Anyway, the Pet Shop Boys have written a piece of music “inspired by codebreaker Alan Turing”, titled *A Man from the Future *(not *The Man from the Future*, the 2011 Brazilian classic), and it was performed for the first time on Wednesday as part of the BBC’s Proms season.

It’s not my cup of tea in the least bit, but we’ve covered every other bit of never-ending Turing centenary news so why not this one?

You can listen to the performance on BBC Radio 3 but, thanks to The Unique Way the iPlayer Works, the actual program starts about six minutes in.

]]>The trailer for the highly anticipated new film about mathematician Alan Turing was released this week. Alan Turing was not only a mathematician, but also the father of computer science and World War II code breaker. The trailer itself looks fantastic and has me super excited to see the film when it is released this November.

The Imitation Game stars Benedict Cumberbatch as Alan Turing and Keira Knightley as Joan Clarke. Clarke herself was a mathematician, Bletchley Park code breaker and, briefly, Turing’s fiancée.

The script featured on Hollywood’s blacklist, a list of the best unproduced screenplays, and tells the story of Turing’s early days at Bletchley Park, his work breaking the infamous German Enigma code, and his relationship with Clarke. An early draft of the script caused concern that it over emphasised Turing and Clarke’s relationship, and was accused of “straightwashing” the story of Turing, who was later arrested and convicted for homosexuality.

After seeing the trailer I am more confident it’s going to be done right. So let’s break it down:

Nock:

What did you do during the war?

Turing:I worked in a radio factory.

Nock:What did you really do during the war?

Turing:Are you paying attention?

Looks like the film is going to be framed by Turing’s arrest in 1952. Plus, Rory Kinnear adds five bonus points in my book.

And with that look, thousands of Cumberbitches develop strange feelings towards a mathematician. I know I did.

Stewart Menzies:

If you speak a word of what I’m about to show you, you will be executed

And here we see Turing walking towards, is it Bletchley Park? Not when Turing was recruiting in 1938, so maybe some other location for the Government Code and Cypher School. Or probably the film is indulging in a little bit of time dilation as we also see Mark Strong as Stewart Menzies who was Chief of MI6 from 1939. The threat of execution for revealing the secret work of Bletchley Park was a very real one.

Turing:

It’s beautiful

And there’s the source of all the trouble, the German Enigma machine, with its box of rotors and everything. Not that they had a machine at this point. At best they had replicas, but even I don’t expect them to explain the workings of an Enigma machine to the cinema-going audience while Cumberbatch looks at circuit diagrams. I agree, it is beautiful.

Matthew Goode as Hugh Alexander looks confused. That might be because he was head of the John Lewis research department at the time and didn’t reach Bletchley till 1940.

Gordon Welchman may have been a better choice and is strangely absent from the trailer. Welchman was Turing’s counterpart in that he was in charge of Hut 6 breaking army Enigma codes, while Turing was in charge of Naval codes in Hut 8. Welchman also worked with Turing to design the code breaking machines.

Hugh Alexander eventually took over the running of Hut 8 from Turing, became head of cryptanalysis at GCHQ and was a chess grand master. Also, did you know John Lewis has a research department. Working on advanced scatter cushion technology.

Hey, also maths on blackboards. Is that frequency of pairs and triplets of letters. That’s reasonable maths in the background.

Turing:

It’s the greatest encryption device in history. The Germans use it for all major communications.

Indeed it was. The machine was used by all branches of the German military and it was one of the best cipher machines around at that time.

This looks like this is meant to be Hut 8, Turing and his team of researchers breaking the naval Enigma. I’m not sure they had actual Enigma machines on their desk as they worked though. Also, it’s World War II so GIANT MAP!

Denniston:

Everyone thinks Enigma is unbreakable

Charles Dance as Commander Denniston, head of the Government Code and Cypher School. He had run the GC&CS for twenty years and knew his parsnips. It was commonly believed, including by Denniston, that Enigma was unbreakable.

Turing:

Let me try and we’ll know for sure

Oh no he didn’t! Setting up some arrogance on the part of Turing. Also, this might be a good time for a comparison.

Charles Dance:

ORLY?

Menzies:

Mr Turing do you know how many have died because of Enigma?

Turing:No, I don’t.

Menzies:Three. While we’ve been having this conversation.

Incidentally, Turing was not so cold as to be unaware of the human cost of the war, and he publicly supported the asylum of Jewish refugees in the UK

Did I mention this is based on a true story?

