The Number Field

Now that it's March, I can post a new video, and have done so. This one features some (but not all) of Elena's different methods of getting from one place to another.

We took Elena to have pictures taken at JCPenney this morning. I tried to pick out an outfit for her while I was shoe shopping last week, and although Jenny approved my choice, a purple velvet dress, it didn't fit properly. This gave Jenny the opportunity to shop for another outfit. She found a lovely blue gingham skirt and matching sweater. Shopping for Elena is getting difficult--she's in 24 month and 2T sizes (is there any difference?), but even those are too small in some dimensions. But the next size up is way too big, especially in the shoulders.

Elena's photo shoot went okay, but she made it hard on us by repeatedly crawling away from the background. She wanted to examine the camera and the remote flash units; maybe she won't be a model after all. Also, the photographer missed the shot several times, which I really don't understand: why couldn't she set her incredibly advanced camera to burst photo mode and start shooting early? I don't want to complain too much--we did get some good shots, and will have the prints in about two weeks.

Last night, some friends came to watch Elena for the evening while Jenny and I drove down to San Antonio to go to the temple. We thanked them with baked goods: Jenny made fresh bread, and I mixed up some cookie dough on Thursday which Jenny baked on Friday. Of course Jenny and Elena sampled the cookies to make sure they were good enough. It's small thanks for their six hours of help, but at least Elena was good for them. She waved goodbye to us as we left, and played happily until her bedtime.

I have to at least mention this week's notable weather event: the Austin version of Snowpocalypse 2010. On Tuesday we had a real snow shower, with a few hours' worth of big, thick snowflakes. There was enough accumulation that some enterprising soul was able to make a small snowman outside our apartment. There wasn't really enough to let Elena play in it, but maybe next year we'll live in a place with a greater chance of winter weather on a regular basis.

A little surprise just snuck up on us. This morning Jenny put Elena down for a nap, but she wouldn't go to sleep. She just cried and cried in her crib, which is unusual for her. Jenny picked her up and brought her to the front room for a little while, but Elena was obviously very tired. So it was back into the crib, and when Jenny put her down again she just laid there and cried.

Then Jenny had an inspiration. That morning, she had taken away Elena's pink fuzzy blanket because it needed to be washed. In the past, we have treated her blankets as interchangeable without any problems. Jenny picked Elena up and together they pulled the pink blanket out of the dryer while it was still warm. Elena took it, cuddled it and started sucking her thumb, and Jenny knew that she could put her down for a nap. She fell asleep instantaneously and slept for three hours, right through her lunch.

This turn of events got Jenny thinking, and she remembered two other recent events when Elena had a hard time sleeping. Both coincided with times when she was without her blanket. The last time Jenny had to wash the pink blanket, because it was covered in birthday cake frosting, Elena wouldn't take a nap, but Jenny attributed Elena's hardship to overtiredness from their busy schedule. Additionally, when we went out for our Valentine's date, Elena didn't fall asleep when the sitter tried to put her down. At the time, we thought it was a result of her no longer fitting comfortably in a Pack-N-Play, but now we suspect the lack of her pink blanket also played a factor.

I had a security blanket when I was a little boy, and I think that my baby box still contains its tattered fragments. I literally loved it to pieces, which is probably why I always identified with the Peanuts character Linus. It's also why my mom sang a lot of this song to try to lighten the mood on laundry day. So far Elena isn't like that--she doesn't need her blanket all the time, just when she goes to sleep. Now that we're aware of it, we're monitoring the situation to see how it develops, and hoping that Target still has this style of blanket in stock.

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.

Elena had her one year checkup on Friday. She soldiered through five shots; the worst part for her wasn't the needle sticks, it was being restrained for long enough to get them all done. Our doctor was still impressed by Elena's good nature and willingness to undergo examination. But the biggest news of the visit was Elena's current weight.

She's still close to the ninetieth percentile for height, which is not much of a change from before. But her weight has jumped way above all the lines on the growth charts. She's now 28 pounds, 13 ounces. At that weight, percentiles don't begin to tell the story. I've done some calculations that put things into perspective. If she were to weigh exactly the same amount in six months, she would still be in the 95 ^th percentile; in one year, she would be in the 75 ^th percentile. Each year in the United States there are only about 60 girls who weigh that much or more at their first birthday. *

It's such a high weight that, when considered together with her large tongue, the doctor has referred us to a geneticist. She doesn't think that there's anything wrong, but thinks we should check things out more thoroughly just to be sure.

Elena has always been a good eater, but we've tried to feed her healthy things, mostly oatmeal, fruits, and vegetables. Despite the video and picture below, we're glad that we can't attribute her high weight to unhealthy eating. But for her birthday, she deserved cake and ice cream, so that's what she got!

* I assumed that infant weight is normally distributed and used a growth chart to estimate the standard deviation and Elena's z-score. I then multiplied that by about 2,050,000, which is an estimate for the yearly births of girls in the United States.

