Hello. My name is Christian and I spend all day looking at maths links on the web.
At least, that’s what Samuel thinks, so he’s asked me to post some of those links here. This will happen to no fixed schedule, so I’ve decided to call these posts “The Internet Maths Aperiodical.”
Let’s start with an FAQ which surely can’t have been asked frequently enough to merit the title.
“Why are there happy puppies on the cover of this Bayesian textbook?”
“The happy puppies are named Prior, Likelihood, and Posterior. Notice that the Posterior puppy has half-up ears, a compromise between the perky ears of the Prior puppy and the floppy ears of the Likelihood puppy. (The puppy on the back cover is named Evidence. MCMC methods make it unnecessary to explicitly compute the evidence, so that puppy gets sleepy with nothing much to do.) If the puppies bother you, see a solution at this blog entry.”
I can’t believe anyone would disapprove of happy puppies on the cover of a Bayesian textbook. Or any book.
“Systems, networks and strategies” (via Metafilter)
A maths course for arts students at the San Francisco Art Institute, which is now about halfway through. Because dynamical systems are very easy to visualise, it looks like a well-chosen syllabus for arts students. The wiki page I linked to is a fun stream-of-consciousness collection of links to fun stuff on the internet related to each topic in the syllabus.
“The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols.”
Summary: Engineer with a gift for graphic design has trouble with algebra; says he was only shown symbolic methods in school/college; creates graphical tools to help get a feel for where solutions to systems of equations lie; writes essay about that; gives it an enormously provocative title. Take from that what you will. I don’t think anybody will dispute that sketching is an important way of getting a grip on a maths problem. Given that his evidence mostly consists of dynamical systems, maybe he should have taken the course at SFAI that I linked to above, and chilled out a bit.
In Soviet Russia, maths problem solves you! (Feel free to delete this one, Sam, it’s in appallingly bad taste)
In order to get into Moscow State University to read maths, applicants needed to pass an oral exam. Apparently, the examiners had a collection of “impossible to solve” questions they would give only to undesirables, in particular Jews. The questions had very simple answers but were worded in such a way as to make them very hard to solve. This paper by the amicable, happy, and not-at-all-odious Tanya Khovanova, along with Alexey Radul, gives both the problems and their solutions.
Baron Munchausen Redeems Himself: Bounds for a Coin-Weighing Puzzle
While looking at that paper I found this one, also by Tanya Khovanova, describing a coin-weighing puzzle. I think these are fairly well-known now, but the Munchausen framing caught my eye because, as is well known, my favourite number is a Munchausen number. I was planning on featuring a paper from my Interesting Esoterica collection each time I make one of these posts, so this might as well be the first!
Benford’s Law and the Decreasing Reliability of Accounting Data for US Firms
Like skateboarding and ska music, every so often the grand wheel of fashion swings around and Benford’s Law enters the public eye again. This is one of those times, and this article claims that accounting data for corporations have been deviating from Benford’s Law more and more since the 1960s. There’s a lot of humming and hahing in the comments about the applicability of Benford’s Law from both people who understand Benford’s Law and people who clearly don’t, which will either excite or frustrate you, depending on your personal policies towards other people’s wrong opinions. A rather good explanation of the idea behind Benford’s Law was posted in the metafilter thread about this analysis.
The Champernowne Constant is a rarity among constants – easy to define, hard to remember the name of. This paper, blogged about by the Math Tourist aka Ivars Peterson, gives a representation of the Champernowne constant derived, as far as I can tell, from a boozy night out. The picture of the author at the end of the paper certainly lends weight to that theory.
And finally, here’s your math masquerading as class war as promised, courtesy of a Mr Obama of the United States.