Introducing The Aperiodical

You may have noticed a new look here on Travels in a Mathematical World. For a while this blog was designed to look like a page from my website peterrowlett.net, but now it is different. This is because I have joined Katie Steckles and Christian Perfect in a collaborative blogging endeavour we're calling The Aperiodical.

A launch post over at The Aperiodical says

The Aperiodical is a new maths magazine/blog aimed at people interested in mathematics who want to read stuff. We post news stories related to maths, opinion pieces, interesting things we’ve found, accounts of monthly MathsJams, maths videos, and feature articles, as well as posts from our own blogs. We also host the Carnival of Mathematics, a monthly blogging carnival.

We've picked today to launch as it is the anniversary of Felix Klein's birth, and we offer some shiny Klein goodies to get started. Matt Parker and Katie Steckles investigate the amazing surface which bears his name in a video 'Top N Facts about the Klein Bottle'.

This got us wondering - what did Klein do apart from that ever famous bottle? Christian, Katie and I investigated and found an interesting career both in research mathematics and other contributions to the discipline, including excellent teaching, editorship of a famous journal and encyclopaedia, acting on a strong interest in school teaching and promoting mathematics to the general public. We wrote up what we found in 'Klein: outside the bottle'.

But we aren't just writing our own posts on the site. We're also keen to publish reports, exposition, videos, or anything mathematical and interesting that you want to share. Recently we've carried interesting pieces by Andrew Taylor offering an application of Grime Dice to electoral reform (as heard on the BBC's Material World) and Paul Taylor on how he devised the Hilbert's Space-Filling Crossword on our Features feed. If you'd like to write something please get in touch.

You can find out more about the approach we're taking with The Aperiodical, view pages and get RSS feeds for all our different types of post, and much more by reading the launch post: The Aperiodical.

What a nice job you have

Much has been made on Twitter of the recent list from CareerCast.com and posted at the Wall Street Journal of the 200 "Best and Worst Jobs of 2012" (a tweet on this from the IMA has been retweeted over fifty times). The reason? Mathematician is in the top ten, at number ten in fact.

There are a few issues with this, such as the simple question: what is a mathematician? If you take this to mean academic mathematician then this is a fairly specialist, niche area with few options for most graduates. Wider than this, there aren't many jobs called "Mathematician". I used to have the equivalent result from 2009, when mathematician was top of the list, in my IMA careers talk. The Wall Street Journal article then featured a mathematician working on 3D graphics behind Hollywood movies. I'm not sure she's who you think of when you hear "mathematician". Either way, I'm left wondering precisely what this job "mathematician" is and how realistic an option it is for most mathematics graduates.

I also wonder about the methodology, explained in detail at CareerCast.com but based in part on fairly subjective values. You might wonder, with mathematician (#10) and jobs that could be taken by maths graduates such as those in computing (#1, #9), actuary (#2) and financial planner (#5) at the top of the list, and lumberjack (#200), dairy farmer (#199), soldier (#198) and oil rig worker (#197) at the bottom, whether mathematician is benefiting too much from being a low-risk, indoors job.

Another issue is consistency. Between being first in 2009 and tenth in 2012, mathematician was sixth in 2010 and second in 2011. Have these jobs changed so much in the four years the survey has taken place or is there so little between the top candidate careers that minor variations are exaggerated?

Perhaps I should just be happy that mathematician is a top ten job and not worry about these niggles. Of course, if mathematician weren't in the top ten then we wouldn't pay the survey any notice so perhaps that's bias enough without questioning how the flattering result came about.

Short, short sci fi #TBSFA

I'm not one for producing creative writing but yesterday, thanks to James Clare, I came across a fun idea: the BSFA Tweetfiction Tweetstream challenge. There are bunch of rules on the website but basically it's an original piece of sci-fi or fantasy fiction contained within a tweet with the hashtag #TBSFA. Check out attempts by doing a Twitter search for #TBSFA.

