The Number Field

We've started feeding Roman solids. Even though he's only five and a half months old, we (mostly Jenny) have noticed his food-ready signs for several weeks. Nothing was more telling than his intense focus on us while we were eating--his eyes would follow the food from plate to mouth over and over again, and at those times his drool wasn't entirely from teething.

All that attention to how food works has paid off for him, because he knew enough to dive right in as soon as a cereal-loaded spoon made its way close to his mouth. It will take practice before he's efficient enough to keep a whole bite in his mouth without pushing some of it out, but most of the bite usually stays in by the second or third time we scrape it off his chin and shovel it back into his mouth. He definitely wants the food in his mouth--any short break in the rhythm is enough to make him scream for more. Roman is clearly not meant to live on cereal alone, so his culinary options quickly expanded to include pureed bananas and sweet potatoes.

Roman only eats solids once per day, so most of his sustenance still comes in liquid form, from nursing and formula. We worry about his weight and about how much of his fussiness seems to be connected to food, but it isn't easy to figure out how to solve those problems. Our current hypothesis is that he has a soy sensitivity, so Jenny has altered her diet and we've switched to a specialty formula. There are some downsides to this approach: soy is found in almost everything (including chocolate), and the formula is rather expensive and smells terrible. Although the results haven't been uniformly positive, we have noticed general improvements, for instance in the quality of Roman's sleep. He now weighs more than 14 pounds, which is still on the very small side, but at least he's gaining weight steadily and seems to be tracking along a growth curve instead of dropping off of it.

We'll keep stuffing him full of as much food as we can, and hope he continues to make progress. In the meantime, we continue to enjoy his happy times. Jenny took Elena and Roman to story time at the library today, and someone approached Jenny just to tell her how cute she thought Roman was. It's always nice to hear compliments like that!

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Or: How Apple turned a thirteen billion dollar profit last quarter.

(I shot this with my iPhone.)

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Would you rather: have me cry all day and sleep well at night, or be a happy boy during the day and up every hour at night? Don't worry, you don't have to choose. I'm going to keep you guessing!

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I never imagined that I would feel that the lyrics from one of my favorite songs applied so specifically to me. Well, how did I get here? By here I mean: living in modest accomodations (comparable to a shotgun shack) in the Pacific northwest (another part of the world), driving a large (rental) car, with my beautiful wife (and kids) living in a beautiful house (with some of her family) a couple of hours away.

The short version of the story is that I accepted a unique (perhaps I should say a once in a lifetime ) temporary work assignment.

Here's a longer version: About two weeks ago, we moved everything that wouldn't fit into luggage from our townhouse into a storage unit and gave the keys back to the landlords. We'll miss the good landlords and location, but not the angry downstairs neighbor. Elena spent the main moving day with her grandparents, but we brought her back for our final cleaning day--she was sad and shocked to see everything gone, walking from room to room saying things like "Oh no, my bed is gone! Oh no, where's the couch?" We had tried to prepare her for this by talking about how we were going to move, but she didn't understand what that meant until she saw the house all empty.

I didn't express my concerns openly, like Elena did, but I had some very deep concerns and doubts as we got ready to go. Was I right or was I wrong to pursue this opportunity? After we handed in the keys, the question changed to: what have I done? But the die was cast, and there was nothing to do but shift into adventure mode for our travels.

We're grateful to have family and friends that living at the origin and destination for this trip. We stayed with my parents for a few days before our scheduled departure. After a long day of flying that in the end wasn't nearly as bad as it could have been, our good friends Carrie and Matt opened their home to us. It was lots of fun to watch Elena play with their kids, her friends, Danny and Kaylee.

Predictions for adverse weather conditions forced us to make a tough decision about when to try to travel over the mountains to Jenny's father's house. Jenny and I had some heated discussions about the right course of action, but eventually came to an agreement. It could have gone the other way, but we got lucky by leaving early rather than lingering. Our drive wasn't impacted by the weather, but conditions deteriorated all along the route after we made the trip.

The bad weather had a silver lining for us, because it kept me with Jenny, Roman and Elena for a few extra days before I moved on to my work location. Now that I'm here, I find that I hadn't fully comprehended how different my life would be without them. It's been a long time since I've been on my own this much. My consolation is the thought that by making these sacrifices we can figure out how to work this to our advantage. For one thing, our house down payment fund will grow more quickly. More importantly, we'll learn about whether we like life on the road. We may have other opportunities to travel, and this is a trial to see if we like it.

