Howdy from the West Coast. Another update from California. While I had originally planned only to stay until Monday, a few folks convinced me to extend my stay. Thirty dollars worth of airline fees and five days later, I’m still here. My cousin Spencer just dropped me off at base camp—at his parents’ home—from his new pad. It’s nice. This was the first time in fifteen years that we spent any amount of time together. I enjoyed the space and the time, though he just reminded me of an incident that occurred during our last and first meeting.

I was eight and more than a little squeamish around blood, especially my own. So when I busted my knee on a strange road in a foreign land while biking I just about fainted; he and his twin brother, Evan, had to drag me home. I’m not embarrassed at all that he remembers and thought to remind me of it now that we’re twenty-three. Truth be told, I’m still not entirely over the blood thing; I am most sensitive to my own bodily fluids—I don’t really care if others are bleeding to death. As long as I’m okay, things are fine, thanks to the movie industry and their constant, graphic portrayal of extreme violence. Yet I really like receiving shots of novacane at the dentist’s office. When I was in high school, sometimes I would chew Orajel until my face went numb.

It’s unfortunate that we live so far apart. I’m starting to really dig this family thing. Think about it: automatic friends without the trouble of being friendly. It’s not a bad deal.

For all of those you back East [and elsewhere], don’t worry. I miss you constantly, and the several of you who have forgot the three-hour time difference have very successfully woken me up in the wee hours of the morn’. Don’t think that because I didn’t pick up that I didn’t wake up. But I do appreciate your calling, naturally.

Is this a blog entry or a love letter?

Anyway: with all my heart, good night.

I am once again States’ side. However, at 7:30 tomorrow morning I hop a flight to San Fransisco. Don’t look for me in Boston again until Monday.

I’m like quick silver.

Last night I drove, according to my tripometer, 442.7 miles from Sudbury, ON, back into the States to hand-off DJ to Bob and Trisha, who brought the boys Kyle and Lukie, along for the ride. I can’t help but feel like we were runners for the Underground Railroad, though I don’t remember tourism in Florida being against the law however dangerous it might be. Weedsport, NY, wasn’t a stop I remembered from my sixth grade history texts, either. But the books we used at my school were far from definitive.

Now I write to you from Auburn, NY, in the parking lot of the Days Inn. Last night, around 2:10am, I tooled into town only to discover that I hadn’t loaded the maps for this part of the state in my little GPS gizmo. Lost, I circled back to the gas station across from the Holiday Inn to ask for directions for the Days Inn. The clerk and customer very kindly gave me straightforward instructions detailing some tricky turns despite the hotel’s short distance from us. “You’ll have to take a sharp right—you might not even see the hotel until after that right because there are trees on either side,” the clerk told me.

“Thanks. I won’t drive too fast,” I promised.

And I didn’t. Within seconds, I was in the parking lot—of a Motel 8. It was late, I needed directions, and I already had a confirmation number. I had to go in.

“I know this is bad form, and that it’s late, and I’m sorry to have woken you up, but can you tell me how to get to the Days Inn?” I asked the desk attendant, a man in his late thirties whom I had clearly riled from sleep. He was thin, in an inactive sort of way, like how I imagine Marfan’s syndrome left Abraham Lincoln.

He explained over my apologies and in no time flat, I was where I needed to be. Four and a half hours later, I was awake again. Time to check in on my sister. Back in Sudbury, she had slept even less. She plans to stay in Canada through August with JC and his family. I’m worried about her.

On my way out of the hotel lobby I ran into another guest, Phyllis, who was up from Florida for an extended summer visit. She was leaving, too, but the rain held her inside. Phyllis had grown up around here—a quaint little town surrounded by sprawling pastures, befitting a place in New England or a Washington Irving short story—, but lived in Natick for a time with her husband, a native Bostonian now deceased, thirty years ago. “My how that mall has gotten bigger,” she remarked. We chatted a while more, asked where I was from, where I was headed and why. I told her. She seemed concerned with my driving seven or eight hours back; I didn’t explain that Michelle was on a bus bound for Syracuse, perhaps I ought to’ve to assuage her fears. I did explain that I wasn’t so foolish as to drive just then, in my sleepless condition, but that I would walk across the parking lot and into my car to camp out until I felt better.

