Fahrenheit 2008 
I'm not really sure what to write about this. Part of me is shocked, but most of me isn't. There are worse things happening out there in the world, but this made me shudder in a way I don't very often shudder.

The Assessment and Qualifications Alliance, the largest examination board in England, has decided to pull a piece of poetry by Carol Ann Duffy, written from the perspective of a knife-wielding loner, from one of its GCSE poetry anthologies - on the grounds that "the board had received a complaint ... against a background of fears over teenage knife crime".

Not only that, but they have asked schools to destroy existing copies of the anthology that contain the offending poem.

Yes, we now have state-sponsored book-burning in the UK.

I would advise all readers to destroy any copies of this blog they might have, in case it turns out to be subversive. If the thought police are reading this: it's not my fault. Those people would have gone out and committed the crimes by themselves anyway.

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Two badgers walk into a snake 
As seen in the garden this weekend:



This photo is somewhat out of date, of course, because these things grow at an alarming rate. This morning, the largest one was about twice this size. I should do a time-lapse animation really, if I had the patience.

I'd love to know if they're edible, since I'm cooking mushrooms and pasta tonight anyway and have you seen the price of mushrooms in the shops? But I'm not quite brave enough to take a bite, and not quite cruel enough to test it on the cat.

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Crunch, crunch, crunch 

I remember sitting in a macroeconomics lecture many years ago, being taught about the government bond markets and how the price of bonds (and, thereby, money) is set. The lecturer started with a simple question: what principle is it which ensures that the maximum number of participants in a market - any market - are able to buy or sell at their chosen price?

There was silence. We'd all sat through a term's worth of microeconomics lectures, and most people probably knew the answer - but no-one wanted to actually say anything. This is Imperial College, after all. Everyone's a dork.

"Price differentiation?" said one dork.

There was some muffled smirking. No, that's not the answer. The correct answer, of course, is the principle of supply and demand. Price differentiation is the technique used by a monopolist to increase his revenues, by selling the same goods at varying prices. For example, a "value pack" of orange juice in a basic red, white and blue carton for 50p, or a "regular" carton of orange juice with a prettier label for 80p, or a "premium" carton of orange juice for 95p. Identical contents, but marketed to appeal to as many different segments of the population as possible. This way, they can make more profit than if they just picked a single price and sold a single product.

That dork was me, by the way. But I realised the other day, I wasn't actually very far wrong.

You get bonds. 1 month, 3 month, 6 month, 12 month, 2 year, 5 year, 10 year, whatever you want. You get government bonds, corporate bonds, synthetic bonds, whatever you want. Everything has its price. Everything has its yield. You can buy whole debts, chunks of debts, sliced debts, minced debts, good debts, bad debts, whatever you want. Bought the wrong thing? You can buy insurance in case it defaults. You can hedge. You can buy swaps, options, swaptions, whatever you want. The equity markets are a walk in the park by comparison. But they are all part of the game too. You can buy shares, sell shares, short sell shares, buy puts and calls, short sell short calls by the sea shore, whatever you like. It's like a big money supermarket and everything's on special offer. You can even trade green pieces of paper with presidents on them for brown and purple pieces of paper with "I promise to pay the bearer on demand the sum of" written on them. To your hearts content.

You think you have choice. But it's all an illusion. All you get is a piece of paper. They sell the same piece of paper over and over again. All that changes is the wrapping, and that's a piece of paper too.

It's a piece of paper.



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The Highland Show 

Only a week and a bit late with this one.

The Royal Highland Show is an agricultural show held in a big field next to Edinburgh Airport. I love this countryside stuff. I know next to nothing about cattle, horses, tractors and farming in generally - and what I do know is mostly derived from accidentally listening to The Archers - but shows like this prove that there are still plenty of people out there who really do know their stuff. It worries me that the knowledge and skills involved in working the land are getting increasingly concentrated in the hands of a dwindling number of experts, while the rest of us just blindly buy whatever is cheapest at the supermarket. But enough of my apocalyptic ramblings. Let's look at some hot guys at work.





A Farrier is basically a specialist blacksmith who makes and fits horse-shoes. The hard-working lads in the pictures above were competing against the clock to transform four rectangular iron bars into four curvaceous horseshoes in the space of 45 minutes. They work in teams of two, and with only the most straightforward tools - forge, anvil, tongs, vice, hammer, punch, file, brush. It's most impressive to watch.

Who wants to see some sheep?



OK, so there aren't many actual sheep visible in that picture. But it gives you an idea of the scale of the place. That was just one half of one of the four or so sheep tents. Continuing the theme of fit young men hard at work: where there's sheep, there's sheep-shearing. And these guys are fast.





There were also some more dangerous-looking breeds, who you probably wouldn't want to approach with clippers:




They have all sort of stuff at the show, but I didn't take photos of most of it. The cattle parade is always enjoyable, because there are usually cute but recalcitrant baby animals who have been attached to a rope and entrusted to the care of a small teenaged girl who isn't quite strong enough to pull it in the required direction. But my real favourite are the Clydesdales - the most popular breed of heavy horse in Scotland. The heavy horse competition is called a "turn-out", where the horses are hitched to a trap of some kind (either in pairs side by side or in tandem one in front of the other, or in larger groups) and proceed to be put through their paces in the ring. Some of the carts in the contest were a hundred years old and still road-worthy!




The exact positioning of our seats, combined with the less-than-perfect weather, made it rather hard to get good pictures. But I did my best!