It's hard to believe, but one year ago, at the very moment that I'm writing this, Elena entered the world . So much has happened since that stormy evening, yet it all seems to have gone by in the blink of an eye. But this is not the space for retrospectives. Instead, here's what we've done to celebrate her birthday.

Last Saturday we had a party at Zilker park. We only had a few guests, including Elena's cousins, but it was lots of fun. We played in the playground, rode on the Zilker Zephyr miniature train, and then ate birthday cake. Elena loved it all. She cried when it was time to get off the train, but then forgot her sorrows when she dove into the cake face first.

Later that evening we opened a package from Grandma Nancy. It had two fun activity books in it. One is about a teddy bear getting ready for bed, and the other is about a farm. It includes a bunch of farm animal magnets, which stick to the magnetic pages of the book. Elena had a good time playing with it at church on Sunday, and we liked it because it was quiet. Speaking of church--on Monday we gave her our first present, a Book of Mormon picture book.

Elena got another present Sunday evening: the Allens gave her a scooter/walker combo. Jenny assembled it with help from their oldest son, then Elena rode around on it like a princess while the rest of the kids danced to the musical stylings of Hampsterdance .

We hadn't planned to give Elena any more presents, especially since we recently received a large collection of beautiful, new-to-us toys from some friends who no longer needed them. Last night I decided that I wanted to have at least a little something for her on her birthday, even if she didn't understand the significance of the day. Maybe I was feeling a little bit guilty; I knew I had to leave early this morning and wouldn't be home until later in the evening.

I decided to get her some more rubber duckies, but the store I stopped at didn't have quite what I wanted. I looked around and found the perfect substitute: Squirtin' Sea Buddies . I gave Elena the starfish and penguin just before her bath. They became fast friends and, as expected, joined her in the bathtub for fun time with the rubber duckies.

Jenny sang Happy Birthday to Elena right when first she woke up this morning, then again after her first nap. I sang when I called to say good morning, and my parents called in the evening to sing to her. After all that, I hope she knows that there was something special about today!

Just recently Elena seems to have really started to understand us and respond to our requests and suggestions. When she does, it feels like we're communicating for real. I can think of several specific examples.

She just got a magna doodle, and has partially figured out how to write on it. Sometimes she uses the wrong end of the pen (the end without a magnetic tip) and gets frustrated because nothing happens.

She loves her rubber duckies, and can find them in the middle of a pile of assorted toys when we say "find the duckies."

When it's time for her to get dressed and Jenny says "put your arms to the sky," Elena will do it. This allows her to have more of one of her favorite activities: playtime on our bed.

The other day I was feeding her dinner, and before I blessed the food I asked her to fold her arms. In the past I've accompanied similar requests with some assistance--putting her arms together for just a second. This time she did it on her own. Of course, it didn't last for the whole prayer, and we haven't been able to repeat the success, but I'm sure I saw it.

Last week a friend of ours taught Elena how to give high fives. It didn't take very long at all, and she's kept doing it all week long with us and anyone else who she sees.

The biggest news doesn't have quite so much to do with communication, although that does play some part. Elena has acquired two new climbing skills. First, she has enough reach and leverage to climb up onto our futon, which is about three times as tall as a single stair step. She has to swing her leg up as high as she can, but with just a few days of practice she's already become proficient. Second, she has learned that she can climb down from things by turning around to let her feet down first. For her, this is a much less scary option than taking everything face first. She used to think that was the only option, but we worked with her to show that there was another way. Here's a good example that we caught on video while preparing the equipment for yesterday's big event * :

* Details are forthcoming, but check the flickr sidebar for a preview.

This week I had a chance to watch and participate in some of Elena's daily activities, things I've lost contact with since Jenny started staying home. I'm endlessly fascinated by what she does, so I'll apologize in advance for this post. I know how maddening it can be to hear a father prattle on about the inconsequential little details that he can somehow parlay into convincing (to him alone) evidence of his progeny's brilliance. I'll keep it brief, but if it gets to be too much, just stop reading and be thankful that I got this off my chest before I had to corner someone at a social event and bore them to death.

One evening Elena had eaten herself into a much messier state than usual--mostly the result of a biter biscuit--and Jenny asked me to give Elena a bath. Mostly I just had to watch her while she played in the tub with her duckies. She loves those duckies. One of her favorite tricks is putting a duck in a bucket. Then she pulls it right back out. She was also pretty proud that she was able to hold three duckies at one time, because she only has two hands! Okay, it was much more amusing in the moment.

The next morning Jenny left us for an early morning dentist appointment, so I was there for Elena's waking up routine. Before allowing me to pick her up, she handed me her blankets one at a time, so they could come out to the front room with us. Once we were out there, she became more interested in her other favorite toys. She pulled the duckies out of the toy basket. Then, duckies in hand, she stretched up to reach the next shelf where all the stuffed animals live. Not just any stuffed animal would do; she pushed them all out of the way to reach her favorite Lamby who was all the way in the back.

