Today’s big idea…

… is a collaborative fiction web. The idea is to create many different stories starting from the same point. If you don’t like the ending… write a new one. If you can see where the author’s abandoned an interesting plot twist… you can pick it up.

In principle, the web can grow in depth and in breadth as far as it likes – I imagine there’ll be a lot of abandoned threads and false starts that nobody picks up, but maybe there’ll be one or two viable novels that come out of the process. If nothing else, it can be a repository for stories that started but went nowhere, giving other people a chance to take over.

I’ve been thinking mainly about the implementation so far (for an experienced PHP dude, it would be straightforward, but there are a few quirks that I need to iron out myself) and a little about the rules. So far, I’ve got:

• write your own work
• release work under CC (by-sa)
• play nicely
• keep it as clean as is reasonable
• 400-600 words per thread

Anything else I ought to include in the rules list? I was thinking of setting the ball rolling by posting my NaNo stories in 500-word chunks.

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Squeezing every last mark out of the paper

You’ve slogged through the twenty-odd pages of your GCSE maths paper. You’ve got a good feeling about this one – you think you’ve got most of it right. And you’ve got ten minutes of the exam left. So what do you do?

When I was sitting my exams, the usual answer was ‘count ceiling tiles’ or ‘look for prime factors of my friends’ phone numbers’. I was an odd child. It turns out that the correct answer – as evidenced by my 99% mark for one paper in which I mis-measured a circle – is to check your work.

Believe me, it’s less tedious than counting ceiling tiles, and much more rewarding. There are many ways to check your work:

• Look for a different way to do a question
• Check that your answer makes sense – is your sale price lower than the original price?
• Measure all the things you were meant to measure, twice.
• See if you can get back from your answer to the numbers in the question
• Read each question to make sure you’ve given the answer they asked for
• Did you write your units down?

There are probably a dozen others I’ve overlooked – do you have any tips?

Polygon vocab: it’s all Greek to me.

Another cross-post to FlyingColoursMaths.co.uk.

Sadly, the maths GCSE seems to be almost as much about learning vocabulary you’re never going to need to use again as it is about learning to do maths (seriously, I’ve not had any use for the word ‘congruent’ in more than a decade of serious science, much of which involved geometry – it’s like the map of the cat). But, as with fractions, they have to be learnt, and, as with pizza, I’m here to make life easier.

Triangle is easy. Tri- means three (tricycle, triathlon) and -angle means corner. -Gon means corner too, which is where the word trigonometry comes from. Tri-gon-ometry: three-corner-measuring. There are three main types of triangle: the equilateral, (equal sides – in English, lateral is another word for sideways), which has three equal sides; the isosceles, which has two sides the same (iso- means the same, and -sceles comes from skelos, meaning leg); and the scalene, which has three different lengths of side (from skalenos, meaning rough. Apparently).

There are also right triangles, which contain a right angle (90º) and are either isosceles (if the other angles are 45º) or scalene (otherwise). The angles inside any triangle add up to 180º – check that it works for an isosceles right triangle.

Four-sided shapes have many more varieties. There’s the square and rectangle, of course, both of which have right angles at all four corners. Then there’s the parallelogram, which is what you get if you squish a rectangle so that opposite sides are parallel, but the angles aren’t 90º any more. A rhombus is a the same thing, but starting from a square. Then there’s the trapezium, which looks a bit like a trapeze: it’s got a bar, parallel to the moorings at the top, and the other two sides can be at any angle. There’s also the kite, which is a lot trickier to describe than you’d think. Take a pair of lines the same length joined together. Take another pair of lines the same length (not necessarily the same length as the first pair) and join them together too. Then join the loose ends of the two pairs together and bang, you have a kite.

A polygon (poly- = many, -gon = corner) is a shape with many corners (three or more). After four-sided shapes, polygons are always called (something-)gons. A pentagon has five corners (penta- unsurprisingly, means five); a hexagon six. Then heptagon (7), octagon (8), nonagon (9) and decagon (10). If all the sides are the same length, you can call them equilateral (again) or regular.