The Highland Games was quite a fun diversion. Basically a strong-man contest, this featured weight-throwing, shot-putting and caber-tossing by a number of (you guessed it) fit young men. Except this is a different kind of fitness which seems to involve a lot of pie-eating. Actually I have some videos of this, but I'm not entirely sure how to upload them (and they're in crappy AVI format anyway). The vertical weight-throwing competition was the hilight, as the competitors were trying to break the world record for tossing a 65lb dead weight into the air. They got a couple of audience members to try it first, just to show how heavy these things really are (i.e. extremely hard even to lift above your head, let alone throw). Then up stepped some big Polish guy and launched this lump of metal about 15ft into the air. They didn't break the record, but they gave it a damned good try.

The caber-tossing was won outright by the only Scotsman in the competition (who'd've thought it?). The object of the caber-toss is to launch this massive pole into the air, have it rotate so the top end strikes the ground and the bottom end continues on and over to fall flat straight in front of you. It's the angle of the caber where it falls that determines your score.




Last but not least, there was the obligatory show-jumping competition. Also known as a fun exercise in long-distance photography and adjusting your camera's shutter speed under poor lighting conditions. Needless to say most of my shots didn't come out at all well, but here is one that almost did:



There were one or two nasty-looking accidents with horses running straight into the jumps at full tilt and demolishing them completely, but fortunately no people or animals were seriously hurt.

Next time, we have to go and see the dog agility thing. I need stuff to caption.



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Small, but perfectly formed 

Once more, I find myself abusing bits of the Internet to satisfy my own warped curiosity. (To be honest, I blame the parents.)

This week: TinyURL. If you've never used TinyURL, here is a brief explanation. It's a free web service that helps you to manage long, unwieldy URLs. Just paste an arbitrary web address into TinyURL and hit the button, and it will return a tiny little thing that looks like http://tinyurl.com/LLIvo or something, which redirects to the site you originally specified and is easier to type, remember, send to someone else, write on a post-it, whatever.

So I got to wondering – if so many people are using this service, then how hard is it to guess a valid TinyURL? (More precisely: how densely populated is the TinyURL keyspace?) To find out, I wrote a small script that picks short random strings of letters and numbers and looks them up on TinyURL, returning the website they point to (if any).

The result? Well, for five-character strings, 627 out of my 1000 randomly selected identifiers were valid. So, if you type http://tinyurl.com/ followed by five random letters or numbers, the odds are roughly two in three that you'll get some random page off the internet that someone, at some time, has found interesting or important enough to run through the TinyURL mangle.

The next question is obvious. What sort of pages are people using TinyURL for?

The answer is disappointingly mundane. Most of the links I found were very boring. Maps to boring places, news stories about boring events, boring people's MySpace pages, searches for boring products on boring e-commerce sites, boring images of anime characters.

Many of the sites I came across this way were rather technical in nature, which suggests that TinyURL is (at the moment) mostly used by geeks. Although there were some definite signs of online shoe-shopping as well. No porn, oddly enough (except for one site that appeared to sell anal sex toys, which I wasn't in a hurry to click on. TwCrs, if you're braver than I am.)

There was one interesting-looking page on the list, which was (I think) a news story about a Boston skateboarder who was sueing the city after getting his forehead branded by a manhole cover. Unfortunately, the target link had already expired. Like, bummer.

And finally, there was clear evidence of at least one person taking the output of TinyURL and feeding it back into TinyURL – presumably to see how many levels of redirection they could get away with.

Honestly. Some people clearly have too much time on their hands.



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Why I did what I did on my holidays and in what order 

Actually, I'm not sure exactly why we chose to go to Northumbria on holiday. Other than the fact that we went there last year and it was great. But I'm not sure exactly why it was great. I think it's because no-one really knows about it. So I'm not sure exactly why I'm telling you about it. It just seemed like, you know, a reasonable thing to do.

Just as the reasonable thing to do when one arrives in a new town is to go out and poke around, trying not to look too much like a nosy tourist but still allowing your brain time to translate the preconceived ideas you got from staring at a 1:25,000 map for hours on end into a demonstrable ability to find your way back to where you started from. And then rummage around in the drawers and cupboards of your rented townhouse looking for a cafetiere and a spare AA battery for the clock on the living-room mantelpiece which no-one has bothered to change, nor even just straighten the hands to 12 o'clock or 6 o'clock or something that at least looks presentable.

One drawer, as you might expect, contained Useful Information. I'm always pleasantly surprised when I locate that drawer, and this time was even better, because in it was not just Information, but also Evidence of the Prior Existence of Intelligent Life, or at least a form of life that shares my suspicion of Indian Takeaways with Very Large Menus and had taken the time (and it's a perfectly reasonable thing to do) to calculate the minimum number of different saucepans required to support such a wide choice of spicy fare:

That's encouraging. Someone else is looking for order in chaos. Someone else is finding patterns, rationalizing the arbitrary, distilling sense from the senseless. Moreover, someone else remembers GCSE mathematics. I wonder if they knew, when they were scribbling down their factorials, how happy it would make me when I saw it? Probably not.

Anyway, there was a clock. Not that clock, the other one. This one hadn't stopped, although it was a few minutes fast. It was in the kitchen, on the wall, and it gave me a shock. I'd written about it, you see. It has unusual numbering. But I wrote about it a long time before I saw it. (That's because the numbering is not that unusual, and my imagination is not as fertile as all that. I am well aware of this. Don't start.) The clock looked like this:

It couldn't go unremarked, and I could even do a post clock ergo prompter clock joke, if anyone wanted to hear it. Actually, the clock I wrote about was even more interesting than this one, but that's another story. Literally. Still it feels like I'm getting things out of order here. Fortunately, the Useful Information drawer has a solution to that, too, and it's only a phone call away:

I imagine that was probably caused by an over-zealous spellchecker. But under the circumstances, it's probably not my place to speculate.

