Archive for category Maths

The Sun, 20 mph speed limits, and a lot of nonsense

CONTROVERSIAL 20mph speed limits designed to cut road casualties are not working, official figures show.

So says The Sun anyway*. So, what’s the problem?

A report from the Department for Transport shows there were 2,262 fatalities and injuries in 2011 on 20mph roads in built-up areas — 24 per cent more than in 2010 when 1,827 were recorded.

That compares to a one per cent reduction in casualties on 30mph roads in built-up areas.

How many people died or were injured on roads with a 30 mph speed limit then? The Sun doesn’t say, but the official data is easy enough to find. In 2010, 127,377 people were killed or injured on a road with a 30 mph speed limit. In 2011, it was 125,494.

In other words, that “1% drop” corresponds to almost 2000 fewer people were injured on 30 mph roads, while 400 more people were injured on 20 mph roads. That is a net decrease of 1448 injuries/deaths.

Just looking at the number of injuries on 20 mph roads is not going to tell you about how effective 20 mph speed limits are. You have to compare them with other speed limits. Data about how many 20 mph zones there are is hard to find, which makes making sense of the Sun‘s data difficult, but it certainly looks like a lot of them have been springing up lately, so an increase in injuries is to be expected – if there are more roads, there will always be more accidents!

Studies of 20 mph zones consistently find that the same stretch of road will see fewer accidents and fewer injuries if the speed limit decreases from 30 mph to 20 mph, especially if this decrease is enforced by speed bumps and other traffic calming measures.

* Incidentally, far from being “controversial”, surveys consistently find around 74% in favour of 20 mph speed limits and just 12% against them.

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50 Shades of Babies

Baby boom predicted next year thanks to success of Fifty Shades of Grey books, says theDaily Mail today. It’s such nonsense that I don’t really know where to be being. Let’s have a quick rundown of the problems.

  1. Fifty Shades of Grey did not invent sex, nor did it invent porn. There have been plenty of erotic books written for women before Fifty Shades came along. People like Jilly Cooper were best sellers decades ago, and somehow these authors didn’t inspire baby booms of their own.
  2. The sort of sex Fifty Shades of Grey is credited with inspiring – again, according to the Daily Mail, quoting a poll by a dating website – is going to tend to be controlled and organised. The Twilight fanfic book does after all focus heavily on contracts between sexual partners. It stands to reason that people would be more likely to use contraception if acting out scenes from the book.
  3. There’s no real evidence that Fifty Shades of Grey has led to people having more sex – a few people posting “I had so much sex after reading this!” on Mumsnet isn’t really enough. Fifty Shades of Grey didn’t just magically materialise in people’s houses, they had to go out and buy it. Presumably most of these people would have bought a similar book if Fifty Shades was not available, especially if they were looking to “spice things up in the bedroom”.
  4. The story comes, ultimately, from one Professor Ellis Cashmore (the only professor I know of whose website has an intro video). I’m sure he’s a smart guy, but he’s professor of culture, media and sport, not demography or statistics or anything else that you might expect someone making predictions about the birth rate to be grounded in. He’s in the papers quite a lot too, for sometimes quite disconnected stories. In the past month alone, he’s explained the psychology behind penalty shootouts, the meanings of footballers tattoos, homosexuality in sport, the place of Wimbledon in British culture and the reasons Madame Tussauds is so successful. It’s not proof he’s wrong, of course, just a reason to be a bit wary that he’s suddenly leapt out of his department to give the Daily Mail a juicy story about a particularly popular book.
  5. Come on, seriously, this story is nonsense meant solely to drive traffic to the Daily Mail and boost Professor Cashmore’s profile. In 2010, 723,165 babies were born in England & Wales. To be statistically significant, you’d need the book to lead to tens of thousands of extra births – i.e., ones that were not planned. Even for a book that’s sold a million or so copies, that’s a lot of babies.

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Did GM soy cause allergies to soar? Probably not.

So, California’s planning a referendum on the labelling of genetically modified food. The Guardian has covered this not in it’s regular news pages, but in its Comment is Free section, under the title “How California’s GM food referendum may change what America eats“.

