Today’s TED video is an augmented reality card trick by Marco Tempest. Now, I’m a fan of card tricks but this was a bit too cutesy for me. However, I draw your attention to his computer’s claim (at 3:20) that if you add up all the spots on the cards in a deck then you get 365 which is the number of days in a year. I make the same claim in one of my school talks but I follow it by pointing out that obviously it can’t be right. (Obvious in the sense that you don’t need to get a deck and count but just use some simple maths.) Usually at least one of the pupils gets it. Anyhow, here’s the...
Tails you win: The Science of Chance
posted by Kevin Houston
Last night David Spiegelhalter presented a TV programme on the science of chance. As usual it’s available on the BBC’s iPlayer for seven days. Spiegelhalter is an entertaining speaker, I’ve seen him give talks a number of times, but I felt this programme was a bit pedestrian. There’s lots in it but that just makes it too “bitty”. For example, there is a brief bit about Apple making iPods less random and an overlong bit about a cricketer who was “unlucky” to break an ankle and so on. Nothing was dealt with in depth. Upon reflection I think that the problem (leaving aside that I am not the target audience, but hey, I can have an opinion) is that there is a lack of drama and tension in the programme. It’s just one thing after another. So although the programme did progress through the history of chance there was no sense in these historical pieces of dramatic fights to uncover the truth. In fact, I felt that the only attempt at tension was rather misguided. To create drama Spiegelhalter jumps out of an aeroplane after explaining how at his age the risk of dying is in some sense less than that of a younger person as he is more likely to die in the next few years. As he heads toward the ground the screen freezes, a caption asks “what happened next?” and the programme moves on to another topic, returning much later. Are we supposed to think that perhaps the parachute didn’t open and he tumbled to his death? Well the tabloids would have told us: “Risk Prof dies in ‘unlikely accident'” or the announcer would have dedicated the programme to his memory. So of course there was no tension or drama in this piece. Particularly since the programme titles showed the parachute opening. Anyhow, there were many bits I did like such as the explanation of average age until death and the graphics used. Mercifully, he didn’t do the Monty Hall problem which has rather been done to death. And of course, as I said, Spiegelhalter is an entertaining speaker so at least he wasn’t putting me to...
Robin Ince on science communication...
posted by Kevin Houston
This one is slightly outside my maths remit but I felt that Robin Ince made some serious points (and maybe some not so serious points) about science communication on this Saturday’s Saturday Live on Radio 4. You can hear it here for the next few days provided you can use the BBC’s iPlayer where you are. Ince’s website lists upcoming performances should you wish to see him live in the UK. He is good – I saw him doing non-science when he was promoting his Bad Books Club. (I have a signed copy of the book. I persuaded him to break the spine of the book so that it falls open at the frostbitten hands picture. Read the book to find out...
In Liverpool
posted by Kevin Houston
I’m back in Liverpool. Rob Sturman and I were reprising the British Science Festival talk for the Liverpool Mathematics Society and today I’m giving a research talk at the University. I had hoped to write about all this last night when I was in my hotel, the famous Adelphi Hotel, but they don’t have internet access in the rooms, only in the lounge. I can’t remember when the last time I stayed in a hotel without free wifi access was. Anyhow, I’m currently in an office in the Mathematical Sciences Building. It may even have been the office I had here back in the 90s but I’m not sure maybe it was the one next door. A lot has been happening since I last wrote. Did you see that the University of Leeds held a talk by, Iain Lobbam, the director of GCHQ on Alan Turing? If not then see the Guardian article or the Telegraph...
Criminal Network
posted by Kevin Houston
I’ve been really busy the last few weeks – the usual effect of the academic year starting! I’m running a new course called Maths at Work which is about how maths gets used in the “real world”. One of the projects for this involves the mathematics of networks, such as Twitter and Facebook. As part of my investigations I came across a use of Steiner trees in fraud detection. The University of Alberta press release called Math tree may help root out fraudsters gives the non-mathematical side of the story, the mathematical side can be found in the paper Social network meets Sherlock Holmes: investigating the missing links of fraud. It would be interesting to see if this actually works! Anybody have any...
Wie man mathematisch denkt!...
posted by Kevin Houston
Today is my blog’s anniversary (happy birthday blog!) and, by coincidence, the official release date of the German translation of my book, How to Think Like a Mathematician although I believe it’s been available for at least a month now. It’s called Wie man mathematisch denkt which I think translates more or less as “How one thinks mathematically”. It’s published by Springer no less and you can buy it on Amazon.de. My thanks to the translator, Roland Girgensohn, who put a lot of effort into making sure that the translation was...
