# How to beat “Blue Monday”

So, another Blue Monday is upon us. It’s not clear exactly when Blue Monday is, but we do know it’s upon us. The Daily Mail has gone with last Monday; The Training Room, one of the four billion companies who have used it for marketing, have gone with next Monday. But we can work it out, because we have the equation:

$Misery = \frac{(W + (D-d)) \times TQ}{M \times NA}$

…unless it’s this one

$D = N + M (T+1) C R \frac{B-S}{J}$

but nobody uses that one. Anyway, it’s definitely a Monday, and it’s definitely in January because $T$ is time, which increases with time and so is highest in December, and $Q$ is how many new year’s resolutions you’ve given up on which is also highest in December look don’t think about it shut up.

Anyway, we know these formulæ are real because they make predictions. One intrepid PR man compiled a formula for the perfect marriage which results in thirty-some pre-specified romantic gestures you have to make every month. Since months are of different lengths, that means you need be less romantic in the longer ones.

This formula about a marriage clearly makes the unrelated prediction that February should be the most romantic month; that there should be some kind of festival of romance smack in the middle of it. Since every restaurant I’ve been in lately has taken great pains to confirm that this is indeed the case, the only rational, skeptical or scientific conclusion is that these formulæ represent the very real cutting edge of science.

While it is obviously bad news that we are all scientifically depressed either last or next Monday, it does offer a ray of hope. Here, you see, is the formula for the perfect Christmas:

I’m assuming that the second “divided by 3D” on the bottom is a typo. Firstly because this formula otherwise defines some kind of festive acceleration, which even a cursory analysis of the Twelve Days Of Christmas song teaches us is dangerous, but mostly because if it’s a real fraction then the numerator has an equals in it.

The point of this equation is—

Actually, first I should point out that $W$ appears twice: once to represent a walk, and once to represent a glass of wine. This might be an error, but I prefer to assume it is a deliberate simplification introduced because walking and wine are somehow equal. I say this because this is the Times’ “Offset Your Carbs” wallchart:

It quite clearly shows that going for a walk is equal to garlic bread:

It also shows (although I haven’t got a close-up photo of this) that a glass of wine is equal to some sex. Taking the new result that wine equals walking,

$Garlic Bread = Walking = Wine = Sex$

The strangest thing here is that mathematically, Peter Kay is now the filthiest comedian in Britain.

Anyway, the point is that the $D$ in the formula for misery is Christmas debt. If we can reduce that value we can all-but eliminate Blue Monday. So how do we do that? Well, the formula for the perfect Christmas is:

$P_\chi = \frac{8F \times (4P + £23)}{3D} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

Christmas debt is $8F \times 4P \times £23 = £736$. Quite a whack. But we can reduce it without affecting $P_\chi$ — I’m generously assuming what is probably an $X$ is a $\chi$ — because it’s in a fraction. Dividing top and bottom by 4, we get

$P_\chi = \frac{8F \times (1P + £5.75)}{18 hours} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

That gets us below £50, but that’s still a lot. Let’s dispense with seven family members and divide through by eight.

$P_\chi = \frac{1F \times (1P + £5.75)}{135 minutes} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

Now our only problem is that the times are inconsistent: 135 minutes in the first term, and three days thereafter. Never mind, just divide all the fractions by 32, top and bottom:

$P_\chi = \frac{1F \times (1P + £5.75) + \frac{3}{32}G}{135 minutes} + \left(1+\frac{1}{4C}\right)\frac{\frac{1}{16}W \times 32NR + 5T}{135 minutes \times 32NR}$

This new, abbreviated Christmas is interesting. $G$, for example, represents a nice family game, of which we must play three thirty-second fractions, and while the formula for the perfect family game (obviously there is one) doesn’t readily divide by 32, there is a game that does.

Three Chess Over Thirty Two features six squares with three pieces on them, and luckily for anyone wanting to knock out Christmas in a little over two hours, requires only one move for checkmate.

But however dull a game Three Chess Over Thirty Two can be, however unsatisfactory one sixteenth of a glass of wine (or walk), and however overfilling you find the 32 portions of nut roast you are forced to consume because it was inexplicably on the denominator, the cold, mathematical reality is that $P_\chi$ has not changed and therefore Christmas has been totally and objectively perfect, while costing less than six pounds. This, in turn, means that our formula for misery loses much of its sting, and that is how you beat Blue Monday.