The article is mostly an opinion piece – fair enough – but there’s one statistic buried in there that leapt out at me.

While researchers have not yet found a “smoking gun”, which would prove that GM foods as a class are dangerous, there are troubling signs that they may be a factor in the recent epidemic of food allergies. Soon after GM soy was introduced to the UK, for example, soy allergies escalated by 50%.

The link there doesn’t go to a scientific paper, but to a piece on “News. Controversy. Opinion.” site Opposing Views, and their figures seem to come, ultimately, from American Academy of Environmental Medicine, a group that has some decidedly quackish views on topics like water fluoridation, vaccines and “Multiple Chemical Sensitivity” (a scientifically unfounded belief that everything in modern society contains toxins). It’s not impossible to support some outlandish ideas while being right about things, of course, but it does ring some alarm bells.

Neither article links to any of the studies it referenced, but with a bit of digging, I found this piece at Academics Review which seems to be dealing with the same statistic. Go there if you want the full takedown, but in a nutshell, it refers to marketing information from a group called “York Nutritional Laboratories” (which sell food allergy testing kits) the rise was in people with a particular antibody, not those who reported allergies and the study didn’t find any connection (the rise simply happened at a similar time to the introduction of GM, although it actually took place before GM soy became mainstream).*

I decided to have a look on Google Scholar for papers looking in the allergenicity of GM soy. There are plenty of studies and review papers looking into this – one, two, three, four, five – and all the ones I’ve found so far suggest that genetic soybeans and GM soybeans pose exactly the same risk of allergy (though as far as I can tell, these are all animal trials. There isn’t much data on human soy allergies out there).

In this case, the claim that GM soy may be responsible for a rise in allergies seems to be simply wrong.

* For the other major claim in Opposing View’s piece, about baby rats dying from eating GM soy, see this peer review of the paper, originally from Nature Biotechnology , which expresses grave concerns about the unusually high numbers of deaths in the control group – it looks like bad care killed the rats, not the soy)

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Will driving at 80 mph help the economy? Statistics say… probably not

Last week, the Transport Secretary Phillip Hammond announced plans to raise the speed limits on motorways from 70 mph to 80 mph. This, he claimed, would:

“generate economic benefits of hundreds of millions of pounds through shorter journey times.”

Never mind the debates about safety and the environment, let’s look at this one argument. So, does a shorter journey equal a more economic journey? The problem is that cars need more fuel to travel faster, and so the faster you go, the worse your fuel efficiency is. Statistics that go right up to 80 mph are hard to find for some reason – the big US government study for example only went up to 75 mph – but according to the calculator at MPG for speed (better sources always appreciated), driving at 80 mph uses about 15% more fuel per mile than driving at 70 mph.

So, lets do some maths! For the sake of simplicity, we’ll assume every single journey on the motorways is work-related. The actual figures will be lower, especially on weekends and holidays.

At 70 mph, it takes 51 seconds to drive 1 mile. In this time, a car with a claimed “highway” fuel efficiency of 40 miles per gallon (roughly as efficient as a modern hatchback like a Ford Fiesta) will use about 0.11 litres of petrol. At the current average pump price, that’s 15 pence of petrol.

At 80 mph, you cover that same mile in 45 seconds, saving you 6 seconds. On the other hand, your car is now 15% less efficient. According to the calculator, your 40 MPG car is now doing just 28.8 MPG, using around 0.13 litres of petrol to cover that mile, so the fuel to travel that distance cost you about 18 pence.

Spending 3 pence to save 6 seconds is equivalent to spending £18 to save 1 hour. The average median wage in the UK is far lower than £18 an hour (currently, it’s £12.50 per hour for full-time workers (PDF))* – in other words, if you drove at the speed limit to get to/from work, the money you’d be spending on petrol would mean most people would actually lose out (people who car-share would be in a better position, but few people car-share to work).

All the extra pay taken home by workers would simply end up going straight to the petrol companies – and when the government is trying to increase consumer spending, that’s the last thing the economy needs.