Where was I? Oh yes, that's right - Alnwick. A wonderful, clean, friendly little town which is home to one of Britain's most impressive castles (so impressive, in fact, that almost every drama series or film with a medieval or fantasy setting has been filmed on location there at one point or another, including Cadfael and Harry Potter). The Duke and Duchess of Northumberland live there – actually in the castle, mind you! – and they let people come in and marvel at their collection of 12-foot-high mirrors and ornate Louis-XIV-era furniture and naff china (and I'm not kidding, some of it is really kitsch like you wouldn't believe). The castle looks like this:

Anyway, they don't let you take photos inside so all this talk of fixtures and fittings is pretty much academic. And besides, I'm getting ahead of myself again: it's only Sunday at this point (if we gloss over Saturday night, that is) so we haven't even been to said castle. We thought about it, but it was kinda rainy, and to British people that means that it's an ideal time to do something that involves being outdoors. So Alnwick Gardens, here we come. (Came. Whatever.)

Now Alnwick Gardens are basically the grounds of the Castle anyway, although they're somewhat removed from the fortress itself and have their own admissions kiosk and gifte shoppe. The Duke has been busy of late reshaping the gardens and installing water features. And when I say water features, I really mean one great giant water feature the size of a large car park, taking up a whole hillside by itself:

It's much more impressive in person. And it does feel almost alive, in a way, so I wouldn't hesitate to anthropomorphize. As you climb further up it, you find little streams and pools cut into the pathways, and planted islands within those, and smooth pebbles just under the surface. It feels recursive, like zooming in on a big wet Mandelbrot set.

In one of the pools in the upper courtyard garden, we came across a chaffinch bathing itself, as brash as anything:

It must be a wonderful place to be a bird or a bee or a butterfly. We saw many interesting kinds of all three, but none of them stayed still long enough to be captured on camera. (Can we say "on film" these days? Has the romance gone out of photography, now we've only the harsh precision of the CCD behind our lenses? But I digress.) There is a particularly interesting species of bee with a deep red colouration, and a white butterfly with orange-tipped wings that we immediately dubbed Lepidoptera Stelios Haji-Ioannou, or the EasyButterfly, although that does really have too many syllables, and shortening it to EasyFly would inevitably result in a namespace clash as soon as we discovered an orange-and-white fly, and EasyButter would be more of a no-frills dairy product, so we ended up at just EasyBy. We saw rather a lot of them over the week. Fortunately, not all of the wildlife was so fast-moving. Indeed, bits of it were hardly moving at all, and we'd come at the perfect time to see the late spring blossoms. There was grove upon grove of apple trees:

...and cherries, too, and a beautiful euphorbia that I'd love to grow myself, given a real garden:

We decided to go to the Treehouse for lunch. This treehouse, I understand, is one of the largest in Europe (who audits these things? Honestly?) and houses a well-regarded restaurant in amongst a lot of rope ladders and rickety bridges and such-and-such.

We arrived not long after noon and even though we couldn't get a table straight away, we remained undeterred. The menu really did look enticing, and much more fun than the egg-and-cress sandwiches on sale in the main café. So we killed an hour or so by talking a stroll around the nearby woods. It was an interesting walk: at some point, someone had clearly imprisoned some art students in this forest and made them decorate the place with sculptures and triptyches and other odd installations, like these:

Yes – there is a surreal door standing in the middle of the forest, there, just like the one in my last story. I almost needed a trip to the causality department when I spotted that. (Actually, there were two or three of them, but the novelty wears off surprisingly fast.) One of them had made their art practical as well as decorative, by providing upmarket nesting-boxes in various colours and architectural styles.

Our right hemispheres duly exercised, we returned to the treehouse and waited another forty minutes or so for our promised table to materialise. Normally I find that waiting (particularly for food) stresses me out, but being on holiday makes a lot of difference. And it was worth the wait! The lunch menu inside was very different from the one posted on the door, so we actually ended up with a proper sit-down meal rather than the light snacks we'd been expecting. But the quality of the food was outstanding – local ingredients well-chosen and well-cooked, and enormous portions of everything at about half the price of a city-centre restaurant of the same quality. And the inside is as fantastic as the outside, although the photos I took don't really do it justice. The restaurant is divided up by knots of twisting branches like great walls of wooden spaghetti. (What is it that you can't shake at a large number of sticks, if you have too many of them, I wonder?)

One thing was for sure: we were going to have to do some serious walking to work off the weight gain from this unexpectedly generous meal. Fortunately, the drizzly cloud was already lifting, and the next day was bright and clear and warm. We decided to get up early and see the castle before all the bank-holiday tourists arrived in force.

The castle itself is quite an imposing site. Most of the UK's castles are crumbling ruins, so it comes as quite a surprise to see one that's in relatively good nick. It would have to be, I suppose, if a family of rich people had chosen to make it their ancestral home, but there's no accounting for taste, as they say. (And judging by the grandeur of the place, the Duke and Duchess have no taste for accounting.) Here are some random photos from the ramparts:

One of the most intriguing things about Alnwick castle is the amount of detail to be seen everywhere. There were some big name designers (well, big names at the time) involved in the 18th Century restoration work, but this isn't a history lesson and you know how to use Wikipedia. They bedecked the battlements with ornate gargoyles and life-size statues, most of which have weathered down to indistinct stumps, but hold your gaze the more for all that as you squint to make out what that strange pose might once have been. (When three hundred years old you reach, look as good you will not, hmmm?)

