It’s been a while since I covered this kind of dodgy maths, so let’s go over the basics. “Formula for” stories are seen by PR agencies as a great way to get free press coverage for whatever product they are shilling because the equations can be dressed up as real research. Attaching a “Dr” or “Prof” to your news story is a great way to gain legitimacy, and the media lap it up as another example of what those crazy boffins are up to.

While this is all great for the PR agencies and their clients, it’s terrible for science. These formulas tend to be based on extremely dodgy assumptions and contain variables which can’t be objectively measured. What’s worse, even a simple mathematical analysis usually reveals problems such as division by zero, which can lead to things like cold and lumpy but infinitely perfect pancakes.

With these problems in mind, let’s take a look at the formula for the perfect handshake. It was created by Geoff Beattie, head of Psychological Sciences at the University of Manchester, and is detailed in this the press release:

I’ve broken it over two lines because the thing is so long, and I think that square root is meant to cover the entire equation, not just the first term, but the press release isn’t very clear. We’ve also got a definition for the many variables, along with what I assume is their optimal values:

(e) is eye contact (1=none; 5=direct) 5;
(ve) is verbal greeting (1=totally inappropriate; 5=totally appropriate) 5;
(d) is Duchenne smile – smiling in eyes and mouth, plus symmetry on both sides of face, and slower offset (1=totally non-Duchenne smile (false smile); 5=totally Duchenne) 5;
(cg) completeness of grip (1=very incomplete; 5=full) 5;
(dr) is dryness of hand (1=damp; 5=dry) 4;
(s) is strength (1= weak; 5=strong) 3;
(p) is position of hand (1=back towards own body; 5=other person’s bodily zone) 3;
(vi) is vigour (1=too low/too high; 5=mid) 3;
(t) is temperature of hands (1=too cold/too hot; 5=mid) 3;
(te) is texture of hands (5=mid; 1=too rough/too smooth) 3;
(c) is control (1=low; 5=high) 3;
(du) is duration (1= brief; 5=long) 3.

Both the formula and its variables are looking really dodgy. I’ve literally no idea what terms like {(4<c>2)(4<du>2)}² are meant to mean. I can only think that the angular brackets denote some kind of average, but then why do they only apply to some of the variables? Are those 2s actually meant to be ²? In which case you can rewrite the whole term as (2<c><du>)⁴, which is at least a little bit simpler.

I also take issue with using two letters to stand in for one variable, because they can be confused for two separate variables multiplied together. Measuring “verbal greeting” and “vigour” doesn’t mean that both of your variables have to start with a v – real mathematical equations make extensive use of Greek letters in an effort to solve this exact problem. But even if this equation was beautifully formatted, it would still be rubbish.

All the measurements are completely subjective, and the scales of 1 to 5 indicate the data behind the equation was probably collected from a survey. This even includes variables such as temperature, which can easily be measured scientifically. Remember, subjective measurements are one of the hallmarks of a “formula for”.

I emailed Beattie yesterday to ask how the formula was created, but as he is yet to reply I can only speculate. I think what he has done is ask people a bunch of questions about handshakes, and then tried to fit their answers to some kind of least-squares model, as indicated by the squares and square root in the formula. This method gives you a great equation for “explaining” the data you’ve gathered, but doesn’t necessarily tell you anything about the phenomena you’re examining.

If that is the case, I still don’t understand how the formula is meant to work. You’d expect that the perfect handshake would have a maximum value of PH, and since there is no division or subtraction involve, that just means slotting in the maximum values for all your variables. The optimal values in the press release include a few 3s and 4s though, so PH isn’t going to be maximum. Hmm.

As with all “formula for” stories the maths behind the perfect handshake formula just doesn’t add up, yet it’s being interpreted as a serious piece of research. Comments on the Mail story such as these two show just how much damage this can do to people’s impressions of science:

“So, most of the country is out of work desperately trying to survive and these idiots are getting paid, what – to study handshakes? Sack these people immediately!”

How much time did the nutty professor spend on this useless bit of information?

Mathematical models and equations are a fantastical tool for understanding the natural world around us, but they have to be based on sound assumptions and decent science – things that “formula for” stories such as this almost invariably lack.

