## The Arthur Christmas Problem

Since it’s the season for it I’d like to point new or new-wish readers to a couple of posts I did in 2012-13, based on the Aardman Animation film **Arthur Christmas,** which was just so very charming in every way. It also puts forth some good mathematical and mathematical-physics questions.

Opening the scene is “Could `Arthur Christmas’ Happen In Real Life?” which begins with a scene in the movie: Arthur and Grand-Santa are stranded on a Caribbean island while the reindeer and sleigh, without them, go flying off in a straight line. This raises the question of what *is* a straight line if you’re on the surface of something spherical like the Earth.

“Returning To Arthur Christmas” was titled that because I’d left the subject for a couple weeks, as is my wont, and it gets a little bit more spoiler-y since the film seems to come down on the side of the reindeer moving on a path called a Great Circle. This forces us to ask another question: if the reindeer are moving around the Earth, are they moving with the Earth’s rotation, like an airplane does, or freely of it, like a satellite does?

“Arthur Christmas And The Least Common Multiple” starts by supposing that the reindeer are moving the way satellites do, independent of the Earth’s rotation, and on making some assumptions about the speed of the reindeer and the path they’re taking, works out how long Arthur and Grand-Santa would need to wait before the reindeer and sled are back if they’re lucky enough to be waiting on the equator.

“Six Minutes Off” shifts matters a little, by supposing that they’re not on the equator, which makes meeting up the reindeer a much nastier bit of timing. If they’re willing to wait long enough the reindeer will come as close as they want to their position, but the wait can be impractically long, for example, eight years, or over five thousand years, which would really slow down the movie.

And finally “Arthur Christmas and the End of Time” wraps up matters with a bit of heady speculation about recurrence: the way that a physical system can, if the proper conditions are met, come back either to its starting point or to a condition arbitrarily close to its starting point, if you wait long enough. This offers some dazzling ideas about the really, really long-term fate of the universe, which is always a heady thought. I hope you enjoy.

## Reading the Comics, February 14, 2015: Valentine’s Eve Edition | nebusresearch 7:46 pm

onSaturday, 14 February, 2015 Permalink |[…] deductive logic — would eventually happen, and for that matter, recur infinitely many times. That’s an unsettling thought, not just for the existentialist dread it seems to require when w… but because it seems to defy the notion of entropy as an ever-increasing quantity. And that seems […]

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## How August 2015 Treated My Mathematics Blog | nebusresearch 8:28 pm

onTuesday, 1 September, 2015 Permalink |[…] Of course I understand the “86164 seconds” query, because that ties in to the delightful animated movie Arthur Christmas and the deep existential dread one of its plot points inspires. […]

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## Bringing Up Arthur Christmas Again | nebusresearch 6:00 pm

onMonday, 21 December, 2015 Permalink |[…] I was able to spin out a couple of mathematical and physics questions from one scene in the film. Last year I collected links to the essays — there’s five of them — into a single c…. I hope you’ll consider […]

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