Keira Knightley’s jaw enters a room. Followed by Keira Knightley. *(Little bit rude! – Ed.)*

Avengers Assemble!

This is sort of a line up of Turing’s research team. From left to right we have John Cairncross (played by Allen Leech), Turing (Cumberbatch), behind Turing is Jack Good (James Northcote) (sorry Jack Good, don’t blame me, blame the person who blocked the scene), Peter Hilton (Matthew Beard), Hugh Alexander (Matthew Goode), and Joan Clarke (Knightley).

Turing started working on the problem of the Naval Enigma on his own, then later joined by Tony Kendrick and Peter Twinn (not featured), and then over the next 18 months or so joined by Clarke, Alexander, Good and Hilton (in that order).

Slightly incongruous here is the inclusion of John Cairncross. Not only was he the last of this group to join Bletchley Park, but he worked in a different section of Bletchley breaking a different cipher entirely. He was also passing information to the Soviets. Can you say INTRIGUED!

Clarke:

What is it that we’re really doing?

Turing:We’re going to break an unbreakable Nazi code.

Clarke:Oh

Looking at other comments on the trailer around the internet, I have seen some people react negatively to what they see as a plucky, female sidekick and love interest for Turing. However, Joan Clarke was a real person. Clarke was an able Cambridge undergraduate in mathematics, Welchman remembered her ability and recruited her for Bletchley Park. Initially Clarke was given clerical work, but was soon moved into Hut 8 to work with Turing. Clarke continued to work for GCHQ for many years after.

Turing and Clarke became very good friends. Turing would arrange their shifts so they could be working together, as well as spending a lot of their free time together. In the Spring of 1941 Turing asked Clarke to marry him, and the engagement even survived Turing’s admission of his homosexuality. Clarke was formally introduced to Turing’s family, Turing gave her an engagement ring, and there was talk of the future. But ultimately their engagement did not last beyond the Summer of 1941.

Turns out people who comment on the internet are sometimes wrong.

A shot of Turing running. In fact Turing was a very talented long distance runner. He would run for meetings from Bletchley to London (40 miles), and his marathon time was only 11 minutes short of the world record at the time. I wonder if his running skills will come in useful later in the film?

A listening station and a new message to decrypt.

Alexander:

To pull off this genius routine one actually has to be a genius.

Turing was still a young man of 28 at this time, with many of the other Bletchley Park cryptographers being several years older than him. However, by this point Turing had already solved one of the great unsolved problems in 20th century mathematics, known as the Decision Problem, and laid the groundwork for computing machines.

Denniston:

Why are you building a machine?

Turing:The machine will allow us to break every message and win the war

Turing doing some tinkering, and the final machine. The Bombe was like simultaneous Enigma machines, with deductions from one machine feeding into the others. The first Bombe machine was called Victory and finished in March 1940.

Alexander:

You could help us. But you won’t.

Alexander throw a glass valve (?) at Turing. Not cool man. Things are getting tense. Let’s chill out for a bit with this beautiful shot of a sunset.

Turing to Denniston:

You will never understand the importance of what I am creating here.

The film seems to be setting up Denniston as an antagonist to Turing, which is probably a great disservice to Denniston, who by all accounts understood the difficultly of the work, deliberately recruiting the professor type, and was proud of their achievements. Although the portrayal may be a more accurate reflection of the attitudes of some others in the military at the time.

Turing:

I’m just a mathematician

Menzies:You’ve got more secrets than the best of them

Cumberbatch seems to be doing a great job portraying Turing’s shyness and awkwardness. And it is clear the gay issue will be a part of the film.

Some maths (not clear what) and some Most Secret documents!

After the war they had a big bonfire at Bletchley Park and burnt all the documents. Although Turing himself had moved on at this point.

Hey! Maybe that running does pay off later in the film!

The Bombe machine stops, and these crazy kids may have pulled it off.

The title by the way is Turing’s own name for what is now better known at the Turing Test, a test of whether a machine can impersonate a man. I expect these clever filmmakers have some double meaning in mind.

Clarke:

Sometimes it is the people no one imagines anything of who do the things that no one can imagine.

That’s it for the UK trailer, but the US trailer has some more information, which a greater emphasis on his relationships with the others and extra INTRIGUE!:

Let’s break this down:

Denniston:

Gentlemen, meet Mr Turing.

