# Φ

Phi is one of very few numbers to have three ‘names’ of sorts; the first is, of course, phi (from the Greek letter Φ, pronounced ‘fee’), and the second is its numerical representation, 1.618 (to four significant figures; the number itself is equal to (1+√5)/2). The third comes courtesy of Dan Brown,  semi-conspiracy theorists and lots of gullible people around the world, and generally comes in a form similar to ‘SERIOUSLY IT’S ACTUALLY A THING DON’T GO AWAY PLEASE’.

Y’see, phi is a number with a great deal of myths, or at least half-truths, surrounding it, which lead a lot of people who don’t do enough research into things to believe it all holds a vast array of semi-magical properties, ranging from molluscs to architecture. Many of this myths, some of which shall be explored later, found their way into Chapter 20 of The Da Vinci Code, which (some might say unfortunately) went on to be a bestseller. Dan Brown is an entertaining author, but a great deal of his work is based around these sort of half truths. This is hardly something that only he is guilty of as an author, but unfortunately a habit of including a section named ‘Facts’ at the start of his books and a tendency to at least start from a position of truthfulness has lead a few too many people to think that far too much of what he says is true. Hence why large portions of people get very, very angry at him, and why phi is rarely a concept taken seriously within intellectual circles.

Anyway; back to the number itself. Phi’s unique property as a number is, seemingly, innocuous enough; if you subtract 1 from it, and then divide one by that number, you return to 1.618 (or, to put it another way, 1/0.618=1.618). Go find a calculator and try it if you want; if you set it up to perform this function [1/(1-Ans)=Ans], you can start from any number above 1 and should end up at phi after a few iterations.

Phi was discovered by Greek mathematicians, never ones to leave such a nicely self-fulfilling number alone once they’d got hold of it, and rapidly realised something quite nice concerning phi and rectangles. If you take a rectangle with a short side of length 1 unit and a long side of length Φ units, and then cut away from that a square with side length 1 unit, then the little rectangle you get left over will be the same shape as your original rectangle; the ratio of its side lengths is 1:1.618. It also just so happens that a rectangle this shape looks very… balanced and aesthetically pleasing, and so our overenthusiastic Greek mathematician friends dubbed this shape ‘the perfect rectangle’ and called phi ‘the golden ratio’.

Phi found its way back into the mathematical world several hundred years later in the early 13th century when a Pisa-born (Pisan? Pisaish? Not sure) mathematician called Leonardo Fibonacci started messing about with what would later become one of the most famous mathematical sequences of all time. The Fibonacci sequence is a very simple business; start with two ones and then, for each successive term, add the previous two. So we start with 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 8, 13, 21, 34 and so on. The reason it has a relation to phi is that if you divide two successive terms of the sequence by one another then you get an approximation to phi, with the approximation getting more accurate as you go further up the sequence. It starts off rather vague (1/1=1 and 2/1=2 aren’t even close), but before long things start to converge (8/5=1.6, much more like it), until eventually we arrive at something very very close (610/377= 1.618037, accurate to five significant figures). This, once again has a geometrical analogy; if you stick two squares of side length 1 unit together, and then add a square of side length two units, and then one of side length three and so on, you start building up an increasingly large rectangle; a rectangle, moreover, that starts to look suspiciously like our old friend ‘the perfect rectangle’ the more squares we add.

However, the reason phi has got so many people worked up and excited over the years is its habit of turning up in nature; although, it must be said, it doesn’t do so nearly as often as people think. A good example occurs in flowers; if you count the petals on flowers, the final number is often one of those in the Fibonacci sequence (so you get three-leafed clovers one hell of a lot more than four leaved clovers). One flower of particular interest is the rose, which often has eight on the inside and five around the outside to make 13 overall; 3 Fibonacci numbers. There are even arguments that pineapple skins and sunflowers share this feature, but trying to explain that without pictures is rather beyond my capabilities. Nobody’s entirely sure why this is, but many attribute it to a mixture of luck and confirmation bias; once somebody tells you about phi, it’s hard to stop seeing it everywhere and to ignore the countless occasions when it doesn’t crop up. I mean, 3, 5 and 8 are hardly uncommon numbers off their own bat.