As well as the grounds and the state rooms, the castle has a number of interesting mini-museums dotted around it, including a fascinating collection of antiquities. I was particularly impressed by some of the saxon jewelry. We definitely could have spent all day there. But we were eager to stretch our legs, so we headed off into another swathe of the Duke's territory just next door – Hulne Park. I've never felt so immediately in love with a place in my life. It's like someone distilled and bottled the English countryside and laid it down in a hundred-acre cellar, then let the public wander in and taste it for free. We wandered through fields of pheasants and sheep in the glorious sunshine, and crossed bridges and climbed hills, and took wrong turnings and saw a perfect red squirrel, and could gladly have done it all again if the day had hours enough.

(This is the point where I'm mentally costing up the season ticket and working out ways to persuade my boss to let me move to another country and work from home.)

I ought, at this point, to stop and say something about the word "Alnwick" for the benefit of those of you unfamiliar with English place names. Neither the L nor the W are pronounced; hence it sounds as if it were spelled "Annick". The town is so called because of its proximity to the river Aln, which is pronounced "Aln". Well, the L is just barely there, anyway. The train station for Alnwick is called Alnmouth station, because it's near (but not actually in) the nearby coastal town of Alnmouth. Which is pronounced "Allen-mouth". Almost. Honestly. It took me most of the week to memorize all this.

The next day we walked along the Aln from Alnwick to Alnmouth. (See why I had to put that last paragraph in there?) It's not far; or at least it's not supposed to be. We started out from the beautiful Lion Bridge:

The Lion-with-a-flagpole-up-his-bottom is kinda the symbol of the Duchy of Northumberland. He pops up on the crest of arms, and conceals himself in floral borders, and there's another statue of him on a big pillar on a hill on the other side of town, next to the best bookshop in the world. But more about that later. We wandered around the edge of the town along the river, watching the wildfowl and avoiding patches of bog and getting annoyed by footpaths that disappear without a trace just when you've got far enough from the main road to make it a pain in the neck to turn round and try another way. Even so, it was all going brilliantly until we tried to cross the river.

Most people cross rivers using bridges. But the most pleasant route to Alnmouth took us across country and over the Aln by means of a ford, with stepping stones. It looks really cute on the OS map. When we reached it, we found the ground around it was ankle-deep mud for twenty feet on either side, and the crossing itself was obscured by a bend in the path. Intrepidly we took off our shoes and waded through the wet dirt, to reach the edge of the stream. The day was baking hot but the water was seriously cold, and flowing fast. We found the stepping stones were all but submerged, and certainly no use for stepping. I waded a little way out, and was in above my knees before I could even touch the first of the stones. The current between the teeth was fierce, and it was becoming increasingly obvious that we were going to have to find another way. So we retreated to the dry grassy path, and washed the mud off our feet with water from an Evian bottle, and sat and laughed and ate our lunch while the noon sun dried our legs. He who fights and runs away lives to fight another day.

From hereon in, things went from bad to worse (in nominal terms, at least). The next footpath took us into a field and left us there. The footpath after that wasn't even there, which wouldn't have been so bad except that the sign for it actually was still there. That led us into a reedy, boggy, overgrown field, which we navigated based on the principle that we were somewhere between the river on one side and the road on the other, so we couldn't actually get lost, and if anyone actually owned this place, then they obviously didn't care too much about it. Under a railway bridge we found the path again, for a while. It took us up a hill, under some prickly trees, and dumped us in a patch of brambles. But we could hear the road just ahead, so we scrambled on and over a couple of wire fences until we reached the tarmac. Pausing for breath and to pick the burrs and thorns out of our jeans, we looked up the road and saw a well-beaten track and a neat stile leading back over the fence, just a dozen yards away. Typical.

Of course, this is all part of the fun. And from this point, the rest of the journey wasn't so hard. We only took one accidental detour, and it was scenic enough. We walked around a number of fields with odd-looking barrels placed at intervals around the edges. The small-print on the labels told me they were dispensing a chemical called a "rheology modifier". Even after ten minutes of browsing the Internet, I'm still not entirely sure what they were doing there. Something to do with preventing erosion or landslips or flash flooding, I presume.

We made it, in the end, to the beach at Alnmouth. In case you didn't know, this is what beaches look like:

Then common sense got the better of us, and we caught the bus home.

For our next trick, we decided to do another walk and see another castle. This time, the castle was in ruins and the walk was just a couple of leisurely miles along the seafront. Dunstanburgh castle must have been quite a sight, in its day.

Now it makes a quiet, craggy home for swallows and wagtails, not to mention the hoards of seagulls that mill around the skies and perch in the shelter of the cliffs below the outer walls.

After we'd explored the castle and watched the fishing boats running up and down the coast we popped into the pub at Craster for a crab sandwich, and across the road to the smokehouse to pick up some kippers for breakfast. And some to bring home and stuff in the freezer to be taken out with a triumphant flourish on a rainy day and eaten with baked potatoes and beer.

The bookshop! I have to tell you about the bookshop!

Barter Books is an enormous second-hand bookshop housed in what used to be Alnwick train station (before Mr. Beeching axed all the smaller branch lines in the country and cut off hundreds of thriving communities from the rail network in the name of efficiency). It's bigger than most large libraries, and infinitely more fascinating. They specialise in rare and antique books, with an incredibly diverse collection spanning centuries and continents. I found a wonderful tri-lingual dictionary of engineering terminology from the early twentieth century, and a second-edition Winnie-the-Pooh, an original Mein Kampf, dusty old tomes by Mrs. Beeton, an encyclopedia of Latin phrases used in the Scottish legal system, a guide to creating the perfect rubber plantation... so many treasures, so little time. And the jewel in the crown, which will probably have me sneaking back there with a wodge of banknotes and a heavy-duty airtight watertight container any day now: the first edition of Max Born's treatise on Einstein's Theory of Relativity! I must confess, I nearly rushed and bought it on the spur of the moment. But on reflection, I think it deserves better than to sit in a plastic bag in a box in our attic for the rest of eternity.

