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This page represents only my own views, and not those of any university or other body.
Posted Sunday 20th December 2009 at 8.57pm 12 things I'm leaving Bath on Tuesday, returning to Nottingham for Christmas before I move to Paris on 4th January. I've had a great time here. Here are twelve things (vaguely in chronological order) that came to mind as some of my favourite moments. 1. Moving into Clarence in 2007, and going through the ridiculous inventory. What should have been one of the most boring nights of my life was actually one of the funniest... the highlights being the worn out mop-pole and the 5 broken vacuum cleaners. I think you had to be there. 2. My first "proper" conference - in Warwick, Easter 2008. Hard work but some inspiring stuff, and I made some friends too. 3. "Oi, you. Yeah, you. I want to show you something," says the huge bald bloke walking down the street towards me. I stop, nervously, and he starts rolling up up his sleeve... to reveal a Forest tattoo. He starts grinning and hugs me. (Forest had been promoted from League 1 earlier that afternoon.) 4. The maths postgrad Christmas party in 2008 - a HUGE game of Indian poker. We were planning on starting a little game with four or five of us, but people just kept joining in. This was the start of our increasingly spectacular postgrad socials. 5. Sitting downstairs in the silent and empty Hobgoblin with Geoff, Jim and Gaz, each at our own table, singing Abba and Elton John songs. Again, you probably had to be there! 6. Beating Winsley in the second game of the 2009 cricket season. It was a scorchingly hot day, a flat pitch, and we were playing against a team that included Terry Duffin, who was Zimbabwe one-day captain not too long ago and has a Test 50 made against an Indian attack comprising Zaheer, Irfan Pathan, Kumble and Harbajhan. It was a really good game, and we won by 10 runs - I also captained the side, and made my first ever 50, although the real heroes were Ian G with 91 and Gregory for bowling Duffin. Apparently Duffin has now returned to Zimbabwe to try to regain his place in their side now the situation there - at least the cricketing sitation - seems, hopefully, to be easing slightly. 7. The maths postgrad pub crawl to Bathampton. A fantastic day out made all the better by the fantastic weather.  8. Hitting my first ever 6, in a game against Bradford 39ers. We were batting first in a 20-over game and I had opened the batting. It was getting to the end of our innings and I had started to slog. I planted my front foot down the pitch and was going to slog the ball over midwicket, but it was a bit shorter and straighter than I expected, so I adjusted by straightening my bat and attempting to chip the ball back over the bowler's head. But I timed the shot to perfection, and stopped running when I was half-way down the pitch to watch as the ball just kept going and flew into the tree next to the pavilion. The ground at Bradford isn't the biggest but it made me happy! 9. Drinking champagne out of mugs in a student kitchen with David Aldous (part of one of the "Probability at Warwick" summer schools). 10. The maths football trip to Germany - especially the moment when, with nackensteak mit brotchen in my hand, a random German girl shouted "hey English - dead sharks!" and I had to hit the deck and wave my dorsal fin... 11. Geoff's birthday 2009, Team Orange running through the streets, me high fiving a random member of the public - then realizing I knew her. 12. Last parade drinks - sitting in a field in the dark with Geoff, Ray, Fynn, Tom, James and Euan looking down on a beautiful lit-up Bath. Posted Sunday 13th December 2009 at 9.34pm A few quick mentions Today's BBC Sports Personality award was a farce. I thought we were in for a good one - like last year - when Jenson came second (he shouldn't have been anywhere near, formula one shouldn't even be a sport - it's decided more by the car than the driver - but I thought he would win it). But then Giggsy won!?!? The guy's been a great player for 20 years but nowadays he can barely play 90 minutes of football a week and isn't sure of a place in Man U's best team, whereas people like Mark Cavendish and Andrew Strauss and Jessica Ennis have slogged their guts out for weeks on end to get to the pinnacles of their respective sports. Hmmm. Rant over. The new national rail website is a huge improvement over the old one. You can actually change your search parameters on the fly! If you want to uninstall linux from your dual-boot computer and go back to just Windows, and want to go back to using the Windows bootloader (so get rid of GRUB), use EasyBCD. A fantastic little piece of software that does exactly what it says on the tin - nothing more, nothing less - with absolutely no fuss at all. Worked perfectly for me to go back to single-boot Vista, and looks like it probably works with other versions of Windows too. Instructions taken word for word from someone called Matt