Turing:We’re each to work together then? I’m afraid these men would only slow me down.

Menzies:Popular at school were you?

Here we see Turing as the outsider. And he never did quite fit in at school.

Turing:

You have six minutes to complete the task.

Menzies:Is it even possible?

Turing:No, it takes me eight.

Ten points to Gryffindor! Although I don’t believe Joan Clarke was recruited like this (I’m not sure anyone was). The Telegraph newspaper did organise a competition to complete their crossword in under twelve minutes. Successful contestants were then approached for a job at Bletchley.

Turing:

I’m designing a machine that will allow us to break every message, every day, instantly.

Quite a claim, yet by the end of the war Turing’s Bombe machine could help the code breakers work out the daily Enigma setting in under twenty minutes – breaking the vast majority of messages. I think we’ll allow a little hyperbole, because it’s not much.

Now this is our first big clanger. But I think we can blame the people who make trailers for this one. The Bombe machine was not a computer, as it was an electro-mechanical machine capable of one job. There was another code breaking machine at Bletchley Park known as Colossus, but this machine was not designed to break Enigma code, but another cipher machine being used by Hitler and top level of the Nazi Party. That code was broken by a mathematician called Bill Tutte and Colossus built by an engineer called Tommy Flowers. Colossus is considered by some to be the world’s first programmable computer, (although there are about eleven candidates for that title).

Clarke:

You’re going to need all the help you can get. And they are not going to help you if they do not like you.

Advice and life lessons from Joan Clarke. I wonder how that will go….

… not so well according to that right hook from Hugh Alexander. Who knew mathematicians were such good fighters.

Tensions leading to fisticuffs may be full on poppycock. They make good trailers though.

Denniston:

Have you decrypted a single German message?

Turing:You will never understand the importance of what I am creating here!

Denniston:Our patience has expired.

Again, this does not sound like the Denniston who supported the work of the mathematicians he was in charge of. But does sound like the attitude of other Generals of the time.

The gang enjoying a bonfire and a beer. This may not have happened.

Turing:

What are you doing? What’s going on?

John Cairncross:The navy thinks that one of us is a Soviet spy.

This looks like the catalyst for the navy to investigate Turing’s private life and unearth some secrets. This may not have happened.

SPOILER ALERT: Cairncross did it. Although he wasn’t caught until 1951.

Turing:

What if I don’t fancy her in that way?

Cairncross:You can’t tell anyone Alan, it’s illegal.

You’re a fine one to talk about legalities and keeping secrets, Cairncross!

That’s a hell of a tag line though. I hope the publicity guy who thought of that one took the rest of the day off. Look, it made Alan Turing cry.

It’s not easy to tell much from the trailer, but it looks fantastic. Cumberbatch and Knightley seem to be doing a bang up job in their roles, and it’s a story that I think will be a big hit. Sure there are inaccuracies, but I think that is forgivable in a dramatisation of events. I think the film will actually inspire people to find out more about Turing, Enigma, and the work at Bletchley Park. November here we come!

]]>*The Imitation Game* is an Alan Turing biopic, starring Benedict Cumberbatch and Keira Knightley. It’s out in November, but this trailer has just been released.

*The Man Who Knew Infinity* is a Srinivasa Ramanujan biopic, starring Dev Patel and Jeremy Irons and based on Robert Kanigel’s book. It’s been in development hell for eight years, but according to *Variety* filming will start in Cambridge in August.

*Erdős-Bacon* is a documentary about the Small World Phenomenon, and in particular the quest to minimise both your Erdős number – the number of publications linked by co-authors between you and Paul Erdős – and your Bacon number – the number of films linked by cast members between you and Kevin Bacon.

The producers are a keen and youthful bunch, which means they’ve gone to Kickstarter to raise money. They want \$40,000, and they hope this pitch will encourage you to open your wallets:

This documentary is the handshake that links a famed actor and a legendary mathematician, creating history’s lowest Erdős-Bacon number.

]]>

I don’t know how the American parliament works – did a constituent ask Rep McNerney to talk about this, or do politicians regularly just talk about their interests?

]]>The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>Puzzlebomb is a monthly puzzle compendium. Issue 31 of Puzzlebomb, for July 2014, can be found here:

Puzzlebomb – Issue 31 – July 2014

The solutions to Issue 31 will be posted at the same time as Issue 32.

