Googolplex
Oscar is way into big maths at the moment. Bedtime, in particular, seems to turn his thoughts to philosophical enquiry. He has probably figured out that sensible worldly questions buy him extra minutes with the light on. Maybe even a full half-hour if mummy really gets the wind in her sails! From a parental point of view, it's very hard not indulge your child's genuine intellectual curiosity. Sure, I could bookmark it for the next morning, but there is a danger the moment will have passed, and the opportunity missed.
Part of my bedtime indulgence stems from a fervent wish not to pass on my attitude to maths. I can't say I love it. At primary school, I was very good at maths, but a year or two into secondary school that all changed. I wasn't terrible. Somehow I managed to remain in the top set, but it was a slog. I remember that I literally spent 90% of my two weeks GCSE study leave on maths revision and ultimately got my worst grade in it. It was with relief that I left maths behind.
Except I didn't. "Hello!" all the maths in 'A' level Chemistry, and still more maths in my Biomedical Sciences degree (including a Statistics module - WHAT?!). Even a last minute career path deviation to the Law landed me in the sticky mire of Solicitors Accounts. Yuck.
But the tide may be turning, and it started with infinity.
I think, for many children, the concept of infinity is the first time they really engage with abstract thought. Perhaps in response to the question "What is the biggest number?" a parent or teacher will introduce the idea of infinity. They may struggle with the concept at first, perhaps thinking it just a Very Big Number, but eventually they get a general understanding, often by marrying it up with the notion of "forever". Oscar's eyes were wide and sparkling as he summed up my explanation "I get it! Numbers go on forever"* . Ben took his understanding one step [a giant leap!] further by explaining that there are big and little infinities. I confess, I was learning something new at this point!
Schools are missing a trick in not exploring this with kids early on. Infinity is a gripping and marvellous thought experiment. Maybe my relationship with maths might have been different if I had been exposed to "Cool Maths"! Children's literature seems to get this. While the shelves are not awash with books on the subject, there are a few to look out for. We liked "Infinity and Me" by Kate Hosford. It's a poetic musing on red shoes, noodles and stars and there is an online curriculum to support it.
In some ways, it is surprising to learn that abstract thought is one of the final stages of cognitive development in children. At Oscar's age (5 years), children are being introduced to big new ideas on a daily basis. Their brains seem wide open and accepting. The level of understanding is perhaps not very sophisticated, but Oscar took infinity in his stride.
But there is one thing you can say with certainty about infinity: it goes on a bit. Perhaps this explains Oscar's real enthusiasm, which is for Really Massive Finite Numbers ("RMFN"). The first RMFN that caught Oscar's attention was the googol (or 1 followed by 100 zeroes).
Unless you are seeking a rough approximation of the number of sub-atomic particles in the universe (sure, every day), a googol is not a useful number. But it is cool - look at it:
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Also, ridiculous. It's obviously famed for being purposely misspelled by Larry Page and others when they were seeking a name for their search engine. This kind of takes the shine off for me.
We read "The Day Anthony Counted to a Googol" by Mark North which is a lovely exploration of all the things that a googol is bigger than. It's a bit US-centric and I don't love the illustrations, but Oscar didn't find that off-putting and enjoyed coming up with his own crazy scenarios.
But the lustre of the googol didn't last long, as I broke it to Oscar that the joyfully-named googolplex is even bigger. That's 1 followed by a googol zeroes. Helpfully, these funny guys claim to have "Googolplex Written Down". But before you take them up on their print option (because you were going to, weren't you?), consider that there would not be enough room to write it even if "you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way"**.
The RMFN that gets Oscar really excited is the rather mundanely monikered Graham's Number. This is officially Oscar's favourite number. And a good answer to have up your sleeve in a pub quiz. It's bigger than a googol. It's bigger than a googolplex. The fact of the matter is that there is not enough matter in the universe on which to write this number. Despite this - and this blows my mind - we know that the number is whole, finite, divisible by 3 and ends in a 7. If you want to know more about Graham's number, Tim Urban writes about it in a clear and amusing manner, concluding that Graham's number has made him feel better about death. So there's that.
I feel like I've drifted away from my point that Oscar is so inspired by maths, and this has rubbed off in the classroom. Sure, it's rather more run-of-the-mill maths, but a couple of months ago Oscar came running out of school waving a piece of paper, desperate to show me something "magical". It turned out to be what he calls "grid maths", or what you and I might call column addition(!) And it endures - his teacher gives him column addition as a reward for early completion of his work in lessons.
Are you in the "Maths is Cool" club?
* Or do they? Ultrafinitists don't think so.
** "Mathematics and the Imagination", Edward Kasner and James Newman
