Thursday, 26 February 2015

The Math Hatter

"Dodgson was fond of children, of Tuesdays, and of the number 42" 
Martin Gardner (mathematician), "The Universe in a Handkerchief".

The legend says that, after having enjoyed "Alice in Wonderland", Queen Victoria asked Lewis Carroll to send her a copy of his next book. She received "An elementary treatise on Determinants" shortly afterwards. This story was never confirmed neither denied, but oh how much we wish it was true, and that we also could see the Queen's face!

We all know (and love!) "Alice in Wonderland", and we all might have as well read something on the maths in the book. But some of you might not know that Charles Dodgson (the real name of Lewis Carroll) was also a "serious" mathematician who lectured at Oxford and even had his say on tennis tournaments until mid-20th century. 

He was the third of eleven children and, from a young age, he started showing a talent for writing as well as for mathematics, and he would create stories and puzzles for his siblings, often involving fantasy and numbers. He went to Oxford to study mathematics and, being the top student was the start of a very long and succesful career in mathematical research as well as in teaching.

One of his most popular achievements as a mathematician came from the fact that he found unfair the way tennis tournaments were organised at that time, so he designed a fairer method to ensure that the most skilled players would pass to the latest rounds; this method was in use until 1942. The national election in 1880, along with the election of an architect for works at the University of Oxford as well as the criteria for the selection of university lecturers, led him to write on the limitations on the traditional election methods merely based on majority, and on how to improve them with a system by which every voter could not only vote for their favourite candidate but also for a number of their preferred alternatives. 

He also published mnenotechnical rules to remember dates and numbers, a method for writing encrypted messages, and an algorithm to find out the date of every Easter Sunday until 2499. He could remember the first 71 digits of pi by using a series of nonsense rhymes, and he also applied this system for memorising the logarithms of every prime number under 100.

His pseudonym was invented when the editor of a magazine for which Dodgson wrote stories and puzzles, thought he should distinguish his entertainment works from his academic publications. Charles proposed a few names, and we should thank the editor for rejecting Edgar UC Westhill and selecting Lewis Carroll instead! Carroll's contributions to literature were very influenced by maths, paradox and logic.

His fascination with the number 42 is patent in the following facts:

-Alice's Adventures in Wonderland has 42 illustrations. 

-The King reads Rule Forty-two in Alice's Adventures in Wonderland: "All persons more than a mile high to leave the court". That, despite not being the number one, is the most important rule, and it becomes a problem for Alice when she eats some mushrooms. 

-In the preface to "The Hunting of the Snark", he also mentions a rule 42 as the most important of them all. Later, in the same book, he says the baker had "forty-two boxes, with his name painted clearly on each."

-In his poem Phantasmagoria, he talks about chasing a 42 year old man.

His ability for teaching is easily seen in his guides for students and in his more than 10000 letters to children. Every child he knew would receive a riddle at some point. Many of them required the application of mathematics, but some needed only patience and common sense as they were simply based on a pun or on memory. He used to find humour in the dullest subjects and never underestimated children; he in fact wrote that intelligence seemed to vary inversely with size. His popular stories include horror tales, plays, riddles, and poems that, beyond the mathematical questions, also show the absurdity and lack of common sense when logic is applied.

Once he even proved that 2 x 2 = 5, and challenged his readers to find what was wrong in his deduction: 

Honoured Sir, 
Understanding you to be a distinguished algebraist (i.e. distinguished from other algebraists by different face, different height, etc.), I beg to submit to you a difficulty which distresses me much. 
If x and y are each equal to ‘1,’ it is plain that 2 × (x2 – y2) = 0, and also that 5 × (x – y) = 0. 
Hence 2 × (x2 – y2) = 5 × (x – y). 
Now divide each side of this equation by (x – y).
Then 2 × (x + y) = 5.
But (x + y) = (1 + 1), i.e. = 2. 
So that 2 × 2 = 5. 
Ever since this painful fact has been forced upon me, I have not slept more than 8 hours a night, and have not been able to eat more than 3 meals a day. 
I trust you will pity me and will kindly explain the difficulty to 
Your obliged, Lewis Carroll  

Martin Gardner was a fantastic mathematician, a great fan of Lewis Carroll, and the responsible for the best "Alice in Wonderland" edition so far: "The Annotated Alice". 
More on Lewis Carroll and the number 42.
More on the maths on Alice, here and here.
A marvellous book.
And if you cannot stop wondering about how come two two times is five, here you go this.

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