A billion years ago (give or take), in a galaxy far, far away, two black holes concluded a cosmic pas de deux. After orbiting each other more and more closely, their mutual gravity tugging each to the other, they finally collided and merged into one. Their collision released enormous energy — equivalent to about three times the mass of our sun. The black holes’ inspiral, collision and merger roiled the surrounding space-time, sending gravitational waves streaming out in every direction at the speed of light.

By the time those waves reached earth, early in the morning of Sept. 14, 2015, the once-cosmic roar had attenuated to a barely perceptible whimper. Even so, two enormous machines — the miles-long detectors at the Laser Interferometer Gravitational-Wave Observatory (LIGO) sites in Louisiana and Washington State — picked up unmistakable traces of those waves. On Tuesday, three longtime leaders of the LIGO effort, Rainer Weiss, Kip Thorne and Barry Barish, received the Nobel Prize in Physics for this accomplishment.

The discovery was a long time in the making, in human terms as well as astronomical ones. Dr. Weiss, Dr. Thorne, Dr. Barish and several of their colleagues labored on LIGO for decades. The landmark discovery in 2015 involved more than 1,000 collaborators dotted across five continents. The project exemplifies a long-term vision among scientists and policy makers that is almost unimaginable today, as distant as those colliding black holes.

In the late 1960s, Dr. Weiss taught an undergraduate physics course at the Massachusetts Institute of Technology. A few years earlier, the physicist Joseph Weber claimed to have detected gravitational waves using a device that relied on antennas made of aluminum cylinders, but he failed to convince skeptics. Dr. Weiss assigned a homework problem to his class: Investigate a different way to detect the waves. (Students, take note: Sometimes homework problems herald Nobel Prize-worthy advances.) What if physicists tried to detect gravitational waves by scrutinizing tiny shifts in the interference pattern of laser beams, which had traveled separate paths before recombining at a detector?

Gravitational waves should stretch and squeeze a region of space as they travel through it. Such a disturbance, Dr. Weiss reasoned, would alter the length along which one of those laser beams traveled, putting the two lasers out of phase with each other by the time they both reached the detector — a difference that could yield a measurable interference pattern.

The idea was audacious, to say the least. To detect gravitational waves of the expected amplitude using the interference method, physicists would need to be able to distinguish distance shifts of about one part in a thousand billion billion. That’s like measuring the distance between the earth and the sun to within the size of a single atom, while controlling all other sources of vibration and error that could swamp such a minuscule signal.

Little wonder that Dr. Thorne, one of this year’s LIGO laureates, assigned a homework problem in his influential 1973 textbook, guiding students to the conclusion that interferometry was hopeless as a method for detecting gravitational waves. (O.K., students: Maybe some homework problems can be skipped.) After investigating the idea further, however, Dr. Thorne became one of the most tenacious advocates of the interferometric approach.

Convincing Dr. Thorne was the easy part; attracting funding and students proved much more difficult. Dr. Weiss’s first proposal to the National Science Foundation, in 1972, was rejected; a follow-up in 1974 received modest funds for a limited feasibility study. In 1978, Dr. Weiss observed in a funding proposal that he had “slowly come to the realization that this type of research is best done by secure (possibly foolish) faculty and young post-doctorates of a gambling bent.”

As the size of the anticipated project grew — interferometer arms that would stretch miles, not yards, decked out with state-of-the-art optics and electronics — so, too, did the budget and organization. The project’s increasing complexity required political mastery as much as physics know-how. At one point, efforts to establish one of the large detectors in Maine foundered on political rivalries and back-room deals among congressional staffers — a lesson in interference beyond laser beams.

Remarkably, the National Science Foundation approved funding for LIGO in 1992; it was (and remains) the foundation’s most expensive project. The timing was propitious: After the dissolution of the Soviet Union at the end of 1991, physicists learned with whiplash speed that Cold War justifications to invest in scientific research no longer held predictable sway in Congress.

Around that time, budgetary brinkmanship in the United States entered a whole new era. Planning for long-term projects now has to contend with frequent threats (occasionally realized) of government shutdowns, compounding a budgetary climate focused on short-term projects that can promise quick results. It is difficult to imagine a project like LIGO getting a green light if proposed today.

Yet LIGO demonstrates some benefits of taking a longer view. The project has exemplified a close coupling between research and teaching, well beyond the suggestive homework problems from the early days. Scores of undergraduates and graduate students were co-authors on the LIGO team’s historic first-detection article. Since 1992, the project has spawned nearly 600 Ph.D. dissertations in the United States alone, from 100 universities across 37 states. The studies have ranged well beyond physics, including pathbreaking work in engineering and software design.

LIGO shows what we can accomplish when we fix our eyes on a horizon well beyond a given budget cycle or annual report. By building machines of exquisite sensitivity and training cadres of smart, dedicated young scientists and engineers, we can test our fundamental understanding of nature to unprecedented accuracy. The quest often yields improvements for technologies of everyday life — the GPS navigation system benefited from efforts to test Einstein’s theory of general relativity — even though such spinoffs are difficult to forecast. But with patience, tenacity and luck, we can catch a glimpse of nature at its most profound.