I suspect that they also have a contraption in there which sucks time out of the universe and blows it back out as warm air, but I couldn't quite figure out how they did it.

Our holiday almost at an end, we found that we hadn't had time to visit even half the places on our list. The incredibly warm weather was still with us, so we decided to spend our final day at Howick Hall. This, in fact, is the historical residence of Earl Grey, the nobleman for whom the original Earl Grey tea was created. The walk there took us past a beautiful piece of landscape called Hips Heugh, which I am grateful not to have to try to pronounce. I took several photographs with the intention of stitching together a panorama of this, but I didn't have time to do the requisite post-processing yet. So here is a straightforward snap:

Howick Hall has some of the most impressive gardens I've ever seen, plus a huge arboretum which is still being landscaped. One of the most original things they've done is to sow wildflowers in many of the lawn areas. The effect is quite dramatic!

Not far from the main house was a pond, planted around with some fascinating species, and attracting dozens of butterflies (as well as some less desirable insects).

Amongst the many trees we passed, this acer stood out quite boldly. Standing under its branches, you felt like summer would never leave. And there were blossoms of all shapes and colours everywhere we turned:

And closer to the ground, the flowers were even more vivid (and various). Their gardeners have planned the site expertly; every twist and turn of the path brings something new to see. Even the humble primroses looked exotic, nesting in the shade of the trees and surrounded by so many other vibrant plants.

With all these green and growing attractions, it's understandable that they might be worried about getting an unwanted visitor or two.

I'm just very slightly concerned that the rabbits and hares might not be able to read the sign.

We couldn't help but pay a visit to the tea rooms for lunch. And very impressive they were too. Simple food, but fresh and well-prepared and tasty – with serious portions. The scones were easily big enough for two to share, and came with proper whipped cream (and jam and butter). The tea, as you'd hope given where we were, came in pretty pots, was made with proper loose tea-leaves and tasted quite excellent. I resisted the bakewell tart mostly through being too full to move by the end of the preceding meal.

The rest of the afternoon was spent pootling around the arboretum while I tried frantically to take photographs of moving butterflies. This, incidentally, doesn't really work. But I did get another lovely shot of the wild poppies and tulips, when we were stopped examining the map under the shade of a tree, which I think is my favourite photograph from the whole trip. (That's why I saved it until last.)

On the morning of our departure, the owner of the house we were staying in gave us a friendly telephone call to ask whether everything has been all right. "Yes," I told her, "although the clock in the living room has stopped. It doesn't have a battery in it". I'm not sure that's quite what she meant. She was probably even more confused when she turned up to show her next guests in and discovered that the clock is in fact working perfectly and telling the correct time. (I left one of my spare rechargable batteries in it by mistake.)

What? You didn't seriously expect me to sit in a room with a stopped clock for a week, did you?



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The GoogleFunction 

How popular are integers?

I didn't know, so I wrote a short perl script to find out. I present... the GoogleFunction.

GoogleFunction(n) is defined as the number of results reported by http://www.google.com/search?q=n. Here is what it looks like for integers n between 0 and 100:


And here it is again with the range extended upwards to 1000:


I could go on, I guess, but you get the general idea.

It looks... almost exactly how I would have expected it to look, except that there's a definite and completely counter-intuitive trough at 13 which I can't explain. Spooky, huh?

(Oh, and the first person to suggest I have too much time on my hands gets a slapping.)



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In Other Words (Part 5) 

(This is Part 5. You should read Part 1, Part 2, Part 3 and Part 4 first. Also, a printable version of the whole story, in PDF format, can be downloaded here.)

Doors are seriously underrated.

     Given time, we could probably learn to get by without the wheel, or electricity, or ink. There are cultures without clothes, cultures without fire, cultures without money. But take away its doors, and a society will fall apart in an instant. We are bound together by the very barriers that keep us apart.

     The literary world (in cultures that still have writing, of course) wouldn’t get far without them either. A door, see, can be a metaphor for just about anything. Birth, life, death, destiny, challenge, change, constancy, control, anything. Nor are they simply there to open and close. They can swing, slide, rotate, creek, squeak, bang, click — or be bolted, barred, boarded up, broken, barricaded, slammed, jammed, knocked on, left ajar, lent against. If you’re writing a horror story, imagine what you can say using only an open door: or, if you’re writing a romance, a closed one. Surrealists can leave one standing disembodied in the middle of a forest. Magical realists can lure their protagonists into undiscovered realms merely by planting an unexpected door in their path — only to whisk it away again as soon as they turn their backs and leave them trapped there forever. Fleeing criminals can hide behind the left-hand door and leave the right-hand door ajar. (A good private detective, on the other hand, checks behind both doors.) Saloon doors in Westerns come in two halves, or even four quarters, for reasons best known to the pioneers and probably having something to do with horses. Or set your story on a spaceship or a submarine, and you have at your disposal the airlock: the apotheosis of doors, the door to end all doors, mankind’s last line of defence against the cruel, inhospitable darkness of the Outside.

     So remember: if your plot’s going to hinge on something — why not make it a door?

     The cheesy voice and cheap car-salesman tie of the director of the Fictional Door Marketing Board are the only part of Stan’s dream that he actually remembers when he awakes to find himself on this sofa with one arm hanging down to the floor and a spaniel on his back.

