• The Perfect Day: O + NS + Cpm/T +He, except when it’s [W+(D-d)]xTQ MxNA
  As in the Telegraph, this was repeated year on year on year on year.
• The Perfect Christmas: PX = (8F * 4P +£23 * 8F + 3G + 2W + 2W:3C + 5T:1NR / 3D) / 3D
  As covered previously. Presumably even following this formula Christmas is still worse than June 20th.
• The Perfect Bacon Butty: N = C + (fb (cm) . fb (tc)) + fb (Ts) + fc . ta
  Apparently, “the experts at Leeds University tried 700 variations on the traditional bacon butty.” I did my undergraduate degree at Leeds and I can vouch that this is true, although I had no idea it was research. Dr Graham Clayton is to blame for this.

Out of interest, N = force in Newtons required to break the cooked bacon. C = Newtons required to break uncooked bacon, fb = function of the bacon type, cm = cooking method, tc = cooking time, Ts = serving temperature, fc = function of the condiment/filling effect and ta = time or duration of application of condiment/filling.

• The Perfect Present Wrap: {(d+2h+w)2 2(w+h)2 — whatever that means
  Thanks to Dr Sara Santos at the University of Manchester, “we now know why we put everything in boxes”.
• The Perfect Sitcom: formula not properly explained
  As in the Telegraph. Repeated, presumably on Dave.
• Staying Awake At Work: CDA + CT + KF TMT
  Bear in mind that KF stands for “knacker factors”, so this is Maths. This comes from “experts at fatigue management consultancy Awake”.
• The Perfect Cheese Sandwich: W = (1 + bd/6.5 - s + (m-2c)/2 + (v+p)/7t) * (100+l)/100
  “Geoff Nute and his team” of “sensory analysts at Bristol University” produced this equation, which says that without a tangy sauce, you need infinite cheese. This was in the optimistically named “science and tech” section.
• The Perfect Penalty: (((X + Y + S) / 2) x ((T + I + 2B) / 4)) + (V/2) -1
  As in the Telegraph.
• The Perfect Breasts: the nipple should be 45% of the way down. Apparently.
  “Patrick Mallucci spent many hours poring over photos of topless models in lads magazines and tabloid newspapers to formulate his theory.” Enough said.
• The Perfect Teeth: no formula
  This isn’t strictly a formula. It’s really a set of rules about what makes a nice smile, of use to cosmetic dentists. I’ve seen at least one of them discussed in the British Dental Journal, but that was to debunk it. Hard to say what the truth is. Better at least than “the perfect cheese sandwich”, but still…
• How To Beat The Post-Holiday Blues: ((j+c) x (r+t) - (h+o))/b
  Professor David Holmes of Manchester Metropolitan University “carried out the research on behalf of Churchill Travel Insurance”, who will presumably use it as a basis for premiums on Post-Holiday Blues Insurance. As ever, all the variables are listed on wholly arbitrary 1-5 kind of scales. According to the Mail, b represents “whether gaps between holidays too long”. Yeah. Gaps too long. Also, verbs for losers.
• Will You Get Seasonal Affective Disorder?: X a x ((24-b) x (c+d+e) + f x (g+h+i))
  Here, we learn why you should always use the multiplication sign instead of the lower case ‘x’. Also why you should remember to include the equals sign. This was devised by “consultant psychiatrist Dr David Wheatley” and “commissioned by Kira St John’s Wort, makers of a herbal “happiness” supplement, as part of a study on depression”. It has to be said, the list of instructions is sufficiently varied and complex to give the whole thing an air of credibility. But still…
• How Beer Goggles Work: no formula supplied
  “Bausch & Lomb PureVision, one of the world’s biggest eyecare firms” got “Professor Nathan Efron, Professor of Clinical Optometry at the University of Manchester” to do this. I don’t know why it’s so often universities I’m at where this stuff happens; before I started at Leeds, Dr Clarke, who took our electronics lectures, was asked by some supermarket or other to work out an equation for how to flip a pancake, and I guess they were expecting him to wander off and make something up, but no, he built a huge red trebuchet-looking thing to flip a strange cardboard pancake. I was there for four years, and some of my friends worked on this for a brief period. Partway through my course he retired, an act which made him much easier to locate — his workload went from insane to average. To my knowledge, the only thing this project has ever achieved is to break countless platinum-iridium tips for the tunnelling microscope. I suppose that means that they at least have more credibility than the “oh, it’ll be b times a plus 4d over qpr” crowd, but still…
• When Heyfever Is Worst: 6.02pm on May 29; no formula supplied
  Stay indoors at that time, is my advice. “Dr Adrian Morris, allergy specialist for Boots Health Club, … created the hayfever formula”.
• The Perfect Horror Film: (es+u+cs+t)² +s+ (tl+f)/2 + (a+dr+fs)/n + sin x - 1
  Who says modern films are too formulaic? This is science! Look! It has a fucking sine function in it:

  The experts have taken blood and guts (Sin x) and subtracted it by the stereotypes (1), to make Sin x - 1, saying Jack Nicholson’s character in The Shining turned into the total opposite of a protective father figure.

  See? That’s Science! Don’t say it isn’t! “Mathematician Anna Sigler, … a former graduate from King’s College, London” did this research. A former graduate, no less. Presumably her degree was revoked when they saw what she was doing with it. The Shining won, by the way. “The research was carried out for Sky Movies, which will be showing The Shining and other scary movies this weekend.” Coincidence.

• How To Wash Your Hair: formula not stated
  “Kerys Mullen, technical manager at Dove, said: “A lot of people ask us about the best way to wash their hair so we decided to work out the ideal formula.”"
• The Perfect Boiled Egg: formula not stated
  How to boil an egg, by several chefs. At the bottom, input from “Dr Charles Williams A physicist from Exeter University [sic]“, who “has worked out a formula for the perfect boiled egg based on the ‘heat-diffusion equation for spherical objects’”. Fair enough, but I for one will trust the chefs on that one.
• The Perfect Day To Change Your Life: M x O + Bh (H+R) x S; max. May 18
  This is the handiwork of Cliff Arnall, the same Cardiff University muppet responsible for the best/worst day formula the Mail and the Telegraph obligingly publish twice every year. If anything this is worse than that one: “Under the formula M stands for motivation and O for opportunity while Bh is bank holiday proximity. The H in the second half equals increasing hours of daylight, while R equals reflection time and S, simply success.” Yes. And..? Surely the aim is to maximise S? In which case, shouldn’t it be on the other side of the equals?
• The Secret of True Happiness, no less: P + (5xE) + (3xH)
  Thomson travel got “psychologist” Carol Rothwell and “sports scientist and ‘life coach’” Pete Cohen to “insist their equation is a useful guide to our levels of satisfaction with life”. Because just asking “are you happy” doesn’t work. Not enough maths, see.