So here I am, somewhere off exit 40 on I-90, in the parking lot of a hotel I’ve already checked-out of, hours later, using their amenities—including the sauna my car has turned into, despite its missing from their list of offerings. It’s time to grab some breakfast.

The ejection fraction gives the medical world an index by which they can measure, in some sense, just how well a person’s heart is working. An average, healthy adult has an ejection fraction between 55–60. That means with each beat of the heart, about 60% of the blood that was in it gets pushed out. Anyone with an EF in the twenties is in critical condition, though people have been known to live, for a time, with fractions as low as ten. My mother, before her collapse, was walking, talking, and living a normal life with a documented ejection fraction of twenty-six.

The doctors and nurse staff in the ICU here are flabbergasted by it. Even before she moved to Canada, over three years ago, her medical records correctly reported that her heart was in critical condition. Yet, during check-ups doctors thought that since it seems to work, there’s no use tinkering with it. They were most likely right. The condition and quality of life she enjoyed is stunning to me, and to the doctors. No one can seem to wrap his head around the reality of my mother, her strength, and good dumb luck.

Now her ejection fraction hovers at around ten, sometimes a little higher, others a little lower. Again, it’s hard to believe that my mother has stuck it out these past five days. The doctors have installed a balloon pump to alleviate some of the stress on her heart, but it is only a temporizing measure and can’t stay in longer than five or six days. The same goes for most of the medication she’s on. They’ll keep her on the ventilator longer if need be. She only takes about ten breaths per minutes on her own. They oxygen levels on the lowest possible setting, though, 30%. And they’ve been weening her off the drips and balloon. Right now it pumps once for every two of her heart’s. That’s medium. We’re aiming for low (1:3).

I should note that many of her neural and cognitive functions have not suffered. She is very aware of her surroundings. She knows that she’s incredibly uncomfortable and that she doesn’t want to be in the hospital anymore. She has recovered only enough strength to move her hands, one at a time, from her side onto her stomach. When asked questions she can nod in response albeit slightly, open her eyes for several seconds at a time, focus on others, and once Janice and I believe she blew me a kiss. Her doctor uses a crude scale to quantify the relative condition his patients. When my mother arrived at the hospital, she was a one, perhaps even less. Now she’s a three. They won’t consider moving her until she reaches at least a five, ideally, seven.

Studies on those obnoxious family newsletters demonstrate that families can’t help but put a positive spin on everything. Some items don’t need much spin. “Jordan and Angie have decided to get married. They’ve already got a cute apartment priced within their budget and will move in right after the wedding in April,” for example. Here the spin comes from the adjective, particularly from “cute.” Others require a little work. For massive, reconstructive spin, it is often necessary to tack on an unrealistic and unnecessarily optimistic phrase at the end as in : “David has been charged with a count of DUI and involuntary manslaughter after a messy break-up with his high school sweetheart last Friday, but it looks like he might get off!”. It’s within our nature to hold onto those tenuous threads of hope wherever we can find them. Of course, pessimists are never disappointed. Aware of both approaches, I elect to leave you with this bittersweet, moderate summary in proper positive-then-tempered-with-negaitve order.

My mom is doing outstanding well within the confines of a tremendously bleak prognosis.

Mentioned last time, it’s worth seeing:

Seeing as I’m here, and you’re probably not, I just opened a Flickr account so that we may share my experiences more fully. You can even subscribe to its RSS feed. I will try to update it frequently enough to make things interesting.

Today, day two of our extended stay, we moved downstairs to another room. It must be the children’s suite. The bedding, curtains, and shower curtain all have prints of Sleepy the Travelodge bear in drowsy sports poses. The television in this room is new enough to accept DJ’s Xbox. DJ, however, forgot the power cord. Right now he’s destroying the extension cord I brought with my Swiss army knife in order to provide juice to his addiction: Tiger Woods PGA Tour. I’m a little concerned. He just muttered, “This is going to be rough,” under his breath to the console. He assures me that at worst we’ll blow a fuse. I reminded him that at worst, Janice and I will already be at the hospital.