Dwamon on linuxquestions.org: 1. download EasyBCD 2. install it 3. go to 'Manage Bootloader' tab 4. select 'reinstall the vista bootloader' (this may be different) 5. click on 'Write MBR' 6. go to 'Add/Remove entries' tab 7. select Linux tab (should be something like) type: grub name: neosmart grub drive: (select drive that says something like 'Linux native') 8. Add entry 9. repeat 7 & 8 but the drive should be 'linux swap' I quite liked linux (I was using Ubuntu) but it kept crashing for no obvious reason. Actually the latest version seemed to be a lot better, it seemed to realize that there was something wrong and saved me from the full crashes, but still all my programs would suddenly close for no apparent reason. Probably a hardware clash from my rubbish Samsung laptop. Posted Monday 23rd November 2009 at 2.16pm Maths I've been writing up my thesis - that's why I haven't written on here for a while. I went from 2 pages (which I wrote months ago) to 100 pages in 8 days - and I was pretty happy that I'd nigh-on finished - and then on Saturday evening I spotted a mistake. It was in the very last bit - the last theorem - and I'd lazily said "well, this proof kind of goes like that last one, but you have to be a bit cleverer, basically do this." And basically doing that didn't work. So I spent Saturday night, and all of yesterday, and this morning (I even did some proper maths on the bus on the way up, which must have looked a bit scary to the other people on the bus) trying to fix the problem. I've managed it, I think. But it's unbelievable how close it is to not working. Sometimes, working on a problem for a long time, you get to see enough of what's really going on that you understand something that you can't possibly explain in words. This is one of those times for me. I have this theorem that says "something happens for b less than a third, and something else happens when b is bigger than a third", which is fine - but then I had the problem theorem, about when b equals a third. And trying to figure out how to prove this theorem was like wandering around for ages knowing there's a cliff over there somewhere and I just had to find it and point out where it was. And then finding it was like Maths had appeared at last and gone, in a big booming voice, "YES, THERE IS A CLIFF. LET ME SHOW IT TO YOU. LOOK" and walked with me to an enormous precipice with a great big burning pit of lava at the bottom, and threatened to push me off, before pulling me back at the last second, saying "HA HA HA, HAD YOU GOING FOR A WHILE THERE DIDN'T I?!" and walking off laughing, just to show me who's boss. In other maths-related matters, this page about the number 1729 is quite scary. I also had quite a nice moment on Saturday (before I found the mistake). I was trying to clear up another lazy point in my thesis where I'd said "it can be shown that..." - in this case, let X be a Poisson random variable with mean 2cT, where c is some positive constant. I claimed that "P( X < cT ) is exponentially small in T as T gets big" - that is, there exists k>0 such that P(X < cT) < exp(-kT) for large T. Presumably this seemed fairly obvious to me when I wrote it originally, and indeed after playing about for a bit one can convince oneself that it's true. But proving it was looking tricky - it was looking like I was going to have to do some complicated approximation of sums with factorials and stuff. Then, after a few minutes of thinking about it, I spotted a nice way. Let 1(A) be the indicator function of the event A. Then (just as in the standard proof of Markov's inequality) 1{ X < cT } = 1{ exp(cT) > exp(X) } < exp(cT)/exp(X) where the last inequality holds because if exp(cT)>exp(X) then the left hand side is 1 and the right hand side is bigger than 1, and if exp(cT)<=exp(X) then the LHS is 0 and the RHS is bigger than 0. Taking expectations, P(X < cT) < exp(cT)*E[exp(-X)]. Look up the moment generating function of a Poisson random variable, fill it in and you get: P(X < cT) < exp(cT)*exp(2cT*(exp(-1)-1)) and 2*(exp(-1)-1) is less than -1 (in fact it's about -1.26) so we're done. Of course there might be a nicer way than this that I didn't spot - or this way might be a standard trick that I just don't remember seeing - but either way, I liked this little "backwards Markov" inequality. Posted Saturday 7th November 2009 at 11.56am Judy Two more cricket articles - one horrible, one really good. This one by Mike Atherton shows us one of the many things wrong with the game. Atherton is arguing the status quo - that we must stick to the current fixture list in international cricket, because it's agreed until 2011 and "about to be ratified until 2016". But why is it about to be ratified until 2016? It stinks! Everyone knows it's rubbish! The suggested World Test Championship, come up with by Martin Crowe ("among the brightest, most innovative minds in the game"), is to give teams 4 points for a win, 1 for a draw, 0 for a loss, and take the average number of points at the end of two years