February 25, 2011

Alice in Numberland

You may have noticed that the title of my blog is a nod towards Lewis Carroll's oeuvre, Alice's Adventures In Wonderland. This is pretty much my favourite book of all time. Why? Because it's FULL OF MATHS!

Lewis Carroll is the nom de plume of Charles Dodgson, who was a maths lecturer at Oxford. He was actually more famous for being a children's photographer, but his maths was pretty good too. He was really obsessed with Euclid's Elements and wrote textbooks to go alongside it. He loved logic too, which is what you see most of in his books.

"if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic".

Tweedledee says that. It's one of my favourite quotes from the book. The best logic puzzles appear in his other books, like The Hunting of the Snark.

Here's another favourite quote (it's just as Alice is falling down the rabbit hole):

"I'll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is - oh dear! I shall never get to twenty at this rate!"

Alice's wrong calculations can be explained by using different base systems:

in base 18, 4*5= 20 = 18^1 + 2 = 12

in base 21, 4*6= 24 = 21^1 + 3 = 13

if you carried on the pattern, you'd get:

base 24: 4*7 = 14

base 27: 4*8 = 15


base 39: 4 *12 = 19

base 42: 4*13= 42^1 + 10 = 1X (where X is the symbol for 10 in base 42)

So Alice is right, she'll never get to 20!

Interestingly, it breaks down at base 42. Lewis Carroll seems to have a slight obsession with the number 42, it appears everywhere in all of his books. It has been suggested that Douglas Adams used the number 42 in the Hitchhiker's Guide to the Galaxy because of this. Adams named his chapters of the radio show "fits" which is also what Carroll did, suggesting he's a fan.

My favourite maths thing that Dodgson did though, was his work on voting systems. This is really interesting, it's got some great maths in it, and if you tackled it in a lesson you would be hitting the moral, social and ethical aspects of maths.

So if anyone asks you to come up with ideas for a maths/English connected curriculum day, suggest studying some of Lewis Carroll's work. I love it when literature and maths combine, as they are my two favourite things. Another good mathsy book is Mark Haddon's The Curious Incident of the Dog in the Nighttime, which I love, but the maths in that is very separate from the story, and I don't think it would be good to use in class.

One of my favourite authors of all time is Louis Sachar, who wrote Holes, which is very commonly studied at secondary schools. He also wrote some great maths books, the Sideways Arithmetic from Wayside School series, so if you have a year 8 class studying Holes, it would be cool to do some puzzles from that to run alongside it.

Finally, another of my favourite authors of all time is Koji Suzuki, the Japanese author of Ring, which was made popular by the abomination that is the film The Ring. There are two sequals, Spiral and Loop, and all three books are outstanding on their own or as a series. They include some brilliant codebreaking linked to genetic codes, and some discussion of meta-mathematics which is just plain awesome. I'm not saying bring them into your lesson, but suggest them to sixth formers who like reading and maybe need showing the coolness of maths. And you should read them yourself because they're sooo good!

Emma x x x

PS if you want to find out more about the mathematical life of Lewis Carroll, I recommend Robin Wilson's Lewis Carroll in Numberland. I have a copy if you want to borrow it. I also have copies of all the books mentioned above, but some of them are at my parents' house in Leicester, so I can't get them until Easter.

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