Hagen's approach to the game was recalled in a recent column in this newspaper by Ken Jones. "The notion that games aren't necessarily fun is pathetic and, sadly, a feature of vicarious parental involvement," Jones wrote. Talk to Parnevik about his life as a golfer and the word that crops up most often is fun.
This is something he certainly gets from his father. Bo Parnevik is a famous comedian in Sweden, a cross between Mike Yarwood and Tommy Cooper. Exposed to the funny ha-ha side of life from an early age, Jesper has never been afraid to explore the funny peculiar aspect of the world either. After Bo took up golf, his son found the perfect outlet for his wondering and wandering mind.
The anecdotes are well chronicled. Parnevik believes in reincarnation, meditates while the dawn breaks over the ocean near his home in South Palm Beach, Florida. He eats volcanic sand to cleanse his system, has had his blood analysed by radiation, uses stroboscopic glasses, has had his metal fillings replaced with ceramic ones to reduce mercury levels and has been a pupil of the Russian philosopher who is Mikhail Gorbachev's mentor.
Of course, the most public demonstration that he is not your regular golfing pro comes in his retro, non-colour co- ordinated clothing and the cap with its upturned peak. Parnevik was practising in Florida one winter and wanted to get a tan. He almost won his next tournament and the tradition has stuck. He planned to get a special Ryder Cup version made.
"Any image is a good one," Parnevik says. "Maybe there isn't that much to write about in the golfing world. I don't mind at all. If anyone can have fun on my behalf I'm happy. All those things started with a small thing and they have been building up. It goes in cycles. You get really hooked on something and try it out, but a few months later you don't want to do anything at all. I've been quite normal the last couple of months."
Some of the stories have been perpetrated by his one-time coach, Olaf Skipper. It was Skipper who got Parnevik to visualise a shot by imagining green peas in orbit falling into a hole.
After the Open Championship at Royal Troon, where for the second time Parnevik narrowly missed becoming the first Swede to win a major, Skipper suggested the full moon had contributed to his downfall. "I read that," Parnevik said. "That was taking it a little bit to the extreme. I'm not really into that. We don't work together that much any more."
But Parnevik has done work aplenty in America, improving his ball-striking and his putting. When he was based in Europe, he used to hate putting on ultra-fast greens. Now he loves it. He has come close to winning but not quite managed it. At Troon, his game was not all there and the putts which held his challenge together for three days refused to drop as they did for Justin Leonard at the finale.
The 32-year-old Swede's admiration for golf's oldest crown is undiminished by his ordeals at Troon and, three years earlier, at Turnberry. "The Open is the absolutely best tournament ever, I think. It is the way they build the grandstands. There is no other tournament that do it that way. There is this tunnel down the 18th fairway. When you get the applause and the cheers it is almost overwhelming. When you hole a putt, the roars are a hundred times higher than anywhere else. It's great.
"I don't look back with any regrets, I just think, once it finally happens, it is going to feel so much better. A lot of people ask me if I am disappointed that I have not won this year. I can't be. I've had my best year ever. I know I'm going to have years which are a lot, lot worse and I'll dream about having a year like this."
Parnevik is at a loss to explain his rise into the world's top 20. "Golf is so easy when you are doing well, it's unbelievable. When I won the Lancome Trophy last year I was wondering: `What is everyone else doing?' All you have to do is hit the fairway, hit the green and make the putt. No problem.
"It is when you are struggling, that's the real test about how you can handle yourself. The really first-class players, when they are struggling, they are still trying hard and they are not complaining about this, blaming others and all that. They just try to fight back. Those guys are the true champions.
"I've thought about it a few times with Tiger [Woods]. I think he sends the wrong message to the teenagers sometimes. You know, when he finished second at Pebble Beach and he said: `Second sucks - all I want to do is win'. If you play for that reason, you are going to be disappointed a lot.
"But there is something else that drives you, has to drive you. If you do it because you truly enjoy doing it then all the results will come. But if you try to do it the other way round... It's like when you are a kid, you never stop playing - not because you think at 30 you're going to be a millionaire, you stand there and chip and putt for hours just because you think it is so much fun.
"I think golf is the best game ever invented. I look at all other games and nothing comes near to golf. I think it is one of the last true games. All other games these days almost force you to cheat as much as you can without getting caught. No one in golf ever has that thought going through their mind. Guys who have never seen golf cannot believe if you are in the woods and you have the chance to win $200,000, why don't you move your ball a little bit. No one can see you. No one would know, but it never happens."
Many of Parnevik's countrymen did not think they would ever see two Swedes in the Ryder Cup team, a consequence of which is full television coverage for the first time. "A lot of people in Sweden have never seen golf before and they watch the British Open and they can't believe how nerve-wracking it is to watch and how exciting.
"They think it is a pretty boring sport and nothing really happens, but when they actually watch it, they realise it is a lot of fun. I remember watching the Ryder Cup at Kiawah and it was so tense you did not want to leave the TV." Parnevik, you can be sure, will be enjoying himself this week.