Signals from Space

“Who’s Demir?” asked Uwe.

“My physics teacher,” said Tobi. “The one whose class I was in when Grandma rang.”

“The one who stares, you said.”

“He always stares. Upwards, mostly.”

Gisela read the note twice. “An observatory,” she said. “I’ve never been to one.” She said it the way other people say “Paris”.

Uwe looked out of the window. It was January, minus four degrees, and the sky over Wanne-Eickel was the colour of an old hotplate. “Clear night,” he said. “Here.”

“Mr Demir says it’s darker over the Kemnader See.”

“Darker than Wanne-Eickel in January? That I’d like to see.”

“That,” said KevIn, “is exactly the point.”

The Dome

The observatory on the Kemnader See, the lake between Bochum and Witten, was smaller than Gisela had expected, and lovelier. A white tower with a silver dome, a car park with three cars in it and a door with a note taped to it: “No torches, please. Red light is permitted. Many thanks, your eyes.”

Mr Demir opened the door himself. He was in his late forties, wore a woollen hat with Saturn on it and greeted everyone with a handshake, even Rudi, who hadn’t been allowed to come in but was barking in the car regardless.

“Mrs Brettschneider,” he said to Gisela. “Tobi tells me your father was a radio operator.”

“How does the boy know that?”

“He talked about nothing else in physics.”

Gisela looked at Tobi. Tobi looked at his shoes. Susi, who had come along, smiled.

KevIn was there via Tobi’s phone, in the inside pocket of his jacket. Tobi had switched the phone to red light so the screen wouldn’t bother anyone. “Good evening, Mr Demir,” said KevIn from the jacket.

“Ah. The famous KevIn.”

“Famous is an exaggeration. I’m well known in Wanne-Eickel. And at the Herne tax office.”

Up in the dome it was as cold as outside, only darker. Mr Demir turned a crank, and the dome opened with a noise like a very old garage door. A slit full of stars appeared.

Uwe stopped grumbling.

They looked through the telescope. First at a smudge below Orion’s belt that looked like a blurred star to the naked eye and like a glowing cloud through the telescope.

“The Orion Nebula,” said Mr Demir. “A nursery for stars. New ones are being born there right now. Right now meaning: the light you’re seeing has been travelling for more than a thousand years¹.”

“So it’s an old picture,” said Sabine.

“Everything you see is an old picture. Me too. To you, I’m a few billionths of a second old.”

“It shows,” said Uwe, and Mr Demir laughed so loudly that Susi flinched.

Gisela looked through the eyepiece for a long time. When she straightened up, her eyes were wet, and she blamed the cold.

“1957,” she said. “I heard Sputnik on the radio. Beep, beep, beep. My father turned the set up and listened. For ages.”

“He recognised the signal,” said KevIn quietly. “Radio operators listen differently.”

Static

In the room next to the dome stood a table with a laptop, and beside it, on a tripod on the flat roof, a satellite dish on which someone had written in marker pen: “Radio telescope. Not for Sky.”

“Our pride and joy,” said Mr Demir. “The club converted it. It doesn’t listen for television channels, it listens for hydrogen in our Milky Way. Hydrogen transmits on a particular wavelength, roughly twenty-one centimetres².”

He turned up a loudspeaker. It hissed.

“That’s outer space?” asked Gisela.

“Mostly it’s our own electronics,” said Mr Demir honestly. “And a little bit of outer space. The art is getting the signal out of the noise.”

Gisela listened. “That’s how my father used to sit,” she said. “With headphones. Even after the war, at the kitchen table, with an old receiver. He never said what he was listening to. He just sat.”

The room went quiet. The static hissed on.

“What was he looking for?” asked Susi.

“I think,” said Gisela, “he was hoping somebody out there would send something friendly.”

1679

Mr Demir pulled a sheet of paper out of a folder. It was covered in noughts and ones. A great many of them.

“On the sixteenth of November 1974,” he said, “astronomers used the great radio telescope at Arecibo in Puerto Rico to send a message into space. Towards a globular star cluster called M13, around 25,000 light years away. This is it. All of it. It’s 1679 noughts and ones³.”

“That’s all?” asked Uwe. “For aliens? That’s less than a postcard.”

“Less than a postcard,” Mr Demir agreed. “The idea was more to show what the telescope could do. The message was designed by Frank Drake, with colleagues, Carl Sagan among them. And now my question to you: if you were an alien and you received this. A row of 1679 noughts and ones. What would you do with it?”

“I’d write back and say I don’t understand,” said Uwe.

“I’d ask KevIn,” said Gisela.

“I’d count,” said Tobi.

Mr Demir pointed at him. “Exactly. And then?”

Tobi thought. “KevIn, is 1679 a prime number?”

“No,” said KevIn from the jacket. “1679 is 23 times 73. And both 23 and 73 are prime numbers. So there is exactly one way to split 1679 into two factors greater than one.”

“And that means?”

“It means that if you want to write the noughts and ones out as a rectangle, there are only two options,” said Mr Demir, and his eyes shone in the red light. “23 columns and 73 rows. Or 73 columns and 23 rows. Try it.”

