Yesterday on Men Who Knit, Hugh Mannity (note pun) wrote that he wanted to make a pair of Fibonacci socks, but he wanted the series to start at the heel and work outwards in both directions.
Yarmando is intrigued. A strange construction method and design-by-math?
I was lying awake at 3:00 a.m. thinking what ways could be used to start socks at the heel. When Dodger had his usual midnight snot attack (Wouldn't it be great if cats could just blow their nose? Or if you could just give them Sudafed?) I got up and tried a couple of the ideas out. I think I see how it can be done.
One way is to do your favorite tubular cast-on (mine is Turkish), knit your favorite short-row heel, and then begin knitting your tube. On the first round, knit half a round in waste yarn. You then either knit up towards the ankle or down towards the toe. When you're finished, remove the waste yarn, pick up the freed stitches, and knit the other half of your sock.
Another method that works but is significantly more cumbersome and confusing (particularly at 4:00 a.m. and with the "magic loop" method -- better to do it with double points I think) is this one: after knitting your heel, put aside half your stitches on a string holder. With your working yarn and a strand of waste yarn, work a provisional cast-on (alternative directions) for the required number of stitches -- at least half of your circumference, more if you want a roomier instep. Connect back up with the live stitches on the opposite side from where you started the provisional cast-on, and then continue knitting either down the foot or up the ankle, reducing any extra instep stitches you added.
Yeah, this is all too much trouble and offers no advantages over other sock construction methods. But it was an interesting experiment to work through when I couldn't sleep.