I felt an attempt should be a contained, whole story (premise to resolution). The much Retweeted example is by @steven_moffat, current head writer of Doctor Who:

The worm became an idea, which hid itself in words, until it could climb, devouring all, through the eye of the reader of this tweet. #TBSFA

— Steven Moffat (@steven_moffat) April 6, 2012

This is good because something is set up (the worm that became an idea and hid in words) and happens (it climbs through the eye of the reader) within the tweet. Even though you don't know where the worm came from or what results from it being in your eye, I feel that this has structure. Some of the tweets I've seen are more like snippets. Many are making creative use of language but they lack either the establishment of a premise or its resolution, or sometimes both. I don't want to pick on a particular example so I've made one up:

The monster was only inches away as I cowered. I needed to run away but somehow I couldn't make my legs start working again. #TBSFA

You don't know what the scenario is, where the monster came from, or what happened in the end. Crucially, nothing happens. Perhaps it's fun to fill in these details (arbitrarily) yourself but I think then the story hasn't really done its job. A really good example, in my view, is this that I saw this morning by @mjkirkham:

As the soldiers were kicking down my door, I clicked 'Unlike' on the Emperor's profile page. Rebellion felt good. :) #TBSFA

— Mark Kirkham (@mjkirkham) April 7, 2012

In a few short words this conjures a world, an event happening within it and makes something happen. So much is evoked that isn't said. We imagine an Orwellian society with extreme, state-controlled social networking. Our hero has disobeyed, been caught and now manages one final act of rebellion before being taken away by the state. In a few short words, you are led to invent an entire story.

Given that the medium was Twitter, I felt acknowledging this by writing a piece of Twitter dialogue was appropriate. You may be aware of the process of commenting on a Retweet (RT, to tweet again someone's message, with attribution). There are various methods for this but I favour putting a comment in front of the RT, so this would look like this: "Message in reply RT @firstuser Original message". Although this means the tweet needs reading backwards it removes any ambiguity over who said which portion. Because of the need to have a complete story I decided to structure a three stage tweet: "First user responds to query RT @seconduser Second user queries original message RT @firstuser Original message".

Anyway, here is my attempt:

Said he was fed up of people asking RT @tim Did he really have a proof? RT @peterrowlett 1st trip in new time machine, to meet Fermat #TBSFA

— Peter Rowlett (@peterrowlett) April 6, 2012

With such a small number of characters in which to tell a story it seemed sensible to appeal to a cliche or two. I tried to hint at a world in which time travel is commonplace (the first tweet reports getting a "new time machine", not inventing one, and '@tim'^* doesn't seem surprised), and consequently history is overloaded with time travellers (Fermat is tired of the question yet his Last Theorem wasn't known until after his death, when it was discovered by his son in the margin of his copy of Diophantus' Arithmetica; he must, therefore, be being bothered by visitors from the future), with the implication of consequent issues for causality.

I chose the issue of whether Fermat actually had a proof, or simply felt he saw one and didn't check the details, as a suitably unanswerable question. (Given that Fermat's conjecture is correct,) Without travelling back in time and asking Fermat to write out the details of his proof (how do you broach that question without breaking causality?), we cannot really know the answer.

I like this idea of having such a short space to bring forth an idea. I hope you like my attempt. I encourage you to have a go. (You're supposed to do it by midnight Tuesday to enter a competition, but perhaps it would be fun anyway!)

* I didn't realise until after I'd sent my tweet that there is actually a user @tim! I meant to check and forgot. I just wanted a short name so it didn't take too many characters, and there's a whole tim-time thing. Thankfully @tim's most recent tweet says he is logging off Twitter for a month, and he has so many followers hopefully he won't see and be confused by my apparently putting words in his mouth!

Carnival of Mathematics 85

85 by brighterorange

Introduction

Welcome to a new Carnival of Mathematics! Traditionally the Carnival opens with facts about the number, this time 85, but first I have an important point of admin to address.

From Carnival of Mathematics 59 in November 2009 until Carnival of Mathematics 84 in December 2011, the Carnival was coordinated by Mike Croucher. Mike said in a blog post (of course!) that he had "had a lot of fun doing so" but that: "Recently, however, I have struggled to find the time to give the CoM the attention it deserves and so it is time to hand over the baton." We should all be very grateful to Mike for his effort over these two years. You can still find Mike blogging over at Walking Randomly.

