Leonardo da Vinci was our greatest switch-thinker. He drew with his left hand while simultaneously writing with his right. He was a left-brained engineer of flying machines and a right-brained painter of the Mona Lisa. He found mathematics essential to his art and art essential to his mathematics and became proficient in every human endeavor but one: golf.

Jim Kaat, on the other hand, does play golf, extremely well, lefthanded and righthanded and often both at once. Some days the former big league pitcher's game is literally a mixed bag of lefthanded woods and righthanded high irons and a left- or righthanded putter. When he says "playing like that can be tough on the brain," he means both halves.

Twice a week Kaat, 75, plays a round against himself—better-ball—with a full complement of righthanded clubs and another full bag of lefthanded clubs. "It makes the caddies happy," he says. "They always root for the righthander to win."

That's because the righthanded Kaat is an underdog, even though Righty Kaat has been playing 26 years longer. Lefty Kaat, who won 283 games over 25 seasons as a southpaw pitcher, has three holes in one and is a seven handicapper, while Righty Kaat is a 10. But three-time major champion Nick Price, a fellow member of MacArthur Golf Club in Hobe Sound, Fla., prefers Righty Kaat's swing. "Something about my shoulder plane," says Kaat, who has difficulty keeping his swing flaws straight.

Kaat was a 32-year-old pitcher for the Twins in 1971 when Vikings placekicker Fred Cox invited him to play his first round of golf at Minnesota Valley Country Club in Bloomington. The club pro only had righthanded clubs to lend Kaat. He was hooked, as were many of his tee shots, and blissfully played righthanded for the next quarter century until short-game troubles compelled him to try chipping lefthanded. For two years he obstinately whiffed or topped the ball lefty. "No one wanted to be my partner," Kaat sniffs.

At a tournament in 1995, Kaat ran into famed instructor Jim Flick, whose golf school he had once attended as a righty, and said, "Coach, I'm coming to your school again, but as a lefty."

It helped that Kaat was an elite athlete and warhorse who threw 19 complete games in 1966 alone, and that he appreciated the most ironclad axiom of guydom: The more pointless your pursuit—visiting every ballpark, alphabetizing your albums, pursuing a white whale—the more noble it is.

Switch-golfing became Kaat's Moby-Dick. He had seen enough ambidextrous baseball genius as player and broadcaster to be emboldened. The lefthanded pitcher Tug McGraw and the righthanded third baseman George Brett could both throw beautifully with their glove hands. On Sept. 28, 1995, Expos reliever Greg Harris, a righthander, used a six-fingered glove of his own design to pitch an ambidextrous inning against the Reds, retiring Reggie Sanders righthanded, walking Hal Morris lefthanded, retiring Eddie Taubensee lefthanded and retiring Bret Boone righthanded.

Day after day Kaat struck more balls than the cast of America's Funniest Home Videos and became, over many years, a better lefty golfer than righty. Just shy of his 71st birthday in 2009, at Glen Falls Country Club in New York, Kaat shot his age lefthanded. He has done it at least five times since.

In golf, shooting one's age is a holy grail that has been realized by players as young as 59 and as old as 103, though the vector lines of golf scores and golfer ages intersect most ideally—for a few blessed seniors—in the mid-70s. And so it was that on Dec. 7, playing against himself at MacArthur, Righty Kaat—now relegated to Cinderella status—rolled in a 15-foot putt on 18 to card a 75, beating longtime nemesis Lefty Kaat by three strokes. "Do you know what that means?" Kaat asked caddie Mike Adamson, who responded, "You just shot your age."

Kaat, the game's Da Vinci, had become the first golfer on record to shoot his age as a lefthander and as a righthander. Until octopi take up the game, his feat cannot be broken, though Kaat offers another possible reason: "I doubt that anyone else is trying."

The most ironclad axiom of guydom: The more pointless your pursuit—visiting every ballpark, pursuing a white whale, golfing lefty and righty—the more noble it becomes.

Know of any other great moments in ambidexterity?

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PHOTODAMIAN STROHMEYER/SPORTS ILLUSTRATED ILLUSTRATION

HOLE YARDS PAR R1 R2 R3 R4
OUT
HOLE YARDS PAR R1 R2 R3 R4
IN
Eagle (-2)
Birdie (-1)
Bogey (+1)
Double Bogey (+2)