Mystery Chord Update
posted by Kevin Houston
The story of the A Hard Day’s Night Chord appeared in numerous papers since my talk with Rob Sturman and Ben Sparks at the British Science Festival. I was also asked to appear on BBC Radio Merseyside which you can hear at http://www.bbc.co.uk/programmes/p00xn5jh for the next 6 days if you are in a territory where iPlayer programmes are available. Start at about...
The Beatles’ Magical Mystery Chord
posted by Kevin Houston
I’m giving a talk at the British Science Festival on Saturday. Details are here. To accompany it I’ve made a video on how mathematics can be used to analyze the opening chord of A Hard Day’s Night by the Beatles.
Maths projects
posted by Kevin Houston
Last week I updated my personal and work web sites for the first time in far too long and I changed the look of this blog. It doesn’t work perfectly yet as some of the colours and spacing are wrong. And I should get rid of that banner at the top – it’s looking a bit old. On a different topic, I’ve been criticized over on the TES forum for my mechanic analogy. I thought it was good analogy, but PaulDG disagrees: As with all analogies, and having only read those few paragraphs of his work, I’m afraid it looks to me as if he’s the sort of “expert” who’s got us into the problems we’re currently in. Ouch. He then gives a straw man a thorough thrashing and finishes with Houston appears from his analogy to be in favour of understanding without skills. This seems rather illogical: Houston wants students to do more of A and less of B therefore he doesn’t want students to do any B. To be honest I can’t see how anyone could have such a reading of what I said. I was tempted to jump into action with a shout of “Someone is wrong on the internet, I must intervene” but after some reflection I decided to just read the rest of the thread. So, the thread itself is about a very important topic — maths projects in schools. As someone who is trying to prepare a projects module for second year students I am aware how difficult it is to prepare good projects. The problem at all levels, school or university, is that it is very hard to set “medium strength” projects – they are either too easy or too hard. I think the key difficulty is...
Painting by numbers – restoring frescoes...
posted by Kevin Houston
You may have seen in the news this week that an elderly amateur attempted the restoration of a religious fresco. The result is pictured below. I took the picture from the BBC article that you can read here. By coincidence this week I saw an article by Carola-Bibiane Schönlieb on the mathematical technique of inpainting. This allows restoration of damaged pictures by using some mathematical process to fill in the damaged part. A particular common method is to use diffusion equations – the idea is that we use something like the heat equation. Imagine the ink on the border of the damaged region as being like heat and the heat travels into the region through conduction. Compare the two images below take from a preprint by Schönlieb and others. The top one is a vandalized picture and the bottom is the version restored through a diffusion equation method. Most people probably wouldn’t realize that the picture had been repaired unless they’d been told. Schönlieb and others have worked on restoring the following Austrian fresco Here’s a picture of the proposed restoration (unfortunately only in black and white): The pictures come from a paper which contains the details. The article I saw this week is more accessible and can be read in the Matlab Mathworks...
The algorithm that runs the world...
posted by Kevin Houston
A colleague in the School of Mathematics, Richard Elwes, has the front cover story of New Scientist. You can read the full article on the Simplex Algorithm...
Hannah Fry: Is life really that complex?...
posted by Kevin Houston
Mathematics talks at TED are rather rare so I was keen to link a recent talk from TEDxUCl by Hannah Fry which was about the applications of mathematics to complex problems such as human behaviour. After watching it I hummed and hawed. On the one hand this is a very well presented and explained talk (and this is even more impressive as the speaker is a fairly newly-minted PhD). On the other hand, it doesn’t feature much maths and crucially, for me at least, I wasn’t sure that anything has been proved. It wasn’t clear to me that any models have been developed. The wording at the end is fairly vague. Saying “Once we have done this…” leaves open the possibility that it has not been done yet. She also says “we can almost begin to talk about…” which is again too vague. Anyhow, in the end I decided to link to it. It’s only 10 minutes long and does give you some idea where things are headed. The end of the talk is mostly about predicting crime, something I looked into a few years ago when a local policeman contacted the School of Maths for help after watching the TV programme Numbers about a crime fighting mathematician. Unfortunately I was unable to help him with his enquiries as at the time the mathematical models for crime prevention and detection were very poor. The current video sort of claims they have been improved. I...
