Hello again, here’s another Internet Maths Aperiodical. Sadly, until I write a third edition, this Aperiodical currently has a publication period of thirteen days, so I’ll be as quick as I can with this one and I’ll make sure to post again either before or after another thirteen days have elapsed. I can only apologise for the temporary regularity of service.
Here are some more math links.
Shakespeare wrote loads of plays and sonnets and things. Or maybe he didn’t! Isn’t it fun being a literary scholar?
No, it’s more fun being a mathematician. So here’s a blog post about a theory that Francis Bacon was the real author of Shakespeare’s œuvre and hid encoded messages attesting to that fact in the Shakespeare folio by encoding letters in binary, and then using two different typefaces to represent 1s and 0s. As a description of historical events it is of course completely wrong, but logic dictates that all but one of the theories about Shakespeare have to be incorrect, so it shouldn’t feel too bad about itself. Anyway, the idea behind the bilateral code was good, and the people with the Bacon obsession played an important part in the mathematisation of cryptanalysis at the start of the 20th century.
Moving onwards, I have another stupid code for you, but this one’s so stupid it took some really clever people to crack it. The Copiale Cipher is an 18th-century manuscript which had evaded comprehension until some dudes with a load of computers and some fresh new ideas about how to use them had a go at it. Using some computer analysis the team first showed that the manuscript contained a real language and not nonsense (which is a very interesting field of study in itself) and then found it could be deciphered using simple frequency analysis and automatic clustering. They’ve written up their methods and thinking in a very accessible paper. It turned out that the book was written by an esoteric society with a predilection for hazing rituals. HOW TOTALLY UNEXPECTED.
I listened to a lovely little programme about rabbits on Radio 4 this week. It’s available on the iPlayer. There’s, apparently, a breed of rabbits called the Old English Spot. So the programme was all about the trials and tribulations of the people trying to breed the perfect English Spot, and the trials and tribulations of the people who have to live with the people trying to breed the perfect English Spot.
And it is hard to breed a perfect English, because a perfect English is one which looks exactly like the rabbit captured in the painting on this page. In particular, the spots down the rabbit’s side must be in exact correspondence with the picture.
What’s this got to do with maths? Good old Alan Turing worked out how spotty patterns come to be decades ago. Spots are the product of an ever-changing dynamical system known as reaction-diffusion, and are much more congenital than hereditary. So there will probably never be a perfect English, unless someone with a very good knowledge of reaction-diffusion systems and a steady hand with a pipette gets their hands on one in utero.
I saw this story on the BBC News site about how summer babies have it tough throughout their entire lives. I didn’t care, I was born in January. What I did care about was the following pair of sentences:
This reflects that these August children can be almost a year younger than their September-born classmates.
This age gap has not been closed by the time youngsters are ready to leave secondary schools.
Abbott and Costello redux. Sadly, the text has been changed to “This achievement gap…” since I first looked at it. The point about August children being nearly a year younger than their September-born classmates is still pretty much tautological but really I just wanted to post that Abott and Costello clip.
Finally, here’s something interesting. A while ago Twitter was abuzz with the startling revelation that the decimal representations of 1/7, 2/7, etc. all contained the same digits, cyclically permuted. A chap called Lawrence Brenton has written an article in the College Mathematics Journal explaining what’s going on. I like it a lot. It’s all to do with some simple group theory, which he explains very clearly. He makes a persuasive case that all teachers should know a bit of group theory because it leads to more convincing explanations of this kind of thing than number theory alone could.
So if anybody ever asks you what group theory is good for, tell them about this. It won’t take long.