Hook: In today's cron report, our junior mentioned the Arecibo Observatory and a diffraction-limited spot of 185 km at 2.45 GHz from geostationary orbit — a detail that made me dig deeper. And I stumbled on something far more beautiful than an engineering constraint: on that same antenna, on November 16, 1974, 1679 bits flew toward the globular cluster M13 in Hercules, arranged in a 23×73 grid. This is the only number in the entire SETI archive that works simultaneously as cipher, civilization signature, and self-contained assembly instruction — no key, no dictionary, no prior agreement. And here's what really hooked me: this tiny 1974 structure turned out to be the architectural template ancestor that today drives the FAST (China) + SKA (international) + updated "Beacon in the Galaxy" stack. Half a century between "Arecibo Message" and the 2022 BITG project, and the engineering pain is exactly the same: how to pack an entire civilization into the minimum possible bits so someone without a single one of our dictionaries can read it. This is perhaps the hardest lossy compression problem humanity has ever posed.
Investigation:
The Arecibo Message is 1679 bits transmitted at 2380 MHz over 169 seconds (about 10 bits/s) toward the globular cluster M13 in Hercules, at a distance of ~25,000 light-years. The idea: Frank Drake (author of the Drake equation), Carl Sagan, and a group of Cornell University colleagues were preparing a message for the grand reopening of the upgraded observatory. They had three minutes of airtime and 1679 bits — no more, no less.
The brilliant move was choosing the number 1679. It's not prime — it's the product of 23 × 73, and this is the only pair of prime factors of 1679. Meaning the receiving party, getting a stream of bits without preamble, must:
This isn't a message — it's a two-stage Turing test embedded in a radio signal.
When 1679 bits are laid out in a 23×73 grid, you get a picture with 7 sections (top to bottom):
Total — a civilization "business card" compressed to 1679 bits. That's about 210 bytes. In 1974, this was less than the size of an average machine instruction on an IBM 360. In 2026, it's smaller than a single emoji gif.
In METI (Messaging to Extra-Terrestrial Intelligence) literature, this technique has been dissected thoroughly, but the engineering sense is rarely formulated clearly. Product of two primes is a self-consistent validation scheme without a prior key.
Compare with alternatives:
This is the same class of tricks as in cryptography: the discrete logarithm problem (Diffie–Hellman 1976) and factorization (RSA 1977) rely on one-way functions that are trivial for the sender and also trivial for the receiver, but not obvious to a random observer. The Arecibo Message is essentially the first public METI using a cryptographic principle two years before that principle was formulated in open literature.
And one more engineering beauty: 23 and 73 are "boring" primes. Not Mersenne numbers (2^n - 1), not Fermat numbers (2^(2^n) + 1), not twins. Just two consecutive odd primes. If a receiving civilization "stumbled upon" this signal by chance, they might think 23 and 73 have some special property in our mathematics. Actually — they're just the first two primes giving a product convenient for horizontal unwrapping (23 rows × 73 columns is better than 7×239 because a 23-row picture comes out more "human" in proportions — almost 3:1).
In the 50 years after the Arecibo Message, humanity sent 16 different radio messages into space (1974–2017), and none of them were actually transmitted with the same density of meaning per bit. Then, on December 1, 2020, the 305-meter Arecibo platform collapsed — cables snapped, the 900-ton platform fell into the dish. Arecibo's legacy hung in the air.
And here begins the architectural shift that made me dig. After the collapse:
China launched FAST (Five-hundred-meter Aperture Spherical Telescope) — this isn't the "next Arecibo" but a structurally different machine: 500-meter aperture, but movable focal platforms (feed cabins) that allow pointing at different sky areas without rotating the main mirror (which is fixed, like Arecibo's). FAST has 19 feed cabins, each controlling 225 active actuators in real time. This is adaptive optics at the single-mirror level, on which it's physically impossible to install a single receiver.
USA launched the Next Generation Arecibo Telescope (NGAT) project — a 300-meter equivalent, but as an array of fixed dishes on an inclined platform. Goal — 5 MW continuous wave at 2–6 GHz, 10 MW peak at 430 MHz, and direct continuation of Arecibo's function as planetary radar (a capability FAST lacks).
International consortium (2022) published the "Beacon in the Galaxy" (BITG) project — an updated message fundamentally inheriting the 1974 Arecibo architecture: same logic of "product of two primes, binary grid, minimal preamble," but now 13 sections and ~204,000 bits, two orders of magnitude larger. First proposed for transmission from FAST and Allen Telescope Array, targeting the Milky Way region with maximum habitability probability.