This is adapted from part of my Stupid Formulæ Talk which can come to your local Skeptics in the Pub or similar event if you think your audience would enjoy hearing me be approximately this silly for the better (or at least longer) part of an hour.

# A round-up of a mathsy week

Maths!

First of all, I’ve written an article for the Aperiodical, an irregular maths blogging collective kind of a thing. It’s about voting systems, crazy dice, paper, lizards and Spock.

Grime Dice” are a set of five coloured dice with unusual combinations of numbers on them. The red die, for example, has five fours and a nine. The blue one has three twos and three sevens, so it loses to the red die about 58% of the time. The green die has five fives and a zero, and will lose to the blue one in 58% of rolls. What makes them interesting is that the green die will beat the red one in 69% of rolls. These three dice behave rather like rock-paper-scissors — in mathematical terms, they are ‘non-transitive’. The full set of Grime Dice also has a purple and a yellow die, so a better analogy would be rock-paper-scissors-lizard-Spock.

You might ask which is the best Grime die, and the obvious solution is just to roll all five dice at once, a hundred times, and see which one wins the most times. This is why you should never believe something simply because it is obvious.

I’ve been quite reasonably asked what Ranked Pairs did to deserve omission, to which my only answer is “be a bit inelegant and have a boring name” (not that I have any particular room to criticise it for either of those). If you’re interested, in Ranked Pairs, you start with the strongest preference the voters expressed (say, Labour are better than UKIP), “lock it in”, then keep locking in preferences, in decreasing order of strength and skipping any that would create Grime-dice-style cycles, until you’ve figured out an ordering on all the candidates. The winner is the one who beats every other candidate in the final, locked-in pairings. It’s not so very different from Beatpath (which I did include) but even after Paul’s recasting of it in more elegant terms it still feels a bit clunky to me. I appreciate that “a bit clunky” is not a completely valid mathematical criticism.

Secondly, my maths-based comedy rant thing about stupid formulæ in PR newsfodder will be on at the new Kingston Skeptics in the Pub group on Thursday 2 August. It’s at the Ram Jam Club, which is here:

Come down if that sounds like somewhere near where you live. You’ll learn how to derive the existence of tiny shoe-horns using quantum physics and a cheap advert for some guy’s book. (Connection fans may note that the golf club to the east shares its name with a popular electoral system.)

Lastly, here is some maths I found scattered around the web, which I may bring out at Manchester MathsJam tonight (spoiler alert). It’s about counting, binary, puzzles and hypercubes (as is all maths).

Picture a counter, like the ones used to count people into clubs or on the obnoxious Lynx adverts a few years ago. When a digit ticks over, all the digits to the right of it also tick over to zero. If you had a really big club (or a really noxious deodorant) you might end up changing hundreds of digits at a time. Binary is no different — but sometimes having to change all those bits at precisely the same time causes problems, so you’d much rather only change one digit at a time. To this end, Frank Gray invented a revised binary counting system where that is exactly what happens. In 3-bit, you start as normal at 000, then 001, and then you go to 011 — the nearest unused number. Next, you go to 010 which you missed out, then skip to 110. Next, comes 111, then 101, and then 100 — the only number left. To get back to zero, you flip that single bit at the front back to 000. To get to eight, you need four bits, and it’s 1100 — again only one bit has changed.

So how do you know which bit to flip? Every second flip, starting with the first, is the right-most bit. Every fourth, starting with the second, is the next rightmost bit. Every eighth, starting with the fourth, is the third rightmost. And so on. I think this is interesting, because it’s also the solution to the Towers of Hanoi game: in that, you move the smallest disc first, and every second move after that. You move the second smallest second, and every fourth move after that. You move the third smallest fourth, and every eighth move after that. And so on. This is a neat way to visualise why the time needed to solve Hanoi increases as 2n. (It’s also the solution to the Chinese Ring Puzzle which, generalising from myself, I shall assume you haven’t heard of and ignore.)

