It is 9 o'clock sharp, Monday morning, in a lovely country house just outside Dundee, where Player and his wife are staying with old friends. I have been sitting outside in my hire car since just after 8.15, because Player does not like to be kept waiting, indeed he loathes sloppiness of any sort. Having heard that he is a fierce evangelist for dietary correctness, I also check my chin three times in the rear-view mirror, lest he spots any stray bits of the reviled fried brid or scrimbled igg.
He doesn't, although he does treat me to a passionate monologue on the perils of over- eating. Suffice to say that junk food addict John Daly is not one of Player's close buddies. "That," he says, "is a very sad story. John Daly had enormous potential and he's a nice man, but something goes wrong. Instead of turning to the right he turns to the left. I think he finds it hard to handle the pressure. And let me tell you, it's understandable. I've seen members on the last hole playing for a couple of golf balls and they can hardly get the putter back. So imagine what it's like being in contention for the British Open. Tommy Armour missed a putt to win the US Open once and the guy said to him, `Tommy, I could have knocked that in.' And Tommy said: `I bet you $5,000 you can't.' The guy said, `Sure.' And Tommy said, `Fine, but you've got to come and putt it tomorrow morning. I want you to think about it all night.' The guy came out next day and didn't get it close."
Player laughs. He has an appealing charm and, up close, is surprisingly dashing, rather like an ageing matinee idol. His heroes, he tells me without embarrassment, are Jesus Christ, Winston Churchill, Gandhi, Mandela and Margaret Thatcher. Golfing-wise, he adds Arnold Palmer and Jack Nicklaus. And Nicklaus speaks highly of him, too, once saying that when you were playing against short-game genius Player and came over the brow of a hill to see his ball on the edge of the green, you thought "thank heavens he's not in the bunker".
Open Championships at Carnoustie have a tradition of producing top quality winners, so it surprised nobody when Player won there in 1968. "It's one of the toughest golf courses that I've ever played," said Player, who tomorrow tees off with Pete Gribben and Corey Pavin. "Especially when the wind blows. Tom Watson won with 275, but I tell you, 300 could win this week if that wind gets going. In '68, the wind blew. And in the final round I hit probably one of the five best shots in my career, at the Spectacle [the 14th]. Billy Casper, Bob Charles, Maurice Bembridge, Jack Nicklaus and myself were all within one shot of each other, and I remember seeing that flag whipping in the breeze and hitting a three-wood this far" - he holds his hands 18 inches apart - "from the hole. And I won by one shot. So when I arrive at the Spectacle, I will kiss the ground."
Player was playing that day with his keenest rival Nicklaus, and their mutual appreciation society thrives still. Last year, when Player won an event on the US Senior Tour, he received a note which said: "You never cease to amaze me." It was signed, simply, "Jack". In turn, Player pays tribute to the graciousness with which Nicklaus finally conceded defeat at Carnoustie 31 years ago.
He was, of course, delighted to beat the world's greatest golfer in one of golf's greatest arenas, and yet the performance he claims to savour above all others was not that one, nor did it come in any of the nine regular majors or nine Seniors majors he has to his name. Nor, for that matter, was it even a winning performance. In the 1969 USPGA, in Daytona, Ohio, Player lost by one shot to Ray Floyd even though anti-apartheid campaigners dogged him throughout, at one point throwing ice in his eyes. "I will go to my grave knowing that basically I won 10 majors," he says, and there is a look in his eye which says argue if you dare.
Instead, I just as daringly raised the subject of Tom Watson, who once asserted that Player had illegally removed a weed beside his ball during a big-money Skins Game. Player insists that the issue is dead and buried, and that he and Watson are friends again, but it clearly still rankles. "What upset me was that he didn't raise it until later. I said to the sponsor: `Look, I will give a million dollars to any charity in the world if I did anything wrong. It's all on camera so let's replay it.' They didn't want to. You know, Nicklaus was feeling pretty upset when he lost the US Open by one shot to Watson, because he thought Watson didn't have the right grooves on his clubs. These little controversies happen in golf. But you should query it at the time, not afterwards. That's what upset me. But Tom and I have agreed not to harp on about it."
