Because of the long travel times between stars, directed messages must be self-contained and easily decoded.

In addition to the Pioneer and Voyager plaques sent into space, astronomers sent a test radio message to the globular star cluster M13 in Hercules in 1974 using the Arecibo Telescope. The message will arrive in 25,000 years.

The message was a repeated sequence of 1679 bits (on/off) of information. This number is the product of two prime numbers (23 x 73) which suggests arranging the sequence in a picture of 23 columns of 73 bits each (see Fig. 20.10 on page 503).

The resulting picture describes:

• binary number system
• the atomic numbers of the primary elements for biology
• chemical formulas for molecules important for life
• a depiction of and the number of base pairs in human DNA
• a stick-figure of a human with height and population
• a Solar System diagram with the 3rd planet displaced toward the human figure
• a depiction of the Arecibo radio telescope and its diameter