(Oops, forgot to mention that this post bears a debt of inspiration to this xkcd comic.)

* Thanks to Lukeablancas in the comments for pointing out that I’ve gone for the median wage. The median wage is good for working out what this means for the average person, since it’s unaffected by extremes, but if we’re looking at the country as a whole, the mean wage might be better – this will take high-earners like company bosses into account, as well as people who work in short but intense shifts, like some freelancers. In 2010, the mean wage for men was £16.00 per hour and for women it was £12.92 per hour (annoyingly the government hasn’t released the combined figures for men and women, but assuming there are roughly equal numbers of both in work the average wage overall is £14.46 per hour). Either way, on average people will end up losing out.

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The Daily Mail blames “brain chemicals” for riots… the research they cite doesn’t

Daily Mail headline: Rioters have ‘lower levels’ of brain chemical that keeps impulsive behaviour under control

Do they? Well, some of them might, but the research in question wasn’t about rioters at all.

Researchers from the University of Cardiff uncovered a link between impulsiveness and levels of the neurotransmitter GABA in a key brain region.

… Around 30 male university students had their levels of GABA measured using a specialised type of brain scan.

They were also asked to complete questionnaires that assessed different aspects of impulsiveness, a trait known to influence self-control.

Participants with more GABA in the pre-frontal brain region had lower scores for ‘urgency’ – the tendency to behave rashly in response to distress or strong emotions and urges.

There was no connection to rioting in the study. Any connection made in the article is being made by journalists – this article has no by-line, being published solely under the Daily Mail Reporter name, but I think it came from the Press Association originally – and it’s a tenuous connection. You see, The Mail is working completely backwards here – they’ve decided that since people who have less GABA tend to behave more rashly, people who they think behaved rashly must have less GABA. You might as well assume that since every MP is in London right now, everyone in London is an MP.

Besides, although the paper in question, “Dorso-lateral prefrontal gamma-amino butyric acid in men predicts individual differences in rash impulsivity” (in Biological Psychiatry not Biological Society, despite what The Mail claims) did find a connection between GABA and impulsiveness, it wasn’t as strong as The Mail claims:

Figure 1 from the paper

Figure 1 from the paper (highlights my own)

That’s a graph from the paper, showing the connection between the amount of GABA in one particular part of the brain (along the bottom axis) and how strong the individual’s feeling of urgency was (along the side axis) in two groups (cohorts). There does appear to be a correlation (the R number is a measure of how strong this correlation is; R = -0.7 is a reasonable correlation) but look at the two I’ve highlighted with red dots in cohort 2. These two people have the same amount of GABA in their brains, but one of them was incredibly impulsive while the other was one of the calmest people in the study. Likewise, in cohort 1, while there was a definite tendency for people with more GABA to be less impulsive, just look at that cluster of dots – there are impulsive people with lots of GABA, and cautious people without it.

The best you could possibly say about this article is that maybe on average a rioter* has less GABA than normal, assuming these riots are entirely impulsive and there is nothing at all planned or premeditated about them. But then, why does this study need to be connected to riots at all? The paper came out in July before the riots, it’s not about riots – or any kind of violence at all – and none of the scientists quoted mention them, and to be honest, blaming the riots entirely on brain chemistry leaves a nasty taste in my mouth. As Mindhacks has pointed out, The Daily Mail seems to be going to great lengths to avoid exploring any of the context behind the riots, and this kind of story helps bolster the Mail‘s line that there is no deeper cause of these riots than “criminality pure and simple”.

Wales Online originally ran this story too (here’s the Google cache, and if that stops working, here’s a screenshot), but they’ve since realised there’s nothing in this proving anything about the brains of rioters and have replaced the story with an altogether more reasonable report on the research. Will The Mail follow suit? Let’s see.

* Male rioters at least – the study only looked at men, so there’s no guarantee this correlation is true in women too.

Edit: The researchers behind the study have published a scathing rebuttal in The Guardian, saying “Let us be absolutely clear. Our research has almost nothing to say about rioting, and certainly can’t be used to justify or excuse any type of behaviour.” Despite complaints from the scientists, The Mail‘s article is still online.