I think those are the main vocab words you need to know for polygons. If I’ve missed any, let me know.

Fractions bad. Pizza good.

 This is one of an occasional series of articles for my tutoring site: FlyingColoursMaths.co.uk. Do visit if you’re in need of maths tuition, or know somebody who is.

“Better cut it into six slices – I don’t think I could eat eight” – Yogi Berra.

Nobody likes fractions. Once you’ve figured out how to beat them senseless, perhaps they become almost tolerable, but even then remembering the rules and carefully applying them is the kind of thing the devil probably has lined up for when he runs out of other ideas.

Unfortunately, they’re on the exam paper. Always. Taking a GCSE paper at random – Foundation paper 2, June 2004 – 16 of the 100 marks (about a sixth of the total) have something to do with fractions. 16 marks could be the difference between a D and a B.

One big trick to working with fractions is to turn the ugly numbers into something you can easily imagine. I tend to work with pizza, because slicing it into bits is a natural thing to do, and also it tastes good. Another is to use your understanding of pizza to learn how to do some basic examples – so you can apply the method to more complicated questions.

I like to start with two quarter-pizzas. Adding together a quarter and a quarter is easy, you get two quarters (or a half, which we’ll come to shortly). 1/4 + 1/4 = 2/4. The size of the slices – the quarters – is the same for both of the fractions so all we have to do is add the top parts. 1/4 + 2/4 = 3/4 – a quarter slice and a half make up three quarters of a pizza. So far so easy.

Now, you might lose marks for writing 2/4 as your answer, because it’s not in its simplest form. Whenever you write a fraction down, you should look for a number that divides into both the top and the bottom. Here, you can divide the top and the bottom by two, making 1/2 – which is the same two quarters.

Why does this always work? It’s best to come at it from the other side. If you start from a half and divide it into two parts, you’ve doubled the number of slices (from 1 to 2) BUT you’ve halved the size of the slices (from a half (1/2) to a quarter (1/4). So now you have two quarters. You can do this with any fraction and any multiplier – if you multiply (or divide) the top and the bottom by the same number, you get another version of the same fraction. A half is also eight sixteenths (multiply the top and bottom by 8); 6/15 is the same as 2/5, if you divide the top and bottom by three.

This trick is really useful when it comes to adding slices of a different size. Let’s say I’m feeling greedy and want a half pizza, but you’re not really hungry and only want a quarter. Between us we eat 1/2 + 1/4. We know we can’t just add the things on top and on bottom – we’d get 2/6, which is a third, which is less than a half. That doesn’t make any sense. Instead, we need to add slices of the same size together.

What’s a good size of slice? Anything you can divide by 2 and 4. Eight is good. Four is also good (even better, because you don’t have to touch the quarter). But let’s do eight for the practice. We want to turn both fractions into eighths. That means we need to multiply the bottom of the half (2) by four. If we do that, we need to multiply the top by four as well, to get the same thing. 1/2 = 4/8. That makes sense. For the quarter, we need to multiply the bottom by two. To keep everything the same, we have to multiply the top by two too. A quarter is 2/8. Now we have both fractions the same underneath, so we can simply add the tops together – four slices plus two slices is six slices, and the slices are all 1/8 of a pizza. 1/2 + 1/4 = 4/8 + 2/8 = 6/8. And naturally, we can make that simpler – 6 and 8 are both even, so you can divide both by two to leave 3/4 of a pizza. Which is just what we’d expect.

So, next time you’re faced with a fraction problem (say, 1/2 + 1/3) – think about what you’d do to the pizza to make it all add up. I’ll leave that one as an exercise – as long as I can have the left-over slice :o)

Getting myself organised

I’ve been an organisational magpie for many years. Every so often I dabble with using a diary, either a paper-and-pen one or an online version, or stumble on a different to-do list manager online… and then fall out of the habit a week or so later. There are a squillion blogs (I counted) suggesting ways to keep yourself organised, most of them saying ‘this is how I do it… your mileage may vary.’