• The Perfect Sitcom: quality = (rd+v)f÷a+s
  Dr Helen Pilcher, a neuroscientist (according to the Telegraph) whored her name to this ‘research’ which was commissioned by UKTV Gold to promote their endless repeating of that clip of Del Boy falling through the bar: f in the equation means “the amount someone falls over”. This is about the level of humour the Telegraph seems to like, because…
• The Perfect Joke: x = (fl + n^o)/p
  In this case, n represents “the amount someone falls over”, and is raised to the power of “the “Ouch” factor”. It won’t surprise you to learn that this is the work of the same Helen Pilcher, although this time helped by comedian Timandra Harkness. It should be some measure of Harkness’ fame that I wouldn’t like to guess what gender the name Timandra indicates. To their very limited credit, the telegraph article does include rants from Jimmy Carr, Bernard Manning and Ruby Wax explaining that the formula was stupid (in their own obnoxious ways). Also Nicholas Parsons, but he’s not obnoxious. Why was this in the news? “The Comedy Research Project, a live stage show featuring Helen Pilcher and Timandra Harkness, will be performed at the Science Museum’s Dana Centre on June 15 and 22 [2006].” I bet that was a fucking blast.
• The Perfect Day: quality = O + NS + Cpm÷T + He
  This was pulled out of the arse of Cliff Arnall (not Lou Reed), a psychologist and former tutor at Cardiff University, because Wall’s Ice Cream asked nicely. The Telegraph notes it “does not take into account the gloomy forecasts for the British economy, fears caused by falling house prices, rising inflation and stagnating pay rises, England not playing in the Euro 2008 and a damper than normal start to the summer”. All the factors in the formula are utterly subjective and the whole thing is worse than most. The comments on the Telegraph pages are fun. This is especially perverse because in 2006 the perfect day was three full days later. (The Telegraph really do obligingly report this, from either end, every time they’re asked.)
• The Perfect Bra: formula not supplied
  This one is actually real (albeit slightly over the top) research! It could genuinely improve your life (moreso if you are a woman). I know; I was as surprised as you are.
• The Perfect Rugby Kick: KP = CSP - s + w + r + yⁿ + cr + sc + mt + xⁿ + ctw
  This is just a shopping list of things that affect a rugby kick. And “y to the power of n represents other factors”. My word. This drivel comes to us no thanks to “Andrew Cushing and Prof Paul Robinson at University College Worcester for the research company QinetiQ”.
• The Price Of Cleaning: price = time × £6.16/hour
  This is a note that the average wage has increased, listed in terms of how much people lose out on by not being paid to brush their teeth (30p, although it doesn’t say how much they save by not having to get private dental treatment if they don’t brush). Barclaycard convinced Prof Ian Walker, an economist at Warwick University to endorse it.
• The Perfect Marriage: formula not supplied
  “Prof James Murray of the University of Washington” says this formula has a 94% success rate in predicting if a couple will divorce, although really I’d want to know sensitivity and specificity, otherwise you could conduct a survey of evangelical Christians and the terminally ill, say they’ll all stay together, and declare yourself the winner. They later ran a second article about how it was nonsense.
• The Perfect Chip: formula not ready at time of press
  That’s right, because Dr Gama Khan won’t just sign off on whatever nonsense Tesco ask — that, or Tesco asked for a big long experimental phase they can publicise for months. Khan says “The competition is intense because everyone wants to go down in history and finally crack the secret of the perfect frozen oven chip. I am looking at a lot of chips. Some days I’m testing them continuously from 9.30am to 4pm. It actually can get quite sickening, particularly when I always smell of chip fat.” And it’s true. Everyone wants a slice of the elusive Nobel Prize in Fast Food.
• The Perfect Football Penalty: odds of scoring = (X + Y + S)×(T + I + 2B)÷8 + V÷2 - 1 [simplified]
  This was commissioned by Ladbrokes, and is credited to “by scientists at John Moores University in Liverpool”, which quickly becomes “Dr David Lewis, a mathematician”. I think this quote tells you all you need to know about the mathematical ability of everyone involved in this report (emphasis mine):

Dr Lewis and his team found the six variables that influence a successful penalty kick are: V = velocity of ball once struck, T = time between placing ball on spot and striking the ball, S = number of steps in run-up to strike, I = time that the ball is struck after goalkeeper initiates his dive, Y = vertical placement of ball from ground, X = horizontal placement of ball from centre and B = striking position of boot.

• The Perfect Sandcastle: 0.125S = OW
  This simply states the ideal ratio of sand to water. Personally, I would just use the pre-prepared wet sand b the beach, which must surely be about right because it does seem to work. “Prof Matthew Bennett, the head of environmental and geographic sciences, Dr Brian Astin, the head of the School of Conservation Sciences, and Rob Haslam, laboratory and technical services manager, then spent two days testing the samples for their suitability for sandcastle building. … Teletext Holidays, which commissioned the research, will be holding a sandcastle-building championship on July 24 [2004] in Great Yarmouth.” This work was replicated the following year by “an MIT team, led by Sarah Nowak and Arshad Kudrolli” who reached exactly the same conclusion (although they phrased it in a simpler way). This might be nearly useful to some engineers somewhere.
• How To Open Champagne: P = T÷4.5 + 1
  P and T are pressure and temperature. I think this is not made up, although not really that useful in real terms: essentially it says that if you cool the champagne it is less likely to explode on you. This comes from “Dr Steve Smith, a lecturer in wine studies at Coventry University”, who “was commissioned to develop the formula after a Marks & Spencer survey found that 50 per cent of women are too frightened to open a bottle of bubbly because they fear that the cork will fly out prematurely, hitting them or a precious ornament”.
• The Perfect Place To Shop: D=f(m,b,c)
  The function f is undefined. “Retail and consumer trends expert Tim Dennison has come up with a formula to help Yellow Pages calculate how diverse and lively high streets are.” It says little town streets are more diverse than city centre ones. Nobody is surprised.
• The Perfect Newspaper: no formula
  It’s the Telegraph. Shocking. I suspect this is bad self-congratulatory reporting of some tiny little statement the academics made, but then I work for Manchester University so I am biased (although I’m not certain which way).
• How To Pour Gravy: amount of gravy = (W - D÷S) ÷ D × 100
  According to “Dr Len Fisher, an independent food scientist at Bristol University… who was funded by the manufacturer Bisto”, this is important because “more than 150,000 gallons of gravy is left every week.” Hard to see what Bisto have to gain by this, except of course that they’re in a newspaper.
• The Perfect Book: formula not done at time of press
  …although it’s going to be Agatha Christie, says Dr Roland Kapferer.
• The Perfect Biscuit: formula deemed to complicated for Telegraph readers
  This was led by Professor Bronek Wedzicha of Leeds University and “half funded by the Department for the Environment, Food and Rural Affairs and half by United Biscuits.” The researchers insist that this is real research rather than a publicity stunt, and I see no reason not to believe that, especially since they spent £91,000 on it.
• The Perfect News Story: “never trust your own instincts” but rely on “tried and tested formulas, bland ingredients and using up old scraps and leftovers from the day before, particularly the choicest cuts from the Daily Mail - no matter how stale.”

