Here's a series of questions that should be fairly straight- forward, but are actually excruciating. When were you last wrong? What has been your most recent serious screw-up at work? What has been your biggest mistake in your personal life? We all have a weird and paradoxical relationship with our mistakes. We can see that everyone around us makes errors all the time – yet we are always astonished when it turns out we are getting things wrong too. It's because, deep down, we see being wrong as shameful proof that we've been sloppy, or stupid. This belief pervades our culture: we applaud the public figures who "stay the course", even if it's wrong, and boo the ones who admit a mistake and "U-turn" or "flip-flop". But what if – apologies for the irony landslide here – we are wrong in the whole way we think about being wrong?

A brilliant new manifesto has just been published urging us to reassess our relationship with our own mistakes: Being Wrong: Adventures in the Margin of Error by the American journalist Kathryn Schulz. Perhaps the best place to start her story is with an experiment first staged in the University of Berlin in 1902 by Professor Frank Von Liszt. In a classroom, two students began to have an angry argument, until one pulled out a gun. As the panicked students around them drew back, a professor tried to intervene – and a shot was fired. The professor collapsed to the ground. The witnesses, unaware that all three were actors following a script, were then taken outside and quizzed about what they had seen and heard. They were encouraged to give as much detail as possible.

Everyone got it wrong. They put long monologues into the mouths of spectators who had said nothing; they "heard" the row as being about a dozen different imagined subjects, from girlfriends to debts to exams; they saw blood everywhere, when there was none. Most people got a majority of their "facts" wrong, and even the very best witness offered a picture that was 25 per cent fiction. The more certain the witness, the more wrong they were. Every time the experiment is run, the results are the same.

The implications are pretty startling. Human beings can't even accurately describe an event of great importance that we have just witnessed with our own eyes. What does that suggest about our ability to be easily right about much more complex questions? In American Pastoral, Philip Roth calls life, "an astonishing farce of misperception". Our abilities to perceive and reason are painfully limited, while the world is unutterably complex. We are peering at an entire universe through a drinking straw.

So the meaningful question about any human being isn't: does he get things wrong? With these limitations, we will all make big mistakes. The real question is: does he take the time to understand his mistakes and learn from them? But you can only do this regularly if you know how to think about mistakes in a healthy way.

There are a few areas of human life where people have found a way to do this. Revealingly, they are the areas that make things work better than any other – the sciences. To pluck one example of millions, when Barry Marshall and Robin Warren proposed that stomach ulcers were caused by bacterial infections in the 1980s, almost all scientists disagreed. Now, after conclusive tests, everyone agrees. It's not that scientists have less ego than the rest of us, or feel less sting when they are proven wrong. It's that they have developed rigorous techniques for constantly checking their claims against the evidence, and ruthlessly hunting out their errors and figuring out what they mean.

This approach can be extended. After two planes collided at Tenerife airport in 1977, killing 600 people, the airline industry introduced radical new protocols. Crew and ground members are now actually rewarded for reporting their own errors and screw-ups. The result? Accidents fell dramatically, from 0.178 per million flight hours to 0.104.

Now compare that to the way we conduct public life. One of the most predictable applause lines for any politician is to boast that he won't back down, look back, or say sorry. Tony Blair wasn't unusual when he bragged: "I can only go one way, I've got no reverse gear." But a car without a reverse gear would be banned from the roads.

Yet we have structured our public life so this seems like a sensible statement, while anyone who ever admits a mistake is talking themselves out of a job. You can hear the carping interviewers now: "How can we ever trust you again, if you were wrong about this?" We make it easier to continue in error than to admit error and put it right.

If we want to face up to our mistakes more regularly, then we need to change the way we think about them. If we see them as proof of our own incompetence, we will continue to puff out our chests and pretend they aren't there. Is there a different way?

Error is an essential step in the process of finding the right answer. Every scientist leaves behind a trail of disproven hypotheses and papers shot to pieces by colleagues. He doesn't see them as shameful, but as part of a process that was bringing him closer to the truth through experimentation. Similarly, James Joyce, thinking about all the drafts he wrote that failed, said, "a man's errors are his portals of discovery".

But error may be even more fundamental than that. From the moment we are born, human beings are creating theories about the world, based on limited evidence. It's how we survived: if our ancestors hadn't generalised that all lions are dangerous, you wouldn't be reading this. Errors are often simply this necessary impulse reaching too far, or misfiring. So the impulse that makes us wrong is also the impulse that makes us human.

Since reading Schultz's book, I have been trying harder to train myself to think systematically about my own mistakes. Every week, I make a list of what I have got wrong, personally or professionally, and try to figure out how to get it right next time. I can't entirely drain the pain from it, but I do think there's a hunger out there for this approach: the most positive reaction I have ever had to a column was when I tried to publicly explore how I had got the Iraq war so horribly wrong. What I learned from that awful mistake – the true factors that drive US and UK foreign policy, rather than propaganda claims – have led me, I think, to positive insights since. If I had instead run from the error and insisted it wasn't there, I would be stuck in a bloody blind alley, devoid of insights.

Tim Harford of Radio 4's More or Less has suggested an annual prize for the politician who makes the most constructive admission of error. It'd be a good start – but we will best seek a healthier approach to error in public life when we achieve it in ourselves.

You will get something wrong today, and tomorrow, and every day of your life. So will I, and everybody you know. You don't have a choice about being wrong sometimes: mistakes will be your life-long companion. But you do have a choice about whether to approach your error in terror so you suppress, ignore and repeat it – or to make it your honest, open ally in trying to get to the truth.

You can follow Johann on Twitter at www.twitter.com/johannhari101

For further reading