     Now this highfalutin artsy handwavy glossy-brochure propaganda is all well and good, but what happens if one of your characters opens a door and you don’t know what’s behind it? Does the FDMB have a special hotline number you can call? More likely, this is the point where you discover that they deal only in generalities, not specifics, and cannot advise on individual cases, so you’re on your own. But, you know, good luck.

     Stan’s still curious about what could possibly have been in the spare room. I mean, we’re all grown-ups here. If she’d just told him, or let him see, then it wouldn’t have been a big deal. But instead, she has planted a seed of intrigue in his mind. And a seed is an even more potent metaphor than a door. Or something. He’s not sure; there is still a spaniel on his back, and it’s gently padding the base of his spine in time to Debussy.

     Someone is brewing coffee in the kitchen. Carrie knocks and asks how he takes it. “White,” he says, “with half a teaspoon of sugar, and I have a spaniel on my back.” This is, she reassures him, to be expected.

     His mind is elsewhere as he spreads butter haphazardly on his toast between swigs of coffee. The seed, thus fed and watered, is sprouting fast and growing in a direction he would never have expected.

     “Are you all right?” she asks. “You look a bit... did you sleep OK?”

     “Fine,” he says. “I just had an idea. I always get like this when I have an idea.”

     Most of Stan’s ideas are short-lived affairs. But this idea stays with him all through a morning of light conversation about anything but doors, and through an enjoyable lunch at a nearby café followed by a friendly but awkward good-bye, and through an afternoon of train journeys and hanging around at railway stations with an empty notebook in one hand and a silver fountain pen in the other. By the end of the day, Stan has realised that this idea is not going to go away. He has a story to write.

     And, better yet, he has a deadline.

     In the event, it takes him every evening in the whole month of April to put his thought into words. Once or twice he comes close to giving up; some days he just sits and stares at the words on the screen, infuriated and enraged by his own complete inability to say what he means; but, slowly, he pieces his narrative together, and seemingly out of thin air, he brings Miranda Wright to life.

     Miranda Wright is an author. A successful one, at that. She lives in Birmingham, Alabama. She writes crime fiction, and she does it very well — so well, in fact, that even high-brow critics from the New York Times who would dearly love to tear her books to shreds are forced to concede that they are complex and compelling and ingenious and never cease to bring fresh ideas to a genre so desperately in need of them. (Believe it or not, he got half-way through writing this before he realised he’d given her a joke name.)

     He also brings to life Simon Black, a crime fiction devotee with a perfectly innocent name, and who would absolutely be an author if someone would just publish his novel. Until then, he’s an ordinary writer, hanging out in online forums looking for ideas and advice and opportunities to pick holes in the work of the better-selling. That’s where he meets Miranda. He doesn’t know that’s who she is at first, because she posts using the handle Guilty503, but after he submits a couple of shorts to one site for review she sends him a personal message complimenting him on his originality, and introducing herself. Naturally, Simon is flattered. When Miranda suggests that they should collaborate on something, he is positively blown away. When she invites him to get together for a meal sometime, he jumps straight on a plane.

     I’m summarising ruthlessly, here.

     Anyway, they meet up in a nice restaurant and hit it off straight away: they like the same wine, they dislike the same shellfish; he notices her shoes, she notices his cufflinks; he has an idea for a novel about a crime writer turned detective who’s investigating the murder of a detective turned crime writer; she says this sounds much better than the silly idea she’s been working on. Then they take a cab back to her house, a great big house out near Lake Purdy with a grand piano in the front room, well one of the front rooms, where he meets her cats, and they sit together on the sofa chatting and drinking beer and gradually getting closer and closer together and everything is looking very promising indeed except for the door. There’s a door, off the hall between the living room and the kitchen, and there’s a clicking sound coming from behind it. Simon wants to know what it is. Miranda laughs and says she has no idea, and will he just come back and drink his beer, but he’s persistent, and next time she goes to the bathroom he tries to sneak a peek inside, but discovers that it’s locked, and then when he turns around she’s behind him holding a rolling pin, and the next thing he knows he’s waking up on the other side of this door, in a cavernous room full of fluorescent light and desks, each with a laptop and a chair, and in the chairs are sitting a dozen young men: all unshaven, bound in leg-irons, with wild, caffeinated eyes, and all typing away at the laptops like their lives depend on it. And on the desk in front of him is a cup of coffee and a laptop, the word processor’s cursor blinking in the top left corner like a heartbeat, and a slightly crumpled Post-It note on the keyboard bearing the message You Know What To Do.

     (Of course, I missed out all the in-jokes and parenthetical remarks and authorial commentary and everything else that Stan put in to turn an otherwise unremarkable piece of fiction into a fitting birthday present for the woman he admires.)

     (At least, he thinks it will be fitting. He also thinks it’s the thought that counts.)

     The third of May is upon him before he’s even decided on a title. Stories need titles, or we don’t know what they’re about, said his primary-school English teacher. Well, he doesn’t know what this one is about, so he just puts a big enigmatic semicolon at the top of the first page instead. The Establishment hates that kind of thing. But he can’t just send Carrie some shapeless untitled document for her birthday: it needs some sort of message to go along with it, and coming up with the words for this proves almost as hard as writing the story in the first place. So after three abortive attempts, he deletes everything and puts, simply:

     You made me write this.

     And just as he has made up his mind to send it, to be done with it, to dispatch it into the ether, he notices a new message in his inbox. It’s from her, from Carrie. And it’s very short. It says, simply:

     Happy Birthday, Stan! Here, look — I wrote you a story.

