A World of Difference Between Invention and Discovery

It’s a question as old as Plato: Do scientists discover laws of nature, or create them?

Did Einstein discover relativity, or did he think it up?

Do mathematicians invent theorems and proofs, or are these truths out there waiting to be discovered? Do chemists find new molecules, or forge them?

Sometimes, the answer is obvious. Astronomers didn’t create the stars, and physicists didn’t invent gravity. Something out there shines; objects fall.

Yet science’s own long-running creation controversy has deep roots.

According to Plato, numbers and geometric forms exist as independent entities, “out there,” regardless of whether anybody ever discovers them. Like tiny organisms seen only under the lens of microscopes, or distant extra-solar planets seen only with the help of telescopes, mathematical truths are simply there to be found.

Today, few mathematicians remain strict Platonists. Certainly, there are some mathematical truths that are simply “out there,” according to Ronald Graham, a mathematician at UC San Diego. “Perfect numbers have a certain form.”

But proving that something is true, he says, “is a creative and elegant thing.”

Even numbers that we take for granted today were clearly “created,” not discovered. Take zero, for example. The whole idea of a “number” signifying nothing was anathema until a few thousand years ago. It didn’t exist until the Indians invented it.

In the same way, calculus was dreamed up in the minds of Newton and Leibniz--and along with it the bizarre idea of a number that could be infinitely small.

Indeed, mathematician Reuben Hersh argues in his book “What Is Mathematics, Really?” that mathematicians invent every bit as much as they discover--loath as they often are to admit this.

“The majority of those who ponder about mathematics no longer believe in Platonism,” writes Marcia Ascher in her classic text, “Ethnomathematics.” “To us, squares or right triangles or prime numbers are categories that we, in Western culture, have created [not discovered].”

Mathematicians have been tossing this question around for millenniums. What about other sciences?

Certainly, proponents of string theory--the idea that the universe and everything in it results from the vibrations of 11 dimensional strings--are generally adamant in their claim that the theory is being discovered, not created.

“Nobody in this field is clever enough to have invented something like this,” says Harvard physicist Andrew Strominger. “It’s clearly something that we discovered. It’s beyond our imagination to invent” such a beautiful and powerful mathematical structure.”

But others hold different views.

“Is the universe already there--a single entity . . . waiting out there for us to discover?” asks Colgate University astronomer and anthropologist Anthony Aveni. “Or are there infinite ways to piece the cosmos together?”

His own answer is obvious in the title of his recent book: “Conversing With the Planets: How Science and Myth Created the Cosmos.”

Clearly, the process of discovery is a complex equation. Gravity existed before Newton came along, but Newton created the laws that describe how gravity works. Then Einstein invented (or discovered?) a new set of laws (relativity) that describes how gravity comes to be.

Perhaps scientists would view creation differently, argues chemistry Nobel laureate Roald Hoffmann, if science had a different--decidedly less sexist--history.

“The male metaphors of peeking, unveiling, penetrating are characteristic of 19th century science,” he says. “They fit the idea of discovery.”

But discovery, he says, is only a small part of what scientists do--even though the cliche, “‘uncovering the secrets of nature,’ has set, like good cement, in our minds.”

Hoffmann is particularly upset that chemists, of all people, have accepted this metaphor. Some molecules, he allows, are already there, waiting to be discovered, like the Americas.

“But so many more molecules of chemistry are made by us. . . . We’re awfully prolific.” Millions of previously unknown molecules--molecules that never existed before on Earth--have been created like works of art in the laboratories of chemists.

There’s a lesson here, he says: “Had more philosophers of science been trained in chemistry, I’m sure we would have a very different paradigm of science before us.”