Bad Moves entry

Bad Moves: Post hoc fallacies

By Julian Baggini

I used to be a bad boy, but since I got the number I've calmed down and become more focused on my religion. I believe it is a sign from God, and that the number was made for me. It has brought me so much luck it is unbelievable.
Sulayman Ahmed, Manchester Metro, 13 September 2002

Unbelievable indeed. What is this amazing power that has turned Mr Ahmed's life around? The answer is a lucky telephone number. Ahmed paid £5,000 (about $7,500) for a telephone number which contained a lucky sequence of figures based around 786, which in Arabic numerology apparently represents the holy prayer Bismallah al-Rahman al Rahim.

Since owning the number, friends and family have been "amazed at the transformation" in Ahmed, according to the Manchester Metro. What exactly is the nature of this transformation? Details are sketchy. The only specific change of luck mentioned in the report is that "he has been relentlessly pursued by women desperate to go on dates with him." None of these women were available for comment.

It seems, however, that the luckiest thing about the number is that Ahmed is going to be able to sell it on for even more and "start buying property". Talk about selling the goose that lays the golden eggs!

Let us suppose that, in fact, Ahmed has been on a lucky streak since buying the number. Does that prove it possesses magical properties? No it does not. The reason is simple enough, and those who think otherwise are committing a common error known as the post hoc fallacy.

Here's how it works. Think of a conditional statement of the form "If X, then Y", such as "If this is a lucky number, then owning it will bring me luck". This is clearly the kind of reasoning which Ahmed engaged in before buying the number. What happens if Ahmed actually enjoys good luck after buying the number is that he thinks this shows the truth of what is in the "if" clause: "This is a lucky number". But it doesn't because it is not true that he would have enjoyed the good luck only if the number were lucky. There could be other explanations. Luck is distributed randomly, most of us think, and at any given time there is always a chance that you will enter into a lucky streak. So the subsequent run of good luck can never prove that what came before it was the cause of the good luck.

The mistake is even easier to see in other examples. Imagine we are watching a football match and I say, "If I scratch my leg there will be a goal in the next hour". You would not think if there was in fact a goal and I had scratched my leg that the scratching was the cause of the goal. You'd rightly see that the fact that the "then" that followed my "if" actually happened does not show that my scratching my leg caused the goal.

It is remarkable, however, the extent to which people fall for the fallacy. No matter how little evidence there is of actual causal power, people are remarkably quick to attribute causal powers to things that occurred before something else. Many superstitions start this way. Someone wears a hat for the first time and that day their football team wins. From that day on the hat is their lucky hat. "I wore that hat and then my team won, so if I wear this hat my team will win." It's very poor reasoning which is strangely compelling.

What is also amazing is the extent to which people are blind to other much more obvious explanations. In the case of Ahmed, for example, he could hardly have been indifferent to his religion when he bought the number, since he parted with £5,000 for the number on the basis of its religious significance. So saying that having the number is the cause of his renewed interest in religion seems to confuse cause and effect. And being convinced of its luck would certainly have given him a certain confidence that could translate into more success, with women and in other areas of life.

It's a simple explanation but for some reason many prefer to think the alleged but unsubstantiated "transformation" in Ahmed's fortunes is down to a number. People are indeed strange.

Click here so you don't miss an update!