Now, as a result, the Carnival has a new home (including an index of previous Carnivals) at The Aperiodical, a not-quite-yet-formally-announced blogging collaboration between Katie Steckles, Christian Perfect and me. We'll do our best to look after the series for the time being. If you've been following the Carnival for a while you'll know it only works because of a parade of volunteer hosts. The next few Carnivals are lined up but if you'd like to volunteer to host one on your blog later in the year please contact Katie. The other necessary element is submissions, and we have plenty of these this time, so let's get to business.

Funky new Carnival logo by Katie Steckles

85

This is Carnival of Mathematics 85. The ever-faithful Number Gossip tells me that 85 has no unique or even rare properties, being merely composite, deficient, evil, odd, square-free and a Smith number. Beyond mathematics, Wikipedia tells me that 85 is the atomic number of astatine, the ISBN Group Identifier for books published in Brazil and the lower bound (due to incomplete research) found by Jorge Stolfi (2004) for The Hollywood Constant, the smallest non-negative integer that has never been used in the title of a movie.

Serious mathematics

(Not that the rest isn't!)

Brent Yorgey at The Math Less Traveled wrote a series of four posts in response to Depressing Expressions by Patrick Vennebush over at Math Jokes 4 Mathy Folks. In these, he is working to prove why a certain iterative arithmetic algorithm always results in a factorial. Brent says:

In particular I'm proving it using a *combinatorial* proof, a lovely proof technique that (in my opinion) isn't used or taught as widely as it ought. 

In part four Making Our Equation Count, he says,

I go through the different bits of the equation we're trying to prove, and explain (with pictures) how to interpret each of them combinatorially.

Rebecka Peterson at Epsilon-Delta writes Extraneous Solutions of Log Equations--A Graphical Explanation. In submitting this post, Rebecka wrote:

Last semester a College Algebra student of mine asked why we sometimes get extraneous solutions when solving log equations. It was such a good question. I tried to do it justice in this post.

Drawing inspiration from the award of the Leroy P. Steele Prize for Mathematical Exposition to Aschbacher, Lyons, Smith, and Solomon for a work about the classification of finite simple groups, Gianluigi Filippelli at Doc Madhattan offers a post about finite simple groups and connections with physics in The classification of finite simple groups.

Frederick Koh from White Group Mathematics submitted Understanding MATTERS (4) saying:

Of late I noticed quite a few students (in online forums) experiencing difficulties in comprehending the concept of calculating distances between 3 dimensional vector planes in space, hence I am sharing an in depth explanation behind how things work.

Rohit Gupta at Kali & the Kaleidoscope investigates a new visualization of Möbius' Mu, "a notorious function to classify all integers in three different boxes" in The 3 Pills of Möbius.

Art

Thomas Egense from Thomas' mathematical adventures writes about an attempt to create mathematics-inspired art algorithmically using something called "Fractal flames". Thomas defines fractal flames, details the algorithmic work involved, and gives several examples of the generated artwork, including the image below (used with permission).

Thomas Egense also submitted Dimensions (series of nine videos embedded below) calling this an "impressive graphical visualization of hard to grasp mathematical concepts like higher dimensions and topology".

Last week Gathering for Gardner 10, the meeting of mathematicians, magicians, puzzlers and others inspired by the life and work of Martin Gardner, took place. Edmund Harriss, from Maxwell's Demon, previewed his G4G10 talk in a blog post, The 2×1 rectangle and Domes. Edmund begins with the humble 2×1 rectangle, "not one of mathematics most celebrated shapes", and ends up with structures built as accommodation at the Burning Man event.

Pop culture

Matt over at Math Goes Pop! writes in The Probability Games about the process used to select participants to take part in a fight to the death in the book and film The Hunger Games. Matt says "the rules here practically beg for some mathematical analysis" and Katie Steckles, who submitted the post, called this "just the kind of unnecessary mathematical analysis of a situation I like to see".

Video game mathematics

Drawing inspiration from the recent arXiv preprint Classic Nintendo Games are (NP-)Hard bringing video games "out of nerdy obscurity and into cutting edge computer science", Sam Alexander from Xamuel.com writes Toward the Mathematics of Video Game Glitches. Sam noticed a minor error in that article based on a glitch in Super Mario Brothers. Running with this theme, he defines video game glitches, game theoretically speaking, and focusing on "glitches which the player can exploit to win the game faster than intended", defines a theorem (which he describes as "committing horrendous crimes against mathematics"!).

