Some Clarifications - X, S and what the heck is A1?

I recently received an email from a knitter who seemed pretty frustrated by some aspects of Sock Architecture, so I want to try to answer her questions here, in case there are others out there who agree with her. (I also answered her email, so don't worry!)

The beginning of the book has a lot of calculations for the heels and toes. This is so that you can "plug in" your own numbers and make those heel or toe shapes with any number of stitches you like. If you want, you can use these instructions to make up your own socks from scratch or just alter an existing pattern to suit you.

The patterns in the back of the book are a little more spelled-out in a stitch-by-stitch way. If you are using one of the sizes in the pattern, you can just follow the pattern, so your knitting experience will be a lot like using any other knitting book. In other words, you can pretty much not do any calculations at all, if you have the same row and stitch gauge the pattern calls for and you want to end up with the exact size that I have written.

Some patterns combine the  best of both worlds (in my mind). They include an adjustable size, where you plug in your own S (total number of stitches), X (half of S) and sometimes a few more calculations, so that you can customize that pattern just for you. Those patterns have the term "adjustable size" in their sizing notes.

Ok, this next bit is only for people who are looking at page 12:

A1, A2 and A3 aren't always computed, but they are related to each other.

When you are working from the toe up, you should work A1 and use the information from the toe-up section of the book to calculate A3. Then, subract A3 from  the desired length of your sock's foot to see how long you should make A2 before you start the heel (and gusset, if any) shaping (which is A3).

When you are working from the top down, you should work A3 and use the information from the top-down section of the book to calculate A1. Then, subtract A1 from the desired length of your sock's foot to see how long you should make A2 before you start the toe shaping (which is A1).

I hope this helps and I'm sorry if I just gave everyone who didn't like high school algebra hives!