All of Dr. Henry J. Heimlich's achievements bear the same hallmark: They cut Gordian knots.

In fact, they sometimes are so very forceful and so very simple that they take people aback--until they are demonstrated.

In 1955 he was the first surgeon to replace any human organ. Even today in his hotel room--he is here to address the International Platform Association--he has a full-sized human stomach made of felt with zippers, and he will show how he simply cuts a long strip from the stomach and fashions it into a tube to create an artificial esophagus.

Later he invented a drainage valve for chest wounds. It is nothing but a Bronx cheer device, a flat rubber tube that lets air out but not in.

And of course in '74 he invented the Heimlich Maneuver, the almost universally known treatment for choking on food: Grab the victim from behind, ball your fist over the midriff just under the ribs, and jab in and upward, hard. Heimlich tested it on animals, and then suggested via newspapers that someone try it in a choking incident. Within a week a Seattle restaurateur saved a woman's life with it.

Today Heimlich claims it has saved well over 2,000 people. It has also embroiled him in a controversy with the American Red Cross, which recommends a backslap first. Heimlich says the slap could lodge the food deeper. His opponents caution that not everyone who collapses in a restaurant is necessarily choking and that some might be hurt by the treatment.

Meanwhile, lives continue to be saved. And Heimlich has become a household name.

He has also proposed a cure for cancer: Give the patient malaria, thus raising the body heat too high for cancer cells to thrive. Simple, forceful--and controversial.

Now the 62-year-old Cincinnati surgeon has another Gordian knot to cut. He believes he has a plan for world peace. It is called "Computers for Peace," and the idea is a vast increase in trade with our political enemies that will, he thinks, deflect us all from our apparent collision course.

"It works!" he says, deeply tanned hands chopping the air. "The Marshall Plan worked. The economic programs to defuse the racial troubles in '68 worked. Inadequate or not, they reduced the violence. This country and the Soviet Union are potentially the greatest trading partners in history. This is based on hard, practical self-interest."

For example, he notes, if we sold the Soviets consumer goods, they could afford to be less obsessed with keeping their people from learning about the glittering creature attractions of the West and could lift the Iron Curtain a bit. If they paid us in cash, they would have less to spend on weapons, and meanwhile our production would rise and unemployment would drop.

Using the talent for publicity that drives his critics wild, Heimlich has written to presidential assistant Michael Deaver (who saved Ronald Reagan's life in 1976 with the Heimlich Maneuver), asking that the president approve the Soviet gas pipeline to Europe.

"The idea that the Russians would close it down to blackmail the Europeans--and lose $10 billion a year in revenues--is crazy. They've already had two smaller pipelines in place for 15 years, and nothing of the sort has happened."

He and his Heimlich Institute have talked up Computers for Peace with world leaders, and as one of the most popular speakers in the United States, the ubiquitous doctor puts the idea over wherever he goes. He likes to quote Thomas Jefferson: "By wise use of the power to trade what we have been blessed with, we may find in food a substitute for the sword and a means to keep peace in the world."

The computer part refers to our ability to project the future results of economic policies, thus convincing skeptics.

One skeptic is former secretary of state Dean Rusk, who finds the plan naive because "one of the problems is the assumption that people will react reasonably rationally in their own self-interest." He noted that human behavior and economic theory often refuse to coincide.

Retorts Heimlich: "It's true I don't understand diplomacy. But how is it that with the most brilliant minds and the greatest spy systems, we still end up with wars? The time has come for people to react in their own self-interest. I have even figured out the timing on this: We have two years to turn ourselves around before we get hopelessly and finally locked into a war course. By the way, I needed Rusk's comments. Without that I'd be just another doctor mouthing off."

The fight for a nuclear freeze is all very well, he adds, but that won't come until the mutual suspicions are lulled by mutual business successes ("Caterpillar Tractor is losing $90 million and has tractors sitting around unbought; sell 'em to Russia!") and the realization that war is no longer as profitable as peace.

Friends are even talking of running Heimlich for president in 1984 as a Republican on a peace platform. "My name is better known than either Bush or Anderson (whom he backed in 1980) when they were running," he says. "I don't have aspirations to be president, but if it's a way to get the peace program across, I'll try anything."

That sounds like the truth. But there is still one thing he hasn't tried. He has never had a chance to attempt the Heimlich Maneuver in an actual emergency.