A Mathematician Comes of Age by Steven Krantz...
posted by Kevin Houston
I’m a big fan of Steven Krantz. His book on teaching mathematics is the one I recommend most to beginning maths lecturers. The second edition is a must have since it contains short replies to his book from other lecturers, some of them highly critical. Currently, I’m reading his recent book A Mathematician Comes of Age. This is concerned with how a mathematician becomes mathematically mature. From the back cover: “It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs.” I must admit I’ve been diving in and out of the book at random and although I don’t agree with everything he says (or agree with the inclusion of certain topics – why are North Americans so concerned about “Math anxiety”?) there are thought-provoking passages every page or so. The parody of the Evolution of Teaching Math on page 49 is very funny and includes 1980s: A framer sells a bag of potatoes for $10. His production costs are $8 and his profit is $2. Underline the word “potatoes” and discuss with your classmates. Leaving aside the humour, I particularly like the section on Reading and Thinking (p95): It has been observed [No reference given – KH] that the key things that a good teacher does are engage the students in the learning process pace the students teach the students to read Now, reading mathematics is something I’ve thought about and try to get my students to do, see Chapter 2 of How to Think Like a Mathematician (follow the link for free samples of chapters 3 and 4). Like in HTTLAM Krantz mentions the importance of reading with...
Maths compulsory until age 18
posted by Kevin Houston
The House of Lords just published a report recommending that students in the UK study mathematics until the age of 18. This recommendation cropped up last year in the Vorderman review. The Lords report can be found online in html and in pdf format. It’s a fairly long report but my response is as simple as my response to the Vorderman review: Where are the teachers going to come from? We don’t have enough teachers at the moment to provide the best-quality maths education. Giving the current ones more to do would lead to catastrophe. The Lords’ report even states The Department of Education, recognising the role of teaching in increasing the progression of students to A level STEM subjects,… has introduced a number of initiatives to increase the number of specialist teachers (such as, golden handshakes and bursaries), but, by their own admission, “the targets set by the previous Government for numbers of specialists teaching physics and maths will not be met”. Is the best that the DoE can come up with is golden handshakes and bursaries? It is unsurprising that the targets won’t be met. There will be no single solution to the problem of mathematics education in the UK, it will require many areas to be tackled but the solution must surely include higher pay for maths and science teachers. The simple reality is that my students can finish their degrees and get a job that pays them an average starting salary of (according to HESA) 23,160 pounds (according to AGR figures 26,500 pounds) with rapid increases, or spend a year on a bursary of less than 20,000, and join a profession where after a number of years they reach top of scale at 31,552 pounds? And yes I know I should take into account holidays, etc, but even with shorter holidays the working conditions are better in many professions. Looking at the figures, which do you think is the better...
Best of xkcd: Maths I
posted by Kevin Houston
I’m currently at a conference so have been working hard on research-y type things rather than thinking up exciting blogs posts. So here are some of my favourite maths strips from...
Monge and Optimal Transport...
posted by Kevin Houston
Mathematicians are ignorant of their history. They know the names of the greats but generally can repeat only one or two (erroneous) stories about them. For example, if asked for a mathematical story from the French Revolution, then many would plump for a story about Galois, shot at dawn. However, there were many other revolutionary mathematicians. One such is Monge. His name is familiar to differential geometers through Monge form and to analysts of PDEs through the Monge-Ampere equation. Information about him is scant in English. All the important books are in French and so my attempts to study his life in more depth have been thwarted by my lack of fluency. I think I first became interested in him when I was a student. I read a book (the name escapes me) which stated that he had studied the concept of the optimal transport of soil when constructing fortifications. The fact that caught my imagination was that the answer was constrained by the observation that the paths of two particles should not cross. At the time I came up with a counter-example but that was because I didn’t really understand the parameters of the problem. I was greatly interested then when I heard that one of this year’s Hardy Lectures would be about Monge and the optimal transport problem. I was greatly disappointed when I discovered that it clashed with previous commitments. When I was at the conference in Liverpool to celebrate the birthdays of Bill Bruce and Terry Wall Andrew Ranicki told me that the lecture had been recorded. And I’m glad it was, it’s a great talk. It’s given by Etienne Ghys. He takes in the cutting of stones, including how Monge designed a never used plan for the ceiling of...