We all know that science can be complicated and confusing, but don’t let that get you down – Fake Science is here to straighten everything out. Did you know that the periodic table is actually based on Scrabble, or that wind power uses giant fans to make wind? Science has never been so simple.

Want to lose weight? Keep it off your plate

Simply leaving serving dishes on the kitchen counter rather than bringing them to the dining table reduces the amount of food you eat, say researchers at Cornell University. They found that this simple dieting strategy reduces the temptation of second helpings, cutting the number of calories people consumed by 20%.

Brian Wansink, director of the Cornell Food and Brand Lab, said that the same idea can be used to promote healthier foods over sugary snacks – keeping fruit on display makes you more likely to eat it instead of reaching for a piece of cake in the fridge.

Animal privacy? Not in my backyard

Wildlife documentaries infringe an animal’s right to privacy, says Brett Mills, a lecturer in film studies at the University of East Anglia:

“We have an assumption that humans have some right to privacy, so why do we not assume that for other species, particularly when they are engaging in behaviour that suggests they don’t want to be seen?”

I’m a staunch defender of civil liberties, but even I think extending the right to privacy to animals is going a bit too far. Of course, great care should be taken to avoid distributing their natural habits or causing them distress, but I really don’t think animals mind us watching them doing what they do.

Green tax would hurt the poorest

A proposed tax on carbon footprints would hit the poorest households hardest, according to study from the University of Leeds. The carbon tax would cost low earners 6% of their annual income, while the richest households would only pay around 2%.

The difference is the result of poorer households spending more on costs such as heating and electricity – 40% of their income, compared to just 8% for high earners.

Forensic experts are unable to accurately determine the age of bruises on the bodies of crime victims, say researchers at Queen Mary, University of London. A study published in the Journal of Forensic and Legal Medicine, suggests that sentencing of criminal cases involving bruising, such as child abuse or assault, could be based on flawed conclusions.

The researchers evaluated the bruise-judging abilities of 15 forensic experts with the aid of 11 willing volunteers and a suction pump. Each subject used the pump to inflict bruises on themselves, which the researchers photographed daily until they had faded completely. The photos were digitally altered to remove any hints that might aid the experts in estimating their age, such as marks from the suction pump, then randomly presented for them to judge. They were also asked to place a series of photos in chronological order, identifying how the bruise faded over time.

While we’re used to seeing experts on TV pin down the time of a crime to the nearest minute, the reality is somewhat different. The median difference between the expert’s assessment and the true age of a bruise was 26 hours, but some were even further out, with one expert getting it wrong by 454 hours or nearly 19 days.

Fresher bruises were easier to identify, with a 52% success rate for injuries under 12 hours old, but accuracy fell as the bruises faded. There was a slight increase in accuracy for injuries over 6 days old, but this could be due to chance as there were only a few bruises that lasted this long.

The experts fared better at the second task, placing the bruise images in chronological order without too many mistakes. The results seemed to depend on the nature of each bruise rather than the skill of the experts, because some bruises showed clearer changes in size and colouration than others.

Incorrectly judging the age of a bruise could have significant effects on a criminal trial, either by allowing perpetrators to get away with their crime or placing the blame on an innocent suspect. The study authors conclude that forensic experts’ estimates are unreliable at best, which calls into question whether they should be used in court at all.

Pilling, M., Vanezis, P., Perrett, D., & Johnston, A. (2010). Visual assessment of the timing of bruising by forensic experts Journal of Forensic and Legal Medicine, 17 (3), 143-149 DOI: 10.1016/j.jflm.2009.10.002

Science is often applauded as a discipline of progress, the great giver of development and improvement to life. And yet science has deprived a forgotten generation, a generation who suffer the indignity of progress and yet reap very few of the benefits.

My great aunt, simply known by everyone as Auntie, is very nearly 89 years old. Born in 1921 she is basically all my grandparents rolled into one. All my natural grandparents were gone by the time I was seven and so she had to bear the brunt of surrogate grandparenthood. And I wasn’t the easiest of surrogate grandchildren. Being a science geek, and being perpetually unpopular, meant that I won several academic awards during my high school years. Whilst these awards were mostly for science, I did win the Year 8 award for French.

However, what has to be said is that these awards ceremonies were as about as enlightening as a Gordon Brown YouTube video. And yet she sat diligently through several mind-numbingly tedious and over-bureaucratic awards ceremonies.

