Tuesday, January 09, 2018

The Improbability Pirnciple: Why we don't notice the improbability of eveyday life.

     David Hand. The Improbability Principle (2014) Suppose you’re playing bridge. You get a hand of all 13 hearts. How unusual! In fact, this deal is one of  635 013 559 600 possible hands. “Ordinary” hands are much more likely, right? Well, yes and no. The fact is that any combination of 13 cards is equally likely. The all-hearts hand is unusual only in that you notice it. A hand with a mix of values and suits looks normal, and it is, in the sense that there are only four all-suit hands, and billions of mixed-suit hands. But each one is unique. So each one is as unlikely to be dealt as any other. They are all equally improbable.
     And when you have absorbed that fact, you are on the way to understanding Hand’s book. He explores odds and chance, our perceptions of odds and chance, and the tools available for estimating odds and chance more accurately. The exploration shows that “Coincidences, miracles, and rare events [will] happen every day”. He demonstrates several laws of probability that combine to make the improbable happen.
     Hand’s book will help the reader realise how improbable every event is. It’s a good introduction to probability and statistics, with many real-life examples as well the standard text-book ones. It will help the reader see the world in which they live with more understanding, and I hope more curiosity. Hand writes well, his tone is conversational, he allows himself the occasional dry joke.
     Here’s my take on his work. It builds on his book, and other books I have read.
     Improbable events must happen, for there are long and convoluted chains of cause and effect leading up to every event. Call them event-chains. Looking forward from “here and now”, an enormous number of possible event-chains stretches into the future. They intersect and criss-cross in unpredictable ways. The future is a network of possible events. Any one event lies on a node, where several possible paths through the network meet. Which paths through this network could lead to events involving you, tomorrow morning, while you are having breakfast? An enormous number. You can list some of the most likely events (the cat will want to go out just before you set the breakfast table, you will fetch the cereal from the pantry, etc).
     But there are other ones, trillions of them in fact (a meteor will crash into the garden, a storm will strip the leaves from the oak tree, two cars will collide in front of your house, the water heater will spring a leak, etc). The odds that any one of them will happen is small (the microwave will stop functioning). For most of them, the odds are very small (one of the people in the collision is a schoolmate whom you haven’t seen in twenty years). Some are extremely small (on the back seat of the blue car there’s a paperback that you donated to the Goodwill in another town seven years ago).
     One of these unlikely events will happen. True, some event-chains are more likely than others, but in general, there are far more unlikely possible events than likely ones. There are so many that unlikely events are more likely to happen than likely ones. The likely ones just happen more often.
As with the all-hearts hand, most events are equally unlikely. We pay attention to the ones that we feel are strange in some way. But think about it this way:
     You go to buy a box of ball-point pens. Consider the event-chain leading up to your purchase. Many hundreds of people were involved in producing the raw materials, shaping them into parts, assembling them into pens, packaging them, distributing the pens to the store. Then there’s the event-chain leading up to your decision to buy the pens. Today, not yesterday. This store, and not another. And so on. What are the odds that you would buy this particular box of pens, today?
     So why don’t you think of it as improbable?
     We don’t usually notice the improbability of any given event. That’s why we’re flummoxed when we do notice one.

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