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  The Mathematics of it

  British Gas commissioned a mathematician, a psychologist and an economist to put into mathematical terms one particular version of Murphy’s law — that things don’t just go wrong, they do so at the most annoying moment.

  They came up with the following formula:

  ((U+C+I) x (10-S))/20 x A x 1/(1-sin(F/10))

  where:

  U = urgency
  C = complexity
  I = importance
  S = skill
  F = frequency
  A = aggravation
  

  Or in the researchers’ own words: “If you haven’t got the skill to do something important, leave it alone. If something is urgent or complex, find a simple way to do it. If something going wrong will particularly aggravate you, make certain you know how to do it.”

  But here’s some simpler mathematics at work: “Murphy’s Law of Queues”. This is when you go to the supermarket, and there are 12 queues, but your queue never seems to be the fastest.

  Mathematicians would start by looking at the probabilities involved. For example, over a given period of time, on average, each queue will take its turn at getting to the top first. But if there are 12 queues, your chances of being in the fastest queue are one in 12.

  So if you go to the supermarket 12 times, you’ll probably be in the fastest moving queue just once. Then take account of “selective memory failure”, and the fact that you never took proper written notes of your queuing experiences on your trips to the supermarket, and it’s no wonder that you end up thinking that you're never in the fastest queue.

Murphy’s Law And Order

Thanks to “Murphy’s law”, people tend to notice that buses come in threes, toast lands butter side down, and when a body is immersed in water the doorbell always seems to ring. It happens to all of us.

In a nutshell, Murphy’s law says that whatever can go wrong, will go wrong. It’s a particular variant of “sod’s law”, where rush hour is worse when you’re running late, and email crashes while you’re sending important documents.

But what is the origin of Murphy’s law, who was Murphy, and is there a scientific explanation behind it?

The Origins

While “Murphy’s law” is popular in everyday speech and many people assume it to be an old myth, it has relatively recent scientific origins — and there’s a real Murphy behind it.

His name was Captain Ed Murphy Jr (1918–1990), an American aerospace engineer whose team had been doing experiments to find ways of preventing aircraft accidents. They were constantly challenging each other to think up “what ifs” and to spot potential causes of disaster. If you could predict all the possible things that could go wrong, the thinking went, you could also find a way to prevent catastrophe.

After becoming frustrated about some malfunctioning wiring, Murphy remarked: “If there is any way to do it wrong, he [the technician who was wiring the machine] will.”

Murphy’s law was born, and his observation about potential disasters was a useful design and safety principle. But at a press conference later about the project, a journalist turned the law into a joke about life in general, and a modern myth was born.

Buttered Toast Experiments

Perhaps the most popular “Murphy’s law” is about tumbling toast. Basically it says that when you drop a slice of toast, it nearly always lands buttered-side down.

Some people speculate that this is due to the weight of the butter. But for a typical slice of toast the butter’s weight would have little effect upon the toast's centre of gravity.

You could check this by conducting a series of experiments with plain toast — simply write the letter “B” with a felt-tip pen on the side where the butter would have been. If butter really was to blame, then unbuttered toast should now land “B” side down just as often as “B” side up.

Others have argued that height is a key factor. Under typical circumstances at the breakfast table, the toast will first be dragged off the edge of the table, and then begin to fall. As it falls, it usually tumbles. But because most tables are only about a metre high, the toast will only have time to do a half turn. So if it starts buttered-side up, it will land buttered-side down.

In 1991 the BBC science series got volunteers to flip some buttered toast up into the air, and see which way it landed. Out of 300 flips, 148 had the toast buttered-side up, while 152 landed buttered-side down. In other words, the odds were almost exactly 50–50.

One of the world’s leading experts on Murphy’s law, Robert Matthews from Aston University in Birmingham, decided to run his own mass experiments, and came to some very different conclusions:

• Toast really does have a tendency to land butter-side down
• The presence of butter is not the major cause of butter-side down landings
• The principal cause is height: toast falling from waist height does not have enough time to come butter-side up again