Monday 22 July 2019

Why do buses come in threes?

Julian Champkin has found some answers to life's niggling disappointments in a new book about maths Why do you always wait ages for a bus, and then three come along at once? Why are showers always too hot or too cold? Add the question of why you always hit red lights when you are in a hurry and you have some of the most fundamental problems of existence.You thought these things were personal? That someone up there was out to get you? You thought they were variations of Murphy's Law that anything that can go wrong will go wrong?

Not at all.

A new book reveals the truth about life's little disappointments: they are part of the mathematical harmony of the universe. It's not fate that's out to get you; it's mathematical probability.

But don't hate the subject just because of this: it can improve your chances of winning the National Lottery.

Why buses always come in threes

Turn up at a bus stop and wait.

And wait and wait.

Buses may be leaving the depot regularly but people arrive to wait for them in drips and drabs. At some point a sudden burst of hopeful commuters will turn up, and when the bus arrives it will have to stop for longer than normal.

That gives the bus behind it time to get closer. Which means it arrives at the stop soon after the previous bus left, when few people are waiting. So it gains still more on the bus in front.

It is a cumulative process, a vicious circle. The bus behind will always travel faster than the one in front. Which means that, eventually it will catch up. The two buses will end up travelling together allowing a third bus behind them to catch up in turn. Most popular routes are too long to allow three buses to travel together much of the way.

Why you never find a four-leaf clover

Look at any plant tomato, buttercup, chrysanthemum. Count the number of petals, or the way the leaves are grouped.

You will find them set out in pairs, three, five eights or 13s but never fours. Plants, it seems, abhor the number.

Instead they stick to numbers in the series 1, 2, 3, 6, 8, 13, 21 ... where each number comes from adding the previous two together.

This kind of series is called the Fibonacet sequence. Mathematicians love to play with this string of numbers and so do plants, for it turns up and over again in nature.

You will find these numbers in the five seeds you see when you cut an apple, or the 34 or 55 spiral whorls in a sunflower head.

But not only will you never find a four-leaf clover, you won't find a four leaf anything else either.

Why the lights are always against you

When you're in a hurry, traffic lights always seem to be against you. The reason is mathematical. A traffic light spends more time red than green because there's always a period when all the lights are briefly red at the changeover.

So your chances of coming to a geen light are slightly lower than 50pc. If you go through two sets of lights, the chance of both being green is less than a quarter, and so on.

Why you should buy a lottery ticket on Friday

The answer to this one is a trifle macabre.

If you buy your ticket on a Thursday, you're more likely to be killed by a car than to win the jackpot.

Buy your ticket on a Thursday, and your chance of winning the Lottery jackpot is one in a million, but your chance of being run over in the next two days is one in ten million. Buy your ticket on a Friday and the accident is half as likely to happen.

Why do Buses Come in Threes? The Hidden Mathematics of Everyday Life by Bob Eastwood and Jeremy Wyndham, was published on April 30 (Robson £12.95).

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