However, this hasn’t deterred supporters of the theory, who claim phi turns up literally everywhere; far more often than it actually does, in fact. There are three commonly stated examples of complete phi-related bullshit that are particularly aggravating to those who know about them. The first concerns the Parthenon, in Athens, of which it is said that if you look at it front on the shape of its profile fits exactly into a perfect rectangle. Even if it did, this wouldn’t be too surprising, for as we’ve said the perfect rectangle happens to be an inherently aesthetically pleasing shape that it would not be too surprising to see incorporated into architecture to make a building look good, but the fact is that this claim is totally wrong. Pictures claiming to show it always leave out a few stairs at the bottom, or use a slightly imperfect rectangle; the relationship is close, but not ‘perfect’ as some people like to believe.

The Da Vinci connection to phi is, perhaps surprisingly, not confined just to Dan Brown; after Fibonacci, Da Vinci’s tutor Luca Pacioli was the first person to write about it (his book was entitled ‘the divine proportion’, Φ’s other nickname), and did so in a book that Da Vinci apparently illustrated. He definitely knew about the thing, therefore, but didn’t use it to compose either the Mona Lisa or the Vitruvian man. In fact, the name of the latter work gives a clue as to where its dimensions come from; Vitruvius was a Roman now known as ‘the world’s first engineer’, who used proportions of the ‘ideal’ human body (or at least what the Romans thought of it) when designing buildings. His dimensions, however, were based merely on the idea that one’s armspan and height are equal and eight times the height of the head, and didn’t use phi at all. Many phi supporters will tell you that phi does crop up a lot when measuring the human body, and in some people it does; but if we look at anthropometric data to get average data, the number of times phi appears drops markedly. In any case; there is a LOT to measure in the human body, and frankly it would be more surprising if a few of the ratios didn’t end up being phi, particularly what with it being a ratio our eye has evolved to find pleasing.

And then there’s the nautilus; an incredibly beautiful deep-sea mollusc that spends its days bobbing up quite happily in its remarkable spiral-shaped shell. However, some will tell you that such a shell is, in fact a ‘golden spiral’,  getting further away from its centre point by a factor of Φ every quarter-turn (this is the typical way of measuring spirals, because REASONS). Unfortunately, this theory was shot down in 1999 when an American mathematician named Clement Falbo decided that the best way to spend his time was to measure a few hundred shells and work out an average. His results came to an average spiral ratio of 1.33:1, making the nautilus the bearer of just another old-fashioned logarithmic spiral (incidentally, there are other, far less pretty, molluscs that do have ‘golden shells’, but people tend to forget about them for some reason).

The ‘golden ratio’ is an interesting little piece of mathematics, the kind of thing that nerds make jokes about on the internet and inconceivably bored teenagers mess around with on calculators at the back of Friday afternoon geography (I speak from extensive personal experience). It pops up in a lot of places and has several interesting properties; but some divine mathematical instrument with which to describe the whole natural world?

…might be going a bit far.

# “Lies, damn lies, and statistics”

Ours is the age of statistics; of number-crunching, of quantifying, of defining everything by what it means in terms of percentages and comparisons. Statistics crop up in every walk of life, to some extent or other, in fields as widespread as advertising and sport. Many people’s livelihoods now depend on their ability to crunch the numbers, to come up with data and patterns, and much of our society’s increasing ability to do awesome things can be traced back to someone making the numbers dance.

In fact, most of what we think of as ‘statistics’ are not really statistics at all, but merely numbers; to a pedantic mathematician, a statistic is defined as a mathematical function of a sample of data, not the whole ‘population’ we are considering. We use statistics when it would be impractical to measure the whole population, usually because it’s too large, and when we instead are trying to mathematically model the whole population based on a small sample of it. Thus, next to no sporting ‘statistics’ are in fact true statistics as they tend to cover the whole game; if I heard during a rugby match that “Leicester had 59% of the possession”, that is nothing more than a number; or, to use the mathematical term, a parameter. A statistic would be to say “From our sample [of one game] we can conclude that Leicester control an average of 59% of the possession when they play rugby”, but this is quite evidently not true since we couldn’t extrapolate Leicester’s normal behaviour from a single match. It is for this reason that complex mathematical formulae are used to determine the uncertainty of a conclusion drawn from a statistical test, and these are based on the size of the sample we are testing compared to the overall size of the population we are trying to model. These uncertainty levels are often brushed under the carpet when pseudoscientists try to make dramatic, sweeping claims about something, but they are possibly the most important feature of modern statistics.

