In 1973, the physicist James Bardeen figured out that in the right circumstances — if, say, a black hole passed in front of a large, bright background, like a star — it might be possible to see its silhouette. “Unfortunately,” Bardeen concluded, “there seems to be no hope of observing this effect.” Later that decade, the French physicist Jean-Pierre Luminet sought to learn what a black hole would look like if illuminated by the glow from the superheated matter swirling around it. He did his calculations by feeding punch cards into a primitive computer. He drew the results by hand. His black-and-white images looked like twisted depictions of a black Saturn, with a ringlike accretion disk warped like taffy.

In the late 1990s, the astrophysicists Heino Falcke, Fulvio Melia and Eric Agol, motivated by a new generation of radio telescopes then under construction, decided to see whether there were any chance of seeing Sagittarius A*’s silhouette from Earth. They ran Bardeen’s equations through software that predicted how light would travel in the warped space-time around a black hole, and they concluded that with an Earth-size collection of radio telescopes, all of them operating at the highest frequencies of the radio spectrum, all of them simultaneously observing Sagittarius A*, one would see a dark circle ten times larger than the event horizon. At the edge of this circle, light rays would be trapped, tracing a glowing ring. Inside this ring, darkness. Sagittarius A* should cast a shadow.

That this shadow might be visible from Earth depended on an astonishing set of circumstances. Earth’s atmosphere happens to be transparent to the electromagnetic radiation — in this case, certain microwaves — shining from the edge of the black hole, even though it blocks radiation of slightly longer and shorter wavelengths. The interstellar gunk lying between Earth and the galactic center also becomes transparent at those frequencies, as do the clouds of superheated matter just outside the black hole, blocking a view of the event horizon. Later in life, Fulvio Melia compared this alignment to the cosmic accidents that give us total solar eclipses. The moon is just the right size, in just the right orbit, at just the right distance from Earth that now and then it blocks the sun entirely. Fulvio wasn’t religious, but these coincidences were so unlikely that he couldn’t help but feel that the black-hole shadow was meant to be seen. The universe had arranged for humans to see to the nearest exit.

But the exit is poorly lit. Radio astronomers sometimes emphasize the difficulty of their jobs with the following fact: All the combined electromagnetic radiation collected by every radio telescope ever built, excluding that emitted by our own sun, would carry too little energy to melt a snowflake. To compensate for this scarcity — to collect as much energy as possible — astronomers build the biggest dishes they can. The world’s marquee radio telescopes are fearsome creations. The Robert C. Byrd Telescope in Green Bank, W.Va., is a full 120 feet taller than St. Paul’s Cathedral in London. But telescopes like that can’t handle microwaves. Few telescopes can.

A radio telescope’s bowl-shaped reflecting surface — that giant glinting dish — is tiled with metal panels, each one polished to exacting specifications. To accurately reflect radio waves with a wavelength of one millimeter, for example, the panels must be free of bumps or scratches larger than one-twentieth of a millimeter. With enough money, you can make enormous reflecting surfaces that are smoother than this. But there is rarely enough money.

High-frequency radio waves create other challenges. The sharper a telescope’s resolution, the more accurately it must be aimed at its target. Accuracy isn’t simply a matter of being extra-careful when turning the knobs and dials. The entire multimillion-dollar electromechanical apparatus that swivels and steers the hulking instrument must be engineered to higher tolerances. Such precision is expensive, so most telescopes don’t have it. Big dishes also deform as they turn and tilt, and they expand and shrink and warp depending on the temperature and time of day. You can install thousands of independently tweakable, computer-controlled actuators that continuously adjust each surface panel, keeping the telescope in focus, but, again: expensive. For all these reasons, high-frequency radio telescopes tend to be small — generally, no larger than 10 meters in diameter.