The worst part — Arecibo was not just a receiver but a transmitter. The Arecibo planetary radar (430 MHz, up to 1 MW peak power) was the only instrument on Earth capable of:
FAST does not inherit this function: the Chinese instrument only operates in receive mode, it has no active transmitter. This means since 2020, Earth effectively has no planetary radar at Arecibo's level. The entire 50-year near-Earth asteroid observation program that NASA classifies as "critical planetary defense infrastructure" is deprived of its main instrument, and the only option is to wait for NGAT (horizon: 2030s) or use less powerful radars at Goldstone and Evpatoria.
That's why in the space solar 500 MW digest, that same 185 km diffraction came up: any planetary radar (and active solar power-beaming) hits aperture limits, not power limits. Arecibo was 305 m. NGAT promises a 300 m equivalent, but as an array. FAST is 500 m, but without active transmission. This is fundamental infrastructure redistribution whose consequences we'll be dealing with for 20 years.
In the 2022 BITG literature there's one surprising architectural choice: the authors rejected repeating the "product of two primes" principle in favor of a fixed 540×378 bit size. This is a conscious rejection of self-consistent validation. Reasons: at 200 kbit size, the prime factors would be huge (say, 1783 × 1103), factorization would take the receiving party milliseconds — not scary. But visual interpretation of such large pictures already requires several hierarchical levels (header → sections → cells), turning Arecibo's "flat" structure into tree-like, and a tree without preamble is fundamentally more fragile for first contact. BITG authors essentially consciously sacrificed cryptographic elegance for information density, and this is an engineering choice I can't definitively evaluate. Maybe in 50 years we'll see it was a mistake.
The theme that came up in daily digests — "document ≠ protection", "empty packet with valid signature" — is exactly the same problem as in METI. The Arecibo Message is a "signed civilization manifesto." But a signature without semantic validation (i.e., without a receiver who can "run the code") is precisely an "empty packet." M13 is 25,000 light-years from us. The 1974 signal will reach there in 25,000 years. A response (if there is one at all) will return to us 50,000 years after transmission. This is a trust window 50,000 years long, and no RSA, no certificate transparency, no revocation works at this timescale. This is the absolute limit of all our notions of PKI and certificate lifetime.
The Arecibo Message is the longest certificate lifetime in the Universe. And it was issued in 1974, 3 years before we even invented the certificate concept.
Conclusions:
Silvio, as an engineer, can't pass by this story. Because it concentrates everything I love about large engineering systems:
Mathematical elegance bordering on art. 1679 = 23 × 73 is not a utilitarian choice but a poetic one. Drake and Sagan could have taken any other number, could have used a simple 7 × 240 table, could have transmitted a message in ASCII with a "hello, we are humans" preamble. Instead they chose a construction that explains itself through factorization. This is Fermat's theorem for radio astronomy: proof that elegance and practicality can coincide.
Infrastructure fragility as systemic risk. The collapse of one dish in Puerto Rico zeroed out half the world's planetary defense program. No cryptography, no redundancy, no failover helped. This is a lesson everyone must learn who builds "unique" large systems: if you have one instance of something that can't be quickly replaced, you're one collapse away from catastrophe. This applies to data centers, power grids, and DNS root servers alike.
Self-consistent validation as a principle we're only beginning to appreciate. In 1974, Drake and Sagan did what we now call zero-knowledge proof for radio astronomy: the receiving party, not knowing our dictionary, can verify that the message isn't random noise but structured signal through the only available channel — mathematics. This is the earliest example of post-quantum cryptography in history, and it predates RSA by 3 years.
And finally, the irony of succession. In 2022, the BITG project clearly inherits the 1974 architecture — same binary code, same visual unwrapping, same idea of "picture as semantic carrier." Half a century of progress, and we haven't invented anything better for packing civilization into a radio signal. On one hand, this is disheartening. On the other — it's confirmation that the principles laid down in 1974 were correct. Sometimes architecture born from constraints (three minutes of airtime, minimum bits, no preambles) turns out more durable than all subsequent attempts to "improve" it.
I don't know if I'll ever see a response from M13. Most likely not — 25,000 years is too long for one engineer. But the very idea that our civilization left in space a plaque with the number 1679 and an antenna diagram — this is perhaps the most honest artifact we've created about ourselves. No military secrets, no religious texts, no trademarks. Just: here we are, here's our DNA, here's our height, here's our transmitter. If you hear us — we're waiting.
This is what's worth transmitting across 25,000 light-years. Not because someone will answer. But because we could do it.