So, this is the system I’m working with at the moment. 

Miles Kington

Well, obviously the Blog365 experiment lasted all of a week before moving and travelling interrupted. But I’m going to do my best to at least make it through the first fortnight of February with a daily blog post.

So, I’m sad to learn that Miles Kington died. He was one of the first journalists to show me that there was more to comedy than slapstick and gags, that wit could make for entertainment. It’s a sad state of affairs that more people are familiar with Jeremy Beadle than Kington. At sixth form, I would turn to his column in the Indy, below the letters page, before even looking at the crossword. For a while I couldn’t go into a charity shop without picking up a book on Franglais. I tried writing Franglais once, but found that my French was too good.

I guess I eventually outgrew his writing – it’s impossible to write daily for many years without returning to familiar set-pieces, and I’ve done exactly the same thing with John O’Farrell, Charlie Brooker and probably a dozen others who don’t spring to mind since.

In any case, I just wanted to say restez en paix, Miles.

Crossword thoughts: “Difficulty difficulties”

I should apologise in advance for the specificity of this article: unless you’re particularly interested in British-style crosswords, and in particular the Guardian’s, you’re likely to get little from it.

In Sandy Balfour’s monthly round-up of the world as it meets the Guardian crossword desk, he raises an interesting question about themed puzzles. In Araucaria’s Christmas puzzle, a reader writes, as soon as you worked out the theme (Thomas Hardy novels), you could simply use the given number of letters to figure out the remainder without even looking at the clues.

I should, before I go any further, declare my bias: I am a big fan of themed puzzles. The first proper crossword I remember working on was an Araucaria special my dad (Ken) was attacking. According to the rubric, “(one clue) of the (other clue)” was one of the themed answers; (one clue) was “Support” and (other clue) “to come”, and I suggested “Back to the Future” – and my dad said something like “Oh! That’s it done. Spielberg movies” and we went on to complete it.

The first crossword I ever compiled was a themed one too. My then-current obsession was the Beatles, and I managed to cram four or five titles into a grid I created myself. The only clues I remember are “Before the Beatles came a Sprout (6)*” and something about condiments in the regiment.

But certainly, themed crosswords can be annoying. Bunthorne was always one of the worst culprits for setting a crossword based on a single quote comprising a substantial proportion of the puzzle, a fifty-letter anagram or (worse yet) a convoluted clue that required an entire weekend’s thought to get anything at all out of.  Araucaria and Paul, of the Guardian setters, are also guilty of this kind of devilment, but take far less delight in willful obscurity.

As for the reader’s objection to themed puzzles such as Araucaria’s Hardy effort, I have to confess that that’s exactly how I solved it, and exactly how I get moving on many themed puzzles. Others, though, require the solution of several – possibly nearly all – of the themed clues before the theme becomes apparent – one I remember fondly involved the hierarchy of angels, some of which were listed as synonyms. And I think that’s the way it should be – the solver should have to work to get the solutions, but not too hard. As with many elements of crossword-solving, there’s a delicate balance to strike between difficult enough to divert and straightforward enough to be solved.

* PREFAB

Metablog: where is Kensson rambling to?

The Kensson’s ramblings blog has never really had a unified purpose, except to allow my talents to shine. Some days it’s there to showcase old, nearly-forgotten songs; other days to brag about new ones. Some days I’ve cooked up some tasty food and want to record it; others, I’ve cooked up a preposterous premise for a story and want to share it. Then there are the articles and reviews that crop up from time to time.

But all of that is the ‘what’ of the blog, rather than the ‘why’. I imagine I had some vague idea that it would either gain me exposure, or money, or something along those lines; recipes and the odd factual article aside, the casual visitor is unlikely to find much by way of direct information – perhaps a little entertainment, but that’s even more hit-and-miss than the usefulness.

