all of maths would need to be worked out again.”

“So you could have... maybe ... a four sided triangle?” said Gwen.

“Or a cube with 9 corners,” said Jack.

“Vertexes. No, vertices[3],” said Mark.

“That’s silly,” said Jenny.

“Don’t shout out,” said Miss Anderson. “Also it’s not just silly. It’sinsane.

“If maths changed then the whole universe could transform itself. We measure everything with numbers. We wouldn’t know how many or much of anything there was. Time and space would change unpredictably. What we know – what we think we know – would be wrong and the world would seem to be a psychotic nightmare.I told the class the story behind the story and the tutor said she was glad something came out of lesson planning. This is, at it's heart, an old fashioned science fiction story with the science in this case being maths. It's also a bit of an homage to parodies of the Twilight Zone and the Outer Limits, where everything suddenly turns out to be completely nuts.

“But we’ve got distracted from the lesson. Find the prime factors of the numbers on the board.”

The class settled down to the problems. Miss Anderson walked up a row and stopped at a desk with exercise book and pen but no pupil.

“Where’s Jeffrey? I must have sent him to pupil services half an hour ago.”

Mark realised that he couldn’t remember Jeff going through the door. He did the thing with his eyes and looked into the ninth vertex of the room. He could see Jeff’s tortured face amongst the uncountable bones and bodies crammed into that space.

“I don’t think he’s coming back miss.”

(3 x 3 x 3 x 19 = 513 words)

Although loosely based on my lesson plan, Miss Anderson deviates from it by talking about some of the philosophical underpinnings of mathematics. Bertrand Russell attempted to prove from rigorous logical axioms that 1 + 1 = 2, and thought he'd cracked it, but as it turned out he needed to use between one and three axioms[4] that couldn't themselves be proven. Of course, you can prove them if you take some other axioms, but as it turns out these axioms also cannot be proven without yet more... Kurt GĂ¶del's incompleteness theorem proved that any logical system complete enough to handle arithmetic would always have unprovable axioms as part of it. Thank goodness Miss Anderson stops before she gets that far. Anyway, my point is that the story is mathematical-philosophically sound and

*you can't prove otherwise*.

Some of this is based on real experience. As far as I know there is no classroom that is a perfect cube. The old gym being split into four classrooms is true, but there was no accident; it was because another building was being refurbished and so not able to be used for a term. Miss Anderson is borrowed from the largest shared universe of them all, real life, although she doesn't get distracted in this way in class, has acquired a fictional name and never lost a pupil into another dimension. If you're reading this, sorry Miss.

So the (creative writing) class enjoyed this. One of them wasn't 100% clear that verticies are the corners of 3D shapes. Do I need to re-write that part? I explain what prime factor decomposition is, get into the philosophical underpinnings of mathematics and put a twist in at the end

*all in 513 words*which is pretty ambitious I have to say. Maybe I didn't quite get there on 3 dimensional geometry but I'm okay with that. The prime factor decomposition of the word count at the end amused most people.

One class member showed it to his 14 year old daughter who then showed it to some of her friends[5]. They liked it. The "uncountable bones and bodies" bit of ramming a joke against the horror was enjoyed by teenagers. Who would have thought! The main criticism from them was that you don't really get to know the characters. Well, hell, 513 words, two or three mathematical concepts to lead up to all of reality being broken and mass death. I'm sorry my character development isn't all there[6].

Finally, I didn't - couldn't? - write about something that actually horrifies me. So, like yesterday, I've combined things that concern and disgust me, and sidle up towards my fears without ever getting too deep in.

[1] A... for Anguish!

[2] Well... sort of. In fact I'd got the call on the Wednesday morning just as I was heading out and got email confirmation later that day. Being busy all day, I briefly revised Prime Factor Decomposition, went to bed and had crazy mathematical dreams. While eating breakfast I thought of all the things that could go wrong in a lesson. "That's a real horror story," I joked to myself. THEN I sat down to write the lesson plan.

[3] What the hell blogger? Your spellcheck wants to insist on vertexes as the plural of verticies? Both are actually okay!

[4] How many depends on which criticism I'm following at that moment.

[5] The prime factor decomposition lesson was for Year 9, who are 13-14 year olds, mostly 14 at this time of year.

[6] The word limit - 700 words - is pretty tough. My tendency to hammer home the story with a twist or revelation in the last paragraph, sentence or word means I am unwilling to just give the first part, so I wrote this as stripped down as I could, which I think has worked just fine, but does mean something has to give. In this case, we get a description of the classroom, a few clues about characters, but you have to fill in the class yourself. Hopefully most people reading this have been to school, or at least seen a school on television, so can fill in the blanks.

## No comments:

Post a Comment