Some time I might do this for other newspapers, although I’m not sure I could read the ones in the Daily Mail faster than their hacks can produce them, so perhaps I won’t.

Something must be done.

/// <summary>
/// Aligns two images. Uses highly-local, non-affine alignment.
/// Also compensates for local brightness and colour changes.
/// </summary>
/// <param name=”Input”>The image to align</param>
/// <param name=”Reference”>The image to align it to</param>
/// <returns>The image aligned to the reference image</return>
public Image Align(Image Input, Image Reference)
{
    return Reference;
}

• Code Factory Entry Here
• Direct Download Link Here (7.1kB, requires .NET Framework, which you may already have)

Technical notes:

• The settings screen assumes you understand what the Mandelbrot Set is. If you don’t, the point is that for each point on the screen, the colour represents the number of iterations required before the value exceeds a certain cutoff. You don’t need to know what that means, but the cutoff is one of the options. Since some points (those within the Mandelbrot Set) will never get there, so the maximum number of iterations option lets you choose when it should give up. A higher cutoff will produce smoother colours but take longer to process. A higher number of iterations will produce more detail but again take longer to process.
• The colour step controls how fast the colour changes. A low number will give less contrast but a less psychedelic image.
• The minimum spread to zoom, which must be between 0 and 1, controls how interesting something has to be before it will be zoomed in on. Some parts of the image take longer to process than others, so the maximum difficulty to zoom, which again must be between 0 and 1, controls how long a part of the image could take before it will be ignored. If no area of the screen matching these rules can be found, then it will revert to the entire Mandelbrot Set image and start zooming again.
• After a great many zooms, you start to hit the limits of double-precision floating point numbers, so changing the maximum zooms option puts a hard limit on how many times it zooms before going back to the start. I find the 40th zoom is where it starts going wrong, though to be fair by that point you’re looking at an area that would have been 1% the size of a hydrogen atom at the original zoom level.
• There’s no frame rate limiter in this. If you have a ludicrously fast PC at low resolution, it may run too fast. You could try increasing the first two numbers to silly levels. That ought to slow it right down.
• I have no idea what happens to this screensaver on multiple monitors.

Steven Bryant began studying Einstein’s theory of relativity in the mid 90’s with the intent of returning to graduate school to pursue a PhD in physics. During the process, he identified mathematical inconsistencies in each of Einstein’s derivations of the Special Relativity transformation equations. Correcting the problems has led him to produce the model of Complete and Incomplete Coordinate Systems, offering an alternative view of space and time. … Steven has a Bachelor of Science and a Masters degree.

Steven seems unaware that someone with a Bachelor’s degree is a bachelor — that’s why they have a bachelor’s degree. They do not have a bachelor. That would be crazy, but then, there’s a very good chance that Bryant is crazy.

His main thesis is that the derivation of ξ in Einstein’s 1905 relativity paper is wrong. It’s not wrong. I’ve checked it myself, and I also have a Master’s degree (and the knowledge required to correctly apostrophise it) so I must be right. I did it literally on the back of an envelope. It was an envelope from The Cooperative Bank, who will doubtless be pleased at my recycling it so. But wait, Bryant has proof that the derivation I just did was wrong. He invites us to substitute numbers into the various forms of the equation. If they are all equivalent, he reasons, then the answer should be the same every time which, he imagines that he demonstrates, it isn’t:

You can try it. All the answers in the results column are correct for the given values. What he’s done, either cunningly or stupidly, is to use values that don’t correspond to any possible physical universe. The derivation of ξ is done using other equations which state that x′ = x − vt and t = x′v ÷ (c − v), and his values of x, v and t don’t satisfy those equations. It’s like saying “Newton says that F = ma, but given that F = 5, m = 2 and a = David Duchovny, we can plainly see that Newton’s law is flawed.” You can’t make something true using only the word “given”.

So we’ve established that Bryant can’t do maths, punctuation or semantics. He also can’t do physics. As well as the imaginary maths error, he also says that the Michelson-Morley experiment was wrong. The experiment, done in 1887, was designed to measure the absolute speed of the Earth, and the result was that it didn’t have one. Bryant says that this analysis was done wrong, because he’s redefined frequency to include an extra, redundant length term. Then he’s incorrectly added this term into the equations and discovered that now the Earth is going about 30km/s, and therefore relativity is wrong.

He also doesn’t understand that Special Relativity only holds when things aren’t accelerating. He claims that an advantage of his idea is that “the twin paradox goes away”, but it also goes away under General Relativity. His proof appears to involve a lot of talking about cats and birds in cages on trucks. I honestly don’t understand it well enough to find specific errors. It would be like looking for continuity errors in Jabberwocky.

The upshot of all of this is that the universe is broken and E no longer equals mc². It now equals mw², where w is defined as “the speed of the phenomenon in question”. Presumably, therefore, we should put nuclear power stations on trucks and drive them around so they make more power. This also implies that nuclear power should produce a hundred million times less energy than we expect (and observe) it to. You would think that someone would have noticed that.

Bryant has not noticed that.

They all have names like “good science”, “suppressed science” and “remedy reality”, and they all update every few days about homeopathy. This is somewhat pointless, because homeopathy hasn’t changed since it was invented in the nineteenth century, except for the addition of a few extra remedies and the decision to start making their magic water using preposterous machines instead of dilution and succussion (which is fair enough since neither works anyway so you might as well do it the quick way). One of my favourites is Homeopathy4Health. I think it’s always a good sign when a website carries a disclaimer like this:

Disclaimer: I am not the owner of any website named homeopathy4health.