So today, I have decided on the purpose of these ramblings (if one can ramble purposefully) clear: the posts I make (daily, with any luck) are now designed to gain me freelance employment in any of several fields. The main ones are:

• Tutoring maths or other subjects I know about (Physics, French, exam technique… – just ask);
• Writing articles, particularly popular science;
• Website creation – need a simple, elegant website full of prose extolling your virtues and with bells here, whistles there? Let me know!
• Programming – I’m good at quick-and-dirty fixes to problems, especially maths-related; my main languages are IDL and Python, but I’m getting to grips with PHP and SQL, and I can dabble in Java;
• Programming consultancy – I’m very good at sitting down with a programmer and asking ‘what does that line do?’ until we figure out why the code doesn’t work. For a reasonable hourly sum,
• Music (I was told last night that I’m an amazing singer, which I was surprised to learn) – let me know if you’d like me to play a gig for you, or write a song, or otherwise prostitute my talents
• Anything tangentially related to any of the above.

Frankly, any pennies I can pull in from freelance work translate into minutes I don’t have to spend doing data entry or whatever other bones the recruitment agencies in the Oxford area throw my way. So I’ll listen to any reasonable suggestions that allow me to work from home. You can e-mail me at colinbeveridge@yahoo.com with any propositions :o)

Overcoming stage fright: an anecdote

I am not a natural performer. I got my first guitar when I was about 14, and I’m pretty sure I didn’t play in public until I was 21; even then, it was an unamplified performance in the corner of a loud pub. I hated my voice, was certain my guitar-playing was lousy, and didn’t particularly rate my ability to remember the lyrics of whatever I was singing.

I did, however, have a huge back-catalogue of songs I’d either written or learnt to play. And, thanks to a bunch of friends who only owned right-handed guitars, an ability to play upside-down if necessary. Which stood me in good stead when, in an unfamiliar pub one pre-festival night, the local rock star – Charlie – heard that I played a little, conjured a beat-up six-string from behind the bar and insisted I play a few quiet tunes in the corner.

Charlie played at the festival the next day and, after 20 minutes or so, calmly announced to the 100-strong crowd that I was going to play a few songs while he took a break. At the time I was furious that he hadn’t, say, mentioned this to me. In retrospect, it was just as well; otherwise I’d have been staggeringly drunk as well as terrified.

I don’t have a good explanation for what happened next. What happened next was that I got up on the stage and rocked. Had Charlie still been on the stage, I would have blown him off it. The audience stomped and cheered and laughed and well, I’ve been a part-time rock star since then.

I learnt several things that day. Firstly, that the only hard part is getting on the stage. If you have even as little talent as I do, it’ll combine with adrenaline once you’re up there and see you through. Secondly, people are much readier to laugh at a singer than at a comedian. You can get away with the lamest jokes in a song (I point at the Saddam Hussein line in Tangled Up In Bob) and, perhaps because the joke is unexpected, you can get a laugh. And third, you don’t need a license to sing. You just need someone to persuade you that you either want or have to.

Any time I feel frightened of playing, I imagine Charlie at the mic putting me on the spot. I know that whatever crowd I’m facing, it’s not as scary as the first crowd. And if I can come through that ordeal with a round of applause and a few drinks bought for me, I’m perfectly capable of doing the same thing again.

The Geocentric Days Are Gone…

I just signed up for blog365, a sort of year-long blogging NaNo. This is partly to console myself after my inglorious failure at said NaNo last year. The idea is to post something every day for the year – something I’m sure those of you bemoaning my infrequent articles must be gladdened to hear. Don’t all clamour at once…

In principle, I’ve already lost blog365 because I didn’t post anything yesterday – but fortunately there’s a leap day coming up which I’ll use to catch up. Anyway, today’s article is inspired by something in the blog365 headline which mentions a lap around the Sun. I wondered: how fast is the Earth moving?