I met greatness on Tuesday afternoon and she was as sinewy as a greyhound, had the manner of a minor saint and owned a game that was unforgiving in its precision. In the first point of the tie-breaker, Simona Halep arched her back and cuffed a serve down the line.

Ace.

The person at the other end of the court was me and I was thinking: Whatever happened to mercy? But I was also, for the first time in my life, delighted to be aced.

As a writer, I want to interact with greatness, investigate it, delve beneath its talented skin. I want to ride pillion with Valentino Rossi and get a chessboard tutorial from Magnus Carlsen. I want to get inside the game, to observe from within, and so when the WTA Tour asks if I want to play with Halep, the world No. 1, I say yes, of course, when?

Then I panicked.

To play against the great athlete is to undergo a ritual of humiliation. In 1923, the writer Paul Gallico approached the heavyweight boxing champion Jack Dempsey to ask if he could spar a round with him. The reason? "So," wrote Gallico "that I might write a story on how it felt to be hit by an expert".

To which Dempsey replied: "What's the matter, son. Doesn't your editor like you any more?"

Halep is no heavyweight and yet she's pound-for-pound the best tennis player around. At 1.68m she's shorter than any of the 11 women who've held the No. 1 spot since Justine Henin in 2008, but like Gallico said to Dempsey, I am here to get hit by her. In a manner of speaking.

I've been fortunate to play golf with LPGA stars but tennis is one-against-one, allowing you to feel a rival's game and discover that TV is unable to convey speed and topspin. Only when you're there on court and Halep's perfectly weighted shots arc over the net, sometimes with a little fizz as if she's decided to attach an extra electricity, sometimes with a side-spin that curls a serve out of reach, do you get a hint of her mastery.

The anticipation of playing a world No. 1 is more terrifying than its reality. I sleep badly, fuss over my rackets, check grips, find a lucky wristband, stress about stretching, wonder about my heart rate, think up excuses and quietly appeal to Spes, the Roman goddess of hope.

Then, abruptly, I am on a slow Centre Court at the Singapore Indoor Stadium, the playing surface lit, the stands dark, the feeling lonely. Darren Cahill, Halep's coach, says he'll warm me up and it strikes me I'm hitting with a mellow Aussie who tamed Boris Becker 6-3, 6-3, 6-2 on his way to the 1988 US Open semis.

Then Halep, winner of 15 titles, walks on court. World No. 1s don't usually agree to casual hits but Halep has always been unusual, a player who wears her unpretentiousness like a scent and whose grace and honesty after her French Open final loss this year should be turned into an instructional tape.

Off the court Halep has a humanity to her, on it she wields an elite player's casual control. Our warm-up is more exhausting than the tie-breakers that follow because the ball keeps coming back. She's like a piece of complex engineering, every part humming and polished, her legs and arms and brain locked in some finely coordinated marriage.

Tie-breaker, I ask. Sure, she says.

Later I will study a film of her fluent feet and also my heavy-footed crimes against technique. Amateurs, I once wrote, should never watch a video of themselves at play because it dismantles every myth we have built of our own skills. Only in our imaginations are we fluent.

But I have one moment whose video clip I am going to set to John Williams music and send to everyone I know. Deuce court. I serve crisply down the line. Halep lunges and her backhand just gets over. I'm on the way in, move sideways and tap a forehand drop shot over the net. She can't reach it.

I will only win one more point all day.

People who play Roger Federer say everything goes too fast and it feels like that. Just constant pressure. Almost no point goes beyond three shots because I'm always too late, too inept, too baffled.

She wins the tie-breaker 7-2.

"Hey thanks, Simona," I say.

"No problem," she replies. "Want to play another?"

Yes. Please.

Then she asks, do you want me to hit the ball to you and extend the rallies? No, I say. I don't want her to plummet to my level but to gain insight into hers. As Gallico wrote of his encounter with Dempsey: "It taught me that painful as it may be to acquire it, there is no substitute for experience."

Gallico finished up on the canvas, "mouth bleeding, grinning foolishly". I lost the second tie-breaker 0-7 to Halep and beamed in defeat.

We shake hands, chat briefly and then she's gone. I haven't, of course, seen the real Halep because I haven't earned that. That adrenaline-propelled, stern-faced, baseline-painting thing which is the great athlete is reserved for rivals.

Still I ask her, how much per cent were you playing? "Eighty", she says and I smile. I met greatness on Tuesday afternoon and I think she's a beautifully kind liar.