Counting in Gray Code is also equivalent to visiting every corner of a hypercube without visiting any twice: if you think of a binary number like 101 as a set of co-ordinates (1, 0, 1), then the numbers 000 to 111 denote the corners of a cube. 00 to 11 give you a square, and 0000 to 1111 give you a four-dimensional hypercube. Obviously you could visit them in standard binary order (0000, 0001, 0010… 1111) but that means taking diagonal tracks through the cube. Gray Code’s system of only changing one bit at a time means you can do it just tracking along the edges — and because you can always change that last bit to get back to zero, you can do a full Hamiltonian cycle, just along the edges, by doing nothing more taxing than counting.

I honestly don’t remember what possessed me to look up Gray Code. It had been sitting in the back of my mind for about two years, and suddenly I thought maybe it was interesting enough to mention at MathsJam. It hadn’t occurred to me that it might have any relevance to traditional wooden puzzles, hyperdimensional navigation, or indeed anything else. But it did. And that is why maths is awesome.

# Maybe from boredom?

The very worst joke I have ever heard from a professional stand-up comedian is (roughly) as follows:

I don’t trust Barack Obama. Call me paranoid, but the last time a black man with an imperialist agenda had that much military power, it was Darth Vader.

It did raise a laugh from some of the audience, but I’m forced to assume they were drunk because the joke makes no sense. It makes no sense because it relies on the audience subscribing to his somewhat contentious views on Obama’s politics, but mostly because Darth Vader is white. He just dresses in black, as has every US president since forever. Basically the uncontroversial similarities he’s found between Obama and Vader are that they’re both in charge of powerful armies and while that’s a fair reason to be wary of them, it’s not funny and I’m not capable of finding something funny if it relies on me selectively ignoring facts.

In The Salmon of Doubt, Douglas Adams makes much the same argument about the joke “if the black box is so indestructible, why don’t they make the whole plane out of the same stuff”, which he described as “the teller and the audience complacently conspiring together to jeer at someone who knew more than they did”.

No, I like my comedy to be smart, and to mock people who, either through dishonesty or ignorance, promote nonsense. So this sounded fairly good to me:

You have a 0.000043% chance of dying during this show. We can’t tell you what you’ll die FROM. It could be heart attack, shark attack, or insertion of a sharp object into an orifice. But we will make sure you at least die laughing.

Stand up mathematician Matt Parker and comedian Timandra Harkness got sick of reading ill-founded stories about how eating this or doing that was going to add six months to your life span, or halve your risk of dying from something or other. So they got a grant from the UK’s biggest biomedical charity, the Wellcome Trust, to do the research and bring you the most definitive comedy show ever about dying.

But then I noticed one detail: Timandra Harkness. I’ve never seen her perform, but it’s a distinctive name and one I knew I recognised, and I just worked out whence: in 2004 she helped publicise ”the formula for the perfect joke” in order to promote her show. The formula was

x = (fl + no) ÷ p

where f is “the funniness of the punchline”, l is “the length of the buildup”, p is “the number of puns”, and just in case this seemed a bit too reasonable, n is “the amount someone falls over” and o is “the ouch factor”. Science often throws up unexpected results, and here we learn that because War and Peace has very high values for both l and n, and a very low p value, it is in fact provably hysterical (although my preferred formula x = f doesn’t throw up this anomaly). This is just an advert posing as bullshit posing as maths posing as science.

I wholeheartedly agree that the simplistic “+6 months” reporting of health stories is annoying and I’d love to see a show that poked fun at it in a clever way, but frankly I don’t for a second believe that Timandra Harkness is the person to do it. Partly this is because once you sell your (and science’s) credibility in this way, I think you forfeit your right to “get sick of reading ill-founded stories about [science]“, but mostly it’s because I agree with Nicholas Parsons that

The formula has obviously been thought up by somebody with no sense of humour.

No, I like my comedy to be by people with a sense of humour.

# The Respectable Face Of PR Science Formulae

I was going to throw this up on Google Reader and let FriendFeed tweet it at you all, but since I have apparently become the standard reference for ‘perfect formula’ stories, I thought I’d stick it up on here. Presenting… The Respectable Face Of PR Science Formulae!

