BULL FIGHTING: A seat in the shade costs more than a seat in sun, but we figure that if you are going to be swooning, well then, a seat in the shade is probably the place to be swooning in. We buy four seats en la sombra. The sun vanishes.

For an additional euro each we can spare ourselves the discomfort of the concrete bleachers and hire a threadbare lozenge-shaped cushion upon which thousands of Spanish backsides have been placed over the years as their owners watched bullfights here in Madrid.

Could this cushion once have been crushed beneath Hemingway's mighty arse - or would Papa have considered the cushion an effete touch? Las Ventas isn't full this afternoon, far from it, but it is gorgeous and dramatic anyway, its perfectly circular Moorish architectural form rising up seemingly organically from the sand which forms the ring itself.

Everything within has a little theatre to it. The men and women who show you to your seats have large, almost comical, black hats perched on their heads. The hawkers are nimble and quick-eyed, apart from the gone-to-seed man in a white jacket who peddles Cutty Sark and wanders through the crowd shouting, Whiskey! Whiskey! He holds a bottle in one hand and glasses in the other and looks balefully at the rows of sober visitors.

The crowd today has at least as many tourists in it as it has aficionados. Underneath the brass music all afternoon will be the whirring of video cameras, the purring of digital cameras, the whispering of dumb questions.

At seven, though, there is a tootling of trumpets and a rolling of drums and two men on grey horses enter the ring. They are dressed entirely in black except for white cotton collars and great red and yellow feather plumes that arc and swoop out of their hats. They circle the ring and come to a stop at the far side.

Then the matadors enter and the band strikes up again. Each matador has a cuadrilla, or a team of helpers who will assist with the preparation for the kill. These are the picadors, who will enter the ring on horseback, and the bandilleros, who will do so on foot. The programme, or la corrida, is made up of three matadors and six bulls.

Tonight, the matadors names will be Rafael Osorio, Rafael de Julio and Luis Vilches. The bulls names are Jaecero, Churrascon, Hospedero, Cubajoso, Secretario and, a little pitifully, Delicado. Unless there is an upset the score will be 6-0 to the matadors. That, though, is not the point.

The point is the show. The display of bravery, of arrogance, of hubris, of style. It is the triumph of will over cowardice, the imposition of art on urgency. The overlaying of control and creativity on a situation of heart-throbbingly primal rawness.

Each matador is pencil thin and wearing a traje de luces, or suit of lights. These are jackets with boxed-off shoulders and large swathes of gold and silver fabric giving way to tight capri trousers which disappear into the pink knee socks, the hosiery of choice for all matadors.

Everyone, bar the bulls - of whom there is as yet no sign - approaches the president of the corrida, a large man in a beige suit who stands at a balcony and accepts the coquettish flourishes of the matadors hats, or monteras, as his due. Then more music and a man who looks like an old-fashioned cinema usher enters the ring as the camp circus which has preceded him evaporates.

The usher has a sign tacked to a pole. The sign gives the vital statistics for the first bull of the day.

Introducing, Jaecero.

Now to business. The bull, Jaecero, is oddly low-slung and handsome, all haunch and brisket, not like the chap of your imagination with the ring in his nose and steam fuming out his ears.

The fighting bull has been bred this way; his head low so that when he charges, his weapons of matador destruction pass below the level of the knee; his horns spectacular, but curtailed over the generations so that they don't spread too wide and catch a leg or a torso as the bull is engaged in a pass through the muleta, the small red cape used in the final act.

The bull is bred to be dangerous but not too dangerous, to be predictable but not too predictable, to be brave and to never get the chance to learn those things that with its natural intelligence would save it. This afternoon, the sight of the men on horses will be familiar. Dealing with men on foot will virtually be a new experience. Seemingly mesmerised by the small movements of the dancing red cape, the bull is in no state to figure out that the goods are standing in a suit of lights just beside the cape.

They reckon that one half hour of rough tuition is all the bull would need. And after that the animal will know forever not to try for the lure of red cape, but to make for the matador.

These bulls who will fight this afternoon are all between four and five years old. When each bull is two years old it is taken briefly from its idyllic life on the grassy range of Castilla or wherever and placed in a small bullring where a man on a horse with a 12-foot long pike called a pic awaits. Everyone pauses to see if the young bull will charge the horse and if he does how will he do it. How will he react when the pic drives into the thick wedge of muscle at the back of his neck? Or will he charge at all?

If not, he is useless. Having charged and his bravery having been gauged, he is allowed go free again. Those who need to know such things note well if the bull lingers in the ring looking back, longing for a second charge, or if he gallops away freely and blithely. Whatever he does, it is important that he does it at two years old. He will have forgotten this brief experience by the time he gets to the corrida.

Two picadors on horses are in the ring with Jaecero now. The horses are blinkered and thoroughly padded in outfits which look like long quilted, eiderdowns.