to see who wins. How did he ever come up with that? Giving people points for a win, fewer points for a draw, nothing for a loss! And - here's the clever bit, that would have flummoxed all but Crowe - the teams play different numbers of games, so we'll take an average! Genius! This article by Peter Roebuck (again) is far better. Slightly pompous and one-eyed, as Roebuck often is, but it's full of good points and I especially like the line "In some places, admittedly, cricket depends on its migrant population (England and Canada spring to mind). Elsewhere the locals are taking to it." I also love this picture. Whether or not it's a fake I don't know, but I can imagine it's not, as I remember doing these piss-easy reading tests as a child and I wish I had had the temerity to object like this - I love the idea that there's a 7-year-old kid somewhere running around not giving a damn about what reading age the government thinks it's important to have, and not afraid to tell her teacher that in the funniest way possible!  Posted Thursday 5th November 2009 at 12.26pm The Stark truth John Stark (another Bath PhD maths student) posted this nicely written note on facebook the other day. I have recommended that my first year tutees read it. Every year I try to explain to first years that mathematicians aren't machines, and that they should write in sentences rather than using endless strings of symbols that don't make any sense to any real person, and it always takes them about 3 months to realize that I'm not joking. In the meantime I have to try to mark their endless strings of symbols, which invloves hours of writing the same comments - "Don't start with what you want to prove", "This doesn't make sense", "??", "What is n?", etc. I figure John explains it better than me, and also if they see two people telling them the same thing they might be more likely to believe us! Any budding young mathematicians (i.e. A-level or early undergrads) could do worse than to read it. Another well-written piece about an obvious (to me at least) truth is this article by Peter Roebuck. Roebuck is one of the most highly regarded cricket journalists around - I'm not his biggest fan, occasionally he's an idiot and writes complete crap or tries to show off, but this time he's struck home nicely. This xkcd comic is fantastic. Posted Thursday 29th October 2009 at 5.46pm Pianos and spanning trees There's a graduate lecture course running at Bath (and, thanks to the taught course centre, simultaneously at Oxford, Warwick and Bristol) this term called "The Uniform Spanning Tree and related models", run by Antal Jarai. I always find it very hard to concentrate for these things, because they go on for two hours in one warm, quiet room... and the high-tech TCC lectures are worse than the old-school ones because generally no-one dares speak except for the lecturer. This term I have too much to do already, so I haven't had time to catch up with the lecture notes out of the lectures - basically I've just been going along, sitting there and trying to absorb as much as possible. It turns out (I decided today) that this isn't a problem for this course. Lots of the proofs seem, when you're sitting there trying to stay awake in an environment tailor-made for sleep, quite boring. But if you think about them, you realise that if you were given this setup and told to prove one of the main theorems, you would have no idea where to start. The methods for the proofs are almost off-the-wall. It's just that once you see how the proof's going, there's a fair bit of messing about (and the TCC room doesn't help there with its high-tech board that's obviously better than a blackboard for telling someone miles away what's going on, but also far better than a blackboard at slowing everything down by being generally lame and getting things wrong) and concentrating on the details is a bit of a killer. So I've started trying to get the idea of the proof at the start, and then wondering for a while how one might have come up with that method, before more or less switching off till the proof gets to the end. It means I'm able to last to the end of the lectures without completely blanking out, and get a decent overview of what's clearly a really nice subject with a huge variety of ideas. Something else came back to me during today's lecture. I suddenly remembered being sat in Irena Borzym's office in Catz College, in a very easy Topics in Analysis supervision, and complaining about how my director of studies had made me do all the courses in the second year when people from other colleges (like Catz) only had to do slightly over half of them (which was a much better way of getting a good mark in the second year exams). Anyway, she just laughed and said that I'd be grateful one day. And today, as Antal went through a proof that used a load of linear algebra, analysis and probability, with a sprinkling of geometry and numerical analysis, I thought: well, I guess she was right. In completely unrelated news (except