Previous issues of Puzzlebomb, and their solutions, can be found here.

]]>You may be familiar with the method of building cubes from rectangular business cards, which is often used by recreational mathematicians to build versions of the Menger sponge fractal by joining together 20 cubes to make a cube with holes through it in each direction. If you’re really keen, you can then join together 20 of these sponges to make the next iteration of the fractal.

Matt, in collaboration with MoMath’s Laura Taalman, is taking this idea to its limit (well, closer to it) and hoping to build the world’s largest attempted Menger Sponge from cards, this coming October. The colossal construction will take place in 20 locations around the world, with each site building a huge level 3 sponge model using over 60,000 cards and measuring around 1.5m across. Together, the 20 local sponges will add up to a distributed international level 4 sponge, the largest the world has ever seen.

The website for the project, which pre-launches today, is at megamenger.com, and Matt’s looking for expressions of interest in either hosting one of the 20 international build sites, or helping out at a local event. The build will take place in the week of the Gathering For Gardner Celebration of Mind in October, and builds will need to happen from 20th October, with all 20 sponges completed by the end of 26th October. Matt himself hopes to be at the Manchester Science Festival build, at which not one but two sponges will be constructed, one on each of 25th and 26th. If you’re interested in joining in, please get in touch via the website, and follow the @MegaMenger twitter account for updates.

If that’s not enough for Matt to be doing in October, he’s also got a book out! His new popular maths tome, titled *Things to Make and Do in the Fourth Dimension*, is out on 30th October. Here’s the blurb:

Things to Make and Do in the Fourth Dimensionis an alternative maths lesson. In it, Matt Parker argues that maths is difficult because it’s one of the few subjects that requires us to train our brains to think in an entirely new way, and to confront things with no direct analogy in everyday life – snowflakes that only exist in 196884 dimensions, imaginary numbers and objects beyond infinity – and shows us why it’s worth the effort.

The book is available to pre-order on Amazon now, and will also eventually be available in good bookshops. It’s already made the Amazon Bestseller list for popular maths books.

A level 3 Menger sponge built from business cards by Jeannine Moseley

*Things to Make and Do in the Fourth Dimension* on Amazon UK and Amazon US

*Things to Make and Do in the Fourth Dimension* – more information from the publishers

Interviewees include a neuroscientist, an archaeologist, a graphene biologist, a structural engineer, a mathematical modeller, a games developer, a radar engineer, a research mathematician, an astrophysicist and a CERN physicist. Who better to front such a podcast than two thirds of the handsome Aperiodical editors, Peter Rowlett and Katie Steckles (that’s me). We’ve been scouring the UK for people with maths-related jobs (and some less obviously maths-related jobs) and interviewing them.

The resulting recordings will be posted on the FMSP website, RSS feed and on iTunes. The podcast launches at this week’s MEI conference at Keele, and will be posted one a week for the next couple of months, and will then restart in September.

It’s aimed at teachers and students in years 10-13, and takes some piece of maths and looks at someone who uses that maths (or a more advanced version of it) in their work. It covers a variety of topics on and off the A-level syllabus, as well as finding out about some interesting career options for people who are into maths. Each episode lasts roughly 25 minutes, and includes a maths puzzle for you to get your teeth into.

iTunes feed for the Taking Maths Further podcast

RSS feed for the Taking Maths Further podcast

Podcasts page on the FMSP website

Further Maths Support Programme.

$abc$ first: in August of 2012, Shin Mochizuki posted a series of papers containing a proof of the $abc$ conjecture to his website. Since then, people have been trying to work out whether it holds up, and Mochizuki has been modifying his papers in response to requests for clarification. If you need to get up to speed, we’ve got a few posts covering the story so far.

Clearly *something*‘s still happening, because Mochizuki is still updating his papers – his website says the last update was to paper II in May, but as far as I can tell nobody’s said anything in public about which way opinion is leaning.

And then there’s Kazakh mathematician Mukhtarbay Otelbaev’s proposed solution to the Navier-Stokes equations (Warning: it’s in Russian). We never got round to posting about it here (sorry!), but Otelbaev is an eminent mathematician and his paper was taken seriously. There was a lot of hullabaloo in the popular media, including of course New Scientist and Kazakhstan’s international news agency, but it also garnered some quick coverage on BBC Radio 4 (where it got the usual expertise-free handwavey treatment).