I think you have to question the mental state of someone who would say that at homeopathy4health.wordpress.com, under the name homeopathy4health. Many of the posts do at least allow public comments, although I’m given to understand there’s some censorship there. But some posts have no comments on them. An example is “Medicine: blind and in the dark?”, which is essentially a long attack on evidence based medicine for blinding studies. The anonymous author’s thesis seems to be that looking at more than one subject is bad because it means using “statistics which are incomprehesible to the lay person and which are subject to statistical interpretation bias” instead of just looking at one patient and trusting yourself not to indulge in any confirmation bias. That, and

The foundations of the scientific approach are suspicion and doubt: both are deeply negative mental processes.  I am told that a good scientist should doubt his results as his first reaction; I would say that this is an unhealthy reaction in most normal situations: someone who doubts his reactions has poor intuition. Someone who is doubtful isolates themselves from experience. Suspicion causes peers to doubt each others results and slows progress.

…

Sceptics believe that the scientific method is the answer to medical problems, I am unconvinced.

That sounds like Biblical thinking to me. The whole idea of “negative mental processes” leading to negative outcomes sounds like something Master Splinter would say. But just as I was thinking he was crazy, I saw a link in his blogroll that put that into perspective. The “Freedom of Science” blog is proper crazy. Honestly, I’m not totally convinced it’s not an elaborate joke, although the archive goes back over a year and that’s dedication if it is. It’s inextricably linked with “Alphysics”, which I think is a joke, but is a rather stupid one written by a crank in the style of Facts For Life in an attempt to discredit physics by equating it — I think; it’s not clear — with alchemy.

It’s very telling: there’s always the chance that the author of Homeopathy4health genuinely has had the astonishing good fortune claimed, and that the range of symptoms described on the “about” page genuinely did vanish just after taking homeopathic remedies. I could see something like that being very convincing, and once you’re there it follows logically that anyone who dismisses it is being overly suspicious of it. But no amount of coincidental remissions could justify listening to the cranks at Freedom of Science (which really should be called Freedom From Science). It is a website devoted to “removing Newtonism from the education process”. It says, with no apparent trace of shame,

Physics is Newtonian religion. Physicists are priests who believe in Newton’s laws as their immutable faith. Physicists are the enforcers of Newton’s occult laws in the name of God.

Now I am a physicist and I’d be the first to tell you Newton’s laws are wrong. They’re wrong because they break down when you look at very small objects. They’re wrong because they’re an approximation to the truth; an expectation value. They’re wrong because they don’t account for relativity. But they’re not wrong because

Occult does not exist therefore Cavendish did not measure the Newtonian force. 

“Occult” is the author’s favourite word to describe force:

Occult does not exist outside physics. Occult may be the official faith of physics and every physicist must believe in it as part of their professional faith but occult does not exist in nature.

This is especially vexing, since he says on the same page:

If we look at the Newtonian force closer we see that force is not really occult.

He is of the opinion that what he calls “physics” is actually a religion devoted to pushing Newton’s politics and never questioning his Laws:

In order to understand what force is a scientist must question it. A scientist, unlike physicists, is not bound by Newton’s authority. For a scientist there is nothing sacred about Newton’s arbitrary definitions. To understand force a scientist must take it apart and then put it back together. Since this is forbidden and illegal in physics a scientific investigator must look at the Newtonian force from outside of physics.

It’s brilliant. The lengths some people will go to be wrong has never failed to astound me. I suppose it starts with one unshakable belief in something — homeopathy, Jesus, racism, whatever — or a fundamental and equally unshakable disbelief in something — relativity, vaccination, science, maths, the holocaust, whatever — and from there you quickly hit a contradiction. Clearly either your pet theory is wrong, or else something very sinister and slightly stupid is going on, and clearly the pet theory can’t be wrong, so you end up justifying it in increasingly moronic ways…

[Force] is a placeholder because it cancels. We cannot cancel radius R and Period T from R3 = T2. But if we write it as Newton did as

Force = R/T^2 = 1/R^2 = Force

we can cancel the superfluous terms of force. We can also write

Newton’s soul = R/T^2 = 1/R^2 = Newton’s soul.

Or

Newton’s wig powder = R/T^2 = 1/R^2 = Newton’s wig powder.

So planets may be powered equivalently by Newton’s force, Newton’s soul or Newton’s wig powder. The last two are as good as force.

Well done for proving we can give a quantity a different name, although the idea that if something cancels it must therefore be antique powdered starch is a rather strange one. Freedom of Science thinks that Newton’s Laws are just made up, and that the actual fundamental law at work here is Kepler’s Third Law, which he calls “Kepler’s Rule”. This is, you may remember, much the same idea that Mark McCutcheon utterly failed to defend when I emailed him.

The site is also hooked into a “wiki” (which is not a wiki at all — it uses Wikimedia but it’s not a wiki because, like with Homeopathy4health’s more preposterous claims, I can’t edit or comment on it) with similarly strange ideas:

We know that Newton started from Kepler’s rule and wrote it as

where R is the radius and T is the period of the orbit. Newton then multiplied both sides by a label he invented, mass, then labeled each side by another label he invented, force, and labeled each side Newton’s laws

This guy thinks that mass is made up. Indeed, he thinks this of all quantities which cancel out even if there are other equations from which they do not cancel. Mass cancels in discussion of gravitation because the gravitational force is proportional to mass and therefore acceleration, and therefore speed and position, aren’t affected by it. Force is a slightly redundant concept when discussing gravity, although it’d be hard to discuss electrostatics without it. Presumably, therefore, he would be happy to play my game: he drops a 4g mass on my head from a height of one metre. Then, I drop a 2-tonne mass on his head from the same height. Then, assuming he survives, I give him £50. See how strong his faith in a massless universe is.

Essentially, he’s angry with Newton because he’s replaced k² with GM (when I learned this at school I never for a second imagined I’d hear even one person take umbrage with it, and here’s at least the second) and arbitrarily defined another quantity as “force”. He seems to consider this a pointless (and indeed politically motivated, although what the politic in question might be is unclear) obfuscation of Kepler’s elegant theory, which indeed it is, as long as you never want to discuss anything but planetary motion. The moment you want to discuss apples, Kepler’s Laws, brilliant as they are, just don’t apply. One of Newton’s greatest achievments was thinking in terms of general theories, rather than having one theory for planets and a separate Theory of Apples. Furthermore, introducing the concept of “force” (which we could always simply call “rate of change of momentum” which is a physically manifest quantity — although so is force if you want to talk quantum) means that we can then add three other forces and describe the whole of the universe, or at least what Richard Dawkins calls “Middle World”, in a few short equations. That has to be better than knowing how fast planets go, doesn’t it?

