THE shopping centre had a special activity for half-term, a sort of cross between trampolining and bungee jumping.

It was a relentlessly wet day and there were children queuing up to be strapped into the harnesses.

The grandson and I had been banished from the flat because the builders were in, so I took him to watch.

Some of the children were nervous, finding it a lot more scary than they'd thought. Others shrieked to go higher and higher.

The best view was from the first floor, level with the highest jumps, so that's where we went. The grandson loved it, watching enraptured from his pushchair.

After a while a man sat down on the seat near us. He was in late middle-age, balding, plump, wearing a pink shirt. He smiled at the grandson, who smiled back. "What a lovely little boy," the man said. "How old is he?"

"Six months," I told him.

"That's a lovely age," the man said. He held out his hand and the baby clutched it. The man beamed.

He obviously loves children, I thought. Maybe his family has grown up and moved away, so he doesn't see them often. Maybe he's lost touch with them. All right, it did cross my mind that he might have had darker, even dangerous motives for talking to my grandson (who's a blond, blue-eyed, appealing child), but I told myself that not every stranger who loves children is a paedophile.

Besides, I wasn't going to let the little one out of my sight and he was firmly tethered in his pushchair.

The man talked to him for a bit and grandson gurgled back in his friendly way.

It all helped to pass the time until we could return to the flat for lunch.

About two months later on a bright summer day, I wheeled the pushchair to the park and sat down on a bench near the children's play area so we could watch the world go by.

There were people sunbathing or picnicking, skateboarders, mothers with prams and pushchairs, toddlers tottering along in the drunken way of the newly-walking, cyclists, dog walkers (one woman had seven dogs in tow - the grandson adores dogs), people chatting on mobile phones, youths kicking balls around or tossing frisbees, children feeding the ducks.

A man came and sat down on the other end of the bench, a plump, middle-aged man in a pink shirt.

He smiled at the baby. "What a lovely little boy. How old is he?"

"Eight months," I said. You know that feeling you get that you've been here before, that sense of deja vu? That's what I was feeling now. Alarm bells were ringing in my head.

"That's a lovely age," the man said.

I don't think he remembered us at all. I think that was what he always said.

I no longer felt he was probably just a lonely man who loved children. I no longer gave him the benefit of the doubt. I began to see a pattern, a threat. He couldn't do us any harm just by sitting there and talking, but I wasn't comfortable.

Time to move on, I thought. I stood up. I don't want my grandson to grow up being rude or surly, so I said to him: "Say bye bye now," which he did, with a little wave.

Then I wheeled the pushchair briskly away.

I still don't know, of course. The man might have been entirely harmless. He certainly didn't do or say anything to justify taking any sort of action against him.

He didn't do us any harm, nor threaten to do any. If he was just a lonely man who loved children, the man I'd first thought he probably was, then I'm sorry; I deprived him of innocent enjoyment, of a few more privileged minutes in the company of my happy little grandson.

But I didn't want to take the chance. Being in the company of a baby makes the world a friendly place where complete strangers readily talk to you.

But I wasn't happy with this particularly friendly approach. I wasn't convinced it was friendly.

It's a sad world where you can't trust people, though I'm glad we didn't treat him rudely, just in case he wasn't a threat.

It's all right now, when the grandson's never out of adult sight, but what happens as he grows older? How do you teach them to be safe, while not allowing them to be rude to others, even strangers? Are we going to raise a generation of suspicious, cynical, unfriendly children? I do hope not, because I'm not sure that sort of world is one any of us would want to live in.