Cool proof of the Fundamental Theorem of Algebra...
posted by Kevin Houston
Despite being on holiday I can’t resist looking for cool proofs. This one is not so much cool as interesting in a Why-didn’t-I-think-of-that way. The fundamental theorem of algebra — that any polynomial has a complex root — is well known to be a theorem of analysis rather than algebra and many proofs are known. The proof I use in my course relies on Liouville’s Theorem and the Maximum Modulus Theorem. However, there is a more direct route using only Cauchy’s Integral Formula and the Estimation Lemma. I found the basic idea in Complex Proofs of Real Theorems by Peter Lax and Lawrence Zalcman. Here’s my modified version: Every polynomial , , , has a root in . The proof is as follows. Suppose not and derive a contradiction. Since for all the function defined by is differentiable on all of . Now, for , So there exists an such that implies that . Thus for such . As is differentiable on all of we have for all , by Cauchy’s Integral Formula, (and where denotes a circle of radius centred at the origin), The right hand side can be made as small as we like by taking large enough. Thus . This is impossible so we have a contradiction and therefore has a...
New Maths Journals
posted by Kevin Houston
I’m on holiday at the moment so don’t have much time to write. If you are interested in the recent fuss about academics fighting for reasonably-priced journals, then pop over to Tim Gower’s blog to see this announcement on new journals. There’s also a little bit on Terry Tao’s blog. It looks like this could be...
Why I’m not celebrating Tau Day...
posted by Kevin Houston
Tau day, celebrated on June 28th, is almost upon us again. Last year I had great fun making a video about tau and appeared in national newspapers and on radio and TV. Though I had helped kick off a story that went viral igniting millions of pixels across the globe, even I felt that it received more coverage than it merited. Don’t get me wrong, it was great fun. Anyone who watched my video could tell from the sound effects, the newspaper headline about Pi is 5.14 and the code hidden in the digits of pi that for me this was not obsessional rage coming out but was instead a reasonably light-hearted look at an irrational bit of maths. Unfortunately, I received a lot of flak and a fair amount of abuse such as being called “peace of sh*t”[sic], “burro” (it’s a Portuguese insult, shame on you BBC Brasil!) and even, rather strangely, bald-headed. (You can hear the inside story in a Math/Maths Podcast.) However, it is not insults that cause me to pass on two rounds of pie this year. Insults are not a problem, I’m a grown up and know that sticking my head above the parapet will give at least someone the opportunity to take a shot. Instead I have two main reasons. 1. The issue is controversial and although controversy and debate are vital for any subject it should be about the significant issues. Tau is important but not major league important. I don’t want disagreements between mathematicians to obscure our central message that maths is vital to society (see here for example). One of our responsibilities is the health of our subject and a basic tenet, like a doctor’s, should be “Do no harm”. In this case I think...
The origin of x in maths...
posted by Kevin Houston
I’m still wrestling with the fallout from marking exams. Despite this, I found time to watch a short TED video posted recently that features Terry Moore explaining why x is used as an unknown in mathematics. Watch the video – only 4 minutes – or jump to the spoilers below if you want to know more. The main idea is that the we use x because the Spanish used (chi) as the first sound of the Arabic word for “something” because they couldn’t say the correct “sh” sound. I recollect a similar argument made somewhere else with slightly different details, though, sadly, I cannot remember them precisely, nor their location. I was unable to track down references at the time to verify this argument and so dismissed it as a Just So Story. Since it has resurfaced it would be interesting to see evidence. Does anyone know of any? My reason for asking is that I’ve spent the last few years learning about Greek mathematics and I am interested in how it has been transmitted to us via the Arabic scholars and scientists. So far I’ve only read the popular accounts, Science and Islam: A History by Ehsan Masood and Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili. The latter is good but spends the first few chapters explaining the history of Islam and various empires. Furthermore, one of the first bits, maybe the first bit, of science to be explained in depth is Eratosthenes’ measurement of the Earth, i.e., a high point of Hellenistic science. Obviously providing a context is important in a book but I still feel as though I don’t know much about the science from the Arabic world between the end of the Greek era and the beginning...