Well, you would think. But apparently there is what I shall generously term “some debate” about it.

Nintendo’s PR company know this too, because they’re Very Clever Scientists. They’re a company called Cake, and they’ve done two pieces of Very Clever Science lately. The first was for Nintendo, and it was a study into how much energy you burn playing Wii. And it turns out, it’s not much. Though they have to be commended for doing a proper, albeit very small, trial and publishing the result anyway.

Cake’s other recent foray into the world of Very Clever Science was for The Children’s Society, a charity whose beliefs are fairly self-evident. They have issued a press release called “Have a mathematically perfect Christmas!”, in which they say (and you’ll have to imagine the phrase “sic” in brackets liberally sprinkled on this quote like some kind of Latin Christmas snow):

The University of Plymouth has Christmas all worked out! Professor & programme director of the School of Applied Psychosocial Studies, Rudi Dallos, has calculated the scientific theory for a perfect Christmas, it is:

PX = 8F x 4P + 23£ x 8F + 3 G +3 W + 2W:3C + 5T:1NR
_____________________________________________
3D

Professor Rudi Dallos devised the formula, which guarantees a perfect Christmas for families across the UK, to compliment the new Christmas book from The Children?s Society…

The perfect Christmas formula (PX) considers the number of family members (F), cost (£) and number of Christmas presents given (P), number of walks taken (W), number of games played (G), the amount of wine and chocolate (W:C) consumed and the ratio of turkey to nut roast (T:NR)!  Divide all that by the total days (D) you spent with your family and you have the perfect Christmas!

There are many, many things wrong with this, so let’s list just as many as we can find! But first, an aside. Obviously I’m in favour of charities in general, and I don’t know much about this one but it sounds like something I’d approve of, but this kind of thing is very bad for the public perception of science and while it annoys me when companies shit all over important things to turn a quick buck, charities should know better. I tend to think they should avoid doing things that will damage society, especially since they’re doing it on the back of donations. So, on with the list…

• This is not a “scientific theory” until he has proved it. That’s what the phrase “scientific theory” means.
• If he did prove it, it would still not be a theory, because it is an equation. That would be a law. The theory would be the underlying mechanics. It is not possible to “calculate” a theory.
• If it was possible to calculate a theory, and this was a theory, it would still not be true that Rudi Dallos had calculated this one. It would be more accurate to say that he had made it up, and more accurate still to say that he’s whored his name out to it.
• There is an equals sign in the numerator of a fraction. I am willing to give Dallos the benefit of the doubt here, as Cake’s typesetting skills are not great (unless their client really does spell their name with a question mark). This is also, I assume, why the lower case letter ‘x’ is used in place of the multiplication sign, and why a row of underlines are used in place of division. And to be fair, their typesetting is just marvellous compared to The Daily Mail’s version of this formula, which not only replicates this error, but duplicates the division so that revellers have to spend nine days with their families every day in order to have the prefect Christmas.
• The symbol “W” is used for two quite separate quantities.
• The pound sign goes before the number, genius.

And then there’s the subtle stuff. Some people have suggested that this equation suggests that one can have an infinitely good Christmas by spending zero days with the family. Personally, I think that’s reading it wrong. The letters are really units rather than variables. I think this is really a definition of a new constant PX, which is in the unusual mathematical units “man (presents + pounds) + games + walks + ml/g + turkeys per portion of nuts) per hour”. (In the Daily Mail’s version, this is per hour squared, making it some kind of bizarre festive acceleration constant, like a kind of Yuletide gravity. Possibly you are expected to buy everyone four more presents every day for nine days, a bit like Hannukah or that Twelve Days Of Christmas song.) That said, it’s still open to the same kind of abuse — if you don’t drink alcohol then you can’t have any chocolate or else the ratio is upset (that, or you have to have some chocolate to prevent undefined divisions), and if you only have one family member then you have to counter this by — I swear this is what it says — spending only 9 hours with them, and in that time playing three eighths of a game, taking three eighths of a walk, eating 166% more chocolate and nut roast than you’d really like.

If you want to spend less than £23 on each of your presents, you can compensate by spending less time with your family so the ratio is the same, however to balance the rest of the proportions, you also have to give proportionally fewer presents, go on fewer walks, and play fewer games. And eat more chocolate and less turkey. It also places no upper limit on how drunk you can get provided you’re willing to balance it with chocolate.

What we have here, you see, is not maths. It’s one of those crappy adverts that says “you plus our product equals profit er I mean happiness”. “The perfect Christmas is 4 presents each for 8 family members, £23 each for 8 family members, 3 walks, 3 games, 5 times as much turkey as nut roast and 3 times as much chocolate as wine, all over 3 days.” It’s nothing more than a description of a perfectly nice Christmas phrased a bit like maths. Then written as a formula.

And it can piss off.

He used a fairly standard distortion that most packages call “twirl” or “whirlpool”. This was not smart. Had he used “blur”, he’d still be loose. Had he used “pixellate”, he’d be on the streets. Those effects destroy image information. But he used “twirl”. The thing about “twirl” is that it’s technically a transform: it doesn’t remove any information from the picture, and that means you can reconstruct the original, with a little patience and preferably a copy of MATLAB. Unfortunately, my laptop with MATLAB installed is currently not working, so I can’t fire it up and show you how to do this, but I can explain it. First, here’s the image he released and the image the police reconstructed from it:

Image source: AFP

The effect is pretty simple, and you’ve probably already figured out how it’s done, but to make it explicit, here it is in mathematical terms. Working in polar coordinates, you shift the image in θ, where the shift (which we should call φ) depends on R. (If you’re not familiar with the notation, R is the distance from the centre of the swirl and θ is the angle that distance is at.) For full nerd points, here’s the equation:

θ_f = θ_i + Sφ(R)

More generally it should be θ_f = θ_i + φ(S, R), but the art package designers probably didn’t set out to make this difficult. They probably didn’t expect it would be used in this way.

I’ve used S as the strength of the effect that you get to choose. The simplest way to undo this effect is to simply apply the same distortion in the other direction: subtract Sφ(R) and you get θ_i back. First we need to know where the centre of the swirl is, but that’s relatively simple. The patterning behind him shows us the edge of the circle, so finding the centre isn’t too hard, and that’s led to people (such as what is at the moment the only commenter on the Times article above) saying that this should have been an easy fire-up-PhotoShop-and-press-twirl fix. Problem is that all paint programmes use a slightly different φ(R). So really you’re just left playing around with something like MATLAB to find a φ(R) that works. That’s why the reconstructed image above still looks a bit like he’s hypnotising you with his Scary Eye.