Once, in Hemingway's time, horses were part of the sacrifice and, unprotected, they suffered the gorings of a fresh bull and died in their thousands in the rings.

Even today, padded and stolid, the horses are remarkable. Jaecero attacks the horse on the far side of the ring, going in low and shifting the animal perhaps a yard or two. The horse remains standing and calm.

While the bull has his head buried in the belly of the horse the picador high on the horse's back controls the horse and buries the pic into that big crest of muscular flesh behind the bull's head. A scarf of raspberry blood begins to flow from the wound.

The picadors job looks easy as he leans in like a pole-vaulter, yet the deaths of picadors come when the pic breaks under a man's weight or the saddle shifts and the picador falls on to the horns of the bull below, there to be tossed like hay on a pitchfork.

While he is in the ring with the picadors, the bull is at his most fearsome. The bandilleros walk around the sand flourishing their large pink capes to entice the bull from one picador to the other. When Jaecero finally attacks the second horse on the near side of the ring he leaves a long smear of his own blood on the quilting. His wounds are making him progressively weaker now.

It is in the nature of the corrida that things must move swiftly. Trumpets sound and the picadors exit. The bandilleros are alone with the bull. They must make him turn and twist and tire him. Through all this, the matador Rafael Osorio - a young man from Jerez making his debut in Las Ventas - must watch and learn the habits of the bull. Does he pull his head this way or that when passing? Does he hold his horns high? Does he charge in straight lines or veer this way or that?

The other job of the bandilleros is to plant gaily coloured sticks called bandilleras into the neck of the bull. This is achieved by abandoning the cape and approaching the bull with a bandillera in either hand shouting the words Toro! Toro! Then with a burst of speed to match the bull's sudden indignation, the bandillero runs, swerves away from thedipped horns and plants the sticks in the animal's upper neck.

Osorio is a newish matador and his caudrilla today aren't top class. One of his bandilleros is entertainingly plump. The audience today gets some amusement out of the fat bandillero's attempts at evasion and flight and when he makes his way towards one of the little bolt holes in the wooden circumference of the ring there is always the possibility he will get stuck therein. Which would, of course, be a tragedy but here in the bleachers we have a guilty secret: we are here to see blood. We are blood brothers and sisters. Conspirators.

When each bandillero has planted his sticks the second act of the bullfight is finished. Now Rafael Osorio steps forward and with a gesture asks the permission of the president of the corrida to make the kill. He walks to one side of the ring and embraces his father. The two other matadors on the bill give him hugs till they merge into one big ball of lights. Finally Rafael's small red cape blooms and the real work begins.

It doesn't take long, but it is compulsive. Jaecero paws the ground and dips his head as Rafael Osorio walks slowly towards him. In the quiet you can hear the sticks in the bull's back clicking off each other.

Suddenly, the bull moves. He charges straight for the red cape Osorio is holding out. Not just holding out. Osorio's feet are together planted on the ground. Movement of the feet when the bull is coming is considered poor form. His feet are planted and his hips are thrust out towards the cloak in a camp, voguish pose that places the entire middle of Osorio's body almost in the path of the bull. The cloak is twitching beguilingly.

The animal sweeps through the cape, its flanks brushing the matador, who swirls away and takes the applause of the crowd. This pass, the bread and butter of matador choreography, is known as a veronica. A series of these passes with different flourishes and moves thrown in serves to fix the bull eventually in the same place.

At times, the bravery of bull and man makes one suck in breath sharply. The bull is wounded, but is never pathetic. It never stops trying to figure out a way to win this encounter. And Osorio fights him with confidence and some elegance. Once, he turns his back to the bull and while facing the other way jiggles the cape in front of himself so that to get to the cape the bull would have to pass first through the man.

Occasionally, he pulls the red cape across himself at the last minute trusting that the bull won't have time to follow the path into his body, but will turn and brush past his behind. The closer the fighter works the bull to his own body the better the victory is deemed to have been.

Osorio is good, but not good enough to draw the white handkerchiefs which fans wave in appreciation of a great fighter. That will take time. That will take more learning than he has now.

It's tempting to do so, but you can't separate what Rafael Osorio is about to do as the final flourish in the final act, the suerte de matar. You can't separate it from a culture or a history.

The lore is wondrous and engaging. From bullfighting's Moorish origins to the stories of Juan Belmonte and Joselito El Gallo and Rafael Gomez and Ignacio Sanchez Mejias; contemporaries and rivals, buried together in a graveyard in Seville, two of them sent to their graves by bulls.

And Manolete was sent that way two. A slender man with a constant look of surprise on his face, he rewrote the rules as regards the style of bullfighting and became an idol of the post-Civil War generation. He died from a goring in the ring at Linares.

And El Cordobes, a hard, tough man from Cordoba who once sued his own son for trying to begin a career using the name El Cordobes.

