Summary
The feeling that "if something can go wrong, it will" (known as Murphy's Law) is generally taken to be a facetious expression of the world's inherent perversity. But Murphy was a real person - and an accomplished engineer. His law is based on sound observations of the way in which plans go wrong and led him to develop mechanisms for combating technical errors.
Scientist Robert Matthews thinks that Murphy was onto something important. In this article he investigates the scientific basis for some of the best known manifestations of Murphy's Law: the proposition that buttered toast tends to fall butter-side down and that if you carry an umbrella, it is bound to be a sunny day. These are more than just psychological perceptions - they are grounded in the laws of physics and statistics. But do such trivial matters really deserve the attention of a serious scientist? Absolutely, says Matthews, who argues that the greatest breakthroughs in understanding often come from careful analysis of mundane phenomena.
The science of Murphy's Law
Murphy's Law states that "If something can go wrong, it will", and as such has entered popular culture as an expression of the perversity and cussedness of everyday events. While many people jokingly blame their misadventures on the existence of Murphy's Law, most scientists appear to regard it as a silly "urban myth", without basis in fact. In this paper I will show that, contrary to orthodox opinion, many of the most notorious manifestations of Murphy's Law do indeed have a basis in scientific fact.
A rueful observation
The suspicion that some things in life are intrinsically likely to go wrong and cause us misery can be traced back centuries. As long ago as 1786, the Scottish poet Robert Burns captured the essence of Murphy's Law in his poem To a Mouse , with the famous lines:
The best laid schemes o' mice an' men
Gang aft agley [Tend to go awry]
A century later, the Victorian satirist James Payn incorporated perhaps the most famous manifestation of Murphy's Law in his 1884 parody of Thomas Moore's The Fire Worshippers:
I had never had a piece of toast
Particularly long and wide
But fell upon the sanded floor
And always on the buttered side
The modern version of the law first emerged during the late 1940s. Like many aspects of popular culture, however, the concept of Murphy's Law has accumulated an entire mythology of its own which has tended to conceal its real origin and meaning...
Yet Murphy was a real person... he became Research and Development Officer at Wright-Patterson Air Force Base, Dayton, Ohio... When Murphy learned of [a] foul-up, he observed that if there was way for one of the technicians to make a mistake, that would be the way things would be done. This rueful observation was the germ of what eventually became known as Murphy's Law.
At a subsequent press conference, one member of the project team said that they had become firm believers in Murphy's Law, that "If it can happen, it will happen". This throwaway remark was seized upon by the press as a pithy encapsulation of the all-too-familiar cussedness of inanimate objects, and the Law soon took on its classic wording: "If something can go wrong, it will".
Murphy's Law of Umbrellas
The weather and the accuracy (or otherwise) of weather forecasts are two frequent topics of conversation among Britons. Being situated in the path of no fewer than five different airstreams, UK weather is notoriously fickle and hard to predict reliably. This can prompt even the most rational of Britons to suspect that behind the overcast skies some malign force is at work . The famous Cambridge number theorist G H Hardy devised his own ingenious method for preventing this malign force from ruining a good day's cricket. To ensure that rain did not fall, he would tell an assistant to go outside with an umbrella, and announce "I am Hardy, and I am going to the British Museum". This being the ideal rainy-day activity, the perverse nature of the weather would duly ensure that the sun would blaze down - thus giving Hardy himself precisely the weather he required.
Many less distinguished people have suspected that the mere act of carrying an umbrella can be enough to guarantee that it will not be necessary, in other words that "If an umbrella can be redundant, it will be". On the face of it, the idea that possession of an umbrella can affect the probability of rain falling seems absurd. However, as I now show, when looked at in the right way, one finds that there is more than a grain of truth behind Murphy's Law of Umbrellas.
The explanation lies in our reason for deciding to carry an umbrella. Perhaps we have heard a forecast of rain, or we believe the skies seem to foretell a downpour. Either way, our decision is ineluctably tied to the probability of rain falling, via the so-called Base Rate Effect.
Suppose that we are planning to take a lunch-hour walk, and that we have heard a weather forecast predicting rain during that hour. Should we take our umbrella, or not ? There are four possible outcomes affecting our decision, shown in Table 1. This has been calculated using real meteorological data showing that, roughly speaking, there is a 10 per cent probability of rain during any given hour in the UK, and Meteorological Office forecasts of rain are now about 80 per cent accurate. The precise meaning of "accuracy" is somewhat ambiguous, but here I shall take it to mean that 8 out of 10 occasions of rain are correctly forecast, and similarly for occasions of no rain. The table allows us to read off the key figure of interest when we are trying to decide whether to carry an umbrella or not. Running along the first row, we see that the probability of rain given that the Met Office forecasts rain is not 80 per cent, as one might expect. It is 80/260, i.e. about 30 per cent. Similarly, the probability that it will not rain, given that the Met Office says it will, is 180/260, or about 70 per cent. In other words, when the Met Office warns of rain falling during our hour-long walk, the 80-per-cent accurate forecast is more than twice as likely to prove wrong as right. The reason for this decidedly counterintuitive result is not that the Met Office is being economical with the truth in its claims of accuracy. Rather, it is because the low hourly "base-rate" for rain of just 10 per cent overwhelms even an apparently impressive level of forecast accuracy.
