I'm mystified also but I have given it a shot. Perhaps some of what I've found can be pooled and we can come up with something. My first stop was to the Moonmilk/Urth archives. Surely someone had addressed this question in its 13 year history. Only Borski (of course) had a hint of a guess. His post-
In _Nightside the Long Sun_, on p. 29, Wolfe has Maytera Marble presiding over a mathematics lesson, "watching the children take nineteen from
twenty-nine and get nine, add seven and seventeen and get twenty-three."This, however, is only possible in a base 9 numbering system, and a strange
one at that, since a conventional base 9 system would only include the digits 0 to 8 (there should thus no 9, 19, or 29).
The following questions therefore ensue:
Since the number 9 is present, are we to assume that one of the other numbers has been retired? (If so, it's not evidenced in the Seal of Pas,
which contains all ten digits from 0 - 9. But could these sequences be artifacts of the pre-launch numbering system?)
Equally possible, I suppose, is the notion that the Whorl, like the ancient Romans, uses no 0 --meaning that the sequence after the first and second
enneads runs ...8, 9, 11, 12... and 18, 19, 21, 22. But can this be supported by text citings: i.e., do the numbers 10, 20, 30, etc., occur
anywhere in the narrative?
Also, if we accept the validity of the base 9 system (doubtless enacted by the Whorl gods to reinforce their sanctity, just as Pas's children have
co-opted the days of the week), how does this change the facts, figures and chronology of the Long and Short Sun books--from ages of the characters to
lengths of the year--or even, say, the hypothetical distance between Blue and Green at apogee and perigee?
Robert Borski
Well, it is an attempt. Are the children's math results errors or an odd version of Base 9 as Borski suggests? Since he doesn't pursue the idea in the archive or in his books I have to guess he was unable to crack the code (if there is one). If it is Base nine it would seem to suggest The Nine gods of the Whorl. Perhaps 1-9 for the regular gods and the extra digit Borski notes is the zero (0) for The Outsider? The Seal of Pas is found in Chapter Nine. There are nine groups of digits. That numeral does seem especially conspicuous.
Now I will ramble a bit-
For me, base 9 automatically invokes the idea of being nine-fingered (as our normal base 10 is based on the usual # of fingers). And this, of course, calls to mind LOTR and Tolkein as both Sauron and Frodo become nine-fingered. I know Wolfe was a great admirer of Tolkein. A foreword to LOTR by Tolkein has always made me wonder if the author was missing a finger:
..it had to be typed and re-typed: by me; the cost of professional typing by the ten-fingered was beyond my means
I've looked and not found any mention of a missing finger on the web. He was in the war. I"ve scoured Tolkein photos..he might have a piece of his left ring finger missing but impossible to say for sure.
This brings back my long wondering on whether Gene Wolfe is lame in one leg. Again no mention of it in web bios. He also was in a war. There is a mention of a bad childhood leg injury from a bike accident in an interview with Larry McCaffrey. Many of the photos of Gene Wolfe show him with a cane...but they are all recent photos. Nothing from the 70's when BotNS was being written. I must continue to suspect leg and finger are important for similar reasons in the works of Wolfe and Tolkein.