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We often make New Year's resolutions without reflecting on what we've accomplished in the previous year. Last year was a very full one for us, so I think that it would be reasonable for me to to resolve to do less this year--not less in the sense of watching more TV, but less in the sense of increased focus on that which is most important. I may not be able to act on that resolution, especially considering that we're almost halfway through January, and I'm only just now writing about my New Year's Resolutions, which surely breaks some social convention, similar to the lower right corner of this comic .

I don't remember all of my resolutions from last year, but I remember my blogging goal was to post something every five days. I stuck to the schedule, at least on average, until Roman arrived. Even after he joined us I managed to post on a somewhat regular basis until I felt the full weight of our holiday projects. I don't think that I should try to sustain that same schedule this year. Instead, I'll try to put something up every week. It may not always be written--with my new phone, it's much easier for me to capture video. I have big plans to introduce the world to Elena's unique versions of her bedtime songs.

Although I love to have an audience, I write first for myself, and second to have a record that my children can read someday. Because of that, I plan to continue searching for a good way to communicate my thoughts about the connections between technical topics and parenting. I know that everyone's eyes glaze over as soon as they see this title , and click off the page as quickly as they can. But I think that I just haven't found the right lexicon, and I'm going to keep trying until I can make it work. I probably need to treat these types of post as crafted and revised essays, not free-form blog entries.

After Roman eats, we can often tell when he still has to burp; it's just clear that there's something inside that needs to come out, and we gently bounce and massage him until it does. That's the way I feel about these ideas--they're inside, and I want to get them out. Please bear with me. I ask for your feedback, and promise that I will make the posts more palatable by increasing the number of cute pictures of Elena and Roman that accompany my more experimental writing.

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With the lack of updates in the past month, I can only suppose that those who will read this post are those who know us well enough that most of what I have to report here will not be news. I want to have some record of what has occupied our time and thought in recent weeks, and now that some of our projects are over and the new year has arrived, I want to return to the habit of writing.

We've kept ourselves very busy jumping from one project to the next and juggling more than one thing at a time. After the success of the Thanksgiving basket project , Jenny again answered the call to serve by coordinating a "Sub for Santa" activity. As a smaller project, it didn't require quite the same level of dedication on her part, but I suspect she spent more time on it than I realize.

Jenny also put in long hours working on the first stage of our annual Christmas package project. Earlier in the year we surreptitiously collected all the old home movies we could find in our parents' homes. She started the process of digitizing the VHS tapes, breaking the footage up into coherent pieces and trying to figure out correct dates for all of the events. After she did that, I copied everything back to DVD and burned copies for all of our family members. We even added LightScribe capability so the discs would look better. In all, we did about 20 hours of video from each side of the family. As usually happens with these packages, I underestimated the amount of work that would be required, and was still burning and printing DVDs two days before Christmas. I think it was worth it--the gifts have been well received, and I hope that Elena, Roman, and all our nieces and nephews will eventually appreciate having these records. (The packages also included some taffy along with the DVDs.)

Somewhere along the way (perhaps because our eBay adventure was winding down, giving her just a little breathing room) Jenny decided we should make Christmas cookies and treats for delivery to some of our local friends. She made cake balls, butterscotch brownies, chocolate chip cookies (both pumpkin and regular), chocolate bark, fudge, and peanut butter blossoms with Reese's mini peanut butter cups. Elena carried the goody plates from our car up to the front doors for delivery, then say "Merry Christmas!" when the door was opened. The first plate got pretty jumbled up, but on subsequent deliveries Jenny helped her hold the plates steady.

In the midst of all this, we still had to attend to our normal parenting duties and holiday activities, like decorating, buying gifts, and spending time with family and friends. Elena and I went on a trip to the mall two weeks before Christmas to look for presents for Jenny and Roman. Elena didn't last long in the toy store; she wasn't bad, it just didn't hold her interest long enough to find something for Roman. We searched all over the mall for things that Jenny might like, and settled on a new sweater (Elena sort of picked the color) and some bath scrubs.

