Junk Knowledge

Multiplying fractions is junk knowledge, so the TES told me this week.

That’s junk knowledge that enables someone to work adeptly with number.

That’s adeptly working with number that enables someone to abstract with algebra.

That’s algebraic abstraction that enables someone to understand calculus.

That’s understanding calculus that allows someone to become, say, an engineer.

That’s becoming an engineer that enables someone to design the building (and model and analyse its perfect conditions) that houses the servers on which the TES is located.

All so someone on the TES can call multiplying fractions ‘junk knowledge’.

I thought of lots of loops through mathematical knowledge with this same start and finish. It was quite good fun.

Beating the Odds

I was running a training session for new maths teachers last week and over lunch someone mentioned the weekend’s huge lottery draw, with the largest jackpot in UK lottery history of £66m, shared by two winners.  I remember when the National Lottery started, one of my first thoughts about it being, “if someone had enough money they could buy up every combination and guarantee the jackpot”.  We talked about this over our jacket potatoes with chilli and I started to consider the practicalities.  And, of course, the maths.  So here are my musings…

Flight and Fight

Back in 2010 I, and 12 million other people, became slightly addicted to a little game called Angry Birds.  I stopped playing after a couple of months, like I always do with these things, not sure what happened to it then, probably petered out like so many other overnight success stories.

The premise of the game was to get your little birds to destroy some nasty green piggies who were stealing your eggs by launching them from a slingshot at the pigs’ defences.  I can see why those birds were angry, I would be if I were repeatedly being launched, projectile-style, at towers of wood and ice and stone.  That’s gotta hurt.

The programmers use some fairly simple mathematics to get those birds to move in a realistic way.  You intuitively expect the birds to move through the air in the way they do because all objects move like that, unless some force causes them to change their path.  Picture it now – imagine throwing a tennis ball, what shape does the path of the ball take? What about a diver jumping off a diving board, or a bullet flying through the air, or water spouts from a fountain?

Good Vibrations

It was King Solomon who lamented that “there is nothing new under the sun”.  This is borne out again and again: story plots, terrorism, facial hair, blog posts, popular music.  Let me demonstrate the latter to you, or rather, let Axis of Awesome demonstrate it:

Next time you listen to the radio, you’ll hear those chords.  In fact, you’ll notice it a lot now you’re aware of it.  This is called the Baader-Meinhof phenomenon, like when you settle on which new car to buy, and suddenly it’s everywhere.

Power-ful Computing

We’re generally familiar with the term exponential growth:

“Her business has been growing exponentially since its start 6 months ago.”

“My number of followers on Twitter has been growing exponentially since I started sharing cat memes.”

It’s doubtful how often the use of the term is mathematically correct, it seems to have slipped into common parlance.  What does it actually mean?  Well, it’s really quite simple.