Despite her willingness to suffer such torture, science, the subject that enforced her to endure such an ordeal, hasn’t been kind to her. Scientific progress has meant that she now lives in a world where it is commonplace for people to reach her age. And yet the human body is simply not designed to last that long.

Our younger generation laud science as the bringer of technology. Science gave us the internet, the iPhone and HD TV. Yet she was born between world wars, in a time when such ideas were fanciful. What has science done for her? It has extended her life so that she now has to deal with dementia, her body wearing out under the strain of scientific progress. Last week she sneezed and fractured a vertebra. A woman who served in WW2 as part of the Women’s Auxiliary Air Force (WAAF) now needs four care visitors a day just to help her stay in her home.

If, as she will soon surely need, she has to move into a care home, it will cost around £1000 per week. The travesty is that if she hadn’t worked hard all her life and had no savings then care would be provided. But my point isn’t a political one.

Is the subject that I love causing such problems? On our exponential march into the future are we leaving behind those that don’t reap the benefits? Those of a religious persuasion are sometimes shaken in their convictions by a lack of faith. Just sometimes I wonder whether a world without science would be kinder….

Here’s an extract from an article I wrote for New Scientist in honour of Pi Day today.

The stars overhead inspired the ancient Greeks, but they probably never used them to calculate pi. Robert Matthews of the University of Aston in Birmingham, UK, combined astronomical data with number theory to do just that.

Matthews used the fact that for any large collection of random numbers, the probability that any two have no common factor is 6/pi2. Numbers have a common factor if they are divisible by the same number, not including 1. For example, 4 and 15 have no common factors, but 12 and 15 have the common factor 3.

Matthews calculated the angular distance between the 100 brightest stars in the sky and turned them into 1 million pairs of random numbers, around 61 per cent of which had no common factors. He got a value for pi of 3.12772, which is about 99.6 per cent correct.

A serious science survey?

The BBC reports that one in 10 children believe the Queen invented the telephone, while others suggest Charles Darwin and Noel Edmonds. The results come from a survey of 1,000 school kids, but rather than despairing at the state of science education, I’m actually amused by this story.

These types of articles seem to crop up fairly often, with children giving nonsensical answers to questions about historical facts. Everyone always interrupts them fairly seriously, but I think it’s far more likely that the kids are just having a laugh.

High-gravity lava lamps

Would a lava lamp work on Jupiter? There’s only one way to find out – build a giant, semi-lethal centrifuge out of Meccano, and take your lamp for a spin:

If that’s true, I’m incredibly disappointed. I understand that in a time of global economic turbulence, space exploration may not be Obama’s top priority, but his new vision for NASA seems incredibly short-sighted.

Instead of “boldy going”, astronauts will spend another ten years floating around the International Space Station. NASA will concentrate on Earth-based projects – mostly climate change related – and private companies will take over the Space Shuttle’s job of ferrying cargo in to orbit. The moon and Mars will just have to wait, it seems.

This worries me, but not because of some romantic idea of humans exploring the final frontier – my concerns are far more practical. I believe getting off Earth and colonising other planets is essential for the continuation of the human race. At the moment we’ve got all eggs in the proverbial basket – if an asteroid were to strike Earth, it could potentially wipe us out completely. Colonisation simply spreads the risk.

Building a base on the moon and then eventually Mars would not only be an incredible feat of human ingenuity, but also a kind of species-wide insurance policy. It’s a project that would take decades, and unfortunately politicians only think in four-year terms. I understand that Obama is under attack because of his healthcare plans, and the budget has to be balanced somehow, but cutting Constellation isn’t the answer.

Next stop, outer space

Even London natives can struggle with the complicated spiderweb that is the Tube map, but surprisingly enough it is actually intended to simplify getting about the capital. Inspired by its iconic design, Harvard scientist Samuel Arbesman developed a similar map for getting about the Milky Way:

But where is Morington Crescent?

The coloured lines correspond to an arm of the spiral galaxy, and each stop is a star or other astronomical object.

Mental time travel

You won’t be journeying to the age of the dinosaurs just yet, but psychologists at the University of Aberdeen have discovered a strange form of time travel. Apparently thinking about the past or future causes people to move backwards or forwards. The researchers suggest behaviour could be the origin of temporal metaphors such as future = forward and past = backward.