My preferred approach would be to knock up a MATLAB interface that let me draw a φ(R) on a pair of axes and then showed me the image it resulted in. I reckon I could detwirl that image to a recognisable whole in an afternoon. And yet…

The hunt began three years ago when German police discovered about 200 photos on the internet of a man sexually abusing young Asian boys. But the man’s face had been digitally scrambled and it was only 11 days ago that German police were finally able to reconstruct an identifiable image of the man who had eluded them for so long.

I can’t imagine how you could spend three years on that. If you can’t do it to a good approximation in a week then it’s probably impossible, and if you can then I don’t see how there could be three years of work in it.

There are 200 images, of course, but it’s safe to assume he’s used the same software to do each one. There aren’t many distorts that don’t destroy the image information, so probably many of those images were useless. The rest, you can reconstruct in the same way. They’ll use the same φ(R).

It’s not as simple as it looks at first glance, but… I just can’t see three years’ work in that. Doing it in a couple of months would have got him caught much sooner. Also now, of course, they have to computer-graphically age the image three years.

Well. Perhaps if my laptop is mended I shall have a go and see how hard it actually is, and then I’ll be able to say properly. But probably by the time my laptop gets fixed I shall be too distracted by the flying pigs and so forth.

Still, it could happen.

To help with these arguments, mostly as a resource for myself, I shall now compile as full a list as I can of flaws with the Imperial and US customary measurement systems. It won’t be a full list, because listing all of them would be like spotting errors in The Core, a task I have previously likened to counting raindrops, but here goes anyway. Feel free to add more to the comments section.

When Is A Pint Not A Pint?

Answer: when it’s in America. Because an Imperial pint is roughly (but of course, not exactly, because that would be too simple) 20% bigger than an American one. Americans call their units “Standard”. Interesting. This means, of course, that if you read the word “pint” in, say, a recipe, there’s really no way to be sure what that means. From here on in I shall switch back and forth between US and Imperial units with no warning because that’s what real life does. In my experience, most Americans are unaware of the difference between the two systems anyway (which of course exacerbates this problem enormously). Metric does not suffer from this problem.

How Long Is A Piece Of String?

All rods, poles, perches, cables, hands and feet are the same length. All chains are the same length. They all comprise 100 links, and they’re all exactly 100 feet long…

Who’s Asking?

…unless, of course, you work as a surveyor, in which case a chain is sill 100 links, only now it measures 792 inches as opposed to 1200. I don’t give the conversion in feet because a surveyor’s foot is very slightly longer than a standard foot. This makes show shopping difficult. Also, of course, if you’re a sailor then a mile is a different length than if you are a motorist. This does not happen in Metric.

Non-integer Conversion Units

This, of course, means that to convert (surveyors’) links into inches, the conversion factor is 7.92 inches to a link. There are two-and-two-seventy-fifths yards in a fathom. There are five-and-a-half yards in a rod, which is the same as sixteen-and-a-half feet. These aren’t extreme examples: these are typical. Imperial was formed largely from feet and inches, but people made new units by multiplying them by whatever seemed convenient and then made yet more by dividing those down. Once you start manipulating them in any serious way you end up with ludicrous conversion factors running to many, many digits. All Metric conversion factors are not only integers, they are powers of ten. All of them. It is impossible to manipulate Metric units and end up with any conversion factor which isn’t just a one, some noughts, and maybe a decimal point.

What’s In A Name?

As well as having names with more than one unit attached, Imperial and US measures also have units with multiple names: as mentioned before, a link is (sometimes) equal to a foot, but a rod is the same as a pole and they’re both the same as a perch. Not only that, but the names bear no apparent relation to the sizes of the objects involved: a foot is the size of three hands, and a link in a chain is the size of a football. Imperial handcuffs must look decidedly strange. Not only that, but a hundredweight is not 100 of anything. It is 112 pounds. Imperial advocates will tell you that this factorises easily. Well yeah, but it divides by seven. What use is that to anyone?

A Bit Much…

Imperial has far, far too many units for any human to remember. To use Metric for almost any purpose, you need to remember maybe four units and three prefixes. Imperial has a dozen weights, two dozen lengths, a handful of areas, and some volumes, and there’s no way to work out what any of them mean. When you have to look up what the units mean that is inconvenient. When, having done so, you discover that they are identical to units you did know, that’s just adding insult.

…But Still Not Enough

Despite its surfeit of units for everyday metrics like length, Imperial is shockingly bad at (for example) force, resorting to multiplying the pound (which has suddenly been defined to be a unit of mass rather than weight) by g. Metric has a dedicated unit for this, the Newton, which is readily converted into seconds, metres and kilograms. The “poundal”, the rather silly Imperial unit of force, is equal to 32-and-a-bit pound feet per second squared. What use is that? The equivalent conversion factor in Metric is simply 1. It’s convenient for discussion of forces, and it follows the Imperial rule of keeping to units people can easily judge, but you should never have a conversion factor like 32.1740486.

There’s also no Imperial unit small enough to measure atoms or large enough to measure galaxies. Metric, with its cunning use of log scales, has several units smaller than an electron, and another equal to about a hundredth of the width of the universe. The Imperial system simply doesn’t scale.

Bad Science

The upshot of this is that you simply can’t do science in Imperial units. It’s just not practical. It’s possible, of course, but it would be a fantastically stupid thing to do. For any halfway complex task, it would be quicker to learn Metric and use that than to use the Imperial system you already know. Partly because, as mentioned, the units are ambiguous. They are designed only for use by chefs on Earth. Chefs on Earth really need no distinction between mass and force, and so they didn’t make one. When you do need one and find it isn’t there, problems arise.

The Long And Short Of It

I appreciate there are sound historical reasons why “pound” abbreviates to “lb”, but I’m unaware of any such excuse for spelling “ounce” with a ‘z’ or those downright fucking bizarre symbols used in Apothecaries’ weights. And whatever the reasons, it’s still a whole bunch of other asystematic stuff that needs learning.

Update (24082007): When Is A Cup Not A Cup?

Answer: when it’s a unit of measurement. If a recipe, say, is translated by a computer or a person unfamiliar with the system, the unit names will be turned into the objects they’re named for. And who knows what size cup the reader might have? Using names of objects for units will lead to confusion. This problem doesn’t happen with Metric. Similarly, if you’re not translating them, a reader may not know that a “cup” can also be a unit. They might think it refers to, say, a cup. And they might have massive cups. There’s no danger of that with a “litre”.

