Free Factoring Humanity by Robert J. Sawyer

simplicity of the first eleven messages: straightforward representations of the Pythagorean theorem and chemical formulas and planetary systems. Although, she had to admit, even those posed some puzzles: the chemicals specified by the formulas had been synthesized on Earth, but no one had ever figured out what they were for.
    Heather got herself a mug of coffee and sat down to look again at yesterday’s message.
    As always, the message was shown as two rectangular grids. Each message was sent as a string of a hundred thousand or so binary digits, over a period of two or three hours. The total number of digits in each message was always the product of two prime numbers, meaning that the digits could be arrayed in two possible ways. According to the header from the Alien Signal Center in Karachi, Pakistan, this message was 108,197 bits long. That number was the product of the prime numbers 257 and 421, which meant that the digits could be set up either as 257 rows of 421 columns or as 421 rows of 257 columns. Sometimes one image looked more intuitively correct than the other—squares or circles would appear in one, while the alternative decoding would simply result in a mishmash. But since no one had yet determined what the messages were supposed to represent, one couldn’t be certain which was really the correct interpretation.
    When the messages had first started arriving in 2007, millions of people had pored over each one. But as the years had passed, the numbers had reduced. Although there was a popular screensaver that downloaded each day’s message from the aliens and magnified various portions of it in turn, Heather knew there were now fewer than three hundred researchers actively analyzing each new message.
    The more correct-looking version of today’s message showed three rectangles and two circles in what otherwise seemed to be a random sea of black-and-white squares; the black squares represented zero bits and the white squares represented ones. Heather stared at it, frustrated. She felt sure she had to be missing something simple. Somewhere in the hundreds of millions of bits of data already received from Alpha Centauri there must have been a Rosetta stone—a key that would let all the other messages make sense.
    There were dissenting views: one researcher in Portugal had long argued that the key would come as the final message, not as one of the initial ones; that way, the aliens would automatically weed out any races that lacked the patience required for interstellar communication. And others had opined that the alien senders were simply too alien—that we were incapable of communicating. A third camp argued that humanity simply wasn’t bright enough, or advanced enough, to figure out what was being said. The aliens might indeed still be on what they considered basics, but the material had already gone over the collective head of humanity.
    Heather was a Jungian psychologist. She believed that all human minds shared a vocabulary of symbols and archetypes that formed the underpinnings of thought. The Centaurs, she felt sure, simply had a different set of underlying metaphors and symbols, and if she could figure out what those were, she could crack the code.
    She took a sip of coffee. This message was as baffling as the others. Maybe it was all a giant crossword puzzle, she thought. The grids of black-and-white squares certainly suggested that, although filling in the blanks was a human concept, possibly—if she could wax Freudian for a moment—related to our sexual biology. Still, it wasn’t the first time she’d wondered if the messages might be deliberately incomplete—yin, but no yang—and the aliens were waiting for humanity to provide the complement, to make it all whole.
    But, of course, we hadn’t yet replied at all; another popular interpretation was that the Rosetta stone was being withheld until humanity did reply.
    There’s an old concept in SETI that said that signals would likely be sent