Often we feel as if we live in more dangerous and risky times, especially at the moment.

We could comfort ourselves by looking back over the century. In 1918 the situation was much worse. About one in 20 of us could expect to die as a result of an “accident”, the popular term for an unintentional injury. But it didn’t take us long to make improvements. Throughout the 20th century we came up with all sorts of advice about how to be more careful. “Look both ways before crossing a road” and “Keep out of reach of children” for instance. There were also drink-driving laws, health and safety regulations and seat belts as standard.

The ideas came one after another and there was an impressive decline in fatal injuries. By 1992, the chance of an injury-related death had dropped to 1 in 40 – even when we were living almost 25 years longer.

But in 1992, this trend reversed. The fatality rate stayed where it was for the next eight years and then began to rise. So although we’ve made progress, being careful today seems harder than it was. This is partly due to the pace of our innovations and inventions. Cars are faster, and there are more of them. We have smartphones and wearable technology to distract us while we contend with busier roads. Meanwhile the number of prescription and over-the-counter drugs continues to rise, along with the side effects and dangerous interactions between them.

But look around and you get the impression that there’s a health warning or a safety strap or guard rail on everything in sight. We’re dispensing safety messages like never before, and yet I believe that we’ve come to the end of a really good run.

Somehow the next safety revolution is going to have to happen in our own minds. Which means understanding our vulnerabilities – a key one being our perception of risk. Suppose someone invited me and my young daughter kayaking. The first thing I do is summon in my mind what I know already. Shooting through rapids; white water rushing over jagged rocks. I’m already thinking, “No way.” But I could have called up a different image: kayaking on a still pond on a contemplative morning surrounded by ducks.

What’s happening here? In the absence of facts, we make choices about risk using particular examples that stand in for all available knowledge. What do I really know about kayaking safety? Nothing. So I pull up examples that happen to have passed in front of me during my life.

A feature of our memory is that rare and unusual events are the easiest to remember. After 9/11, air traffic dropped to a historic low and people opted for driving instead. Given what had just happened, flying was terrifying. Yet the number of people who died in traffic collisions rose well above those who would have died in aeroplanes.

So how do we protect ourselves against the problems we have assessing risk? A first step is to acquire real risk numbers in our heads – to stop counting the number of injuries and deaths we’ve seen on TV and start relying on actual data.

One study says that on any given day of whitewater kayaking, there’s a 1 in 330 chance that you’ll need medical attention. But how much risk are you taking when you speed through an amber light? Or let your elderly parents walk down a flight of stairs? Or accept a new medication, no questions asked? You probably don’t know, but you need to. Well-informed judgment can reduce these so-called accidents to something much more rare. We have the power to make them not happen. Take care.

Careful! by Steve Casner, is published by Pan Macmillan at £18.99. Order a copy for £16.14 at bookshop.theguardian.com