     Excitedly he opens the attachment and starts to read, almost incredulously at first, and after the first couple of pages he’s hit by a vicious wave of adrenaline as if he just walked into a door.

     (How many doors must a man walk into, before you can call him a man?)

     It’s the same story. She wrote the same story.

     And it’s completely different.

     He reads on, his own deficient offering all but forgotten, as her flowing words pull him into the world of Jacob Schumann, an artist, a painter, resident of Primrose Hill; not successful, but neither without talent; unattached, but not without charm. Jacob divides his time between studio and gallery, yet while his skill lies in sketching and painting it is sculpture that he seeks out to study wherever he can. And lately he’s been visiting exhibitions all over the country in pursuit of Descabella, a pseudonymous sculptress whose work has enraptured and bewitched Jacob since he first set eyes on it. One day, he promises himself, he will possess one of her pieces for his own, but until then he will be forever wandering down to the Frith Street Gallery to admire the subtle, sinuous lines of Descabella’s Canción del loro, and exchange meaningful glances with the dark-haired young lady he sometimes meets there, who one day breaks the silence and asks him why his hands are so many different colours, which of course he explains, and much to her delight, for while she herself is a sculptress it is most of all in the works of painters that she loves to immerse herself.

     Maria Izquierda is her name, or one of them.

     And they carry on talking, first over coffee, then over dinner, and then before long they are meandering through the streets together in the falling dusk, back towards her Edwardian house on the edge of the Heath where you can really see the stars from the garden and the corner window of the study looks out over the drowsing city and the trees are full of chattering sparrows, and only as they walk up the drive together and he descries dark, twisting figures of stone and shadow on the twilit front lawn does he realise who she really is. Then, inside, too enchanted to be awestruck, he gladly accepts a glass of wine and they sit watching the daylight retreat and the city sparkle below them, and talk solemnly about past times neither of them knew and futures they may never see, and as they speak he feels as if the world around him is become a picture that is painting itself, the brush strokes falling delicately one after another, and everything has dropped into place and revealed its true meaning except for the door. There’s a door, in between two bookcases in the study, and there is music coming from it. Jacob wants to know what is behind it, and Descabella laughs. “I will show you, if you will do as I ask,” she says. “I will,” he says. So she takes from a drawer a fine scarf of silk, and with it she blinds his eyes, and then taking his hand in hers she opens the door and together they step through it, and the music grows like the wind at dawn, and he feels joy like a fine mist on his face, and a scent of lavender overwhelms him.

     Then she reaches up to his face to loosen the blindfold, and he opens his eyes, and the door closes softly behind them.



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In Other Words (Part 4) 

(This is Part 4. You should read Part 1, Part 2 and Part 3 first.)

The train is just sat there at Earl’s Court, and no-one has the faintest idea why. Everyone who wanted to get off has done so. Every so often someone comes dashing up the stairs from the underpass and races towards the open doors, throws themselves into the carriage and sits down panting for breath, then looks briefly annoyed, and slightly embarrassed, as the doors fail to close behind them. Every so often someone gets up from their seat to poke their head out and look up and down the platform for signs of life. Every so often the train makes a sort of hissing sound.

     “You could write a novel about this,” says Stan. “The Train to Nowhere.

     Carrie smiles. “Yeah, The Train that Never Left. Or how about The Slow Train to Ealing?”

     “Or maybe the train does leave, but the entire novel takes place in the ten minutes when it’s stuck in the station for no reason.”

     “It would either be a complete load of cobblers, or it would win the Booker Prize.”

     “Or both.”

     “The Stopping Train. That could work”

     “They Should Have Taken a Taxi.

     “We still can, if you promise to win the Booker Prize so we can afford it.”

     “What is the Booker Prize, exactly?”

     Carrie looks at him as if he just admitted he never actually learned how to tie his own shoelaces.

     “It’s the biggest literary prize you can win, apart from the Nobel Prize, of course: look, surely—”

     “Yeah, I’ve heard of it,” says Stan. “I mean, what do you get? Is it some sort of trophy, or do you get a big brown envelope full of cash, or what?”

     A palpable wave of relief washes over Carrie’s face. “Oh, I see what you mean. Erm... now that you come to mention it, I honestly have no idea. I think the point is that people win it, rather than they actually get anything for winning it. I expect they give you a great big cheque — and nothing else — assuming you’ll probably just frame it and put it on your wall. And then you’re famous.”

     The train doors close. Three seconds later they open again. The train hisses like a recalcitrant cat.

     “You’re sure this is no trouble? I mean, apart from the obvious.”

     “Of course I’m sure. Like I said, we have a spare room. At least, I think it’s a spare room. I don’t think anyone’s actually been in there for about nine months. Maybe Grandad’s been secretly converting it into an aviary or something. But we can’t let you stay in some nasty hotel in King’s Cross for the night, when there’s a perfectly good bed for you in my house. I mean, our house.”

     “It’s very kind of you, anyway.”

     “Not at all. Anyway, I wanted to say I thought your thing about the insurance guy was really good. I can’t do character portraits. I just get skittish and make them all move around and do things and have conversations. But with yours... well, I really felt like I knew the guy, at the end of it, you know?”

     “Thanks. I could say the same thing about yours.”

     “Really? The Usha one?”

     “Yes, that one. It was captivating. I really, you know, connected with it. And that doesn’t often happen with me.”

     “Well, thanks. It’s not my usual sort of subject matter, so I wasn’t quite sure where I was going with it.”

     “Then go there. And you’ll find out.”