SNES vs. Xbox Triple60 by avail

Performance and puzzles

Ben Nuttall writes about his experience as a maths busker.

“What is Maths Busking?” I hear you ask. Maths Busking is a street performance of mathematics whereby the buskers demonstrate mathematical ideas and engage the public in thinking like a mathematician

As well as a fuller explanation of maths busking, Ben shares some of the 'busks' he performed, his thoughts on the experience and some photos.

Birmingham City Centre by Maths Busking

Katie Steckles, writing at The Aperiodical, discusses a variant of a popular mathematics 'mind reading' trick. I don't want to spoil the puzzle in case you want to play along at home, so go over and check out On Disreputable Numbers.

Paul Taylor, also at The Aperiodical, writes about a puzzle he designed for Katie Steckles' Puzzlebomb. Puzzlebomb is a monthly puzzle sheet featuring all-new types of puzzles. Following the release of the April Puzzlebomb, Paul made the following claim on Twitter:

I guarantee there has never been, and will never be, another puzzle quite like Hilbert's Space Filling Crossword

In Words to Fill Space he justifies this assertion and describes how he created the puzzle.

Paul also writes, again at The Aperiodical, about a class of puzzle in which a number of prisoners are all given hats and their fate depends on their ability to correctly determine the colour of their own hat. Paul offers "a nice variation on the theme that I heard about at a recent MathsJam" as Another black and white hats puzzle.

Maths Jam is a monthly meeting of maths enthusiasts in pubs worldwide to share stuff they like. "Puzzles, games, problems, or just anything they think is cool or interesting". A recent development is blogging roundups of what happened at Maths Jam meetings. Recent outings, full of puzzles and mathematical goodies, include: Newcastle (February), Manchester (March), London (February) and Melbourne (January), and a set of photos from various February Maths Jam meetings.

Maths Jam London February 2012

Last month I attended Newcastle Maths Jam. While there we played with a puzzle that Out of the Norm states as:

By relabelling the faces of two dice, can you design a new, unusual pair of six-sided dice that achieves rolls with the same frequencies as a pair of normal dice? All the faces must have a positive number of spots.

Dice and Dissection: a puzzle discusses this puzzle and gives a nice diagrammatic way to view the solution.

History and society

John Cook of The Endeavour writes about a wedding invitation written under the collective pseudonym of that "semi-secret group of French mathematicians", Nicolas Bourbaki. In Nicolas Bourbaki’s wedding invitation, John explains some of the mathematical references and reveals how the invitation "nearly cost Bourbaki member André Weil his life".

A post on Pat'sBlog goes to primary sources to highlight an error in Wikipedia in relation to the origins of the four-fours problem. That is,

using four fours and whatever mathematical operations that were allowed to make a number, or a set of numbers. 

The origins of the problem apparently lie in earlier similar problems, including a problem of four threes. Read about it in Before There Were Four-Fours, There Were Four-Threes.

Guillermo Bautista at Mathematics and Multimedia writes A US President's Proof of the Pythagorean Theorem about the proof of the Pythagorean theorem formulated by James Garfield, the 20th president of the United States of America.

Alexander Bogomolny of CTK Insights offers a little piece of mathematics in the history of chronology given in Florian Diacu's The Lost Millennium in a post entitled Chinese Remainder Theorem: an Application to Chronology. Submitting this post, Alexander said:

Chinese Remainder Theorem is a staple of early puzzle books, both European and Eastern. This is very satisfying to learn that the theorem finds practical and important applications in the science of chronology. The book by Florian Diacu where I found this application is an exquisitely written compendium of history and mathematics of calendrical calculations. The book deserves every praise and gets my wholehearted recommendation.

In a blog post here on Travels in a Mathematical World, I was very taken with an answer given to a question about working outside traditional academia by Neil deGrasse Tyson in an interview with Samuel Hansen for the Strongly Connected Components Podcast episode 45. The whole interview (18 mins) is worth listening to. My reflections can be found as Culturally an academic.

