“To learn all that is learnable; to deliver all collected data to the Creator on the third planet. That is the programming.”
Imagine a vast growing sphere centered on the Earth with a radius of fifteen billion miles, the distance a beam of light travels in a day. This is the anthroposphere: the patch of the universe into which humanity and its artifacts have spread. At its periphery – indeed, defining its periphery – is a one-ton device hurtling away from us at forty-thousand miles per hour while sending radio signals toward Earth with a broadcast power of twenty watts. That’s only a tiny fraction of the wattage used by commercial radio stations on Earth, yet somehow Voyager 1, with its puny transmitter, is still executing its mission of gathering data about our solar system and relaying that data back to far-off Earth. And part of the technology that makes this feat possible is an algebraic construct that nobody even dreamed of two centuries ago: the arithmetic of finite fields.
Actually, I shouldn’t be so confident that nobody back then dreamed of finite fields; Carl Friedrich Gauss (1777–1855) may have. He was known for not writing up his ideas until they had matured sufficiently, which in some cases meant never writing them up at all.