I am not a Mathematician, nor am I especially gifted at maths. But I just love exploring mathematical ideas.
Many of us are turned off maths at an early age because of the way it is taught.
Too much rote learning of “number facts” and methods of doing long multiplication and division sums
Too much emphasis on getting the right answer and not enough on seeing why the answer is right
Not enough exploring ideas and using maths as a stimulus for imagination
Many kids become bored and frustrated and decide they are “not good at maths”. This can be worth a bit of street cred if you want to join the tough kids.
A few of the lucky ones, and I count myself among them, break through this mindset and see maths as a way of seeing and finding meaning in the world around us. And seeing the world through a mathematical lens enhances rather than detracts from its beauty.
Imagining beyond small numbers
We all have an instinctive idea of small numbers of things. We can see at a glance that there are three apples on the table or five people in the checkout queue. As preschoolers we learn to count small numbers, up to ten, then up to a hundred and so on.
But after we learn to count to a hundred a couple of things start to happen:
We start to chunk the numbers 100… 200… 300…, then 1000, 2000, 3000 etc
And we get our first understanding that numbers just keep going on and on for ever, to infinity what ever that means
Now we can use phrases like five thousand, seventeen million, or three and a half billion and make sense. But we have lost a picture in our mind of what these phrases actually mean. How can we envisage these numbers.
How big is 1.4 billion?
The population of China is about 1.4 billion. The number rolls off the tongue easily but what does it mean?
I have come up with a little mental prop to help me understand just how big 1.4 billion is.
I live in Melbourne, Australia. We don’t have an opera house or a harbour bridge like our flashy neighbour, but we do have a sport stadium called the MCG. Its name is actually the Melbourne Cricket Ground but Aussies are a bit lazy with language so we just call it MCG or ‘the G’.
It’s a big stadium and it holds 100,000 spectators. That’s a lot of people. I know, I’ve been there in such a crowd.
So let’s use the MCG to see if we can get a picture of how big 1.4 billion is. What if we wanted every Chinese citizen to visit the ground for a football match.
So let’s get 100,000 people into the ground to see a game. Tomorrow we can get another 100,000 and let’s keep going at 100,000 every day till all 14 billion have shared the experience. Every day another 100,000 people visit the G, with no days off for Boxing Day Good Friday or Chinese New Year.
How long will it take for all 1,400,00,000 to see the game?
The answer is over thirty-eight years. Yikes! That’s more than half my lifetime.
Only 30,000
The idea for this story, which might one day be a book, started when I was startled by a headline sometime early in the Millennium which read
What if There are Only 30,000 Genes?1
This was one of many headlines at the time. The conventional wisdom2 beforehand was that there was at least 50,000 human genes. Earlier estimates were much higher but had been trending down for decades. We humans are important and the pinnacle of creation so we must have lots of genes.
So we were all in a lather because our wonderful civilisation and the superb brains that created it could be encoded with a mere 30,000 genes. But worse was still to come.
What about 22333?
As the Human Genome project was being completed the number settled on by some scientists as a likely number. Actually it is probably not exactly that number but let’s use it because it is interesting. Firstly it’s prime factors are 23 and 791. An amazing coincidence because as everyone who knows a little about human genetics knows that 23 is a very significant number. We might have some fun with 791 as well!
More about Big Numbers
This is an actual headline of an article in Science Magazine at the time. I’m sure there were lots of similar headlines at the time.
This is an ironic phrase meaning “commonly held misconception” coined I think by economist John Kenneth Galbraith. He was a very clever man but people didn’t always understand his irony and now they think conventional wisdom is the truth. Conventional wisdom is often stifles new ideas and becomes the enemy of truth.