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A punny reply from the TaxPayers’ Alliance

A couple of days ago, Primly Stable commented on the post from last month about the false claims that the NHS was buying loaves of bread for £32 a piece, pointing out that The Express had issued a retraction of the story (though it remains available online), and Tabloid Watch followed this up with an excellent post pointing out that The Sun had quietly deleted the story too.

At Tabloid Watch’s suggestion, I emailed Emma Boon of the TaxPayers’ Alliance, who was quoted by a number of papers (including The Mail and The Telegraph) as saying

“It smacks of incompetence that the Welsh NHS is paying so much more for these goods than they are available for in the shops.

“The cost per unit prices are way above supermarket prices for gluten-free products in some cases which is really worrying.”

“This doesn’t look like taxpayers are getting value for money.”

to ask if she or the TPA would be retracting the comments, and whether the TPA would remove the claim from their website. Here, in full, is her reply:

Thank you for your e-mail. £2.82 is still an awful lot of dough for a loaf. A cursory glance around my local supermarket or online reveals gluten free loaves are sold for much less.

Whichever way you slice it I stand by every word of my comment.

Best,

Emma

The reply may not have addressed any of my concerns (for one thing, the claim that the NHS spends £32 on bread is still up on the TPA website), but those are some excellent puns, I’m sure you’ll agree. I’d say Boon should consider writing for a tabloid in her spare time, but judging by how often she and the rest of the TaxPayers’ Alliance are quoted in the papers, it seems a little redundant.

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How to inflate figures and scandalise people

A number of papers this week (Daily Express*, Daily Mail, Daily Mirror, Daily Telegraph, Wales on Sunday) have all carried the same story, claiming that, in the words of the Daily Mail, “NHS officials pay £32 for gluten-free bread that costs £2.25 in the shops”.

Though it’s not impossible that a big organisation like the NHS has inefficient bread-buying schemes, it seems a bit unlikely that something as widely prescribed as gluten-free bread is being bought for more than 10 times its shelf price. So where did the figures come from?

Well, it looks like the story comes from this Welsh government data about prescriptions. Sure enough, if you look it says that the 27 prescriptions of a particular type of bread, Lifestyle Gluten-Free High-Fibre Brown, cost £32.27 each.** But doctors aren’t prescribing one loaf of bread at a time.

The important column is the one marked “quantity”, which tells you how many grams of bread were prescribed. For Lifestyle Gluten-Free High-Fibre Brown, doctors prescribed a total of 123,600 grams. Divided between the 27 people, that’s 4,577 grams each, or about 11 loaves of bread per person. So that £32.27 figure is the cost of buying 11 loaves of bread, not 1, and as the Welsh government points out, it works out at around £2.82 per loaf.  This is still slightly more than the cheapest online cost of the bread, so I assume there is still room to bring prescription costs down, but NHS Wales is certainly not spending more than £30 on a loaf of bread.

* Turns out James Delingpole writes for The Express too. Huh.

** If you want to check for yourself, it’s in section G-O under the name “Lifestyle_G/f H/fbre Bread Brown”.

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Happy birthday Neptune?

Neptune

Happy birthday!

Just a quick post: according to The Observer, tomorrow (July 11) will be one Neptunian year since the discovery of the planet Neptune. Except…

One year on Neptune is 60,190 Earth days. Neptune was discovered on 23 September 1846, so Neptune’s first birthday will be 60,190 days after this date.

23 September 1846 + 60,190 days = July 10, 2011

Neptune’s birthday is today, not tomorrow! We’ll all be celebrating on the wrong day!

Never mind phone hacking, this is the real scandal.

Edit: The BBC is even more wrong, claiming Neptune’s birthday is July 12. The philistines!

Double edit: In fact, it looks like we’re all right! July 10 is one average Neptunian year after the date of discovery, July 11 is the day when Neptune will have made precisely one orbit around the solar system’s barycentre (i.e., its centre of mass when you take the Sun and all the planets into account), and July 12 is the day that Neptune will have made precisely one orbit around the Sun. (A figure of July 13 is floating around as well, most likely as a result of an Indian newspaper article which has taken timezones into account). Thanks to Up, Blogstronomy and the Wikipedia users on Talk:Neptune!

