Many facets distinguish the minds of children from those of adults, among them imaginative capacity, the repression of reason and the mysterious condition of innocence. But perhaps one of the most telling divisions is between the things adults fear and those that worry children.

I recently asked one of my youngest daughters what she feared most. She answered without hesitation: failure. This disturbed and surprised me. I had always thought of fear of failure as an adult preoccupation, but it seems that one of the effects of the climate of the times (and the media saturation that expresses it) is the importation of adult fears to childish minds. The fear of ghosts is being replaced by the terror of underperformance.

This “adultisation” of fear is underlined by a survey I came across on the internet suggesting that children’s fears had changed considerably over the past few generations. In this survey, from Johns Hopkins University in Baltimore, the top five fears 30 years ago were animals, being in a dark room, high places, strangers and loud noises. In the updated survey, kids were afraid of divorce, nuclear war, cancer, pollution, and being mugged.

A more recent poll, carried out in the UK a little over a year ago, points up some enduring traditional fears, including spiders and bugs, witches, the dark and clowns. However, being bullied, being approached by strangers and school performance all featured.

Children’s fears are a litmus test of the society we live in and they are clearly changing – becoming more concrete – as society becomes more performance-driven, insecure and saturated with threatening, upsetting facts. Refreshingly, missing from either of the lists was fear of terrorist attack or paedophile abduction – the sort of thing parents have nightmares about – but it is clear that the imaginative arena of anxiety is undergoing a transformation and perhaps an intensification.

I don’t know what to do about fear, given I suffer fair amount of existential fear myself, even knowing, as I do, that fear for the most part is useless. “To conquer fear is the beginning of wisdom,” said Bertrand Russell, but unless one is singularly lacking in imagination, one never conquers fear completely.

I was once asked what single piece of advice I would proffer my 17-year-old self and the answer I came up with was, “Don’t be so afraid.” Nevertheless, I spent much of my early years frightened, like my daughter, of failure or rejection. Many of my later years, too.

Fear can be shameful. The film that most recently gave me the chills was Force Majeure in which a father runs away from his wife and children when he is faced with a situation of sudden danger. My secret terror – and I imagine the fear of many men – is that some ignoble primal instinct in such a situation would render me similarly unheroic. How would one live with oneself after that?

I cannot sincerely tell my children there is nothing to be afraid of in life. What I can say with conviction is that fear, for the most part, is useless. It tarnishes your soul, yet does nothing to protect you against the situation you are anxious about. It is the most terrible waste of time. I agree wholeheartedly with Aung San Suu Kyi – “The only real prison is fear and the only real freedom is freedom from fear.”

Courage is not being free from fear, however. Courage is not allowing fear to distort your purposes and cramp your life. We all have secret fears and to deny it is to deny some essential element of our personalities. But if you can do one thing for your children, show them bravery, so that they learn bravery themselves. For courage is the wellspring from which an authentic life flows.

• @timlottwriter

• Tim Lott’s new novel, The Last Summer of the Water Strider is published by Scribner on 18 June