We use a base 10 (decimal) system of because we have 10 fingers and 10 toes. Similarly I presume we have the concept of odd and even numbers because we have two hands, two feet, two eyes, two ears etc. In that case odds and evens would be alien to aliens who have three hands, three feet etc. They probably have odd and treven where a treven number is a number divisible by three.
The aliens may not have the concept of mathematics or even the concept of counting and logic. The numbers themselves are no more natural than the number systems that describe them. Perhaps counting the stars is a passtime for the allien rednecks, while the allien intelligentsia just enjoys the sky without an attempt to classify, measure, or otherwise examine the heavenly bodies.
Originally posted by John Smith: The aliens may not have the concept of mathematics or even the concept of counting and logic.
Perhaps. But then these will be the aliens that never leave their planet, so it's highly unlikely we'll ever meet them. Aliens we're likely to ever encounter will have developed mathematics at least similar in power, if not in conceptual basis, to our own.
I'm not at all sure that our concept of odd and even derives from our bilateral symmetry. I think it's more likely to come from sharing. That is, someone realized that when you're dividing up food (or whatever) among two parties, it's easier if there are 2, 4, 6, or 8 than if there are 1, 3, 5, or 7. The relevant factor here how many people do you need to share between? Of course, the moment you need to share among three people, or four, the usefulness of "odd or even" is diminished. However I still think it's likely that division between two would be the first case discovered and named, even by three-legged aliens. Unless perhaps they have a reproductive system which requires three sexes, rather than two...
Aliens we're likely to ever encounter will have developed mathematics at least similar in power, if not in conceptual basis, to our own.
John's alien rednecks could still do it!
I don't think trilaterally symmetric aliens are very likely - anything evolving near the surface of a planet will need to deal with two primary directions, 'up' and 'down' - but if they did, trinary might be more natural to them than binary. I think they would have three terms, though - one for things just less than divisible by three, and one for things just more than divisible by three, as well as 'treven'.
Such aliens' computers would undoubtedly use balanced ternary rather than binary. Unfortunately, their web page seems to be down at the moment.