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Defending tau

The Daily Mail today has a piece about the proposed alternative to the number pi, tau (τ), equal to 2 x π.*

Basically, the reason we might want to change to tau is simple:

Pi is defined as the circumference of a circle divided by its diameter. We came up with this definition thousands of years ago, before modern geometry had taken off, and it’s a perfectly good number.

However, we now know that the diameter of a circle – the distance all the way across – isn’t really the best way to measure a circle. Instead, it’s better to measure the distance the radius of the circle – the distance from the centre to the edge. For example, if you’re working out a planet’s orbit, the distance from the planet to the Sun (radius) is a nice logical thing to measure, but the distance from the planet to the other side (diameter) of its orbit doesn’t really mean anything important.

Since the radius is half the diameter, circumference divided by radius is twice as big as circumference divided by diameter, which is why tau is twice as big as pi.

The definition of 1 radian. The red line (radius) and blue line (arc length) are the same length. By Stannered, CC-SA-BY-3.0

Tau is also nice because it makes working with angles a bit easier. The most natural way of measuring angles – the way you have to do it if you’re doing maths or physics – is to measure them in radians. The radian is defined in terms of the circle’s radius – one radian is the angle you get if you walk around the circle for a distance of one radius. If you travel 2π radians, you travel a distance which is 2 times pi times the radius, or pi times the diameter; in other words, you travel the length of a full circle, 360°.

However, that 2 in there is a bit of a pain. It basically means that, in physics or maths, whenever you’re dealing with a circle or a wave you get annoying factors of 2 popping up in your equations, and unless you’re very careful, it’s easy to forget a factor here or put an extra one in there, making your sums completely wrong. For example, to switch between ordinary frequency and angular frequency (effectively, switching from revolutions per second to radians per second), you multiply the frequency by 2π. This is a change we need to make a lot when working with waves, and it’s so easy to lose a factor of 2 when you’re working with a bulky equation.

That factor of 2 is only in there in the first place because we made the mistake of basing pi on the diameter instead of the radius. If we replaced pi with tau, 1 circle would be τ radians, and that factor of two would disappear. It wouldn’t be a groundbreaking change, but it would still be quite nice, and it would make the mathematics of circles a bit easier to understand. Of course, the hassle of teaching people to use tau instead of pi is probably greater than the benefits, so its unlikely we’ll ever give up pi.

Unfortunately, the Mail is quoting from a (paywalled) interview in The Times with University of Leeds lecturer Kevin Houston, whose and they seem to cut down what he’s said to just:

‘Mathematicians don’t measure angles in degrees, we measure them in radians, and there are 2pi radians in a circle,’ Dr Houston said.

“That leads to all sorts of unnecessary confusion. If you take a quarter of a circle, it has a quarter of 2pi radians, or half pi. For the number of radians in three quarters of a circle, you have to think about it. It doesn’t come naturally.

‘How much simpler it would be if we just used tau instead of pi,’ Dr Houston added. ‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You don’t have to think.’

Trimmed like that, it sounds like Houston is only promoting tau because he’s too stupid to work out three quarters of two (his Youtube video, linked by the Mail, explaining the mathematics of tau, shows this is not the case). So perhaps naturally, Daily Mail commenters have leapt at the chance to prove that they’re smarter than a mathematician, because really, what do mathematicians know about mathematics?!

If an ‘A’ level Maths student has trouble with the difference between Tau and Pi, then they should be on another course. Any excuse to dumb down the kids and stop them thinking for themselves!

Alan, Frankfurt, Germany (ex pat)

Right on! How dare we dumb maths down by making it slightly clearer!

‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You don’t have to think.’ …..It may be appropriate for DM readers who like not to think, but I’m afraid mathematicians do think, and aren’t interested in tau, thank you very much.

rupert, Yors4hire, UK

Except for all the mathematicians and scientists who support tau I daresay because they think.