In our wanderings, we saw several fun things that Elena wanted to do, but I asked her to choose one of two options: taking a ride on the choo-choo train that goes up and down through part of the mall, or having a frozen yogurt treat in the food court. She was determined to ride on the train, but when we got to it the operator was taking a break and there was no sign indicating when it would start up again. I suggested that we should go finish our shopping, then come back, but she didn't want to. After thinking about it for several minutes, she decided to switch her preference and we got some yogurt instead.

As we were about to head home, I noticed a new barbershop that was running a grand opening sale. Jenny had talked about getting Elena's hair cut for some time now, so I asked Elena if she wanted to go in and get it done and she agreed. The stylist was very gentle with Elena's somewhat knotty hair, and tired Elena stayed calm and still the whole time. The only problem was that I didn't get a lock of her hair to preserve as a first-haircut keepsake.

Roman is developing by leaps and bounds. After several days of trying and almost making it, he rolled over from back to front for the first time on Christmas Eve--it was his present to us. The next day, when we visited my parents' home, he put on a show and did a couple full rotations, back to front to back again. He likes to grab at anything he can get his hands on, including the ball and tag blanket he received as Christmas presents. Often he's ticklish all over and full of giggles, especially when 'wrestling' with toys. He also likes to test out his legs by standing up whenever he can, using as little support as possible.

We do have some concerns about Roman, mainly that he isn't gaining weight at the rate that we would like--at his four-month trip to the doctor, he tipped the scales at only thirteen and a half pounds, which put him only in the tenth percentile, which was lower than his previous measurements. We'd like the downward trend in percentile to reverse itself or at least stabilize, but for now the doctor isn't too worried. We're trying to work out some feeding issues which are almost certainly a contributing factor to the weight gain concerns. Along with a different approach to reflux treatment, Jenny is researching different theories about effectively nursing an easily-distracted baby.

I was going to write more about Christmas shopping, but this post has gone on long enough. I have just one question: why is it that the only non-My Little Pony options for toy horses at Target cost either one dollar or more than thirty dollars? Even though I wasn't thrilled with it, Elena has been happy with the one dollar option.

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Now that we live within driving distance of two sets of grandparents, we're into our second year of alternating holidays. For Thanksgiving that meant our first major road trip with Roman, and a new trial for our potty-trained Elena. We had a great time, but even with lots of people to help out, Roman and Elena kept us fully occupied. I'll spare most of the details and only touch on some of the highlights of the trip.

• Frozen Yogurt : We hadn't been to a self-serve frozen yogurt place in a long time, because there isn't one close to us. We always enjoyed them back in Texas, and it was nice to do that again at the Sweet Frog.
• The Bike Ride : I may have been the only member of my family to keep this tradition alive. Thanksgiving morning was perfect for riding, with blue skies and cool temperatures. It was my first ride in the area, and I loved the scenery but could have done without some of the hills that were steeper than I was prepared to handle.
• The Thanksgiving Feast : Jenny's mother did most of the work, and everything was delicious. My meager contribution was a chocolate pecan pie, which did get good reviews.
• Black Friday Shopping : Jenny argued was that we were probably going to be up at midnight anyway because of Roman's feeding schedule, so we should go out looking for deals. I went to bed early in protest, but she woke me up when it was time to go. The lines outside of Target and Best Buy were unbelievable, so we ended up at Kohl's. The speed of their checkout line impressed me, especially since it's always been a weak point of shopping there.
• Date Night : I don't feel bad saying that it felt great to take a break from both children at the same time. We went to see The Help , which is probably out on DVD already, but there's nothing like seeing it on the big screen with a bag of theater popcorn. I wish we had a second-run theater around here.
• Peaks of Otter : We threw lots of rocks in the water and saw a heron while hiking at this lovely recreation area along the Blue Ridge Parkway. After our picnic lunch, Elena and I played by the stream. The weather was too cold for wading and splashing, so we threw sticks and leaves in the water and followed their routes as the current carried them along.
• Game Time : The grown-ups played Settlers of Catan , but Elena found some other things that were more her speed. Once she started to play Hungry Hungry Hippos she didn't want to stop and had no problem handling multiple hippos at once. Another time we sat down to a couple of rounds of Dora the Explorer-themed Memory , and I was impressed by how well she was able to remember and make matches.

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While I was designing our Christmas cards, I thought about doing something math-related, and the obvious choice was to use some variant of the Penrose tiling as the background. I took the card in a different direction, but the process gave me an opportunity to reflect on life with a new baby.