that it's a bit random), the BBC website keeps telling me about semi-humorous (I think) but also semi-useful or informative articles. There was one yesterday about the four colour theorem, and another today about "viewing and purchasing an upright piano". All good stuff, I remember having a reeeeaaaaally crap piano for years when I was learning. Unfortunately the internet didn't really exist back then so I didn't know this stuff. Any seven-year-olds reading my blog and wanting to know how to choose a piano - well, you could do worse than reading this article! Finally, just when I though PhD comics was past its best, he's come up with another good one:  Posted Thursday 29th October 2009 at 11.39am Mad car parking skillz This problem is taken almost word-for-word from David Williams' book "Weighing the Odds". Simon, my supervisor, was going to put it on the third problem sheet for the second year probability course but decided against it - it might appear on a future sheet but there's no reason why the students shouldn't be able to see it here beforehand so here goes: There are sites 1,2,...,n spaced a car's length apart. A car occupies the space between two numbers, so the interval [i,i+1] for some i=1,2,...,n-1. Once a car is parked in [i,i+1] no other cars can then park in [i-1,i] or [i+1,i+2]. The car park starts empty. Then the first driver comes along and chooses one of the n-1 available spaces uniformly at random (so with probability 1/(n-1) each). Then another driver comes along, and chooses one of the remaining available spaces uniformly at random. Then the third driver comes along, and so on until sites no good for parking are left. Show that if n=5, P(cars parked in [1,2] and [3,4]) = P(cars parked in [2,3] and [4,5]) = 3/8 and P(cars parked in [1,2] and [4,5]) = 1/4. Now, for general n, let p(n) = P(right-most site ends up isolated), that is p(n) is the probability that at the end no-one has parked (indeed no-one can park) in [n-1,n]. Show that (n-1)p(n) = p(1) + p(2) + ... + p(n-2) and deduce that p(n) = 1 - 1 + 1/2! - 1/3! + 1/4! - 1/5! + ... which converges to exp(-1). Now let p(i,n) = P(site i ends up isolated), that is the probability that by the end there are no cars in [i-1,i] or [i,i+1]. "Argue convincingly" that p(i,n) = p(i)p(n-i+1) (which is close to exp(-2) for almost all i when n is large). This obviously depends on your interpretation of "argue convincingly". The general idea is quite easy to see after thinking for a while; proving it rigorously is slightly harder but doesn't use anything a first year student (in fact most A-level students) wouldn't know. It's fun though. Also fun is this parking game. I remember playing it against my housemates in my third year of undergrad. Good times. I scored 384 just now. Posted Wednesday 21st October 2009 at 5.12pm Bikes There seem to be some bike thieves round where I live. A few weeks ago I was walking home and found my bike about 20 yards down the road from my house; slightly confused, I picked it up and put it back where I had left it. Then yesterday, while I was still at work, one of my neighbours knocked on the door and told my housemates that they had seen some people who they thought were trying to steal my bike, and that my bike was now lying on the pavement outside our house. My housemates thankfully brought the bike inside. I had been leaving the bike (just locked to itself) in the front garden, so from now on I'll put it round the back instead where it's harder to get to. But it does beg the question: how incompetent can bike thieves be? I mean, bike theft is pretty easy to do if you've got some kind of lock-cutting device. You walk up to a bike when there's no-one around, cut the lock, and cycle off. Even if anyone tries to stop you, you then have the advantage that you now have a bike and they don't. What you don't do is pick up the bike, move it a few yards to alert everyone's attention, then go off home and get your lock cutters, giving the owner time to rescue his bike. These photos of comedy cycle lanes also made me laugh. Posted Sunday 18th October 2009 at 9.09pm Ideas I have this joke that I often use in my talks, about how my supervisor says spine martingales make everything look easy and make people think "what's he been pissing around at for three years?" (Maybe I have to think of a new joke now I've used that one up here.) Well, I'm currently rewriting our "unscaled growth along paths" paper - it's almost done but I've been trying to come up with some interesting examples to put the results into context. I think it's almost done now, I've just been trying to finalize one last thing which involves going back through the proofs in a certain critical case. And I got to part of the proof which I hadn't really thought about in a while, and tried to get my head around it in this special case, and I was like, how the hell did I ever think that up? I tried to take a shortcut with the special case and couldn't do it at all, so how did I ever get the general case to