At the Rio Olympic Arena, an epidemic of hugging has broken out. Everyone is hugging everyone, all the time. Everyone is almost tiny enough to fit in an overhead airline locker. Everyone is proof that size means nothing for they are more nerveless than heavyweight judokas at these Games. They elegantly hurtle off a bar, flip precisely in the air, perfectly catch the bar on their way down. With arms extended and toes pointed, if you please.

And, yes, what do you do for a living, Sir?

The hugs are a bonding mechanism, a congratulation, but maybe also an acknowledgement that they know what precise courage is required for every performance. Because this is the Olympics, this is gymnastics, this is stripped-down Cirque du Soleil where you don't get laughs but scores. This is a fast, ferocious, flip-spring-twist routine with a degree of difficulty that has the person next to me with her hand on her mouth three times in 10 seconds.

Did I just see that?

Like the Wolf Turn, which is as scary as it sounds. Wherein the gymnast squats on the beam, with one leg fully and gracefully extended, and then swivels 360 degrees on the other leg. Think of it as ballet on a tightrope.

This is what Simone Biles is doing and this is why I am here. Like opera singers or painters, some athletes like her call us. We hear of their art, we even witness it on TV, but we wish to experience it. It's like Michael Phelps: you don't go to an arena just to see him swim, but to feel it, to hear it, to taste it.

Biles is the hero of a modern time when we reverse an ancient ritual: once you had to win Olympic gold to be great; now, like her, you're considered great and must merely win Olympic gold to confirm it. But this is pressure, this is what makes gymnasts - who are so practised they could do blindfolded routines on a ship's plank - fall off beams and bars.

All of this happens on Tuesday. Mistakes happen. Even an errant Biles happens. Perfection is a gymnastic ideal, not a reality and for a sliver of a second her arms bend on the uneven bars. Yet the mistake humanises Biles, it does her a service, it actually increases the wonder. For when she's majestic later on the floor, you cannot believe a human is capable of such inhuman skill. Same blood and bones as us, slightly different skill set.

I am not keeping score for this is not a day for such trivialities. This is a day for joy, not jottings. I pity the judges, for it's like holding up placards with numbers and judging dancers at the Bolshoi.

America is winning the team event easily anyway for they are deep in talent and adept at this more athletic, more difficult gymnastics which makes Nadia Comaneci not seem like from another world but from another sport. Grace has bent to explosiveness.

Biles is only 145cm tall but in a raucous stadium, on a crowded floor of four different apparatus and eight competing teams, she commands you to watch her. She will get the day's highest score on the vault and beam but it is on the floor where the afternoon's memory is made.

On one side of the floor exercise square is painted the Olympic logo of the five rings. Biles is standing right on those rings, like a woman on top of the Games and also her game.

Some feet away from me, a fan is wearing a Nasa space shuttle hat. It is appropriate for that's where Biles is travelling. As Anna, a former regional-level gymnast from America volunteering here, tells me, Biles literally reaches heights no one else does. If it makes her moves more visually dramatic, it also offers her more time to create.

It has been a dazzling evening where merely watching these disciplined acrobats limber up is riveting. They see life differently from us folk who find toe-touching a feat. Sometimes they do handstands, standing straight yet upside down, unmoving and unconcerned, just staying like that as if their view of the world is a better one.

But right now people are looking at Biles on the floor. Even the judges at the vault and the uneven bars, whose jobs are done for the day, have turned in their chairs to look at Biles. One will later even applaud her. For all the brilliance they regularly see, she is the exceptional one.

Biles' score on the floor is 15.800, the gold is won and her greatness has an Olympic glint. She comes down from this stage she owns and her team-mates are waiting.

To hug, of course.