An aperiodic tiling, among which the Penrose tiling is the most famous, is a way of covering space with simple geometric shapes, with an interesting feature--you could go on forever in every direction, and there would never be a repetitive pattern. No region would ever look exactly like another (as long as you're looking at regions that contain more than a few tiles). There are ways of doing this that use just two different tile shapes, which astonishes me. That's not to say that different areas don't look similar--that's unavoidable--but they're never exact copies. I see a similarity with an infant's life. Although his repertoire has been growing, it used to be that Roman could only do about four things: eat, sleep, cry, and (rarely) be calmly awake. Every day is a mix of those activities that is sometimes frustratingly repetitive, but never exactly the same. We have to keep on our toes and adapt as best we can, which isn't easy but is certainly preferable to the monotony of doing exactly the same thing over and over again.

There is a point to all of this rambling. How can we be sure that a tiling really is aperiodic? What if there's some spot out in the distance, out close to infinity where nobody has charted yet, where everything looks just the same as it does right here? One way of proving that can't happen is to show that a tiling has hierarchical structure--certain motifs that reappear at ever-increasing scales. If the pattern of tiles ever repeated, then there would be a largest motif size that it could contain, so if the maximum size of the motif is unlimited the tiles can never repeat. It's similar to an argument that proves that there are infinitely many prime numbers . Down in the trenches, holding Roman while he's going through another bout of inconsolable screaming, it's hard to understand what's going on. Every day we lay another few tiles that help to expose the larger structure, and hope that the actions we take will effect positive influence on the larger structures of personality and character.

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We're happy that we have family living close by, so that we can share special holidays with them. This was the first time that I helped Jenny decorate a cake. It featured flags from places Leisa has visited in her extensive worldwide travels--some are harder to figure out than others.

It was very nice of Leisa to let Elena help open presents--we all enjoy Elena's wow reaction, no matter the present.

Just one more thing: a big congratulations to Leisa and Sam!

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This is a guest post from my sister Leisa.

Mark claims that grandparents are the magical people who calm down cranky children. I can't refute the pictures Mark posted, but I would argue that there is an extra-special bond between aunts and uncles and their nieces and nephews. Mark and I grew up far away from our extended family, so we didn't spend much time with our grandparents, aunts and uncles, and cousins without our parents close by. Over the last few months, Elena has had the chance to go on extended family adventures without her parents. Like many children, she’s displayed a special attitude when her parents aren't around to guide her through a new situation.

Adventure 1: To the Mountains
When our oldest brother's family was visiting from out of state, Elena wanted nothing more than to spend time with her rambunctious and adventurous cousins. Her aunt and Grandma convinced Mark and Jenny that she should go hiking with us at a favorite Mountain Park , then stay overnight and meet up with her parents when they came to dinner at Grandma and Grandpa's house the next day.

Elena doesn't act differently when her parents aren't around, but there is something about those situation that feels liberating. Elena felt comfortable and safe enough to walk right up the middle of the stream like her older cousins, and she also got to search for mud puppies, fish for minnows, and enjoy splashing all around.

She simply expected someone to be there to balance her as she walked up the stream on the slippery rocks and through the deeper pools. She trusted herself to be able to balance--a skill she didn't quite have the strength for, so I ended up hauling both of us up the river. At lunch she loved eating nearly unlimited cheetos and cookies.

Adventure 2: To the Shore
While Jenny and Mark were at the hospital for Roman's birth, Elena had an adventure of her own with us. We spent the first day having fun (and not doing much napping or sleeping) at Grandma's house, and then we went to the beach.

Unfortunately, Elena was overwhelmed by the waves, which wouldn't obey when she told them to stop. She definitely preferred the water in the mountain stream of our previous adventure because it only came up to her knees at the deepest spots. Luckily, she did enjoy digging in the sand and chasing seagulls.

For some reason, she decided that the best way to show her love for the sand was to lay face-down in it and tell her two doting aunts to cover her with sand. Originally, we had encouraged her to let us cover her feet with the sand, but she liked that enough to have us cover her and Grandma with it. Elena giggled as we covered her just enough before she broke free, only to want to be covered again.

When it was time to go make the drive back to meet new baby Roman, Elena was very sad to go. She fussed through having at least four people try to wash the sand off of her--maybe she didn't know the bundle of joy and the extreme changes that were awaiting her. We hope Elena will have some more adventures with us soon, whether her parents are around or not.

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