I'm still a little confused about the 122... maybe that's because math makes zero sense to me. Sorry. I also don't understand why it can't be base-16, especially after being confirmed by Brandon.
I thought this might come up eventually.
Here's a primer on how numbers work.
Our number system is big-endian, positional, and base-10
. Big-endian means that, when reading a number from left to right, you encounter the big end first. Positional means that the value of a numeral depends on its position within the number. Base-10 means that the mathematics that determine what a numeral in a given position means are based on the number 10.
In positional systems, in order to determine the value of a number, we multiply each numeral by bp
, where b is the base and p is an exponent whose value is dependent on the position. In the first position, the exponent is 0; in the second, it is 1; and so on and so forth forever.
Let's look at an example number: 385. The value of this number is determined by the following expression: 3*102
= 385. In other words, 300 + 80 + 5.
This way of thinking about numbers looks daft until you realize that it allows for numbers in bases other than the familiar 10, which can occasionally be very useful. The only example I know of is computers, which only have two numerals to represent information, and so have to use base-2.
In base-2 (or binary), our example number is 110000001: 1*28
= 256 + 128 + 1. Of course, binary numbers are hard for humans to work with, so to make our jobs easier, programmers started using base-16, or hexadecimal. Our example in hexadecimal is 181: 1*162
The chapter numbers cannot
be a positional system, at least not in the way we use them. Consider chapter 17, which is numbered (16 1). If this were a base-16 system, that number would be 16*161
, or, IOW, very much NOT 17. Instead, the two numerals are added together, much like Roman numerals.
The only way to get those chapter numbers to work in a positional system is to posit that every TWO numerals occupy a single position. In such a system, you add pairs of numerals together before applying the base. So, in the three-digit number (6 16 10), you first add 16 and 10 together to get 26, then apply the base: 6*161
= 96 + 26 = 122.
Such a system is not without problems, as eri has pointed out:
Sorry, but it can't be base 16 system, if it has 16 digits plus zero (which we've seen used on the map).
It is true that all of our positional number systems use the same number of symbols as the base. Thus base-10 uses 0-9, base-16 uses 0-F, etc. In this system, there are 17 symbols: Spike-Duralumin. I realized this when I proposed it, but I ignored it because it's not an issue. All it means is that there is more than one way to represent certain numbers, but this system would have that property anyway due to the two-numbers-per-position thing.
So, yes, it's an inefficient and stupid way to write numbers. But, then again, so are Roman numerals, and the greatest empire of the ancient world used them to create feats of engineering never before seen. And speaking of Roman numerals, that's another system that has many ways to represent some numbers.
If we abandon the notion of shoehorning these numbers into a positional system, we'd end up with a system where all numerals are added together, except for those that are preceded by a letter, in which case that number is multiplied by some value before being added. In the edition number, under this system, the two unknown letters would be value-modifying prefixes on the numbers 15 and 6.
I'm pretty much convinced the numbers work in one of these two ways. Now, we just need more information, which means that someone needs to bug Brandon (or we could RAFO, but that's no fun
Nobody likes a sham, except when it comes to poo.