After our noontime visiting half-hour at the hospital, we’re going to the Dynamic Earth underground mining exhibit to complement yesterday’s trip to the parking lot in Copper Cliff at an actually mining plant, to stand next to a giant Canadian nickel, and then walk across—not over—Onaping falls, about forty minutes away, on the suggestion of Mike who previously managed the CD and DVD store in a sparsely populated “mall.” Two days ago Mike gave his notice; he’s not allowed back in the Zeller’s next-door nor does he ever want to go again. He loves fishing and promises that Onaping, while far away, is well worth the distance. Mike is not a professional cartographer, but he did get us to the movie’s last night.

Jason, soon-to-be Superboy, is going really to resent Superman once he gets a little older. Lois shouldn’t leave Richard; this situation is just no good.

DJ just successfully McGuivered his Xbox; the rest of us are leaving to avoid a fire.

We begin day three in Sudbury, ON, at about the same time we did yesterday. Apparently it wasn’t the travel that knocked us out until one in the afternoon, it was just us. Although, it could also be the air. Mom, JC, and Janice have touted the superiority of the so-called fresh Canadian air up here. Having lived in Toronto before, I wasn’t convinced of its immediate and pristine perfection.

Sudbury is a small city to me, but up here, with a population in excess of 150,000, the Greater Sudbury metropolitan area a behemoth in the Near North. I am constantly baffled by this mismatch of opinions. Mining is the primary industry, and it seems that most people have a personal connection to it, either directly, or through family ties. We met another couple here to see their mom. Like ours, she had been airlifted from hundreds of miles away for heart failure. Like ours, too, she is young; this one even younger, clocking in at only 47 years. Sudbury’s renown for cardiology, at least in Ontario, is wide-spread. Sonny, a man at the the Peddler’s Pub, told me that the first bypass surgery was done right here, and that he knew the patient. Sonny is an old man. We have plans to visit him on his seventieth birthday, November 2, 2009.

The daughter’s name is Mel. She and her boyfriend Jason were the first to arrive. They agonized during the mandatory wait period. Janice and I visited our mom, who was relatively stable by comparison, and left them. Before leaving, I ran to the car to fetch the camera from the car. DJ and I had been working on a 500-piece jigsaw puzzle of Paddington Bear, the smallest, least complicated puzzle we could find. While we did not finish it, we had assembled enough of it that the image was recognizable. And the scattered, extraneous pieces, which were mostly of a solid color and filler anyway, framed the interior nicely. So nicely, in fact, that we thought it fitting to capture the whole set-up for later.

When I returned from car in the adjacent lot owned by CTC college—the adjoining building has space to lease if anyone’s interested—, I discovered Jason tooling about the elevator in the main lobby. He paced back and forth, stopping only long enough to decide whether we had met before. I spoke to confirm his suspicions, and to be nice, “So, we meet again.”

He responded, “I hate this place.” I had to leave Jason. I was on a mission; Paddington and his toggles were waiting.

Janice and I made it back for the next round of visiting hours. We didn’t expect to see the doctor. I was told she wouldn’t be around until the morning, but she was there now. So were Mel and Jason. This time a huge crowd of people accompanied them. Family, Mel told me.

Janice has found the courage to walk into the room and sometimes even speak to my mother. However, her focus and strength are not unlimited. From time to time dizziness overcomes her and she has to leave the room to sit. The doctor winked at the nurse, Bonnie, “It must be all this fresh air.”

“From those two smoke stacks,” Bonnie agreed.

Because of the mining culture, the three hospitals that serve Sudbury see all sorts of perverse diseases caused by airborne nickel and sulfur in uncommonly high concentrations. So much for that fresh air.

We’re looking into medivac options to bring mom to Boston. She has to go somewhere else for the transplant, anyway. She’s well beyond a bypass.

Everyone else is doing fine. We haven’t used the pool yet, but I plan to tonight.

Presently I am in the bed nearest to the bathroom in a hotel room across the hall from but within the same hotel as my mother’s fiance and one of his boys. My sister is with them just now. DJ is trying to sleep in the other double. Our window looks out onto the offices of Dr. U. O. Kau across the street. This place is a city by Canadian standards, but in Massachusetts, hamlet might be more apt. The traffic is no more dense than in my small hometown. On the other end of the city, there is a hospital. On the fourth floor, the floor parallel to mine, in the critical care unit, is another room. There, a nurse observes my mother’s body from the corner of the room.