Another weapon for the poor statistician can be the mis-application of the idea of correlation. Correlation is basically what it means when you take two variables, plot them against one another on a graph, and find you get a nice neat line joining them, suggesting that the two are in some way related. Correlation tends to get scientists very excited, since if two things are linked then it suggests that you can make one thing happen by doing another, an often advantageous concept, and this is known as a causal relationship. However, whilst correlation and causation are rarely not intertwined, the first lesson every statistician learns is this; correlation DOES NOT imply causation.

Imagine, for instance, you have a cold. You feel like crap, your head is spinning, you’re dehydrated and you can’t breath through your nose. If we were, during the period before, during and after your cold, to plot a graph of one’s relative ability to breath through the nose against the severity of your headache (yeah, not very scientific I know), these two facts would both correlate, since they happen at the same time due to the cold. However, if I were to decide that this correlation implies causation, then I would draw the conclusion that all I need to do to give you a terrible headache is to plug your nose with tissue paper so you can’t breath through it. In this case, I have ignored the possibility (and, as it transpires, the eventuality) of there being a third variable (the cold virus) that causes both of the other two variables, and this is very hard to investigate without poking our head out of the numbers and looking at the real world. There are statistical techniques that enable us to do this, but they are for another time.

Whilst this example was more childish than anything, mis-extrapolation of a correlation can have deadly consequences. One example, explored in Ben Goldacre’s Bad Science, concerns beta-carotene, an antioxidant found in carrots, and in 1981 an epidemiologist called Richard Peto published a meta-analysis (post for another time) of a series of scientific studies that suggested people with high beta-carotene levels showed a reduced risk of cancer. At the time, antioxidants were considered the wonder-substance of the nutrition, and everyone got on board with the idea that beta-carotene was awesome stuff. However, all of the studies examined were observational ones; taking a lot of different people, seeing what their beta-carotene levels were and then examining whether or not they had cancer or developed it in later life. None of the studies actually gave their subjects beta-carotene and then saw if that affected their cancer risk, and this prompted the editor of Nature magazine (the scientific journal in which Peto’s paper was published) to include a footnote reading:

Unwary readers (if such there are) should not take the accompanying article as a sign that the consumption of large quantities of carrots (or other dietary sources of beta-carotene) is necessarily protective against cancer.

The editor’s footnote quickly proved a well-judged one; a study conducted in Finland some time afterwards actually gave participants at high risk of lung cancer beta-carotene and found their risk of both getting the cancer and of death were higher than for the ‘placebo’ control group. A later study, named CARET (Carotene And Retinol Efficiency Trial), also tested groups at a high risk of lung cancer, giving half of them a mixture of beta-carotene and vitamin A and the other half placebos. The idea was to run the trial for six years and see how many illnesses/deaths each group ended up with; but after preliminary data found that those having the antioxidant tablets were 46% more likely to die from lung cancer, they decided it would be unethical to continue the trial and it was terminated early. Had the Nature article been allowed to get out of hand before this research was done, then it could have put thousands of people who hadn’t read the article properly at risk; and all because of the dangers of assuming correlation=causation.

This wasn’t really the gentle ramble through statistics I originally intended it to be, but there you go; stats. Next time, something a little less random. Maybe

# I’ve been expecting you…

As everybody has been incredibly keen to point out surrounding the release of Skyfall, the James Bond film franchise is currently celebrating its 50th birthday. Yes really- some absolute genius of an executive at Eon managed to get the rights to a film series that has lasted longer than the Cold War (which in and of itself presented a problem when Bond couldn’t simply beat up Commies all of a sudden and they had to start inventing new bad guys). But Bond is, of course, far older than that, and his story is an interesting one.