One of the reasons Player hates to see blemishes on his extraordinary record is that he is, by his own admission, a perfectionist, and arguably also a teeny bit of a control freak. Having won nine majors on a regular tour, he was determined to match the feat on the seniors tour. And did. Like Sam Snead, he has won in each of five decades and next year will be trying very hard to make it six. Don't bet against it. At the recent Tournament Players' Championship he was dissatisfied with a 65 because it could easily have been a 63, which would have made him the youngest man to shoot his age on the Seniors Tour. In the meantime, his schedule would wreck men half his age, indeed he reckons to have notched up 11 million air miles in his career, which might even interest Norris McWhirter. He told me with a certain pride, moreover, that he knows exactly where he will be every day between now and Christmas.
He is, of course, slightly richer than Croesus (although slightly poorer than Arnold Palmer) yet maintains that he has to keep travelling to sustain his 11,000-acre stud farm between Johannesburg and Cape Town and the 150 people on his payroll. Farming is even closer to his heart than golf, he says. He owns 300 thoroughbred racehorses and - surprise, surprise - calls home every day to check on their well-being.
It is all a far, far cry from the humble Johannesburg suburb where he grew up. "In fact, I was talking to my wife about it yesterday on the plane, and got quite choked," he said. His father worked down the gold mine. His mother died when he was eight. Fleetingly, his big brown eyes glisten as he talks movingly about his childhood, about the day his grandfather died, about leaving for school every day at 6am and returning home to an empty house. A shade irreverently I find myself thinking of the Four Yorkshiremen sketch - "That's nought..." - but at the same time it is hard to think of anyone who has rewritten their own destiny quite so spectacularly. With this in mind, Player is worth listening to when he makes pronouncements on the modern game. And one of the latest bees in his bonnet concerns the ambiguous golf coach. "I've been lucky," he says. "I've had very few bad spells. And you know why? Because I stood on the practice tee and worked it out for myself. Golf swings are like fingerprints, everyone is different, and when you change somebody's swing, you are trying to erase their fingerprints. Look at Jack Nicklaus, Arnold Palmer, Ben Hogan and Sam Snead. None of them swing alike. Ernie Els swings completely different to Tiger Woods. This is a game of contradiction. Trevino takes the club way outside. Arnold takes it back on the inside. Nicklaus takes it straight up in the air. So what is the right swing?
"If one of these coaches today saw a guy like Jack Nicklaus or Miller Barber, with a flying right elbow, they'd say no, you mustn't do that. I never had a coach standing there all the time saying `you're doing this, you're doing that'. If I had, I would have stopped thinking for myself. And if you're going to have a coach, have one coach. A lot of guys get over-coached. Nicklaus went to Jack Grout for fine-tuning now and then. I had my father-in-law who helped me. But that was it. Now, I don't profess to know the answer when guys like Faldo and Ballesteros start playing badly. But I do know that I haven't heard one thing about the swing in the past 15 years that I hadn't heard before."
Wise words, although, like many golfers of his generation, Player is also capable of pious piffle. "Golf teaches you so many lessons in life," he says. "It teaches you not to get cocky. It teaches you to be punctual. If the world could be run like golf, there would be no murders, rapes and drugs. Because in golf, they don't tolerate it." I bite my tongue, for daring to wonder what the world would be like if everyone wore Pringle sweaters and women were kept out of the Spike bar. Player, meanwhile, is warming to his theme. "My advice to young people: play golf. I look at Michael Jordan, retiring at 36. And look at your soccer players. Bobby Charlton, he stayed around, didn't retire until he was 35 or something. In golf, that's when you're in your prime. Steffi Graf, this legend, this old lady of tennis. She's 30. Let me tell you, when these sportsmen and women retire at 31 or 32, they go into great spates of depression. The public don't know this. But I know, because I've talked to them. Now, when I was 62 I won four tournaments on three continents. So the answer is to play golf."
Actually, the answer is to play golf like Gary Player, which is a different proposition entirely.