Otelbaev set up the problem a bit differently to the way it’s normally stated, so there was some confusion about whether his solution would qualify for the Clay Millennium Mathematics prize. According to this math.stackexchange question the two problems *are* equivalent, so we just needed to find out if it works or not.

To add some more doubt into the mix, Terry Tao published a paper titled Finite time blowup for an averaged three-dimensional Navier-Stokes equation to the arXiv, which states some limits on what a solution to Navier-Stokes can look like, but comments on his blog post about the paper say that it doesn’t rule out Otelbaev’s solution.

But in the end, with no fanfare, and no mention on Radio 4, Otelbaev sent this message to Stephen Montgomery, which he reproduced on another math.stackexchange thread about the solution:

Dear Prof. Montgomery-Smith,

To my shame, on the page 56 the inequality (6.34) is incorrect therefore the proposition 6.3 (p. 54) isn’t proved. I am so sorry.

Thanks for goodwill.

Oh well! Maybe next time.

]]>*Jordan Ellenberg is an algebraic geometer at the University of Wisconsin and a blogger at Slate. His book *How Not To Be Wrong* was new when he sent The Aperiodical a copy to review ages ago.*

*How Not To Be Wrong *sets out its stall in the introductory chapter, *‘**When Am I Going To Use This?’.* Mathematics doesn’t consist of the repetitive exercises that take up so much of school maths, but is “the extension of common sense by other means”, a skill you can bring to bear to enhance your existing reasoning power.

This assertion is backed up by the story of Abraham Wald, a Hungarian mathematician who, having emigrated to the US following the Nazi invasion of Austria, worked at a classified statistics programme during the Second World War. He was asked to study the pattern of bullet holes on returning aircraft to determine how best to place the limited amount of armour that the planes could handle. His insight was that the intuitive answer – to protect the most bullet-ridden parts of the returning planes – was exactly wrong: those are the parts of the planes that can take damage and still have the plane return. The parts that need protection are the ones that down the plane on their first hit, so the skewed sample of the returning planes show no damage to those areas. Whether you think this is sounds like a genuine mathematical insight or a flash of inspiration that a trained social scientist could equally have arrived at, we see plenty of evidence that Wald’s maths training played a huge role in properly utilising this realisation, including a page of his actual mathematics, typewritten in the terrifying pre-LaTeX days. Wald’s story recurs throughout the book as the mathematical concepts underlying it are fleshed out.

The bulk of *How Not To Be Wrong* is split into five sections: *Linearity*, *Inference*, *Expectation*, *Regression*, *Existence*. The first four-and-a-half of these are collections of clearly and entertainingly described discussions of “maths in real life”-type topics (plus a decent amount of pure maths to keep people like me happy). If you’ve followed Ben Goldacre’s crusade to popularise evidence-based medicine or spent 2011 reading angry blog posts decrying the quality of debate surrounding the AV referendum, you may find yourself covering old ground during the lengthy discussions of *p*-values and electoral paradoxes. But there is plenty otherwise to keep you occupied, including a brilliant explanation of why everyone will (not) be obese by 2048; the maths of the Bible Code; why you should miss more trains; and a hearteningly excellent discussion of topics related to the 1+2+3… furore (the recently-controversial series isn’t directly mentioned but a brief diversion into the Grandi series and a well-chosen G. H. Hardy quote should settle the nerves of anyone still on edge about the whole affair – very probably just me). A few of these vignettes have been published on the author’s Slate blog as a sort of taster for the book, which you can read and thus render reviews such as this one essentially pointless.

The second half of *Existence, *along with the final standalone chapter *How To Be Right*, seems to comprise the author’s thesis on the nature of maths. From the notion of the axiomatic basis of a mathematical system (cleverly explained through examples of counterintuitive geometries) and its similarity or otherwise to systems of law and democracy, Ellenberg discusses the foundations of maths, formalism, Russell’s paradox and the concept of mathematical genius. The book concludes, as books should, on its soapbox, with a rousing defence of the necessary uncertainty that goes with a mathematical approach to life.

For me as a mathematician, the book, especially in the opening and closing parts, displays exactly the philosophy and tone (and quality of diagram) I associate with the subject. Hopefully readers without a maths background will by the end of *How Not To Be Wrong* understand that I mean that as a strong compliment.

How Not To Be Wrong* is on sale now, published by Penguin Press. Amazon are selling it for \$16.77 in the US and £16.00 in the UK.*