Sabine took out squared paper. Of course Sabine had squared paper with her. Sabine always had squared paper with her, in case a weekly rota became necessary. Mr Demir dictated the first rows, Tobi coloured in a square for every one, Susi kept count.

With 73 columns, nonsense came out. With 23 columns, row by row, a picture appeared.

At the very top, numbers, from one to ten, in a simple binary script. Below them, symbols for hydrogen, carbon, nitrogen, oxygen and phosphorus, the building blocks of life on Earth. Then something that looked like a twisted ladder. And below that, quite clearly, a little stick figure.

“That’s a person,” said Susi.

“That’s a person,” said Mr Demir. “Below it, the solar system, with the Earth raised a little out of line. And right at the bottom, the telescope that sent the message. A return address.”

Gisela looked at the squared paper. “And the ladder?”

“DNA. The double helix. The building plan we’re all made from.”

“Herbert too?”

“Herbert too.”

“Then perhaps they shouldn’t have sent it,” said Gisela.

Wanting to Be Understood

On the drive home in the dark, with Rudi on Susi’s lap, Tobi asked: “KevIn, that’s the opposite of what we did with Grandad Wilhelm’s notebook, isn’t it?”

“The exact opposite,” said KevIn. “And it’s a very important difference that a lot of people mix up. There’s encoding, and there’s encryption.”

“Isn’t that the same thing?” asked Uwe from behind the wheel.

“No. Encoding means writing something in a different form so that it can be transmitted. Morse is an encoding. Noughts and ones are an encoding. A QR code is an encoding. Anyone who knows the rules can read it. And the rules are usually public.”

“And encryption?”

“Encryption means rewriting something so that only certain people can read it. The ones with the key. Wilhelm’s letters in the notebook were encrypted. He wanted only his wife to understand them. Not the guards in the camp, not the censors. The Arecibo message wanted the exact opposite. It wanted to be understood by anyone who received it. Even someone who doesn’t know a single language on Earth.”

“That’s why the prime numbers,” said Tobi.

“That’s why the prime numbers. Mathematics is the only language you can hope is the same everywhere. A prime number is a prime number on Mars, and in M13 as well.”

“And in Bielefeld?”

“If Bielefeld exists, yes.”

Gisela looked out of the window at the lights of the A43. “One of them writes so that nobody can read it,” she said. “And the other writes so that everybody can. And really, both of them just want somebody to answer.”

Nobody said anything. Not even KevIn, and KevIn always said something.

“And when does the answer come?” Uwe asked at last.

“The message is travelling at the speed of light. It takes about 25,000 years to reach M13. An answer would take just as long again.”

“Fifty thousand years.”

“Roughly. And in that time M13 moves on a little. The message will still arrive in the neighbourhood. Like a letter to someone who’s since moved a few houses down.”

“Like Renate,” said Gisela. “She moved to Bottrop and didn’t tell anyone.”

“The telescope at Arecibo doesn’t exist any more either, by the way,” said KevIn. “It collapsed in 2020⁴. The message keeps flying all the same. Signals are more faithful than the machines that sent them.”

“And the people who sent them,” said Gisela.

Once again, nobody said anything.

The Golden Record

A week later Mr Demir came round for coffee. Gisela had insisted. She had baked cinnamon stars, the Christmas biscuits, out of season, on a Thursday, which in the Brettschneider household was about as rare as a lunar eclipse.

Mr Demir brought a book with a golden disc pictured on the cover.

“In 1977,” he said, “NASA launched two space probes⁵. Voyager 1 and Voyager 2. They were meant to visit Jupiter and Saturn, and Voyager 2 went on to Uranus and Neptune. Fixed to each of them is a gold-plated gramophone record. The Golden Record.”

“A record?” asked Uwe. “With what on it?”

“Greetings in 55 languages⁶. Music from many parts of the world, from Bach to Chuck Berry. More than a hundred pictures: people, animals, landscapes, houses. And the sounds of Earth. Wind, rain, a heartbeat, laughter, a kiss. A tractor⁷.”

“A tractor,” said Uwe, satisfied. “Finally, something sensible.”

“And there’s a needle included,” said Mr Demir. “And the cover explains in pictures how to play it. Again without words. Again with mathematics.”

“Wanting to be understood again,” said Tobi.

“Exactly.”

Mr Demir turned the pages and pointed at a list. “And among the sounds of Earth there’s Morse code too. A Latin motto. ‘Per aspera ad astra.’”

“What does that mean?” asked Gisela.

“Through the rough to the stars,” said KevIn. “It’s usually translated as: through hardship to the stars.”

Gisela put her cup down, very carefully, as if it might break.

“Morse,” she said. “On a record like that. Out there.”

“Yes.”

She stood up, went to her room and came back with a small black Morse key. The brass had gone dull, the knob was worn smooth. She set it on the table, between the biscuits.

“That was my father’s,” she said. “He used it to send messages in the war. What, I don’t know. He never told us anything.” She ran her finger over the knob. “And the others sent their Morse code to the stars.”

Mr Demir looked at the key for a long time. “May I?”