work? So I thought back and I remember vaguely standing in Simon's office, and we had this drawing on the board of some curve with straight lines drawn all over the place, step functions below it, step functions above it, and both of us going "yeah, it ought to work...", and then I remember sitting in my office trying to turn that picture (or a subpicture of that picture, or an alteration of that picture) into maths. And then I thought, well, yeah. That's how ideas come. Pictures and talking and hard work. And occasionally a eureka moment. But even the eureka moments usually come after lots of pictures and talking and hard work. PS I happened upon this video of a Flaming Lips gig. It does get a bit of the feeling of being at a Flaming Lips gig across, I think. There are some nice balloon-based moments, like the kid in front catching a balloon and giving it to his short-arse girlfriend to punch, and the guy with the camera suddenly breaking out of his calm camera-holding to punch a balloon himself. (Pity Wayne's voice is shot - although it does get slightly better as it goes along!) Posted Wednesday 14th October 2009 at 10.58pm Thoughts for today So, everyone seems to think Obama shouldn't have got the peace prize. I think he should: what did more for world peace recently than putting a sensible guy in charge of the USA? (I guess by that argument we should give the prize to the American people, but splitting up the cash wouldn't leave much per person.) I had French class again today. It was a million times better than last week. Most of the already-fluent speakers weren't there. I still panic every time I try to speak, and my brain goes blank and I can't think of any words or what order to put them in or what the correct endings are. But this week it was actually fun (bar the times I tried to speak and ended up stammering / giving up / blushing). I've been listening to the new Mountain Goats album today. It's good. Also tried listening to the new Flaming Lips again yesterday as it's getting a load of good reviews. It grew on me a bit but I still don't really get it. I remember trying to put a CD on in the car on some family outing once, and everyone complaining, and my mum saying "sometimes you just want a nice tune", which I took as a real blow, because that's what I'm all about, the nice tunes. Call me boring, closed-minded, one-dimensional, I don't care. But don't tell me I'm not all about the nice tunes. To kill one Pitchfork review with another: "There's a moment in last year's documentary, The Fearless Freaks, where Wayne Coyne is playing a song he was writing during the time of the Clouds Taste Metallic sessions. With only his strumming to accompany him, Wayne sings, "Cats killing dogs, pigs eating rats..." The song is "Psychiatric Explorations of the Fetus With Needles", and on its way to actualization, it will acquire a weird intro and a stranger instrumental bridge, and will be puffed up large and colorful enough to suit the rest of that big, glowing album. But even as Coyne plays it alone on guitar, you can hear something special. Listening to At War With the Mystics-- the Flaming Lips' first new album in almost four years, and the product of many months in the studio-- it's difficult to imagine a similarly inspiring glimpse into one of these songs' construction. Much of the record sounds like chords and melodies were written later, as an afterthought to flesh out production experiments. The goofy noises, glitches, and wafts of Wilsonian harmony in "Haven't Got a Clue", for example, seem to be more central to the track's focus than the melody (of which there is almost none) or the lyrics ("Every time you state your case/ The more I want to punch your face"). But the sounds are certainly interesting." What there doesn't also apply to Embryonic? OK, so the lyrics are probably better on Embryonic than Mystics. But where are the tunes, Wayne? Posted Saturday 10th October 2009 at 3.35pm Ladybirds invaded my room today.  Posted Wednesday 7th October 2009 at 10.14pm Entre les murs Bath uni offers free language courses for postgrads. I started on the advanced course today - I did the improvers and intermediate courses in my first and second years, and so advanced is the only one left to do. Boy was it hard work. Most of the people there had, I think, already spent some time living in France, and their French was far more fluent than mine. It was a real effort to keep track of what people were saying - I was just about able to keep up most of the time but got lost several times. And as for speaking, I'm just so slow! It takes me ages to form sentences - I have to go through "decide what I want to say in English, translate into French, try to remember that word that means ______, try to think of synonyms for _______ that I might be able to translate, check through grammar and correct" before I say anything. I think I'm technically reasonably capable: when I saw a paragraph one of the other attendees had written, I thought to myself "that word should be that, and that should be that" - and then the teacher came over and said exactly the same thing. So I can do it - but I need to do it a hell of a lot faster! I think I know now what it feels like to not understand in school! I can sympathise with the kids who messed about in lessons and made life hell for the teachers - when you're struggling to keep up it's so tempting just to give up. By the end of the two hours my brain was fried, and that's with barely saying a word myself, just trying to keep track of what the teacher (and others) were talking about.  