Ian Fleming had served as an intelligence officer during the Second World War, being involved with such charismatic spies as Dusko Popov (who ran an information exchange in Lisbon and traded signals on a roulette table), before returning to England during the 1950s. He later made a famous quote, based on an event that occurred in 1952:

‘Looking out of my window as the rain lashed down during one of those grey austerity-ridden days in post-war Britain, I made two of the biggest decisions of my life; one, never to spend winter in England again; two, to write the spy story to end all spy stories’.

He began writing the first Bond novel (Casino Royale) in February of that year, retiring to his Goldeneye estate in Jamaica to write it (Bond spent the majority of his time in certainly the earlier novels in the Caribbean, and Goldeneye would of course later become the name for Pierce Brosnan’s first Bond film). He chose the name from American ornithologist (and world-renowned expert on Caribbean birds) James Bond, saying that he originally wanted his character to be a normal person to whom extraordinary things happened, and whilst this brief got distorted somewhat through his various revisions this drab name, combined with Bond’s businesslike, unremarkable exterior, formed a contrast with his steely edge and amazing skill set to form the basis of the infamous MI6 operative (Fleming also admitted to incorporating large swathes of himself into the character).

The books were an immediate hit, demonstrating a sharp breakout from the norms of the time, and the film industry was quick to make its move towards them. As early as 1954 a TV version of Casino Royale starring the Americanized ‘Jimmy Bond’ had hit the screen, but Fleming thought he could go better and started a project to make a film adaptation in 1959, with himself acting as screenwriter. However, the project bombed and it wasn’t until 1961 that Albert ‘Cubby’ Broccoli (along with partner Harry Saltzmann) bought the film rights to the series. This project too was plagued by difficulties; despite Sean Connery being said to ‘walk like a panther’ when he came to audition for the part, Broccoli’s first choice for the Bond role was Cary Grant, and when he said he didn’t want to be part of a series he turned to James Mason. Mason made similar bones and so at last, with some misgivings, they turned to Connery. Said Fleming, ‘he’s not exactly what I had in mind’.

He had even worse things to say when Connery’s first film, Dr. No, was released; ‘Dreadful. Simply dreadful’ his words upon seeing the preview screening. He wasn’t the only one either; the film received only mixed reviews, and even a rebuke from the Vatican (never noted for their tolerance towards bikinis). However, Dr. No did include a few of the features that would later come to define Bond; his gun, for instance. For the first 5 Bond novels, Fleming had him using Berreta 418, but munitions expert Geoffrey Boothroyd subsequently wrote to Fleming criticizing the choice. Describing the weapon ‘a lady’s gun’ (a phrase Fleming himself would later use to describe it), he recommended the Walther PPK as an alternative. Fleming loved the suggestion, incorporating an adapted version of the exchanged into his next book (which was, coincidentally, Dr. No) and giving the name of Bond’s armourer as Major Boothroyd by way of thanks. Boothroyd’s role as a quartermaster eventually lead to his more famous nickname; Q.

Not that any of this saved the film, or indeed ‘From Russia With Love’, which succeeded it. Reviews did improve for this one if only for its better quality of execution, but many still rallied against the very concept of the Bond movie and it hardly kickstarted the franchise. What it did do, however, was prompt the release of the film that did; Goldfinger.

This was the film that cemented Bond’s reputation, and laid the tropes on the table for all subsequent films to follow. Pussy Galore (Honor Blackman) became the definitive Bond girl, Sean Connery the definitive Bond (a reputation possibly enhanced by the contrast between his portrayal of Bond and the aggressive, chauvinistic ‘semi-rapist’ portrayed in the books), and his beautiful, silver Aston Martin DB5 the Bond car- one such car sold in the US some years ago for over 2 million dollars. According to many, Goldfinger remains the best Bond film ever (although personally I’m quite fond of Live and Let Die, The World is Not Enough and Casino Royale), although rather sadly Ian Fleming died before he could see it.