From the b3ta newsletter, it’s OK Cupid’s analysis of what words and phrases are more successful than others at eliciting a response to a first-contact message. Essentially, it’s a formula for the perfect on-line chat-up line, and it basically reads ‘spell right, don’t be a creep, and mention specific interests’. It’s just a blog post, so it’s still not really Proper, Peer-Reviewed Science, but there are enough mentions of N and f and statistical significance — all used quite correctly — as well as a note about anonymisation, that my instinct says they probably did it right. And the results are a nice mix of the obvious (read the other person’s profile), the counter-intuitive (confidence is bad) and the interesting (mentioning a religion is good but mentioning atheism is better).

In any case, it does what the original ‘perfect formulae’ story tried to do (or at least what its creator claims he tried to do and I see no reason to disbelieve him), which is to combine clever PR with an actual attempt to show how science can be relevant. And it worked, because here it is in the Telegraph, alongside a photo of attractive young people kissing each other, for purely illustrative reasons, naturally. Wouldn’t it be nice if companies realised they could get the PR without the sneers of intellectuals if they just did these things right?

Also I’m inclined to like it because it seems to say that self-effacing male atheist physicists are sexy. And I think we can all agree that that’s basically indisputable.

# My NewsBiscuit Annual

From time to time I submit stuff to Newsbiscuit. More occasionally they use it. Their submission board is pretty awkward to work, though, so I thought I’d post my favourites on this blog also, where I can keep an eye on them. First, the ones they used:

Next, some of the ones they didn’t. I’ll put most of them after the fold, since there are a lot of them. Also, some might be offensive if you’re easily offended. First, though, my favourite, from early to mid October:

Gordon Brown has new kitchen sink installed under anti-terrorism laws

Prime Minister Gordon Brown has had his kitchen refitted under laws brought in in the wake of the September 11th and July 7th terrorist attacks.

The refit was proposed in August, as part of a larger reorganisation of Number 10. Brown’s wife Sarah raised objections to the plans at an early stage, saying that the new system would make cooking difficult and that she didn’t like the colour. It seemed that the deadlock was unresolvable until September 17th, when the Prime Minister realised he could use existing anti-terror laws to push the installation through without first gaining his wife’s approval.

Critics have claimed that this is “a clear abuse” of the power handed to the PM’s office by these new rules. One backbench MP said that while he understood the need to have special new measures to deal with the new kind of threat faced today, the government had taken advantage of the fear to pass laws granting themselves more power than they had ever been elected to. Other recent applications of the anti-terror laws include freezing the assets of Iceland UK, resolving the double-booking of a conference room in Parliament, and the emergency resolution on Tuesday which mandated it was James’ turn to do the washing up.

Brown has insisted that neither he nor the government has abused the trust placed in them by Parliament, saying that there are “other kinds of terrorism” besides violent attacks on civilians, and that these might be said to include refusal to wash dishes or bad taste in kitchen units.

The House of Lords is expected to overturn the decision, but James Brown has said that as he’s already done the washing up, it’s too late to reverse the damage and a system must be put in place to prevent these situations from arising in the first place.

# The Perfect Formula II: The Mail

This is the same thing as I did for the Telegraph, but for the Daily Mail. This one was harder because their search function is bad and their website unreliable. Also the dross between the formula stories was more depressing. But then, it did turn up the brilliant formula for the perfect horror film, so that’s something…

• 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) × (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 × O + Bh (H+R) × 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 + (5×E) + (3×H)
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 Formula

Here is a list of “mathematical formulae” and “scientific equations” which detail every aspect of our day-to-day lives, all “calculated” or “devised” by “scientists”, “academics”, “economists” and “mathematicians” from various embarrassed universities. These are all taken from the Telegraph. Don’t imagine other newspapers are better…

• 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 + no)/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.

# Christmas Cake

There’s a shortage of Nintendo Wiis at the moment, because they’re popular and it’s Christmas. This has led to crazy people suggesting that Nintendo have engineered this shortage deliberately, which is true only in the rather weak sense that Nintendo’s objective is to sell consoles rather than horde them in shops. The fact is there’s no reason Nintendo would do such a thing – the only people who profit from a Wii shortage are canny eBay users. Nintendo make more money by selling more consoles. This is very basic stuff. Nintendo know this.

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)!Â  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.