Not too long after that Jenny came home from a triumphant no-cavities visit, and I headed to school. Twisted heights of algebraic numbers will never be as fun as playing with little baby, but it might be slightly easier to unlock their secrets.

Yesterday, I didn't arrive home until late. Elena had long since finished her dinner and even took her evening bottle before Jenny and I sat down to eat a delicious breakfast dinner of whole wheat pancakes, bacon, and grapefruit. Although Elena played with her toys for a little while at the beginning of our meal, after just a little while she crawled over to see what was happening in our area.

I'm surprised by how tall Elena has grown. When standing, she can almost see the table top, and at this particular moment she had an excellent view, so she could tell how much we were enjoying dinner. Even though she had eaten more than enough already, she wanted in on the action and started whining. I didn't respond to her advances, so it went on for a few minutes.

Then Jenny intervened. In a very normal voice with no gestures or other cues, she said "Elena, Daddy isn't sharing with you, but if you come over here maybe Mommy will share with you." Upon hearing this, Elena immediately let herself down, crawled all the way around the table, pulled herself up and started begging at Jenny's knee. Jenny told Elena she wouldn't get any pancake unless she signed for "more." As you can see below, Elena complied. At least in my mind, this clearly demonstrates that she understands what we say. Also, the big smile and laugh after she gets the pancake is probably because of the syrup, a rare and tasty treat for her.

Just before bedtime we tried do some fingernail trimming. Usually Jenny files them, but Elena has increased her resistance and Jenny asked for my help. I decided to give the supposedly baby-safe nail clippers a try, and managed to take care of one or two of them, but when I set to work on her left pinky I miscalculated or flinched and nicked her fingertip. Elena didn't seem to mind it at all, but it started bleeding enough that we put a band-aid on it. I wonder how many other babies have their first nail clipping and first band-aid coincide? Unless I'm just the clumsiest father alive, I'm sure there have been more than a few.

I know that Christmas is long gone, but I still want to record the theme and contents of the packages we sent to our families * . Elena did a great job with her part , and Jenny and I spent a lot of time putting them together. I was quite happy with the results, and we got very favorable reactions from the recipients.

This year's theme was Elena's Nursery Rhymes . We picked several classic nursery rhymes and included a small item to go along with each one. Most of the gifts were ornaments for the tree, but there were a couple of exceptions. Jenny put together a booklet with all the nursery rhymes and a picture of Elena that matched each one, but the recipients had to figure out which item went with each rhyme. I hope it wasn't too hard--you be the judge. In no particular order, here they are:

• Ladybug, Ladybug : Jenny put together refrigerator magnets like the ones described here , using ladybug stickers under the decorative marbles.
• Twinkle, Twinkle, Little Star and What are Little Cowgirls Made Of? : We ordered these ornaments from Oriental Trading Company.
• The Muffin Man : Jenny made a chocolate chip muffin mix. Everyone absolutely loved these; I'll add the recipe when I get a chance.
• This Little Piggy : We made plaster casts of Elena's foot, then painted and decorated them. We made one attempt at pressing her foot directly into the wet plaster, but she was just too wiggly (it was good we put paper down to protect the carpet). While regrouping and reformulating our strategy we stumbled upon Moon Sand , which holds its shape when molded. Pressing her foot on the sand was quick and made a perfect impression, on top of which we poured the plaster. The process preserved a surprising amount of detail.
• Row, Row, Row Your Boat : The implementation on this one was more than I bargained for. Rowing is my sport, so I really wanted to use this rhyme. I couldn't find any good ornaments to purchase, so I decided to make some instead. First, I found instructions for making paper clip people . The base was half of a styrofoam ball painted to look like water. We cut out the boat from some quarter-inch thick wood planks, fashioned the riggers from popsicle sticks. Finally, toothpicks were just the right size and length to serve as oars; since he's mid-stroke, I didn't have to worry about making blades for the oars. We hot glued all the pieces together, then snapped the assembly into a clear plastic ornament.
  

Even though the rower took the greatest amount of time and effort, it might be something that would interest other people. Jenny and I have toyed with the idea of refining our process so we could manufacture and sell them next year. What do you think? Would you buy something like that for the rower in your life? If you're not a rower, imagine that a similar ornament was available for other sports--skating, basketball, baseball, rock climbing, or whatever else. What would be an appropriate price? Would you be interested in custom orders so you could specify a color?

We're already thinking about a theme for this year's package, but we plan to keep it a closely guarded secret until after Christmas. You can probably expect that Elena will have an even bigger role. In fact, just last night Jenny showed me Elena's first artwork.

* It occurs to me that I never wrote down the theme of our 2008 packages, which was A Taste of Our Travels . We included a treat from each of the special places we had visited during the year: hard candy from our Caribbean cruise, salsa mix from Fredericksburg, steak seasoning to commemorate Dallas, Austin's favorite pancake mix , and a tub of baby food to represent our future.