### (A post on ancient alien contact protocols)

Picture a sandy beach long ago near Cyrene in ancient Greece. A man writes a list of numbers and marks one as special. He then circles two and crosses out all its multiples. He circles the next untouched number, three, and crosses out all its multiples. He continues until all the numbers in the list are all circled or crossed out. If we use red for the circled numbers then the following picture gives your part of his result:

The circled numbers are 2, 3, 5, 7, 11, 13, and so on, the *primes*. Primes are numbers whose only positive divisors are themselves and one – and they are required to have two different divisors. The man is Eratosthenes of Cyrene, and the method of finding primes is the Sieve of Eratosthenes. How is this an alien contact protocol?

We have not yet found a natural process that generates the primes, sequentially, in the above fashion. This means that a signal in pulse-code like the red and blue dots above would be a simple, easy to recognize signal of intelligence that transcends language. H. Beam Piper’s story Omnilingual develops the theme that math, physics, and chemistry might permit translation of an alien language – as long as the aliens knew math and science. His thesis is that math potentially forms a Rosetta stone between technological civilizations.

Prime numbers have another role in alien contact protocols. Suppose you want to send a simple raster picture – black and white pixels on a grid. If you transmit a long string of ones and zeros then the receiver needs to know the size of the grid. If the string of ones and zeros – pulse code – has a length that is the product of two primes then there is only one way to decode the pulses onto a grid. Astronomer Frank Drake used this technique for Project Ozma with the following picture:

The picture was transmitted to Tau Ceti and Epsilon Eridani, about ten light years from our sun, with a 73×23 grid of black and white squares. There has been more than enough time for a reply, so no dice this time. This alien contact protocol relies on the self-evident nature of the primes in mathematics. It clearly assumes that aliens are people we would want to contact and that they are paying attention. Occupy Math would love to talk with aliens, but has never met any. If you want to be able to talk with them, and are not relying on them to do all the work, then study math. As Piper, Drake, and numerous others have noted, it is a literally universal language.

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics

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