Harry’s 2025 Christmas Miscellany

What could be more Christmassy than a fireside tale by our old friend Charles Dickens? “What could be?”, I hear you reply, to which I can only respond: a spooky fireside tale by Mr Dickens. A ghost story that will freeze your marrow, chill you to the bone and leave your teeth chattering. Here, courtesy of the Internet Archive is an 1891 print of his story, To Be Read at Dusk. Perhaps it should be read at dusk, in which regard I suggest, since we are all nerds here, browsing the sun’s movement across any location. (With apologies to Copernicus and his many acolytes!) Of course A Christmas Carol is probably MORE traditional. Enjoy!

If you prefer fiction over fact, then maybe this Agatha Christie story will suit you instead. Peter Sallis plays the indomitable Hercule Poirot in a BBC radio production of Hercule Poirot’s Christmas. https://youtu.be/0lsrJIbWlAI?si=ddq8kmhaiGePJAgR

Everyone knows that the apparent 3 dimensions of our world are really just the start, and whether you are interested in relativity (4 dimensions), string theory (at least 10 dimensions) or quantum physics (infinite dimensions) you have to try to wrap your head around the strange and wonderful geometry that the extra dimensions allow. One of the most beautiful objects in these higher dimensional world is the 120 cell, a tessellation of the 3 dimensional sphere which is the set of points at distance 1 from the origin of 4-dimensional space (or spacetime if you prefer). The tessellation is by regular dodecahedra, and we can’t build an accurate model in our 3 dimensional universe, but just as you can sketch a sphere or a cube on a 2 dimensional page, you can build a sketch of the 120 cell if you have the patience, and in this video Thomas Kerne shows you how!

Apologies for repeating an item from last year, but John Finnemore’s publisher did not entirely meet their part of the bargain and he was left with a stock of copies of his extraordinary graphical mystery. It’s a more a game than a story and is not for the faint-hearted. We can’t give it away (the poor man has to eat and his publisher is not doing anything to help with the bills) but here is a link in case you want to spend some Christmas money!

Last year we wallowed in the dulcet tones of a group of musically gifted mathematicians from Northwestern. If you enjoyed that you will almost certainly like this – a twist on the classic Twelfth Day of Christmas by Straight No Chaser. You have almost certainly heard this before, but you might have missed the OG from 1998! I don’ t know if any of the singers are mathematicians, but something about it suggests that some of them might be.

This is the National Cipher Challenge, so I thought you might like this. A guide to breaking the Playfair cipher by hand. It was written by Oran Looney and includes python code for those who like to speed things up, but what I really like is the analysis behind it all.

For something closer to home, here is a description of how to effectively brute force a Hill cipher written by an anonymous member of the National Cipher Challenge community!

This video is both charming in its naivety and full of dated references, but watching it from the perspective of the large language model era, it is remarkably prescient in the sort of things these machines would one day (as in, now) be able to do!

A last treat for you this year – an account of how the Bombe was used to break the Enigma cipher in the Second World War. This contribution comes from contributor upsidedown, and we are really grateful that they offered it to us. Later we will publish a version of this containing solutions to the exercises, but knowing our audience we suspect that many of you will be glad to have this version for a while first!