Since then, the franchise has had to cope with a whole host of ups & downs. After ‘You Only Live Twice’ (in which the character of supervillain Ernst Stavro Blofeld is first revealed), Connery announced that it would be his last Bond film, but his replacement George Lazenby appeared just once (On Her Majesty’s Secret Service, in which his performance received mixed reception) before claiming that he didn’t feel the character of a gun-em-down chauvinist such as Bond could survive the ‘peace & love’ sentiment of the late 60s (Lazenby was also, on an unrelated note, the youngest man ever to play Bond, at just 30). After Connery was tempted back for one more film (Diamonds Are Forever) by an exorbitant salary, the gauntlet was thrown to Roger Moore, who simultaneously holds the record for oldest Bond ever (57 by the end) and most number of films (7, over a 12-year period). Moore’s more laid back, light-hearted and some might say graceless approach to the role won him some plaudits by its contrast to Connery’s performance, but despite increasingly negative audience feedback over time this style became ever more necessary as the series came under scrutiny. The feminist lobby (among others) had been gaining voice, and whilst they had once been pleased at the ‘freedom’ demonstrated by the likes of Playgirls and other burlesque performers (seriously, that was the attitude they took in the 50s) by now they saw them as the by-products of a chauvinist society. This quickly meant Bond’s all action, highly sexual and male-dominated atmosphere came under fire, forcing the character to retreat into steadily tamer plots. It was also rapidly running out of ideas (the same director had been working on the project for several films by now), retreating into petty jokes (ie the name ‘Holly Goodhead’) and generally mediocre filmmaking. The series limped on with Moore until A View To A Kill, and for two more with Timothy Dalton after that, but it then took an 6 year break whilst another Dalton production fell through. Some felt that the franchise was on its last legs, that a well-liked and iconic character would soon have to wink out of existence, but then came Pierce Brosnan.

Whatever you do or don’t think of Brosnan’s performances (I happen to like them, others think he’s fairly rubbish), there can be no denying that Goldeneye was the first Bond film to really catapult the franchise into the modern era of filmmaking. With fresh camera techniques to make it at least look new, a new lead actor and a long break to give everyone time to forget about the character, there was a sense of this being something of a new beginning for Bond. And it was; seven films later and with Daniel Craig now at the helm, the series is in rude health and is such a prominent, well-loved and symbolic character that Craig adopted his 007 role when pretending to skydive into the stadium alongside the Queen during the London 2012 opening ceremony (which I’m sure you all agree was possibly the best bit of the entire games). There is something about Bond that fundamentally appeals to us; all the cool, clever gadgets, the cars we could only ever dream of, the supermodels who line his bed (well, maybe a few people would prefer to turn a blind eye to some of that), and the whole smooth, suave nature that defines his character makes him such a fixed trope that he seems impossible for our collective psyche to forget. We can forgive the bad film making, the formula of the character, the lack of the artistry that puts other films in line for Oscars, simply because… he’s Bond. He’s fun, and he’s awesome.

Oh, and on a related note, go and see Skyfall. It’s absolutely brilliant.

# So… why did I publish those posts?

So, here I (finally come)- the conclusion of my current theme of sport and fitness. Today I will, once again, return to the world of the gym, but the idea is actually almost as applicable to sport and fitness exercises generally.

Every year, towards the end of December, after the Christmas rush has subsided a little and the chocolates are running low, the western world embarks on the year’s final bizarre annual ritual- New Year’s Resolutions. These vary depending on geography (in Mexico, for example, they list not their new goals for the year ahead, but rather a list of things they hope will happen, generating a similar spirit of soon-to-be-crushed optimism), but there are a few cliched responses. Cut down on food x or y, get to know so and so better, finally sort out whatever you promise to deal with every year, perhaps even write a novel (for the more cocky and adventurous). However, perhaps the biggest cliched New Year’s Resolution is the vague “to exercise more”, or its (often accompanied) counterpart “to start going to the gym”.