Bond. Strange Bond.

The Royal Society of Chemistry continued it’s tradition of strange PR stunts this week by announcing a search for a Sean Connery lookalike.

As if devising a new ending for the Italian Job or cooking the perfect Yorkshire pudding weren’t enough, they want to use the lookalike in a bizarre photoshoot designed to highlight the importance of British research keeping the nation healthy. No, I don’t get it either.

The Mail and others have leapt on a rather silly paper by Peter Backus, a University of Warwick economist. He’s used the Drake equation, which was originally intended to estimate the number of alien civilizations in our galaxy, to explain why he doesn’t have a girlfriend.

You can visit Wikipedia for an explanation of the Drake equation, or alternatively check out Colin’s dissertation for the full details. The basic idea is to break down all the requirements for alien life in to individual factors, such as the chance of a star having planets or a planet supporting life, then multiply them together to get the number of civilizations out there in space. Trouble is, we don’t have very reliable evidence to back up most of the figures, so estimates vary wildly.

Backus has used the same principal to find his perfect woman, and “discovered” that there are only 26 women in the UK that are suitable for him. That’s a one in 285,000 chance of meeting “the one”, apparently. Of course, the exact same criticism of the Drake equation can be applied here – most of his numbers are entirely subjective and not backed up by evidence. Pick some different numbers, and you’ll come up with an entirely different answer.

I can’t really blame Backus for his formula, as it’s not like he’s trying to sell anything or has got the maths wrong. What I find annoying is the way the media leaps on the figure of “one in 285,000″ as an absolute fact, and describes maths no more complicated than multiplication as if it were some sort of advanced calculus that should only be attempted by a genius. Let’s just hope no one discovers the ancient art of “division”, or our heads just might explode.

I actually had some success, and after more than 12 hours of work was rewarded with this rather understated error message:

Quite. Sadly, in the end I had to say goodbye to my faithful old PC and buy a new one, complete with Microsoft’s latest operating system, Windows 7. It’s quite different to the Windows XP I’m used to, especially as I’d disabled most of XP’s bells and whistles to make it run like Windows 2000. Essentially, I’ve been using the same operating system for an entire decade, and now I’ve been forced to change some long-held habits!

All of which leads me on in a fairly rambling way to what I had originally intended to talk about at the start of 2010 – whether we’re now living in a new decade. The media seem pretty convinced that we’ve abandoned the “Noughties” in favour of the “Teens”, but the maths says otherwise – it won’t be until the end of 2010 and the start of 2011 that we enter the next decade.

It’s the same argument that you probably tired of in the years leading up to December 31st, 1999. At the time, mathematicians said that millennial celebrations should be put off until the start of 2001, while the rest of the world largely ignored them.

Simply put, our calendar system starts at the year 1 AD, not the year 0 AD. One year later is 2 AD, ten years later is 11 AD, and two-thousand years later is 2001 AD. So, new decades start with years ending in a “1″.

But when we speak of the Noughties, we obviously mean the years 2000 to 2009. The year 2010 can’t be a Noughtie, because it doesn’t have a 0 in the right place. And hang on a moment, isn’t the calendar based off the life of Jesus, a man whose date of birth we know very little about? And lets not even start on the missing 11 days of September 1752.

Given the human desire for patterns and our fondness of round numbers, it’s probably best if we stick to celebrating 2010 as the new decade – it’s no less arbitrary than any other choice. Even so, I can’t help wanting to go with 2011. It may be ugly, but it’s mathematically correct!

I’m absolutely amazed that Labour are reducing science funding, while at the same time refusing to budge on wasteful schemes like ID cards or Trident nuclear missiles.

In the past year alone the Government has spent £81.5 million on developing biometric ID cards, and the final cost is expected to be £4.5 billion over a ten year period. This is despite the science behind biometrics not being fit for purpose.

Meanwhile, the cost of replacing our Trident nuclear missiles has been placed at £130bn over 30 years (though the Government says it will only be £20bn). This is counter to the spirit of the Nuclear Non-Proliferation Treaty, if not the actual law, and a fantastic waste of money. Given the choice between expanding human knowledge, or maintaining the potential to blow people up, I know which I’d go for…