The Number Field

Elena took her first steps this week. After watching a video of her cousin walking, I decided that I should let Elena try, especially if she had a nearby target to aim for. So I stood her up a couple of feet from the futon and let her lunge for it. At first it seemed like she was just lunge-falling forward, but she did get her feet going and managed to reach the futon before falling to the ground.

We tried it a few more times while Jenny was in the kitchen working on dinner, and by the time she came out, Elena was ready for showtime. Jenny sat on the couch, I backed up a little bit, and let Elena head forward. She balanced herself and took more deliberate steps as she headed towards her mommy. When she got there, Jenny turned her around and sent her back in my direction.

As we practiced walking this week, Elena had plenty of bobbles, stumbles, and falls. Sometimes she doesn't know exactly where she wants to go, so she just stands in one spot for a while. I think that's quite a feat in and of itself. With every bit of practice, she gets better at walking. But she's made the big leap; before she couldn't do it at all, but now she can.

My calculus students have a test today, and I see similarities in their struggles with the material. Both are examples of the learning process. I know that they don't understand everything perfectly and will still make some mistakes, but I hope that they have crossed over the major barrier of understanding, so that they can feel competent to work through the test and get lots of the questions right.

The same principles still carry over to me, because I am trying to learn to walk in my research. To put a lot of fancy words on it, right now I am trying to obtain a better understanding of orthogonality in local fields with a non-archimedean metric. It's terribly frustrating, since sometimes it feels like I'm so close, but yet I haven't quite seen the path yet. If I can just take the first stumbling steps, I know that I can smooth it out from there.