So should I give up? That'd be the easy option. I have plenty of excuses, the biggest being that I don't really have the time to be taking two hours (plus recovery time!) out every Wednesday. I'm moving to Paris in January and it feels like it would be less embarrassing to learn as I go along over there - at least the French have good reason to be a million times better than me at French! But this latter reason is obviously flawed - if I give up now what makes me think I'll be able to cope when I have people speaking French around me almost all the time, rather than just two hours a week? I think, for now, I'll keep going - it'll make me feel superior to the secondary school class clowns, and what have I got to lose by embarrassing myself with my sssssllllooooowwwww speaking for a few more hours? I just hope I can motivate myself to go along when it does come around again next week. The other option is to find some other people who speak just as slowly as me... maybe I could seek out some stutterers... or some French whales... PS I made some spicy beef and noodle soup tonight. Weird thing was, it tasted strongly of fish sauce, but I didn't put any fish sauce in because I didn't have any. Maybe Thai-style food is just destined to taste of fish sauce, no matter what - the Thai are just going with the flow. Posted Monday 5th October 2009 at 11.20pm Green like a geisha gown My sister, Corran, has just started university. She's studying maths at Birmingham, and she rang me yesterday to say she'd done all the questions on her first problem sheet except one: how many (natural) numbers less than a million contain a 4 or a 6? I didn't tell her the answer - in fact at first I just said she should think long and hard about it. A few hours later I rang her back and gave her two clues that I said were applicable to many maths problems, not just the one she was struggling with. One: if you can't answer a question, think about whether you can answer any related questions - like the "opposite" question (a first year's intuitive grasp of "opposite" being enough that we needn't worry about exactly what we mean). So for example, can we answer "how many natural numbers less than a million don't contain a 4 or a 6"? And two: if your question can be simplified, can you answer the simpler question? Do we know how many natural numbers less than 10 (don't) contain a 4 or a 6? How about less than 100? 1000? Anyway, I don't know if she managed to solve the problem in the end but it got me thinking: should I be giving her these clues? All I know is these are now two of my natural reactions when presented with a problem. I don't know how I got those reactions. More generally, how do we learn to do maths? Clearly it's important to solve lots of problems in a non-prescriptive way, by which I mean that you shouldn't know what method is going to work before you start - the A-level approach of giving you a method and getting you to practise it 20 times, then moving on to the next method, won't do you much good at this stage. But why am I now able to solve a problem in 10 seconds while holding down a conversation over the phone, where seven years ago (I can't believe it's been seven years!) it would have taken me a lot of hard thought and several failed attempts? Is it just because I've seen equivalent problems solved so many times by myself and others, or is it that I have more general problem-solving skills hard-wired into my brain by virtue of having done maths nearly every day for seven years? Maybe it's a bit of both. Can it be a bad thing to be telling my sister, and my tutees in Bath, general ways of solving problems? Should they be discovering them for themselves? I remember one of my lecturers once claiming that it was important for students not to be able to do all the questions, because otherwise they might get the false impression that maths was easy. I agree with that (although I think the comment was actually after someone had pointed out that one of the lecturer's problems was in fact impossible to solve). But I think we should try to teach ways of solving problems. We should try our best to teach them enough general methods to make the problems as easy as possible. And if we can teach them enough to make the problems easy, then we should be giving them harder problems! Posted Sunday 27th September 2009 at 10.16pm What the...?  Posted Wednesday 23rd September 2009 at 8.09pm Mr and Mrs Akhund Many congratulations and best wishes to Immad and Fatema, who married yesterday.  