Clearly, the world would be a very different place if we all stuck to our resolutions- there’d be a lot more mediocre books out there for starters. But perhaps the gym example is the most amusing, and obvious, example of our collective failure to stick to our own commitments. Every January, without fail, every gym in the land will be offering discounted taster sessions and membership deals, eager to entice their fresh crop of the budding gymgoer. All are quickly swamped with a fresh wave of enthusiasm and flab ready to burn, but by February many will lie practically empty, perhaps 90% of those new recruits having decided to bow out gracefully against the prospect of a lifetime’s slavery to the dumbbell.

So, back to my favourite question- why? What is it about the gym that can so quickly put people off- in essence, why don’t more people use the gym?

One important point to consider is practicality- to use the gym requires a quite significant commitment, and while 2-3 hours (ish) a week of actual exercise might not sound like much, given travelling time, getting changed, kit sorted and trying to fit it around a schedule such a commitment can quickly begin to take over one’s life. The gym atmosphere can also be very off-putting, as I know from personal experience. I am not a superlatively good rugby player, but I have my club membership and am entitled to use their gym for free. The reason I don’t is because trying to concentrate on my own (rather modest) personal aims and achievements can become both difficult and embarrassing when faced with first-teamers who use the gym religiously to bench press 150-odd kilos. All of them are resolutely nice guys, but it’s still an issue of personal embarrassment. It’s even worse if you have the dreaded ‘one-upmanship’ gym atmosphere, with everyone’s condescending smirks keeping the newbies firmly away. Then of course, there’s the long-term commitment to gym work. Some (admittedly naively) will first attend a gym expecting to see recognisable improvement immediately- but improvement takes a long time to notice, especially for the uninitiated and the young, who are likely to not have quite the same level of commitment and technique as the more experienced. The length of time it takes to see any improvement can be frustrating for many who feel like they’re wasting their time, and that can be as good an incentive as any to quit, disillusioned by the experienced.

However, by far the biggest (and ultimately overriding) cause is simply down to laziness- in fact most of the reasons or excuses given by someone dropping their gym routine (including perhaps that last one mentioned) can be traced back to a root cause of simply not wanting to put in the effort. It’s kinda easy to see why- gym work is (and should be) incredibly hard work, and busting a gut to lift a mediocre weight is perhaps not the most satisfying feeling for many, especially if they’re already feeling in a poor mood and/or they’re training alone (that’s a training tip- always train with a friend and encourage one another, but stick to rigid time constraints to ensure you don’t spend all the time nattering). But, this comes despite the fact that everyone (rationally) knows that going to the gym is good for you, and that if we weren’t lazy then we could probably achieve more and do more with ourselves. So, this in and of itself raises another question- why are humans lazy?

Actually, this question is a little bit of a misnomer, simply because of the ‘humans’ part- almost anyone who has a pet knows of their frequent struggles for the ‘most time spent lazing around in bed doing nothing all day’ award (to which I will nominate my own terrier). A similar competition is also often seen, to the disappointment of many a small child, in zoos across the land. It’s a trend seen throughout nature that, give an animal what he needs in a convenient space, he will quite happily enjoy such a bounty without any desire to get up & do more than necessary to get them- which is why zoo keepers often have problems with keeping their charges fit. This is, again, odd, since it seems like an evolutionary disadvantage to not want to do stuff.

However, despite being naturally lazy, this does not mean that people (and animals) don’t want to do stuff. In fact, laziness actually acts as a vital incentive in the progression of the human race. For an answer, ask yourself- why did we invent the wheel? Answer- because it was a lot easier than having to carry stuff around everywhere, and meant stuff took less work, allowing the inventor (and subsequently the human race) to become more and more lazy. The same pattern is replicated in just about every single thing the human race has ever invented (especially anything made by Apple)- laziness acts as a catalyst for innovation and discovery.

Basically, if more people went to the gym, then Thomas Edison wouldn’t have invented the lightbulb. Maybe.

# Money- what the &*\$!?

Money is a funny old thing- the cornerstone of our way of existence, the bedrock of modern-day life, and the cause of, and solution to, 99% of all life’s problems. But… well, why? When you think about it, money doesn’t actually mean anything- it is an arbitrary creation brought in for convenience’s sake, and yet it as an entity has spiralled into so much more than a mere tool. Now how on earth did that happen?