On Being Wrong

4 x 4 + 4 x 4 +4 – 4 x 4 = ?

The above arithmetic sentence has been floating around Facebook recently. Can you work out the answer? Apparently (we are told) 73% of people get it wrong. To work it out you have to know a rule: in calculations like this, multiplication and division take precedence over addition and subtraction. That means, simply put, that you carry out any multiplications or divisions before you carry out the additions and subtractions. So it works like this:

4 x 4 + 4 x 4 +4 – 4 x 4 = 16 +16 + 4 -16 = 20.

Most people (73%), though, don’t seem to know this rule. They simply carry out the calculations from left to right:

4 x 4 + 4 x 4 + 4 – 4 x 4

= 16 + 4 x 4 + 4 – 4 x 4

= 20 x 4 + 4 – 4 x 4

= 80 + 4 – 4 x 4

= 84 – 4 x 4

= 80 x 4

= 320

That’s okay. It’s an easy mistake to make, if you have forgotten the rule or never learned it. The interesting part of this is the reaction of many of those who get it wrong. Some insist that theirs is the correct way to do it. Okay, fair enough. They’re wrong, but at least I can understand their position. Other arguments are more bizarre. ‘Different people do things different ways. You can do it any way you want to.’ ‘So someone made a silly rule! So what, I’ll do it however I want to!’ Rather than simply admit that they were wrong, or that they did not know the rule, they adopt a defensive posture. ‘I didn’t know that rule, so it can’t be important anyway.’ ‘No one’s going to tell me how to do it. It’s a free country, I’ll do it my way.’

Arithmetical or mathematical anarchy is not an option, but there is a deeper point here. It demonstrates how difficult it is for people to admit that they are wrong, once they have committed themselves to a position, even on such an apparently trivial—it’s not actually trivial, although many might think so—issue such as this. Instead of saying, ‘Oh, I didn’t know that. I see it now,’ people would rather defend the incorrect answer or adopt the attitude that ‘it doesn’t matter anyway’. If this is possible on an issue that people will have forgotten tomorrow, imagine how difficult it is for people to admit they have been mistaken on what appears to be a more important issue: religious beliefs, political opinions, scientific theories.

Our politicians demonstrate this kind of attitude every day. They obstinately cling to an outmoded policy or point of view today for no better reason than that they held it yesterday. To admit that they might actually have been mistaken…? It can’t be done. And were they to do it—in fairness to them—the media and the public would bay for blood. People cling to religious or superstitious beliefs long after they are even remotely defensible. Pride—and a lack of anything to replace the old view—prevents people from changing their minds. Or admitting that they may have been mistaken after all.

As a society we should applaud scientists, politicians, religious and other leaders—anyone who has the courage to stand up and admit: ‘Yes, I was wrong. I see it now.’