In short, there is exactly one valid reason not to switch to Metric: the switchover itself would be expensive and difficult. But if anyone tries defending the Imperial or US systems in and of themselves, then they are just being obstinate and narrow-minded. The most common attempt to defend the system goes like this: “Metric makes you stupid because you never learn how to divide by twelve and stuff.” This is rather silly. There are two possible scenarios here:

1. There exists a large number of things for which division by numbers other than powers of ten is a useful skill. Therefore, removing one of them should make no material difference.
2. There does not exist a large number of things for which division by numbers other than powers of ten is a useful skill. Therefore, that skill is largely pointless and we may as well save ourselves the bother of developing it by using the simpler system.

Neither of those scenarios offers a good reason to stick with Imperial. Because there isn’t one. Sometimes people claim that Imperial units are more natural. This is true up to a point. Feet and inches are quite handy lengths for rough working. Luckily, they both convert fairly readily into Metric — there are about three feet in a metre and two inches is 5cm. The rest of the units are really only convenient because you’re used to them, or because there are simply so many units it’s hard to imagine how there could fail to be one the length you’re looking for. Well, unless you’re not human.

“Atheists?” said the demon, “there certainly aren’t any atheists in Hell.”
“But,” he started, starting to question his beliefs now, on his first day in Hell, when one might reasonably argue it was a tad on the late side, “all they had to do was believe! How hard is that?”
The demon made a noise somewhere between “oh?” and “hmm,” in the patient manner of one who’d been going over this for centuries and didn’t imagine having to stop soon. “But they didn’t believe in Hell either. It would seem a bit harsh to expect them to follow rules set out by someone they thought was fiction, with a punishment they thought didn’t exist.”
“So what you’re saying is,” he said, watching with trepidation as the demon selected a pointy looking object from a leather roll-up pack and held it over the flames, “that all we had to do to get carte blanche to sin as much as we pleased was to stop believing?”
“That’s right,” the demon said, as it walked behind the lost soul and plunged the instrument into his back (not that he really had such a bodypart any more, of course). “But you’re in luck. God’s laid down a special rule, just for you. To test your little wager. You can go to heaven, if you want to.”
“How?” Pascal shouted, above the pain. Right then and there there was nothing he wouldn’t do to escape the pain.
“Simple,” the demon replied, moving the instrument savagely, “just believe I don’t exist.”
And for a thousand years he tried.
After that he rather gave up. By that stage his tortured soul didn’t seem worth saving anyway.

Personally, I don’t have much faith in Alexa. It measures all traffic by users of the Alext toolbar, and that’s a fairly skewed subset of Internet users. It’s probably alright for big sites, but even then it’s not ideal. For small sites, the numbers are utterly meaningless.

Wikipedia still holds their word as gospel, though.

As everyone in the world knows by now, most websites and forums use “captchas” to try and stop computer programmes from posting fake comments containing adverts. “Captcha” stands for “Completely Automated Public Turing test to tell Computers and Humans Apart”. And as everyone in the world ought to have realised by now, they don’t work.

There exist a number of ways around them, the most cunning and most effective, although the most difficult to set up, is to build a pornographic website and get real humans to solve the captchas for you in exchange for naked pictures.

But mostly, they’re easy to get around because they’re shit. This, for example, is the default captcha that comes with the now obsolete phpbb2:

That is very easy to solve. (It should perhaps be pointed out at this stage that my job is in large part to extract shy information from images.) As with all the algorithms I’ll show you, this is the first and simplest one I could come up with, and it’s only the start. In all cases I will extract a binary mask of the letters for transferal to a more general OCR system. Also in all cases, I will use Matlab 6 to perform the analysis.

Here is the code required to make this captcha machine readable:

function bank=solvefuzzy(bank)

[x y c n]=size(bank);

%First, greyscale the lot by taking the red channel
bank=bank(:,:,1,:);

%Now blur it slightly.
for (i=1:n)
bank(:,:,1,i)=filter2(ones([3 3])/9, bank(:,:,1,i));
end

%Now threshold it.
bank=(bank<0.63);

%Now trim the borders.
bank(1:x,[1 y],:,:)=0;
bank([1 x],1:y,:,:)=0;

Here is the result of this algorithm on four example captchas:

Now that wasn’t hard. And I know that the letter shapes aren’t ideal, but it’s a very uniform font they use, and the letters aren’t rotated, so it’s as easy as pie to extract the characters from this mask.

Of course, cracking obsolete captchas isn’t terribly useful, or wouldn’t be if anyone bothered to update their forums, so here’s a captcha from phpbb3:

The first thing you should notice about this is that it’s gorgeous. But let’s have a look at the code required to break it:

function bank=solveclassy(bank)

%First, greyscale the whole thing
bank=mean(bank,3);

%Now threshold it.
bank=(bank<0.55);

That’s two commands. Now, let’s check the results.

So that’s done it perfectly, with no real image processing at all. Of course, this is a little unfair to the new captcha — it is in reality much tougher than phpbb2’s, because it uses many fonts and angles and sizes. So some kind of cunning would be required to turn these shapes back into characters, but that’s really nothing OCR software doesn’t do as a matter of course. And if you were to take each character individually (even if they overlap, the colours in the original image would distinguish them) and perform, say, a Radon transform on them about their centroids, this would give you a distinctive pattern for each letter and number in each font. The point is that from here it is entirely possibly to crack this captcha. Besides which, phpbb is open source, so training the process by Radon transforming all possible characters would be fairly simple.

But phpbb3 has another trick up its sleeve: a second type of captcha. This is the one used on www.phpbb3.com’s forum, so presumably they trust it:

Aside from the fact that it looks like something from a bad Spectrum game, the first thing you should notice about this is that it has clearly been designed to be almost impossible to crack, by someone who knows nothing about cracking captchas. For example, the uniform background colour. Well over 90% of the image is a single colour and every pixel of every letter is that colour. Then, the individual letters are outlined in distinct and uniform colours, and then, as if that wasn’t helpful enough for crackers, the characters are made up of little square elements (which I will call ‘charels’), so we can reconstruct the characters down to the pixel, generally the right way up. It really couldn’t be more helpful if it tried.

