The question of whether there is an etymological connection between the words “new” and “nine” at the Indo-European level has been debated for the better part of a century based on the similarity between the words in a number of European languages and their seemingly common connection to the root for the word “now”. For example, the new/nine/now complex is neu/neun/nun in German, ny/nio/nu in Swedish, and novus/novem/nunc in Latin, etc.
The existing debate (a short, if technical, summary can be found here) has tended to focus on the reconstructed Proto-Indo-European roots of the words. This debate is both interesting and valid, but is, in my opinion, incomplete because it fails to take into account the symbolic associations of the words. I believe that an analysis of these associations as found in mythological contexts and an understanding of how these associations derive from phenomena observable in the natural world supports the idea that they are fundamentally connected.
In a variety of cultures (at least ones with Indo-European languages), the number nine represents wholeness and completeness. This can be seen in the nine-fold conception of the universe found in Norse and Hindu mythologies (the “nine worlds” and the navagraha or “nine houses, respectively), or the fact that Odin hung on the world tree Yggdrasil for nine nights before acquiring the runes. Alwyn and Brinley Rees devote a short section (pp. 192-196, part of Chapter 9) of their excellent Celtic Heritage to the prominence of the number nine in Celtic culture. One of the connections they mention is that the ancient Celts are believed by some to have had a nine day week, which lends credence to the number being associated with the completion of a cycle.
But why is the number nine traditionally associated with completeness? I know there is a long tradition in numerology related to the number nine and I don’t discount this out of hand. To give just three examples: nine is the minimum number needed to construct a magic square; many significant numbers related to the proportions of the earth and the solar system add to nine; and nine is the product of 3 (a number that is considered special in many cultures) multiplied by itself.
However, I think there is an obvious, common sense explanation that may help to explain the origins of the association of the number nine with the concept of “new”: the period of human gestation is nine months, after which, a new life is born. Viewed from this perspective, when Odin hangs on Yggdrasil for nine “nights”, he is essentially in a period of incubation, at the end of which he is “born” in possession of new, secret knowledge in the form of the runes. When the fulfillment of nine is reached, something new is born, and what is new is that which is happening now.