The human selected to communicate with the aquatic aliens of Cida-2 is surprised to learn that their number system differs from our own. In particular, although our communication with the extra-terrestrials begins as expected (with them sending us a message in the form of prime numbers and finding the plaque on our Pioneer 10 space probe), and although early discussions of integers and rational numbers goes well (apart from a slight theological difference), the aliens object to the notion of "real numbers" as defined by the humans and are terribly offended when the human claims that their series representation for -1 is divergent. They show the human *their* number system, and he comes to realize that it may be as sensible a completion of the rational numbers as our own.
In fact, this story is not so much a work of fiction as a drawn out thought experiment designed to introduce the reader to the notion of p-adic (well, I suppose in this case it would be 2-adic) numbers. There are a few cute touches. Of course, the aliens using a p-adic topology for their numbering system would be much more successful at solving Diophantine equations than humans. And I like the point he makes about the confusing reverse orientation of our writing and number systems. (In many human languages, we read words from left to right but write our numbers from right to left. At first, this confuses the aliens who misinterpret the numbers on the pulsar map of our space probe.) However, like David Ruelle's "Conversations on Mathematics with a Visitor from Outer Space" it is essentially just a mathematician using the concept of aliens as a didactic tool and not as literary as similar works such as Story of your Life, In the River, or Incandescence.
Published in the November 2008 issue of *The College Mathematics Journal* Volume 39 No 5, pp 337-345. (Those interested in this story may also be interested in the non-fictional article that precedes it in the magazine which introduces the closely related "leftist numbers", an extension of the integers allowing infinite decimal representations to the left rather than to the right. I wonder what the inhabitants of Cida-2 would think of that?) |