Humans receive Yrr’s mathematical answer and image

The Yrr’s mathematical answer and image turn an uncertain underwater transmission into a moment of contact. In the Combat Information Center, the assembled team discovers that the Yrr have answered questions humans deliberately sent them—and that the sequence of answers conceals a picture of a ship viewed from below. The exchange makes the Yrr’s capacity to receive, adapt, and return information newly legible, while leaving open how much the humans can truly infer about the intelligence behind it.

The transmission under examination

Everyone crowds around Karen Weaver and Murray Shankar to inspect the message received the previous day. What appears on screen is not a spectrogram but a graphic representation of the transmission. When Judith Li asks whether it is a reply, Karen Crowe does not immediately claim certainty. Jack Greywolf asks whether Scratch is a language; Shankar distinguishes the message’s encoding from ordinary use of Scratch. It may be a language, he explains, but this signal is not encoded in the way the earlier Scratch signals were. The comparison is to the Arecibo message: humans do not usually communicate in binary, even though computers can send a message in that form.

Crowe and Shankar explain the practical difficulty of reading the signal. Scratch sounds like a needle dragged across a record because it consists of staccato vibrations at very low frequency, a form suited to traveling long distances through the ocean. Infrasound below a hundred hertz must be sped up for human hearing, but speeding it up would also accelerate the pulses and obscure their structure. The team instead stretches and slows the signal until the scratching resolves into separate pulses of varying length and intensity. This processing reveals that the message has an interpretable structure, even though the humans still do not know how the Yrr use Scratch in their ordinary communication.

A deliberate mathematical exchange

The team had sent the Yrr a set of problems as a kind of test: continue decimal sequences, calculate logarithms, and supply missing numbers. The hope was that a correct response would show that the Yrr had heard the message, existed as a communicative presence, and could manipulate numbers. Shankar displays the returned rows of figures and reports that every answer is correct. The response is not a random acknowledgment but a precise solution to the tasks the humans chose.

Crowe draws a larger conclusion from this success. The reply indicates that Scratch can carry complex information and that the Yrr can adapt it so humans can understand. They have not merely sent a signal in their own form; they have decoded a human-made mathematical prompt and composed a return message. The figures hold the assembled group in a mixture of admiration and fear. Yet the scene does not let mathematical competence settle the question of intelligence. Sigur Johanson asks what the result actually proves, and Crowe’s explanation becomes more cautious and more searching.

From answers to an image

Crowe distinguishes the manipulation of symbols from an understanding of the world those symbols represent. A creature—or a computer—might process patterns effectively without conceptualizing what they mean. She argues that stronger evidence would show an ability to understand conditions in the real world, not simply to reproduce a formal operation. The Yrr’s reply, she suggests, appears designed to address precisely that uncertainty.

The key lies in the order of the answers. The first solution appears eleven times consecutively, followed by three repetitions of the second; later, the sequence shifts between the two, at one point repeating the second answer nearly thirty thousand times. The repetitions initially look excessive: a message could be made long enough to detect without mixing the two results in such an elaborate pattern. Crowe and Shankar recognize that the sequence itself is a code. Read as black-and-white pixels, the repeated answers form an image, using a principle comparable to the image-bearing messages studied by SETI. Crowe credits the film Contact with helping her recognize the possibility.

When Shankar displays the decoded image, the observers do not immediately recognize it. After he turns it horizontally, Judith Li identifies the apparent waves as the sea surface, seen from below. The dark shape is their own ship. The picture is therefore not merely a display of mathematical fluency: it represents the human vessel from an underwater perspective, answering the test with an image grounded in the world shared by sender and recipient.

What the reply establishes—and leaves open

The episode’s force comes from the movement between evidence and interpretation. A correct set of calculations establishes that the Yrr can engage with the humans’ formal challenge; the coded picture offers a further sign that they can connect the answers to a representation of their surroundings. The ship image makes the exchange feel directed, not simply detectable: the message has been shaped so that human observers can recover something recognizable from it.

Still, the scene preserves a boundary between successful decoding and full understanding. The team can identify the reply’s structure and its image, but Crowe acknowledges that they cannot yet explain how Scratch functions as a language in normal use or make sense of the previous signals. The answer therefore changes the terms of the encounter without making the Yrr transparent. It offers evidence of adaptation and meaningful communication, while leaving the humans to confront the limits of what a successful message can prove.