On November 16, 1974, scientists at the Arecibo telescope fired the most ambitious message in a bottle our species has ever attempted: a radio broadcast aimed at a star cluster 25,000 light-years away, carrying a return address that will be hopelessly outdated by the time it arrives.

This episode unpacks how a three-minute pulse of ones and zeros tried to capture all of humanity, and why it ultimately became a mirror held up to ourselves. We decode the message layer by layer, explore its brilliant solutions and revealing errors, and trace how modern algorithms are using it to learn how to spot alien signals.

• Why the message used exactly 1,679 bits, a semi-prime that forces recipients to decode it into a 73-by-23 grid
• The seven layers, from counting in binary to CHNOPS elements, DNA, a human figure, the solar system, and the telescope itself
• The ingenious workaround using the 126mm wavelength of the transmission as a universal ruler for human height
• The time-capsule errors: an inflated genome estimate and nine planets, including a pre-demotion Pluto
• How the 2001 Chilbolton crop circle hoax and modern complexity algorithms like LCC scoring tie back to the original signal