There's a story about the boyhood of El Cordobes which links him to so many of his predecessors. Eager to test his courage, but not of an age when he might be permitted to do so, he and a friend went to a moonlit field and woke the sleeping bulls, waving improvised capes and performing veronicas and pases de pecho and other moves until dawn.

All the deaths are achingly poignant. Here in this ring in Madrid, here in Las Ventas, they paraded the body of 21-year-old Jose Cubero when he died in the ring in the late 1980s. On his final lap of honour the mourners waved white handkerchiefs and cried Torero, Torero as the body passed.

So with history and culture on his slender shoulders Rafael Osorio stands face to face with Jaecero in Las Ventas. There is silence. The bull's tongue lolls from one side of its mouth. Jaecero is tired and mesmerised. He is haunted by the matador's stare. By contrast, Osorio holds his estoque, or curved sword, in perfect form, eyeing the spot into which he will drive it.

"Toro," he says quite softly. "Toro, toro." And finally, fatally, the bull moves, more of a lumber than a charge now. Straight towards Rafael Osorio. Osorio rises to his tiptoes and drives his sword deep into the flesh above the neck just past where the bandilleras hang. It is a clean entry. Sometimes the sword meets bone and refuses to go in. Now, however, all that remains visible of the sword is the handle sticking from the animal's neck.

There is applause. On the faces of the tourists no revulsion. Nobody is looking away. Most are checking their cameras to make sure that they have captured the moment of entry. Jaecero staggers a little and finally falls, a graceful fall, front legs buckling, so it appears as if he kneels before keeling slowly sidewards.

We never swooned. We weren't as appalled as we'd hoped we might be be. My daughters, two dedicated vegetarians, rooted steadily for the bulls but seldom flinched. Part of us came to see the bloodshed and another more secret part wondered if we mightn't see the blood of a man spilled on the brown sand.

Once, between kills, my youngest went down to the shop beneath the seating. When she was ready she stood for a while at the top of the stairwell and, thinking she was lost, we hollered and waved at her. She went into an elaborate comic mime to indicate her intentions, pretending to be a bull, stabbed through the neck and then staggering woozily about the place. When the next killing was over she'd be back to her seat. She didn't want to impede anyone's view.

Maybe a person's reactions says something about them or something about the tolerance level we have acquired for affronts to human dignity from televised war right down to Big Brother. Maybe not. Perhaps it was just that at Las Ventas even in the acts of purest violence you could detect metaphors: art, bravery, beauty and a connection to a more primal time when we didn't swaddle ourselves quite so thoroughly against the inevitabilities of life and death.

The three acts of the bullfight - the bulls entry and his brave optimism as he charges the horses of the picadors; his confusion and anger as he succumbs to the assaults of the bandilleros; and his final, weakened submission to the gleaming sword - have a theatrical poignancy which is all too easily dismissed.

And the matadors. A man alone in a ring with a charging beast quells his own screaming heart and summons the front for art and stillness. Whose life isn't about faking composure in some way?

In Las Ventas, you could imagine the context and set it against tradition. Hemingway loved the fights but conceded that there was no overwhelming moral argument for them. They stir something or they don't.

On a Sunday afternoon in the still Madrid air you can understand how one could love this life and its lore. The old guys, the ancients, The slow death of Manolete. The tales of El Cordobes and his attitude. And the scent of death. You could see even on this slow Sunday why bullfighting has survived in a plastic world.

A high, hot sun and 25,000 thousand people fanning themselves. A great matador. A feared bull. No drama more real? Perhaps not.

Yet, those moments are fewer. As the details of Churrascon, the next bull, are being paraded to a crowd gulping Coke and Häagen-Dazs, the remains of his brother bull Jaecero are being dragged from the ring, leaving a dark stain in the sand as they go.

Jaecero hasn't departed easily. When Osorio's sword has been pulled back out from his body, Jaecero's sides have still been heaving. A bandillero has had to take a dagger and stab him several times in the brain to draw the final quietness over him.

Whatever sanctity bullfighting had has been washed away by money. You can't separate the corrida from its history. Nor can you isolate it from its present. You imagine the carcasses of Jaecero and Churrascon being stacked carelessly into a beef mountain made up of the other 40,000 or so bulls who will be killed this season and the nobility of the animal becomes the butt of a joke.

The business, the hawkishness, the sheer repetitiveness, the conscious breeding of bulls to be less dangerous, the habit of shaving their horns, allegations that many are drugged, half blinded with Vaseline, the strikes, the star system and the agents. All these things have diminished bullfighting.

It is a ritual, but not a necessary one. An art but a limited art. A contest but an unfair one. All those things, but still compelling enough in itself to make its own case. Three matadors. Six bulls. Odd mathematics for the modern age.

We hit the Madrid evening. Headed for food.