     The carriage jerks forward a few inches and stops, sending Carrie’s head sideways into Stan’s shoulder. Then the lights go off, and come back on, and the doors beep and shut, and the train starts to clank forwards out of the harsh light of the station into the brown darkness ahead. A speaker in the ceiling pops loudly, and the driver’s voice comes crackling wearily through it.

     “Ladies and gentlemen,” he announces, “this is the Slow Train to Ealing.”

     Stan and Carrie take one look at each other, and burst out laughing.

     “You don’t think...”

     “No,” she says, “this is the District Line, not Nineteen Eighty-Four! Spooky, though. Coincidence.”

     “Maybe not so unlikely. He’s probably done that joke a hundred times.”

     “I suppose. But still, don’t you think coincidences happen more often than they should?”

     Stan scratches his ear. “At the risk of sounding like a nerd, there are good mathematical reasons for that. You ever hear of the Birthday Paradox?”

     “Erm... not sure. Was that Iain Banks?”

     “It’s not a novel, it’s a... thing. It demonstrates how often we perceive stuff to be much more unlikely than it actually is. Shall I carry on being geeky?”

     “Ooo, yes please.” Stan can’t quite tell whether the enthusiasm is genuine. He never can.

     “All right, you asked for it. So there were, what, ten of us in the bar this evening?”

     Carrie nods. “Yup.”

     “OK. What do you think are the chances that two of us had the same birthday?”

     “Pretty slim, I’d say.”

     “One in five?”

     “No, much less than that. Like fifty-to-one, at least.”

     “Well, I’m telling you, it’s one in five.”

     “No way.”

     “Yes way. And now you know that, how many people do you reckon we’d need to make it fifty-fifty?”

     “I don’t know,” Carrie shrugs. “Sixty? A hundred?”

     “Twenty-three. Straight up,” he adds, seeing the reaction of her eyebrows. Turns out, this useless fact has the same effect on almost everyone.

     “As it happens, I know that we all have different birthdays. Although Pam’s and Eleanor’s are only one day apart. So it looks like we’re in the four out of five.”

     “When’s yours, by the way?”

     “May the third.”

     “You have got to be kidding me.”

     “No. You’re not going to tell me that we were born on the same day.”

     “I don’t have to tell you. You already guessed.”

     “I don’t believe you.”

     “Aw, c’mon Carrie, no-one lies about their birthday! It’s way too easy to get found out. I was born on the third of May 1981. I have the documents to prove it, and everything.”

     “God, he was born in the eighties,” exclaims Carrie under her breath, staring into space.

     “Don’t worry, I won’t ask you for the year. I know I’m kind of socially inept in many ways, but...”

     “’77,” she says without thinking. “But I still can’t get over this.”

     “A lot of people say I look older than I am.”

     “No, not that, silly! The birthday thing. I mean, what are the chances?”

     “I told you, one in five.”

     “But you said that was when there were ten of us. Now there are only two — me and you. That has to be really unlikely.”

     “Well, one in three hundred and sixty-five then. Give or take.”

     “I don’t think you can reduce weirdness to a number.”

     “Sixty-seven point three percent of the time, you can’t.”

     At each stop the carriage is getting steadily emptier. Expectantly the doors spring open, and dejectedly they close again on thin air. The train rolls on, and Stan and Carrie sit there side by side, rocking to and fro with the rhythm of the rails beneath them, watched only by their own warped perspex reflections.

     “This sort of thing never happens in books,” Carrie muses.

     “I think writers are scared of it.”

     “Coincidence?”

     “Yeah. The last thing you want is your reader putting down the book in disgust and thinking well, that was all very convenient. So you get all these stories which start off with an intriguing coincidence of events, promptly followed by thirty chapters of explaining why it wasn’t a coincidence at all. Or the author goes to a whole lot of trouble charting the actions of each character in great detail, so that when the coincidence finally does make its grand entrance, everything looks perfectly logical. Everyone has an alibi. Nothing is left up to chance. There is no higher power.”

     “Sometimes there’s a higher power. More often than not, I’d say. But convenience is a whole other story. I mean, whenever I’m writing I try to make everything as inconvenient as possible for my characters. Hell, half the time they can’t even get up a flight of stairs without trauma. Because really, who wants to read a book about someone who just had a perfectly normal day? Where’s the fun in that?”

     “Maybe you could sell it to one-eyed cross-dressing undercover crime-fighting Formula-1 drivers who fancy a bit of escapism.”

     “Ah, so you read JR’s latest, then.”

     “Is this our stop?”

     It’s not far from the station to Carrie’s place, if you know where you’re going. At each corner they seem to choose the road with the less expensive cars parked on it, until finally they draw alongside Carrie’s grandad’s Ford Escort with the wing mirror held on by gaffer tape, and climb the steps to the porch. The hall is lit, but the rest of the house is dark. The place smells of paint thinners and burned toast.

     “Don’t ask,” says Carrie. He doesn’t.

     They sit in the kitchen for about half an hour, snacking on crackers and cheese and drinking pineapple juice and chatting about their favourite authors. She has hardly heard of any of his, nor he hers, which Stan finds immensely puzzling. Surely there must be something fundamental they have in common when it comes to writing? But the more they talk, the more he realises what different worlds they inhabit. Except, that is, for the obvious observation that here they are sitting in the same room, discussing books and films and swapping little details about each other’s lives, and making eye contact that seems far too hesitant and meaningful to be dismissed out of hand.

     It’s gone midnight before they climb the stairs. Carrie helpfully points out the difference between the bathroom and the airing cupboard in passing as they shuffle along the hallway in the dark.

     “And Grandad’s in there, and I’m in there,” she whispers, pushing open the door to the spare room and flicking on the light. “And... oh!”

(You can read Part 5 here.)



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