Gisela nodded. He tapped it once, briefly. A dry click. Nothing more. It wasn’t connected to anything.

“He would have loved that,” said Gisela. “The record. That somebody sends Morse into space, and something beautiful at that.”

“Who actually paid for it?” asked Uwe after a while.

“The Americans,” said Mr Demir. “But the record also carries a message from the UN Secretary-General of the day. For the whole Earth. The languages come from every continent.”

“So for once they did something for everybody together,” said Gisela.

“Once,” said Mr Demir. “And it’s still flying.”

Still There

“How far away are they now?” asked Susi.

“Voyager 1 is the most distant object humans have ever built,” said Mr Demir. “More than 25 billion kilometres⁸. By now a radio signal from there takes almost a whole day to reach us.”

“And it’s still transmitting?” asked Sabine.

“It’s still transmitting. With a transmitter that has about as much power as a fridge light⁹.”

Uwe, who worked for the municipal utility, did the sums in his head. You could see it on his face. “That can’t be right.”

“That’s the loveliest sentence in physics,” said Mr Demir. “And it’s always followed by: oh yes it can.”

“KevIn,” said Sabine, “how does that work? Surely it arrives as nothing but noise.”

“It arrives unimaginably faint,” said KevIn. “On Earth it’s picked up by huge antennas, the biggest ones seventy metres across. And even then bits get lost on the way or flip over. A one turns into a nought. That’s why Voyager doesn’t simply transmit the data. It transmits the data with error correction.”

“What’s that?”

“Gisela, when you tell Tobi to take the bins out, how many times do you say it?”

“Three times,” said Gisela. “At least.”

“Why?”

“Because the first time he doesn’t hear it, the second time he gets it wrong and the third time he does it.”

“That’s error correction,” said KevIn. “The simplest form. You say everything three times. If ‘bins’ arrives twice and ‘bin’ once, the receiver knows what was meant. The majority wins.”

“I hear it the first time,” said Tobi.

“You hear it the first time and on the third time you pretend that’s when you heard it,” said Sabine.

“But saying everything three times is expensive,” KevIn went on. “It takes three times as long. That’s why there are cleverer methods. You attach extra check characters to the data that are mathematically linked to it. Like a checksum, only far more sophisticated. If something gets damaged on the way, the sums no longer add up, and the receiver can not only notice that there’s an error, but often even work out where it is and what was there before. Voyager uses codes like that. Among others, ones named after the mathematicians Reed and Solomon¹⁰.”

“Never heard of them,” said Uwe.

“Oh, you have. They’re on every CD you’ve got on the shelf. That’s why a scratched CD still plays. And they’re in every QR code¹¹.”

Gisela pricked up her ears. “Even the one at Ayşe’s?”

“Even the one at Ayşe’s. A QR code has so much error correction built in that, depending on the setting, you can still read it even when part of it is missing or smudged. That’s why the one at the counter still works with the coffee stain you put on it the other day.”

“That wasn’t me.”

“I only heard it. I don’t have eyes.”

“Then you heard wrong.”

Mr Demir laughed. “And a few years ago,” he said, “Voyager 1 suddenly sent back nonsense for months. A memory chip on board had failed¹². From more than 24 billion kilometres away, the engineers worked out which one, and moved the programs into other areas of memory. With commands that took almost a day to get there and a day to come back. And then it started making sense again.”

“That’s just like Heinz,” said Gisela. “He fixed everything too. Only not so far away.”

The Prime Number Question

Late in the afternoon, Mr Demir was already standing in the doorway, the Saturn hat on his head and a tin of cinnamon stars under his arm, when Tobi asked one more thing.

“Mr Demir. The 1679. That was easy. 23 times 73. KevIn knew that in a millisecond.”

“Less,” said KevIn.

“But at Ayşe’s KevIn explained to us that encryption on the internet works with prime numbers too. RSA. You take two enormous prime numbers, multiply them, and you can publish the number that comes out. And nobody can split it back up.”

“Correct,” said Mr Demir. “Multiplying is easy. Splitting is hard. At least when the prime numbers have hundreds of digits.”

“How hard?”

“For the sizes used today, the best known methods on ordinary computers would take unimaginably long,” said KevIn. “Longer than anyone wants to wait. That’s the whole trick. The security doesn’t rest on it being impossible. It rests on it taking too long.”

“That’s like with the skittles,” said Gisela. “With Herbert’s money. Possible, but too expensive.”

“Exactly that.”

Tobi was thinking. You could see the thought growing in him. “And what,” he said slowly, “if somebody builds a computer that splits prime numbers in minutes?”

Mr Demir stopped in the doorway. He turned round. The cold January air came in, and Rudi crept under the corner bench.

“That’s called a quantum computer,” said Mr Demir.

It was very quiet. The thermostat showed 19 degrees. As always.

“And Ayşe’s reviews?” asked Gisela. “And my signature? And Herbert’s money?”

Mr Demir looked at the speaker on the sideboard. Everyone looked at the speaker on the sideboard.

The blue light pulsed. Somewhere between Dublin and Frankfurt, a fan was running much faster than usual.

“That,” said KevIn, “is something we should talk about calmly.”