This tau thing is clearly aimed at mindless rote learners but to those of us who actually understand maths, pi expresses something meaningful which is precisely why we refer to it so much.

Vincent, Glasgow

Pi and tau express more or less the exact same thing – the shape of a circle – tau just expresses it in a slightly more logical way.

As a retired Maths teacher this idea lacks intuitive sense. The whole point of the exercise is to relate the circumference of a circle to its diameter – and the ratio is the irrational number 3.14159… The ratio is NOT 6.whatever! That’s the basic theory. Then there are various formulae needed at basic school level: for example, the area of a circle is pi time radious squared. The new formula would be tau times radius squared divided by four: an extra calculation step. Or the volume of a cone pi r squared h…. and so on. And in times of austerity how many schools could afford a new set of textbooks filled with tau? (And all authored by Leeds people, no doubt!) And then there are the millions of calculators with the pi button built in…. No! This idea is like trying to say that from 2012 we’ll all drive on the right – indeed the idea of tau is worse than that because there are regions of the world already driving on the right….. This is a big UM and No No

Andrew, Cwmbran

No, but the ratio of the circumference of a circle to its radius IS 6.whatever (6.28318… in fact). The fact that the area of the circle becomes a half times tau r squared (0.5 τr2 – there’s no dividing by four involved) is one of the downsides to tau, but as Kevin explains in the video, there is a deeper mathematical reason why we would expect that half to be there, so while it’s annoying it does make sense.

This is the way you can waste a lot of time while avoiding doing anything of real interest or value to anyone. What a waste of brain cells!! Is this supported by public funds? There are real problems in the world today that are worthy of serious consideration, but when academics waste their time on things like this, they prove that they have no value to society at large and should be dismissed.

Samuel, Dubuque, Iowa

One mathematician making a 5 minute Youtube video in his spare time? How dare he! He should devote every second of his life to curing cancer!

Big Wow… Is “2pi” the only mathematical innovation Leeds University can come up with, it’s best 21st Century contribution to the advancement of mathematics? Talented Maths kids doing their 5 science A levels must be crossing Leeds off as even a 5th choice.

Russ H, Bucks

Again, this is one guy working in his spare time. This is not the only thing the University of Leeds Maths department does! (Incidentally, 55% of Leeds pure maths research is “world leading” or “internationally excellent”, and a further 40% is “internationally recognised”.)

BUT….e^([pi]i)]=-1 and this does not work for tau. There are uses for Pi beyond circles!

Miles, Australia

(This refers to Euler’s identity, eπi = -1, which gives us a nice way of representing imaginary numbers using angles. And despite what Miles says, it’s all about circles.)

That’s true, it doesn’t. Instead, eτi = 1. This is even better than Euler’s original version, since we no longer have that minus sign (and all that minus sign told us is that pi radians = half a circle, something we already know). Quite a few comments are like this – “OH NO EULER’S FORMULA IS BEAUTIFUL, WE CAN’T CHANGE PI COS THAT WILL BREAK IT” – and yet no-one actually bothers working out what it would look like with tau.

Professional jealousy. Eienstein acceepted Pi and I can assure you he was more intelligent than this egghead. This man just wants to make a name for himself. Change all the books indeed. He is “daft” !

Ruckus, myrtle Beach SC (ex pat)

And why do we bother speaking English? If German was good enough for Einstein, it’s good enough for us!

All those comments have been upvoted, by the way, unlike this comment, which currently has a score of -1:

I am in full favour of this proposition. Unfortunately, a large number of these comments seem be be from people with only a basic understanding of mathematics. Using Tau in place of Pi would reduce the need for a constant in a plethora of standard calculations involving circles and spheres, the like of which children will be schooled in. Furthermore, the simplicity of the equations using Tau may increase understanding and encourage children to pursue an interest into further mathematics. From my experience of mathematics lessons, the majority of students didn’t dislike mathematics, but rather found it too complicated to enjoy. Once provided with a topic they were able to grasp, students began to enjoy working the problems. Once children have achieved a satisfactory grasp of simple circle equations, the transition to understanding the calculus is a much easier one. I think that should the readers have been taught using Tau the comments here would be better informed.

