Post hoc fallacies
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
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.