Table 1: Outcome of forecasts for 1,000 1-hour walks
Thus there is a sense in which "If an umbrella can be redundant, it will be": if you take an umbrella on your lunchtime walk in response to a Met Office forecast rain during that hour, then two times out of three the umbrella will indeed be redundant... In conclusion, it is possible to beat Murphy's Law of Umbrellas by taking account of the base-rate effect and its pernicious ability to undermine even apparently highly "accurate" predictions.
Murphy's Law of Toast
Undoubtedly the most famous of all manifestations of Murphy's Law centres on the fall of toast: "If toast can land butter-side down, it will do". As remarked earlier, this propensity has been noted for at least a century, and led to my own involvement in the study of Murphy's Law. It was also the centre-piece of a fascinating documentary on BBC-TV in 1991, in which a team led by Professor Ian Fells of Newcastle University investigated various manifestations of Murphy's Law experimentally. In the programme, a group of people was supplied with white sliced bread and butter, and instructed to toss the buttered bread into the air and note which side up the bread landed. After 300 trials, the results were statistically indistinguishable from the 50:50 split expected from a coin-toss.
The Law of Toast: continued
However, this apparent refutation of Murphy's Law is based on the fundamentally flawed assumption that toast typically reaches the floor after being tossed like a coin into the air. Yet reality is somewhat different, with toast usually heading floorwards as a result of sliding off a plate, or being swiped off a table. Dynamically, this is entirely different from a coin-toss, and as we shall see, leads to an entirely different outcome. The BBC-TV experiment did at least demonstrate the inadequacy of one widely-believed explanation for Murphy's Law of toast: the presence of butter on one side.
Order-of-magnitude estimates show that neither the aerodynamic effect nor mass asymmetry caused by the presence of a thin layer of butter should make any difference to the final state of the toast, and this was comprehensively confirmed by the BBC-TV experiment. The key to the dynamics and final state of toast lies in what happens as it reaches the edge of the plate or table. Once its centre of gravity has passed over the edge, a gravitational torque is set up, inducing the toast to spin. The final state of the toast is then dictated by whether this torque is large enough to allow the toast to rotate into a butter-up position in the time taken for it to free-fall under gravity to the ground. Thus the fate of toast is controlled by friction, gravity, and the height of the table.
To first approximation, this manifestation of Murphy's Law can be modelled as a rigid, rough, thin homogeneous rectangular lamina of mass m, side 2a, falling from a rigid platform set a height h above the ground leads to the conclusion. Ignoring the process by which the toast arrives at this state and any horizontal velocity, the dynamics of the toast can then be viewed from an initial state where its centre of gravity overhangs the table...
... [M]aking certain simplifying assumptions about the process of detachment from the table or plate-edge... it emerges that toast sliding off a plate or table really does have a bias towards butter-down landings. Furthermore, the low torque acquired by toast sliding off a table or plate leads to the butter-down effect persisting for all tables of height below around 2.5 - 3.0 metres.
More sophisticated analysis is possible, but ultimately no amount of mathematics is a substitute for a single practical demonstration. I therefore recommend that anyone who is still not convinced about the reality of Murphy's Law of Toast simply places some toast (or any similarly-sized object, such as a paperback book) on a table or plate held at waist height, and observe what happens as it slides off and onto the floor. The tendency for toast to land butter-side down will become all too obvious...
Conclusions
The results presented here provide ample evidence that, contrary to orthodox opinion, Murphy's Law does indeed have a basis in fact. From the proliferation of odd socks to the fall of buttered toast, a whole range of everyday phenomena do have a bias towards the worst possible outcome. There is, I believe, more to these results than confirmation of a supposed "urban myth", however. While conducting my investigations into Murphy's Law, I have often been struck by the fascination the results presented here hold for many people. I suspect that this is at least partly because questions surrounding such "trivial" phenomena as tumbling toast are usually airily dismissed by many scientists, who are supposed to spend their time probing the mysteries of the cosmos, not buttered toast. Certainly, in the contemporary lexicon of science, "triviality" is one of the most pejorative of terms. Yet it is as well to remember that the fall of toast is just as much a demonstration of the laws of physics as the dynamics of distant galaxies: Nature herself does not know the meaning of "trivial".
A dismissive attitude towards everyday phenomena also overlooks the fact that the history of science has seen many cases of "trivial" phenomena leading to seminal discoveries. The most famous, of course, is the fall of the apple which by all accounts did indeed prompt Newton to contemplate the concept of universal gravitation. Other examples include Euler's work on hydrodynamics, which sprang from his involvement in the design of the fountains of Frederick the Great of Prussia, Raman's discovery of the eponymous scattering effect after pondering the blueness of the sea, and Feynman's work on quantum electrodynamics, which was partly inspired by his study of a wobbling dinner-plate.
Who knows, perhaps knot theory, invented in the 19th century and now at the forefront of theoretical physics, might have been discovered much earlier if Euler had spent a frustrating day in his garden shed sorting out knotted rope (after all, he did lay the foundations of graph theory after studying the equally "trivial" matter of how best to tour the city of Konigsberg).
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