Pep, Manchester

Good old Daily Mail comments, eh?

* They claim the idea was invented by Kevin Houston at the University of Leeds. In fact, it’s much older than that – Bob Palais first came up with it in 2001 – and Houston is just promoting it. Also, as a conflict of interest thing, I guess I should point out that Kevin taught me a few years ago, and is a thoroughly nice guy.

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Hard-hitting research from Cravendale

(Hat tip to @TomChivers)

Look at me, boldly breaking press embargoes to bring you the FACTS. What IS the formula for the perfect cup of tea?

You might have thought that George Orwell answered that fairly conclusively years ago, but if you did then you are clearly an idiot. After all, George Orwell was just an author, journalist and political campaigner. What the hell do writers know about tea?! No, to answer this question we need the help of cargo cult science!

Good thing Cravendale’s taken the hit and hired scientists from Northumbria University to tell us the secret of good tea. Spoiler warning: the answer’s “Cravendale”.

Some of the more sceptical among you might be wondering how they tested this, and how awfully convenient it was that this research, which appears to have been funded by Cravendale, just happened to prove that Cravendale made the best cup of tea. Well, how can you argue with this experimental methodology:

Following the brewing process, teabags were removed and varied amounts of semi-skimmed Cravendale milk [0ml, 5ml, 10ml] were added to samples for our sensory advisory panel.

The panel’s results reveal that the ideal amount of milk to be added is 10ml.

Yep! They compared Cravendale milk to no milk at all, and shockingly found that Cravendale tastes better than nothing. This must prove Cravendale is the best milk ever, QED.

Incidentally, 10ml isn’t much milk at all, really – it’s less than half a single measure of spirits, after all. You’d think that if you were trying to test the ideal amount of milk to put in tea, you’d try everything from “no milk at all” to “nothing but milk”, but to be fair I guess the scientists involved had more important things to do than indulge the bizarre PR-driven whims of a milk filtration company.

There’s no mention of sugar in the paper, and certainly no mention of anything more exotic – a spoonful of honey, a dollop of cream, or a splash of lemon, for instance. I assume Cravendale hasn’t figured out how to filter sugar or lemon juice yet. They have however found time to make some truly groundbreaking progress in the field of thermodynamics, however:

The optimum temperature to drink tea at is 60°C. With the addition of Cravendale milk, our brews were able to reach the optimum temperature after just six minutes, two minutes faster than regular black tea.

Yes, adding a cold liquid to a hot liquid will in fact cool the hot liquid down! Of course, this only works with Cravendale milk – as everyone knows, if you add regular supermarket own-brand milk to tea, the tea just keeps getting hotter and hotter!

Still, all this stuff about “things cooling down over time” is pretty state of the art – I mean, Isaac Newton only figured out his law of cooling 300 years ago. Thank goodness Cravendale is on the cutting edge.

Anyway, based on all this research, the scientists at Northumbria have come up with a formula for the perfect cup of tea. Are you ready for this piece of extremely rigorous mathematics? Here goes:

TB + (H2O @ 100°c) 2minsBT + C(10ml) 6minsBT = PC (@ OT60°c)

where TB = teabag, BT = brewing time, C = Cravendale milk, OT = optimum temperature and PC = perfect cuppa.

Look how science-y that is! There are letters and numbers and plus signs all over the place! And they say “H2O” instead of “water” – only a true scientist would do that! Also according to that formula you should keep your tea brewing for 6 more minutes after you add the milk which sounds like a one-way trip to astringency-town to me, but then I’ve never written my tea making instructions down in the form of algebra, so what do I know?

This “research” has been embargoed until tomorrow morning – let’s see if any of the papers are stupid enough to run with it.

Anyway, this was quite a long post, so you should probably treat yourself to a nice cup of tea now. Just remember to use own-brand milk.

Edit: So far, the Mail, Telegraph, Express and Metro have all swallowed Cravendale’s PR rubbish. Sigh.

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