If you're hosting Christmas this year and a familiar sense of dread is setting in, read on for the 'mathematical' survival guide to the day from The Indisputable Existence of Santa Claus
So, the clocks have gone back, winter is taking its grip on the world, and, if you're hosting Christmas this year, a familiar sense of dread might be setting in.
How long does a turkey take to cook? Who will get upset about the size of their slice of Christmas pudding? Will half-hearted cracker-pulling result in tantrums over who gets the magic trick and who is left with the screwdrivers?
But don't despair! With a subtle change of perspective, you'll be able to approach the big day with a new-found confidence and rediscover that elusive good cheer. Simply look at things through the eyes of a mathematician . . .
Let's start with the star of the show. If you look up a turkey recipe online (or - whisper it - in an actual book) it will probably tell you to heat your oven to 180°C, then find the cooking time (in minutes) by multiplying the weight of your bird (in kilos) by two-thirds. However, any mathematician worthy of their protractor and set square will tell you that this calculation is bogus.
Since the heat from the oven reaches the turkey through its skin and has to penetrate all the meat, the cooking time must depend on the surface area (in square units) and the volume (in cubic units). So the relationship between cooking time and weight is more complicated than a simple multiplication!
Luckily, back in the sixties, a chap called Wolfgang Panofsky (evidently unfulfilled by his undemanding job as director of Stanford University's particle accelerator centre) provided a proper answer to this conundrum. After roasting and eating more turkey than medically recommended, Panofsky determined that the cooking time could be calculated by raising the weight of the bird to the power of two-thirds, then multiplying by 1.13.
Quite why this method has never caught on with the public, despite its evident mathematical superiority, we have no idea . . .
After the main course, you'll be moving on to dessert, and if your family is as argumentative as ours are, then the simple task of dividing a Christmas pudding so that everyone has what they want - boozy raisins, cherries, more or less of the fruit - can be nigh on impossible.
The answer is Austin's Moving Knife Procedure. Make a cut to the centre of the pudding, then rotate your knife slowly above it, keeping the tip at the centre. As soon as someone reckons this piece is worth having, they shout 'Cut!' you plunge the knife in and give them the slice. Effectively everyone cuts their own slice, so they can't complain! Cunning, eh?
Of course, a traditional British Christmas dinner demands a traditional British round of Christmas crackers. The unspoken goal of cracker-pulling is that everyone wins a prize (generally a pack of mini-screwdrivers), but the results are inevitably unsatisfactory. One person will win two prizes, someone won't get any, and prizes will be redistributed across the dinner table, usually with a paper hat falling in the gravy along the way.
Now, as it turns out, there is a simple cracker-pulling pattern to guarantee everyone a prize . . . All guests pull both ends of their own cracker. Efficient and effective. Not much fun though, we'll admit.
If this mathematically perfect method doesn't appeal, the approach that maximizes the probability of everyone getting a prize is pulling crackers in pairs, then pairing up again so that winners pull against losers. This method has a probability of success of 0.5 to the power n/2 (where n is the number of people at the table), or to the power (n+1)/2 for an odd number of people.
What's that? You were already doing that? A likely story . . .
So there you have it. With a fresh mathematical perspective, you can overcome your festive fears and sail through Christmas with a smile . . .
There are all sorts of other Christmas tasks that maths can help with. From wrapping your presents to organizing the office Secret Santa; from decorating your tree to winning the annual game of Monopoly - with maths on your side, you'll always be one step ahead.
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How do you apply game theory to select who should be on your Christmas shopping list ? Can you predict Her Majesty's Christmas Message? Will calculations show Santa is getting steadily thinner - shimmying up and down chimneys for a whole night - or fatter - as he tucks into a mince pie and a glass of sherry in billions of houses across the world?
Full of diagrams, sketches and graphs, beautiful equations, Markov chains and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingfuls of mathematical marvels. And proves once and for all that maths isn't just for old men with white hair and beards who associate with elves.
Maths has never been merrier.
NOW WITH A BRAND NEW CHAPTER
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