Human imagination seems seriously limited when faced with the cosmic scope of time and space. We can imagine, through stop-motion animation and CGI, what it might be like to walk the earth with creatures the size of office buildings. But how to wrap our heads around the fact that they lived hundreds of millions of years ago, on a planet some four and a half billion years old? We trust the science, but can’t rely on intuition alone to guide us to such mind-boggling knowledge.
At the other end of the scale, events measured in nanoseconds, or billionths of a second, seem inconceivable, even to someone as smart as Grace Hopper, the Navy mathematician who invented COBOL and helped built the first computer. Or so she says in the 1983 video clip above from one of her many lectures in her role as a guest lecturer at universities, museums, military bodies, and corporations.
When she first heard of “circuits that acted in nanoseconds,” she says, “billionths of a second… Well, I didn’t know what a billion was…. And if you don’t know what a billion is, how on earth do you know what a billionth is? Finally, one morning in total desperation, I called over the engineering building, and I said, ‘Please cut off a nanosecond and send it to me.” What she asked for, she explains, and shows the class, was a piece of wire representing the distance a signal could travel in a nanosecond.
Now of course it wouldn’t really be through wire — it’d be out in space, the velocity of light. So if we start with a velocity of light and use your friendly computer, you’ll discover that a nanosecond is 11.8 inches long, the maximum limiting distance that electricity can travel in a billionth of a second.
Follow the rest of her explanation, with wire props, and see if you can better understand a measure of time beyond the reaches of conscious experience. The explanation was immediately successful when she began using it in the late 1960s “to demonstrate how designing smaller components would produce faster computers,” writes the National Museum of American History. The bundle of wires below, each about 30cm (11.8 inches) long, comes from a lecture Hopper gave museum docents in March 1985.
Photo via the National Museum of American History
Like the age of the dinosaurs, the nanosecond may only represent a small fraction of the incomprehensibly small units of time scientists are eventually able to measure—and computer scientists able to access. “Later,” notes the NMAH, “as components shrank and computer speeds increased, Hopper used grains of pepper to represent the distance electricity traveled in a picosecond, one trillionth of a second.”
At this point, the map becomes no more revealing than the unknown territory, invisible to the naked eye, inconceivable but through wild leaps of imagination. But if anyone could explain the increasingly inexplicable in terms most anyone could understand, it was the brilliant but down-to-earth Hopper.