Cool proofs again
posted by Kevin Houston
In between marking exams, marking essays, external examining, getting my two PhD students to submit their theses, and, well you get the idea, I’ve been trying to come up with a cool proof of a theorem in complex analysis: Let be a power series with radius of convergence . Then, . I.e., the derivative of is what you expect it to be, the termwise differentiation of the series. I’ve not been able to find a good proof of this. My plan of attack has been to show first via the root test that the formal derivative has radius of convergence . The main sticking point is then to show that this formal derivative really is equal to . The clearest proof I found was in James Pierpoint‘s book Functions of a Complex Variable which you can find online here. Like many old books (this is from 1914) I’ve found that, if you allow for slightly odd notation and nomenclature, it contains excellent material that is currently passed over. (Does anyone still teach Raabe’s test?) Anyhow, the proof is on pages 172-173 and relies on pages 84-85. For me the proof is very clear because of equation 3 on page 84: the expansion of via rows can be turned into a power series in by summing the columns. My problem is that when I try to turn everything into a rigorous proof this becomes obscure. Also, we have to prove that all the formal derivatives of have radius of convergence . This in itself is not difficult but it means we have to set up the notion of all formal derivatives rather than just the first one. For me this may be too much extraneous clutter for students. The hunt...
William Noel at TED on the Archimedes Codex...
posted by Kevin Houston
Regular readers will know that I’m interested in the history of mathematics and am a fan of Archimedes. Well, here’s another video on the Archimedes Codex, this time by William Noel at TED rather than one by his coauthor, Reviel...
Euclid and Eratosthenes — Greek or African?...
posted by Kevin Houston
Last month the mathematics author John Derbyshire wrote an online article not about mathematics but on his personal views regarding race. Views which eventually got him sacked as a columnist for the publisher. The Guardian newspaper responded through an article by Jonathan Farley. My post today is not about race but rather about some points made in the comments to Farley’s article. In his article Farley said … Euclid, Eratosthenes and other African mathematicians outshone Europe’s brightest stars for millennia. In the comments section it was asked They are known as Greek mathematicians. Why are they quoted in an article about Black mathematicians? Now, one should avoid getting involved in fights in comments section and fortunately someone had replied in a comment later highlighted by Guardian staff Well, Euclid is ‘Euclid of Alexandria’ which is in Egypt of course and Eratosthenes was born in Cyrene (modern Libya). So I don’t think its erroneous to say they were black mathematicians. Various arguments were made later in the comments about whether North African counted as black. I’m not going to get into this argument either. Instead my post is about the precise origins of Euclid and Eratosthenes. In my geometry and history of mathematics courses I tell my students that when we talk of Greek mathematicians, we should not think of them as swanning around in Athens dressed in togas. Instead they came from all over the Mediterranean, from what we now call Italy, Egypt, Turkey, Libya and so on. Some even came from Greece. (And they didn’t wear togas. That was the Romans. The Greeks wore a chiton, a type of tunic.) A good example of this is the greatest Greek scientist, Archimedes, who was from Syracuse in Sicily. But what about Euclid and Eratosthenes?...
Antikythera Mechanism...
posted by Kevin Houston
I only discovered this yesterday. BBC Four has shown a film on the Antikythera mechanism. It can be found here I haven’t had a chance to view the programme yet so I don’t know whether it is any good. Note that even if you are in a region where you can view iPlayer programmes it is only available for one more day (unless you download to the iPlayer desktop). UPDATE: 22/5/12. I managed to watch the programme last night. It was quite good despite an early lapse in voiceover grammar and some dodgy computer effects (most were ok – just some were dodgy). And who was the mystery woman who walked around the Greek games stadium with the academic who was explaining it to us? Anyhow, leaving aside the minor problems that beset all TV productions the programme did cover the recent revelations of the mechanism by the Antikythera Mechanism Research Project but did not ignore the contribution of Michael Wright of the British Museum. I do have to argue with the speculation that Archimedes had been in some way involved. There is no evidence that his knowledge was used to construct the mechanism. (The programme also repeated the myth that Archimedes had been killed whilst drawing in the sand. Some of Plutarch’s stories say he was working on a problem but none say it was in the sand.) The bit about the front of the device representing the planets also seemed a bit...
Mathematics of History...
posted by Kevin Houston
I teach a course on the History of Mathematics but today’s post concerns a TED talk on the Mathematics of History. This very short talk by Jean-Baptiste Michel serves as a follow up to the one given with Erez Lieberman Aiden on What we learned from 5 million books. The idea is that we can use mathematics to understand history. Unfortunately, the talk is too short to develop a coherent argument and the examples given are not exactly new so I’m not yet convinced that they have something. It should be interesting to see whether this develops...
