Imagine standing under a tent on a karst hillside in Puerto Rico, on an afternoon in November 1974, watching the dedication of a remodeled radio telescope.For just under three minutes it warbles at the sky. Then it stops. The audience around you has just heard humanity’s first deliberate radio message to another civilization broadcast over the speakers.

The math written into that broadcast is simple, and it is the part of the story that has refused to age. The Arecibo message was aimed at Messier 13, a globular cluster of about 300,000 stars in the constellation Hercules, roughly 25,000 light-years away. At the speed of light, the signal needs about 25,000 years to reach the cluster. A reply along the same path needs another 25,000 years. Even granting the most generous case — that someone on a planet receives the message, recognizes it as deliberate, and aims a transmitter of similar power back at Earth on the day it arrives — the earliest possible answer cannot reach us before about 52,000 CE.

Of course, the people who designed and sent the message were not seriously expecting a reply. 

Three minutes, twenty-three columns, seventy-three rows

The Arecibo broadcast carried 1,679 bits of data — a string of ones and zeros transmitted by shifting the carrier frequency up and down at ten bits per second, over a total of less than three minutes. The number 1,679 was chosen because it is the product of two prime numbers, 23 and 73. A recipient who notices the factorization can lay the bits out as a 23 by 73 grid; the ones become shaded squares, the zeros stay blank, and a low-resolution picture appears. Arranged the other way, as 73 by 23, the same bits produce an unintelligible set of characters, which is part of the puzzle.

Reading top to bottom, the image shows the numbers one through ten in binary, the atomic numbers of the five elements that make up DNA (hydrogen, carbon, nitrogen, oxygen, phosphorus), a schematic of the DNA double helix wrapped around a binary representation of the number of base pairs in the human genome, a stick figure of a human flanked by two numbers (average height in units of the broadcast wavelength, and the world population in 1974), a map of the solar system with Earth nudged upward to identify which planet the signal had come from, and finally a sketch of the Arecibo dish itself, with its diameter encoded in units of the broadcast’s own wavelength. The content was designed by Cornell astronomer Frank Drake, working with graduate students Richard Isaacman, Linda May (now Linda M. French), and James C. G. Walker. Carl Sagan and others contributed. Drake had been given about a month.

“From day one, I’ve always thought pictures work,” Drake told National Geographic in a 2014 interview with his daughter, the science journalist Nadia Drake. “Sending pictures is easy. We do that all the time, with great results.” It is a quiet point but the probably right one. Words sit inside a language a recipient may not have; numbers sit inside symbols a recipient may not share; pictures, arranged on a grid built from primes a recipient can recognize, sit closer to the bone.

Aimed at a cluster that will have moved

A standard objection to the choice is that M13 will not be where it is now by the time the signal arrives. The cluster orbits the center of the Milky Way; over 25,000 years it will have moved. Drake addressed this directly: “It will have moved a little bit, but only a fraction of the width of the beam of transmission.” The cluster’s proper motion is small enough relative to the spread of the Arecibo beam at that distance that the message will still arrive near the cluster — not at the same stars Drake’s eye was on in 1974, but somewhere in the same crowd.

The result is the line in the title. Twenty-five thousand years out at the speed of light; twenty-five thousand back at most. The math gives 51,974 CE for the absolute earliest return. Rounded plainly: an answer cannot reach Earth before about 52,000 CE. There is no scenario in which the team running the transmitter, or anyone who knew them, or anyone alive in 1974 at all, was ever going to hear it.

A demonstration, knowingly

The message was not really a conversation opener. It was a demonstration. Donald Campbell, a Cornell astronomer who was a research associate at the Arecibo Observatory in 1974, put the official frame plainly in a 1999 Cornell Chronicle piece marking the 25th anniversary of the broadcast: “It was strictly a symbolic event, to show that we could do it.” The real purpose of the ceremony was to mark the completion of an upgrade to the telescope — the new transmitter could throw a signal into deep space at high power, and the message was the most striking way to show it.

Drake’s own account adds something the official frame leaves out. The message had two recipients, not one. “It was a message that would actually inform anyone who did receive it that we existed, and tell them a little bit about what we were like,” as reported in National Geographic. “And it was also a message to ourselves in that it showed what an intelligent civilization can do to contact other civilizations.”