Over at Second-Rate Minds, Samuel Hansen writes about The True Importance of Friends, explaining the origin of a result in social network theory and its implications in epidemiology. 

I really noticed the absence of the Carnival back in February when I thought I might submit a couple of blog posts which got a particularly warm reaction and found the submissions form deactivated. The posts were Apparently Gauss got in this bar fight with Hilbert... and the follow-up Why do we enjoy maths history misconceptions?

Technology

John Chase from Random Walks writes about the surprising features of Microsoft Office Equation Editor, in which he makes the bold claim: "LaTeX lovers will love it". Find out why at Microsoft Office Equation Editor.

I've saved the last word for this revived Carnival to the previous coordinator, Mike Croucher. Mike's month of math software for March 2012 offers the latest news in the world of mathematical software (a month of math software has been a monthly series since January 2011).

The End

Well, that's that for this Carnival. You can help spread the word by blogging, tweeting, etc. about the revival of the Carnival and directing people to this edition. If you're hungry for more mathematics blog posts then there's the previous Carnival of Mathematics 84, the latest Math Teachers At Play Carnival 48 is over at Math Is Not A Four Letter Word and you can get a weekly selection of blog posts from the Mathblogging.org Weekly Picks.

Future outings for the Carnival of Mathematics are queued over at The Aperiodical. Carnival of Mathematics 86 will be posted in May by Brent at The Math Less Travelled. Submissions for this are now open, so keep your eye out for great posts and get writing!

May I publish a letter from my MP without permission?

A friend of mine recently contacted her MP on a matter of use or misuse of statistics in promotional material and received a reply. She wants to write a blog post about the experience. The fairest way to do this would be to quote the MP's response, since this avoids hearsay and anecdote. Is she free to do this? I have an answer to this question and I share this below.

I googled a lot, to no avail, and asked on Twitter.

Help: If I write to my MP is it okay to publish the reply in full with comment on a blog? URL to reputable source yes or no appreciated.

The answers were unclear. Clearly a private letter from a private individual is copyright of that individual so permission must be sought, and this was the view taken by several respondents. However, a letter written on company time might result in copyright owned by the employer. In this case, the MP works for the state and has their time paid by the taxpayer to perform the public function of representing constituent's issues. Then, is the constituent free to publish the letter without seeking permission? This was the view of several other respondents.

There are also issues of privacy, but if the MP has revealed nothing private and the constituent is happy is that okay?

Or perhaps there is a public interest defence? 

Happily, @singinghedgehog suggested that I ask the House of Commons Information Office. I sent the following query.

Hello,
If a constituent writes to their MP and their MP replies, are they free to publish the response in a blog post?
I have been told that the contents of the email are private and the constituent should write back asking for permission. I have also been told that no permission is needed as the MP's time is publicly funded so as long as the constituent is happy they may make the contents public.
Thank you for your help in clarifying this matter. As I found an answer hard to find, may I publish your response on my blog?
Thank you,
Peter. 

Notice how I cleverly ask "may I publish your response on my blog?"? They didn't reply to that bit! So I emailed back asking if this was okay and got this response (I've taken off the name of the respondent because there is no need to include this):

Dear Peter,
There are no restrictions on publishing emails from this office as we are a public information service.
I hope that this is useful. 

So here is the original response (I've highlighted the key bit):

Dear Peter,
Thank you for your email.
I have spoken to our legal services team and they have given the following response to your question:
Letters written by Members
A Member has copyright in letters that s/he has written. Therefore, the relevant Member’s consent must be obtained before their letter can be published.
Letters written by constituents
Constituents are advised that, if they send a letter to their MP, it may be protected by qualified privilege for the purposes of defamation. However, this protection is likely to be lost if a constituent puts their letter in the public domain.
I hope that this is useful to you. 

So my friend must ask permission. Better, she should have asked permission in her original letter. I don't think the second part applies (though I haven't seen the correspondence in question) but it is interesting to note.

This surprised me because the two seemingly most reputable responses - one originating with someone who works for an MP and one secret "reputable source" ("I'd tell you who but I'd have to kill us both") - both gave the opposite answer. So I'm publishing this here in the hope it is useful to someone.

