Nap When Your Baby Naps?

We woke Sofi up for New Year's so we could get a photo of Sofi's first New Year and after a feeding it seemed like she was going to fall right back asleep but - NO! Three hours later she was ready for her next feeding without managing to drift off once, and I stayed up trying to calm and soothe her. At three I handed her off to her mother (who had been sleeping in the guest room) and managed to get some sleep myself. While she was up, I started reading *Sleeping Through The Night*, a gift from my brother and sister-in-law that says that in the first six weeks you really can't control when your baby is going to sleep or not, and the best thing to do is to nap when your baby naps.
I just can't do it. I've tried several times now. Even though I'm very tired, I lie down and try to nap. This last time, just now, I tried counting prime numbers. I made it into the hundreds and realized I didn't know my over-ten multiplication well enough to go any further. So I started going over my over-ten times tables in my head. I hear the neighbors walking overhead. I start stressing: I better get to sleep soon, or the baby's going to wake up before I drift off. I'm like the overtired child who can't get to sleep because she's upset that she's so tired. Eventually I gave up, got up, and wrote this blog entry.
One thing Cathy and I do that does work is spell each other: every couple nights one of us will let the other sleep in the guest room while they do all the baby-tending. So we manage to get a good night sleep out of every four or five.