One. Zero. Euler’s Number. A sequence of prime numbers in ascending order. One. A sequence of eleven primes. The same eleven primes, but fading out to two-thirds amplitude. The same eleven primes, but even fainter at one-third power. Thirty-four Zeroes. One. Zero. The same eleven primes, three times again, but not fading out. Eighty-four zeroes. The sequence of prime numbers from the beginning, but in descending order. Euler’s number. Zero. Zero.
The decrypted contents of the signal were laid out on a dry-erase board in the classroom the mathematics department appropriated to work on the project.
“That’s…it?” Harlow could not decide if he was impressed or underwhelmed. Well, he felt proud that his idea of Euler’s number being a decryption key worked out so well. Still, the contents of the message were vaguer than what the president suggested in his address.
“That’s the whole thing,” replied Morgan. “Cheyenne’s brought a team of linguist, zoologist, and psychologists on board, but we get to keep working on this because, as you can see, the aliens didn’t really give us anything to work with besides numbers.”
“Okay then, let’s work through some patterns. One-Zero, Zero-Zero. Hello, goodbye.”
“That would be fair, if a little colloquial. Those, with or without Euler’s number, could be standard data headers for the species.”
“Bah, the difference isn’t relevant to me; the meaning’s the same either way.”
Harlow thought there could be layers and layers of hidden meaning behind just the use of One-Zero and Zero-Zero. But he was wise enough to know these types of speculations were best left for someone else. Harlow thought finding patterns and giving them utilitarian meaning would be more productive.
“Primes in ascending, then descending order,” Morgan continued. “That could mean ‘we are intelligent enough to know what this is.’ Just a marker there to tell they aren’t sending this at random.”
“Could be,” Harlow agreed, “but it could also be a title. ‘Here, we are talking about primes.’ And then they follow it up with very specific primes from that sequence. Are those supposed to have meaning on their own?”
“One hypothesis out there is that they’ve assigned a prime to each letter of their alphabet, or syllable of their syllabary, whatever the case may be. So those five specific primes would make up one word.”
That could make some sense culturally. Assigning a number to each letter of the alphabet is one of the simplest cyphers humans have come up with. It could also be their equivalent of ASCII values. But…
“How long would it take for someone with absolutely no knowledge of computers or programming to figure out that the ASCII value 65 is a cypher for a capital ‘A’?” Asked Harlow.
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“I’d bet on it being nearly impossible without any documentation,” answered Morgan.
“So, if you were an alien, and you wanted your message to be understood—because why send a message if you don’t want it to be understood—then using this sort of encoding wouldn’t make any logical sense, right?”
“Is this sort of message sending something I, the alien, am experienced with then? What if this is my first ever message out and I don’t realize what I’ve done?”
“The evidence so far suggests the opposite. You’ve used a copy of an Earth signal. You’ve used Euler’s number to give us both a key and make sure we realized this wasn’t a natural phenomenon. No, no, no. Up to this point, everything about this message has been orchestrated with intent, and I believe that means experience.”
“Therefore, it’s likely that a simple, utilitarian solution is correct over any other,” concluded Morgan in agreement.
“The simplest solution I can think of right now is that these primes mean something on their own or as a group. For example, if I gave you 9-16-25 as a sequence. It’s one level removed from what I actually want to say, but you could figure out that this is just 32-42-55. It’s a Pythagorean triple, which tells you that my message is probably about triangles or trigonometry.”
By now, the other professors in the room gathered around Harlow and Morgan to listen in on their discussion, and hopefully contribute something.
“There’s no logical order to their sequence,” one put in.
“The only thing they have in common is they’re non-negative prime integers,” added another in support.
“Maybe then they aren’t referring to a mathematical theorem, but a practical application,” posited a third.
That one made the most sense to Harlow.
“Radio frequencies, then? They reached out to us on this specific frequency because we would notice it, but really they want us to be listening on these bands for more complex communications? Or they expect an answer on these bands, maybe?” Proposed yet another team member.
“That makes sense to me,” replied Morgan. “I’ll put our hypothesis on the network, and I’ll forward it to Cavanaugh so NASA can investigate it.”
That was a sensible deduction for Harlow too, but it felt incomplete. There was something in the message that made him think this was a red herring. What was it?
“The fade out…” he began.
“Pardon?”
“The fade out in the middle. They present the primes at full power, then at two-thirds power, and then at one-third power. But for the second set, they do it three times at full power.”
“If it’s an orchestrated message from someone with experience, then that’s purposeful.” Morgan considered for a moment. “If it follows the numbers themselves have a practical use, then the fade out is what’s meant to impart meaning to them.”
“That much is sensible…”
“But we can’t know the meaning behind it until we know what the application is. Or can we?”
Harlow didn’t have the answer. “I… I don’t know. I need to consider it further. I don’t have a better idea than what you proposed. But there’s… something I can’t put my finger on that’s bugging me.”