So let’s see some code.

function result=solvefunky(bank);

[x y c n]=size(bank);
result=zeros([x,y,1,n]);

%First, determine that background colours.
%We assume the first colour with five continuous pixels of itself
%along the first row is background.
background=zeros(3,n);
for (i=1:n)
colour=[0 0 0];
j=1;
count=0;
while (count<5)
if ((bank(1, j, 1, i)==colour(1)) && …
(bank(1, j, 2, i)==colour(2)) && …
(bank(1, j, 3, i)==colour(3)))
count=count+1;
else
colour(:)=bank(1,y,:,i);
end
end
background(:,i)=colour(:);

%Next, find areas that are that colour
backgroundareas(:,:,i)=((bank(:,:,1,i)==background(1,i)) & …
(bank(:,:,2,i)==background(2,i)) & …
(bank(:,:,3,i)==background(3,i)));

%Now, find areas of that colour smaller than 15 pixels
temp=bwlabel(backgroundareas(:,:,i), 4);
small=zeros([x,y]);
numberofregions=max(temp(:));
for (region=1:numberofregions)
pixels=sum(temp(:)==region);
if (pixels<15)
thisarea=temp==region;
%This leaves a lot of bits which aren’treal, but we know from
%looking at the captcha that the letters are outlined in just
%one colour, so lets eliminate anything that’s got more than
%one colour adjacent to it. (In fact, we allow one pixel of a
%different colour as this works better.)
adjacentpixels=(imdilate(thisarea, [0 1 0;1 1 1;0 1 0])&~thisarea);
red=bank(:,:,1,i); green=bank(:,:,2,i); blue=bank(:,:,3,i);
ar=red(adjacentpixels); ag=green(adjacentpixels); ab=blue(adjacentpixels);
if ((sum((ar~=ar(1)))<2) && …
(sum((ag~=ag(1)))<2) && …
(sum((ab~=ab(1)))<2))
small=small|thisarea;
end
end
end
result(:,:,1,i)=small(:,:);

end

That results in this rather pleasing image:

Now all I’ve done here is to find the pixels that are part of the larger “charels” which comprise the message. There’s still a lot of work to be done to find the message in ASCII format, but it can be done: you can separate the individual characters by recourse to the original image — each one is outlined in a distinctive colour, and if a colour is reused then it probably isn’t reused in adjacent characters, so a simple contiguity test will catch it; you can reorient and rescale each character by picking a charel arbitrarily and seeing where its neighbours lie relative to it, using the provided coloured outline as a guide and the ’shadow’ colour to define the vertical and/or horizontal axes — this will allow you to build up a reoriented image of each letter, which can be easily checked against the known font to see which it most closely matches.

Those of you who know me should already have worked out that this took me less than one evening, including grabbing all the pictures and writing this entry. I wouldn’t bother if it was going to take longer. You know that. So if you employed a good programmer for a week to crack such a captcha you ought to be able to finish the job off. Then you’d have access to every phpbb3 forum out there.

Clearly there are false positives and things in these processed images: the bottom one in particular has a large false positive in the Z, and the last H has a bit missing where the L overlapped it. I don’t think either of these would actually affect a good OCR algorithm (given that said algorithm would have the font used built into it and have an ideally oriented and scaled image of the letters, albeit with the odd mistake), and even if it did, well, we cracked the other three. If we assume we can crack 75% of these captchas, then we can break into a forum which allows us 5 attempts (which is pretty standard) 99.9% of the time.

phpbb3 also allows the user an almost ludicrous amount of options for their captcha. This is good, as it means that a cracker will have a harder time beating the captcha in the general case. But in the specific case of the default settings, which almost everyone will use, this won’t help at all.

So what’s the solution? Personally, I use a bespoke text-based captcha. Image based ones are hard to programme, which isn’t a problem if you’re doing something like phpbb, because it has to be hard to crack (oh dear) and text based ones really aren’t. Another problem with image-based solutions is that some devices or people can’t read them, so there usually has to be a fallback, and then you have two links, of which a cracker need only outsmart the weakest. (Sorry for the mixed metaphor there.) I think bespoke text-based is good because there’s no really motivation for a cracker to devote any time to cracking it, as they’ll only get access to my websites, and if they do I can very easily change it the following evening. But it couldn’t work for phpbb as you can’t make a bespoke captcha for every user.

Some captchas are obfuscated further than these. Sometimes this is a simple case of drawing lines over and through the text. This is pretty easy to beat — any good photo touching-up software has had this feature since the week after flatbed scanners were invented, and replicating it is not hard, even when the lines must be found automatically. A better solution is to deform the letters themselves, though this involves a very direct tradeoff: anything you do that makes letter shapes harder for a computer to identify will have the same effect for your legitimate users. Again, I would attack such a captcha by not attempting to restore the original image, but by developing an algorithm to characterise each… well, character based on its Euler number, the number of sharp corners in its outline and their relative locations, and maybe the Euler number of the shape you get if you dilate it a bit. I believe this could crack such a captcha with minimal training.

Theoretically, human authentication is the best way, but humans aren’t apparently very good at that. It’s not always apparent from a name and an email address if a user is a human or a spambot. My proposed solution is a deliberately impossible captcha: you find or create an image, possible of random abstract ‘art’, or a landscape, or a sort of randomly generated Rorschach ink-blot test, and ask the user for a vague, one sentence description. Then a human would authenticate the user’s account by seeing if the user’s description of the image relates to that image in any way. It’d be a little subjective, but I really can’t see it being cracked, except perhaps be Derren Brown concocting a sentence that would appear to describe any image. And people would learn to spot that sentence. It would still be susceptible to the porn crack, but then everything is, and honestly I think it’d be fairly easy to tell which descriptions of Rorschach ink-blots had come from the minds of teenage boys looking for naked pictures with a pretty high degree of certainty.

Plus, I think it’d offer a fascinating glimpse into the psyche of all prospective users of your forum.

You can download all the above code, and some general making-it-work gubbins in the Code Factory, but you’ll need Matlab to make it work, and you’ll need the Image Processing Studio, to make it run. If anyone wants to extend the code, do feel free. Complete code is available if you want it, though — people sell it to prospective spammers.

This is not a mathematical essay.

This is a film review.

Twenty-one Alistair Griffins attended the Dave Gorman show.

The local incinerator burned down.

Richard got the wrong change at the maths cafeteria.

For this reason, I chose to re-christen Leeds “Ironyville USA”, for reasons which are many and obvious. And Leeds, for its part, rose to the task admirably. The £1-shop in town is currently having a half price sale. The Bodington Bar in Bodington Hall does not sell Boddingtons. (I have no information regarding the bar at the Tetley Halls.) The Dry Dock is shaped like a ship, but The Ship is not. (The Dry Dock is run by the same people as The Library, who apparently elected to specialise in confusing pubs.) All the cashpoints seem to have no cash (and therefore no point). It’s beginning to get silly, really.