Posted Monday 14th September 2009 at 9.39pm Bangers and mash with spicy mango and apple gravy No progress on the maths post I promised, still looking for time to go through it properly. So in the meantime I thought I'd post another recipe that I made up today. As usual I just threw things in without bothering to measure, so it's all approximate. More guidelines than actual rules. The below makes enough for one hungry student - adjust as you see fit! 2 sausages 1 large potato Rosemary (preferably fresh - way nicer than dried) Lump of butter Dash olive oil 1 medium-sized onion Half a leek 1 carrot 1 red chilli 1 chicken stock cube (I recommend the Knorr ones... they're awesome) Half a small glass of apple juice 1 heaped tablespoon of mango chutney Other veg (I used a few mangetout, green beans and peas). Put the sausages in the oven, and the potatoes on to boil. Chop the carrot into big chunks and add to the pan with the potatoes. After 5 mins or so (use the 5 mins to chop the onion, leek, chilli and rosemary) heat up a dash of olive oil and start frying the onion and leek. Fish the carrot out of the boiling water and add to the frying pan. Once the onion starts looking vaguely cooked, add the chilli (you can add this earlier if you want it spicier), then the stock cube and keep adding water a bit at a time (just pour some out of the potato pan). Once the stock cube has been absorbed add the apple juice and mango chutney. Keep stirring and adding water until you've got a sauce-like consistency - you can add some flour to thicken it up if needed. After around 20 mins of boiling the potatoes should be done, so drain them, add the butter and rosemary, and mash. Add the veg to the gravy for a couple of minutes (or longer if needed) then serve. Posted Friday 11th September 2009 at 3.45pm All my words for sadness 2 months without a post. That's really bad. Well, I've been busy - summer means conferences and cricket. Hopefully I'll get the chance to write another post at the weekend about BBM on a circle. We hosted a UK probability meeting here in Bath this week, where I saw a really good talk by Jeff Steif about circle coverings that I hope will be of help once I've digested it more thoroughly. (There were, of course, plenty of other good talks!) By the way, in response to the posts below, I didn't have swine flu. I may just have had a small stone in my gland. It seems to be better now anyway. Finally, a mention for my grandad, who died two weeks ago today. His funeral was yesterday. He was 87, a few days from his 88th birthday when he died. Posted Sunday 12th July 2009 at 5.13pm Baked new potatoes with carrot and sweetcorn One thing about being forced to sit at home all day: it does give you time to cook. So I made this:  Wash the new potatoes, prick each a couple of times with a fork, and roll them in some olive oil and rosemary. Bake with some whole cloves of garlic at 190C until... baked (45 mins? I'm rubbish with times and quantities, I just guess). Put the carrots and a couple of segments of orange with some thyme in a pan of boiling water and simmer till the carrots are how you like them. Then drain, add a knob of butter, some sweetcorn and spring onion and warm through. Peasy. Makes a nice healthy lunch. Must make sure I have some protein for dinner though... Posted Friday 10th July 2009 at 9.49pm Maybe I have swine flu So. I went to Germany at the weekend. In Germany they have an annual "maths football championships" where postgrad teams from universities across the country meet up and play football against each other. We have a German who also happens to be a good footballer in our department in Bath, so we got invited too. It was great fun, the Germans were massively friendly and they loved our Dead Sharks game. But towards the end I got ill - one of my glands swelled up badly, just below my jaw bone on the left side of my face. (Sympathetic housemate's reaction: "Ha! You look like a toad! You been eating too many flies? Ribbit. Ribbit. Ha ha ha.") I don't have any other symptoms, and it's slowly going down, so I guess it's just an infection - I blame the German diet of steak im brotchen ad infinitum for messing up my immune system. But I went to the doctor yesterday to make sure it wasn't anything serious, and she decided that I should stay at home for a while just in case it's mumps or swine flu (wrong gland for mumps and no flu symptoms, but hey). Staying at home is boring. I don't have anywhere comfortable to do work so I end up doing a bit lying on my bed then falling asleep, or doing a bit on the sofa then watching TV. I've watched a lot of episodes of House. I'd never watched it before a few weeks ago but I like it. Really I ought to watch Delicatessen again, or get some more French films. Posted Wednesday 1st July 2009 at 12.37pm Jens Lekman has swine flu Get well soon Jens! www.jenslekman.com/records/smalltalk.htm
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