"How lovely it is to dream while you are awake." Andre Agassi heard this from his long-time fitness coach, Gil Reyes, who heard it from his mother. This is where Kyrgios is now. There is a touch of Mad Hatter about it all; if Kyrgios had looked over the fence while practising, he would have seen his sister, Halimah, being interviewed to explain her shoes, high heel Nikes. Actually, he did look.

The fact that best explains Kyrgios right now is that he is 19, probably not fully grown, certainly not fully formed. He is one of only two teenagers in the top 100, for men's tennis has become a muscly man's world. He will have to do all the rest of his growing up in public. It could involve pains; who among us would like to be judged as they were at 19?

At not quite19, Martina Hingis indelicately labelled Amelie Mauresmo, then also 19, "half a man" in a press conference. How Hingis, who is now 34 and here playing doubles, must flinch to remember it. How Mauresmo, here coaching Andy Murray, also must flinch.

At 19, Lleyton Hewitt was already a formidable tennis player and a brat, named by Inside Sport as Australia's least-admired sportsman. Shortly afterwards, he called a linesman a "spastic". Bernard Tomic at 19 appeared in court to answer a multitude of driving offences; meantime, John McEnroe accused him of tanking at the US Open.

Comparatively, Kyrgios' rap sheet is trivial: a couple of busted racquets, a snap at a linesman, one audible obscenity which somehow on Monday became an "expletive-laden tirade", and which Kyrgios' family says was directed at someone in his own box anyway, not at the crowd.

Kyrgios is confident, and could be cocky; they are not so far apart. His challenge, and that of his many minders' too, is to keep them apart while the world watches him figure it all out.

"Only boxers can understand the loneliness of tennis players," wrote Agassi, the angriest of teenagers at his beginning, a veritable sage at his end. "Even a boxer's opponent provides a kind of companionship, someone he can grapple with and grunt at. In tennis you stand face-to-face with the enemy, trade blows with him, but never touch him or talk to him, or anyone else.

"Of all the games men and women play, tennis is the closest to solitary confinement."

That is for the future, fast arriving. For now, Kyrgios is revelling in the attention. He and James Frawley only ever meant to hit balls back and forth on Monday, but one of their casual rallies suddenly grew into a serious point, won by Kyrgios after some furious hitting, whereupon he pumped his fist and the crowd cheered as if he was break-point up on Andy Murray.

There's the awake dream. There can be no doubt that Kyrgios brings an indefinable quality to Australian tennis, technical proficiency yes, but also a sense that he knows how to win things. Twice, he has triumphed from two sets down, feats of persistence for which teenagers generally are not known. Twice now, he has reached the quarter-finals of a major, the youngest man to do so since Roger Federer. Even Murray sees in him an assuredness he says he did not have at the same age.

And he is personable, as teenagers in the public eye rarely are. It buys him more slack than Hewitt or Tomic were ever cut. His business-like exit from the practice court on Monday was only ever a piece of stagecraft. After a suitable pause, he turned, grinned, walked to the other side of the court and spent the next 20 minutes signing autographs, and returned again as if for a second encore and a final photograph.