Carnival of Mathematics in a Mathblogging.org world

For a while now (what, over a year?) the folks at Mathblogging.org have been choosing their weekly 'picks' of the blogs coming through their aggregator. The promise at the start of each post has amazed me:

We try to read every blog post that goes through Mathblogging.org. For the Weekly Picks, we collect posts from last week that give you an impression of what the mathematical blogosphere has to offer.

This, to me, seems an incomprehensibly difficult task. There's so much out there and a massive selection of blogs are now indexed at the site. In light of this resource, our current attempt to revive the Carnival of Mathematics did leave me wondering whether we were barking up the wrong tree in 'a Mathblogging.org world'.

Now the incredible level of effort that must be needed for this ever-increasing task has proven unsustainable. In a post entitled "The Weekly Picks are dead, long live the Weekly Picks", Peter Krautzberger outlines a plan to cope with this:

The goal of the Weekly Picks has always been to show off the wealth of the mathematical blogosphere and to offer an accessible introduction to the various types of mathematical blogs out there...
For the next few weeks, we will focus the Weekly Picks on a different category each week.  This will give us the room to present the full spectrum of the community.

This seems to be a reasonable plan to deal with this ever-growing task, and I'm delighted to hear the Mathblogging.org folks are human after all! However, there is a problem:

We realize this means we might be missing some great posts that just happen to appear on a week where we do not cover that category.

Aha, here is somewhere the Carnival can step in. If you feel a post you've written has been overlooked because Mathblogging.org wasn't looking at your type of blog this week, you can submit it to the Carnival of Mathematics. (Of course, it's then up to the current host to decide whether to include it.)

This approach has its problems too - much is missed, or determined by various biases or whether bloggers have heard of it or remember to submit. But while the Mathblogging.org 'weekly picks' represents a completist approach now focused on each category in turn, the Carnival attempts to catch the best posts across all with its anarchic, community-led method. Perhaps there is room in the world for both approaches, after all.

Behind closed doors: the Spanish intelligence service

When I was a student there was a door in the basement of the university library marked "This door must remained closed at all times". I remember joking that perhaps no one could remember what was behind it, and of course they couldn't check.

The BBC are reporting that GCHQ have received two Engima machines used in the Spanish civil war, in exchange for a German four rotor Naval Enigma machine recovered from Flensburg in May 1945, an Enigma rotor box and related documents.

The machines were apparently discovered "almost by chance, only a few years ago, in a secret room at the Spanish Ministry of Defence in Madrid." The BBC quotes Felix Sanz, the director of Spain's intelligence service, saying:

Nobody entered there because it was very secret, and one day somebody said 'Well if it is so secret, perhaps there is something secret inside.' They entered and saw a small office where all the encryption was produced during not only the civil war but in the years right afterwards.

It's good to hear the Spanish intelligence service is taking secrecy so seriously, to almost Monty Python levels of silliness.

An interesting article, it also gives a hint at international co-operation. Mr Sanz is quoted saying:

In today's world it is impossible to work alone. You need friends and allies. I knock at the door of the British intelligence - all three agencies - as many occasions as I need it and I always get a response. And I hope on the occasion where the British services knock at my door, when they leave my house they leave with a sense they have been helped also.

I find this last sentence interesting. It may be entirely coincidental, or a product of translation, but it doesn't actually say that he helps the British intelligence services. This reminds me of a joke in the opening episode of the excellent Yes, Minister, in which the meeting of the Minister, Jim Hacker, and his civil servant Sir Humphrey, contains the following dialogue:

Bernard Woolley: "I believe you know each other."
Sir Humphrey: "Yes, we did cross swords when the Minister gave me a grilling over the estimates in the Public Accounts Committee."
Jim Hacker: "I wouldn't say that."
Sir Humphrey: "You came up with all of the questions I hoped nobody would ask."
Jim Hacker: "Well, opposition is about asking awkward questions."
Sir Humphrey: "And government is about not answering them."
Jim Hacker: "Well, you answered all mine anyway."
Sir Humphrey: "I'm glad you thought so, Minister."