Monday, July 06, 2015

Why and How

A guy I once kind of knew, heard of a girl, whose previous dog's owner overheard a conversation about a foreigner who used those region-hacks for DVD players. You know those ones that stop you watching it because it was meant for another country. The same thing that stops us watching the Trevor Noah clip on colonisation. I imagine that person knows a hack for that too. All illegal of course.

The hacks involve an algorithm of rather bizarre steps that result in the DVD player becoming region free. Something like 'press... right arrow, yellow button twice, mute, help, left, up, 5, box office, up, pause, 3, 7, increase volume, down, boil an egg, tv guide, 4'. Then the screen allegedly goes black and they think they have broken the machine. About two minutes later, lo and behold, they have a region free machine. A mysterious algorithm that if followed correctly does what it is supposed to.

I am busy learning to solve a Rubik's cube via YouTube clips. By stop-starting your way through the video, you can learn what to do. In the beginning the steps are quite understandable. Towards the end there are just algorithms to learn. If you see a yellow fish, make sure its nose is pointing down and then '(R)ight face (c)lockwise, (U)p face (c), (R) counter-clockwise (CC), (U)(C), (R)(C), (U) 2X, (R) (CC)'. The last few stages all have these semi-mystical algorithms that magically solve the cube if you make no mistakes.

It reminded me of some of the things I learnt at university. In one particular subject I was desperately keen not to 'just learn the algorithm'. I wanted to understand why it worked. I sat down with the 700 page text book and started my way through it. Each page took about an hour to understand. I decided to persevere, but after 20 pages my speed wasn't increasing. I did the more simple arithmetic of how many hours it would take to understand the course. I didn't have that much time. I had to suck it up and learn the algorithms. In the case of this course, I didn't even understand the steps! So I had to just learn the various rows of proofs having no clue what they meant. I recognised the symbols, and so sometimes I would spot a pattern. If there was a (-1) at the end you swapped everything around on the next row. Why? Don't know. Fortunately I was not alone. Humility was dolloped out to all my classmates.

Learning how to do something you don't understand can be done through repetition. A university Maths professor once told us at school that if you want to do well at school maths, you can. Just do enough past papers until you recognise all the questions that could be asked of you, and you know the next step. Learn maths like you learn history. He told the story of a girl who had been failing maths, so she did something like 90 past papers and ended up getting close to full marks. Don't do examples till you get them right, do examples till you stop getting them wrong.

There aren't enough hours in the day to learn how to do everything. Fortunately we can solve problems and then share 'simpler ways' to do things. We will likely need the experts when things go wrong. Real understanding comes from knowing the why, not the how. 

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