Discount for Variational Problems in Differential Geometry Book...
posted by Kevin Houston
One for researchers. Last year I, with my colleagues Roger Bielawski and Martin Speight, edited a book, Variational Problems in Differential Geometry. There is currently a US promotional offer for this book: Yes, I want 20% off my copy of Variational Problems in Differential Geometry Feel free to send the link on to people you know who might be...
[Insert technology here] will revolutionize education...
posted by Kevin Houston
In a previous post on the Khan Academy I said in an aside I think that video’s threat to teaching jobs is greatly exaggerated. When the printing press was invented people probably said “No more need for teachers, you can learn from a book”. Every new technology is predicted to revolutionize teaching and to cause the disappearance of the bulk of teaching jobs. People said it about radio, they said it about film, they said it about TV. They now say it about YouTube videos and laptops. I was asked for evidence for the “They said it about film” part. Given that when I was school we watched educational films projected on the wall at least someone was eager to use the medium in education so someone must have said it. However, the quote comes from an interesting source: Thomas Edison. I believe that the motion picture is destined to revolutionize our educational system and that in a few years it will supplant largely, if not entirely, the use of textbooks. I should say that on average we get about two percent efficiency out of schoolbooks as they are written today. The education of the future, as I see it, will be conducted through the medium of the motion picture … where it should be possible to obtain one hundred percent efficiency. Thomas Edison (1922) quoted in Larry Cuban, Teachers and Machines: The Classroom Use of Technology Since 1920. Whilst researching this quote I came across Quote Investigator which discusses the history of the quote. This led to an interesting article using the quote to comment on the current Let’s-give-all-the-kids-laptops/iPads movement. Of course, I could have easily found a dozen such articles. And when was television the answer to all educational ills? Well, recently...
Pi is 4 (again)
posted by Kevin Houston
I’ve been busy this week. On Monday I gave my new Auto-Tune talk to the School of Maths (I spent the previous Saturday reading the patent for Auto-Tune. Very interesting.) And yesterday I was in London to give a talk on Teaching Analysis. The meeting was also interesting but poorly attended as just about every project is running conferences and workshops. During my talk I showed my Pi is 4 video as an example of something I am using in my lectures. You can see it here. Anyhow, Vi Hart has a video on the subject which is worth...
Martin Gardner – free pdf...
posted by Kevin Houston
I only realized recently that an edition of College Mathematics Journal dedicated to Martin Gardener is freely available for all rather than just subscribers. You can download it here: College Mathematics – Martin Gardner Special Issue. The issue is, as one might expect, a mixed bag. Of interest is a reprint of Gardener’s original article on Hexaflexagons (these were a childhood favourite for me); in the provocatively titled Martin Gardner’s Mistake Tanya Khovanova discusses the errors in solutions to Tuesday’s child problem (a problem which surfaced at Gathering for Gardner before ricocheting around the internet); Arthur Benjamin has a very simple (I mean that in a good way) article on Squaring, Cubing, and Cube Rooting. There’s also an article by Ian Stewart, who (I suppose it goes without saying) has a new book...
Khan Academy videos: Instructive or destructive?...
posted by Kevin Houston
Over the last few weeks I’ve been thinking about producing more videos. I’ve certainly fallen behind my planned schedule of producing them – too many other tasks get in the way! Anyhow, I have to produce some so that my school can complete a project for HE-STEM. As part of this I’ve had to consider what makes a good video and for me one of the most interesting debates about videos in education has been triggered by the huge success of Salman Khan’s video series. You can see him explain the history and the philosophy behind it in the following TED video: Looks good doesn’t it? However, his videos have been strongly criticized. This is not surprising, educators were always going to object to an ex-hedge fund manager – backed by Bill Gates and with no educational training – coming in and saying “This is how you do it”. Nonetheless, many of their criticisms have foundation. I’m particularly against the “gamification” of education. Whilst games can be a useful tool in education when you wrap all learning in a game, then students lose sight of the importance of education; they see it just as collecting points for their scorecard. Audrey Watters gives a good explanation of the arguments against Khan and various links in her post The Wrath Against Khan which arose as in response to an article in Wired on the Khan Academy. (Aside: I think that video’s threat to teaching jobs is greatly exaggerated. When the printing press was invented people probably said “No more need for teachers, you can learn from a book”. Every new technology is predicted to revolutionize teaching and to cause the disappearance of the bulk of teaching jobs. People said it about radio, they said it about...