A vast array of medical equipment surrounds a bed placed in primary position. To the left, a number of IVs drip medication to keep her blood pressure low enough for what’s left of her heart to maintain a pulse. She receives liquid nutrition through a tube that enters through her nose. Another, snaked down her mouth, aids her breathing. Her medical outfitting is extremely unconfortable, and when she is awake, she is very adamant about letting her medical staff know. They tell me she tries to take out the tubes, complains that her throat is sore—she first went to the hospital because her throat was sore; she exhibited serious flu-like symptoms, common for women, and diabetics in particular during heat failure—she is so violent in her opinions and actions that they have tied one foot and arm to the bed and doubled her sedation treatment to keep her more comfortable and more manageable. My mother’s strong, stubborn personality is to her benefit. The nurse marvels at her surviving this long. Right now she’s resisting everything, treatment and death alike.

Her body makes a small amount of urine, which proves that her kidneys are functioning, however slightly. The same is true of her lungs. If her condition does not improve quickly, her organs will fall into disrepair due to their disuse. The heart medication also damages the kidneys. Unfortunately, last night she was not strong enough even to be transported to another hospital for a transplant. I will check today soon.

When I woke up yesterday, something told me I ought to go back to sleep. To celebrate the fourth, DJ and I hit up Christopher’s in Porter Square after we saw off Steve in a cab headed for his ship with his crewmate (Uncle) Dizzy, someone whom I had only just met but had immediately adopted me as his own because I refill my pint glass with an athletic celerity.

Scott, the bartender, told me that last call on the fourth was scheduled for midnight. DJ and I left, the last ones to leave, close to 1:30am. Just months after my college graduation, I’m too old and too out of practice to close a bar and not pay for it twelve hours later. The sun is too unkind. The trees are too loud.

After work, Janice picked me up at the Braintree T. She was tinkering under the hood in a no standing zone near the main entrance. Her car burns oil and we had quite a drive ahead of us, and it was already close to midnight.

“JC called. Mom had a heart attack,” she told me as she helped me load my bag in the trunk.

“I told her to go to the hospital yesterday when I talked to her. I thought she needed a few liters of fluid,” I answered.

This morning JC called again. This time I picked up. My mother was air-lifted about four hundred miles away to a hospital in Sudbury, second best in Canada he said, but things looked bad. Her heart had failed her. Only about a quarter was still functioning, the rest of it was probably dead. I stood in the middle of Commercial Street, the main thoroughfare in Provincetown with my father, sister, and her boyfriend Andrew. We were on a mission: to find Andrew a bathing suit. I had just picked up a pair of navy blue running shoes for myself, a purchase about a year over due.

“Thanks for calling. I appreciate your taking care of my mother,” I told him with utter sincerity.

“Well, I didn’t do a good enough job, now did I?” he answered. JC and I have never exchanged more than 250 words, less than a middle school book report. Now his voice was shaking. Emergencies can make strangers into family.

I replayed critical scenes every movie I’ve ever seen in mind head, measured my words, and tried to be comforting and appropriate. “You’ve done the right thing. There’s nothing left to do. All we can do now is wait.” My voice was noticeably flat. I put on a smile for my audience to explain that my mother was ill and almost certainly going to die. Now I know why couples break up in public. No one was angry. No one cried. We continued on our way to the next shop, to find Andrew a suit.

On the way I snapped at my father and apologized.

Once there, I ducked out again, this time to talk to my grandmother for the second time that day. I thought we were done talking, but she interrupted our goodbye with a very simple and moving prayer. I winced but the public setting saved me. I didn’t cry.

The walk back to the hotel lasted about twenty minutes. On the way Ellen, Paul’s wife, pulled me out of the crowd. She was with her daughter Gracie, who was happily nursing in the stroller, and Alice, their dog. A moment later Paul bounded out of the cigar store across the street. I walked into him, head down, and quickly. It seems to surprise everyone every time. For a moment I was able to suspend the severity of reality; I smiled without thinking too much about it. He reminded me that I find out about a job tomorrow. Even if I don’t get it, “there’s still purpose to your life,” he told me.

On the walk back, I pondered what that purpose might be. My dad filled the time with talk of submarines. The Germans or the Swedes, he couldn’t remember which, have developed a new submarine that leaves an almost invisible signature. It uses diesel and fuel cells rather than conventional nuclear technology. The hull is rubberized to absorb sonar, and all of the metal, even the dishwashers, are magnetically neutral. Maybe I’d take that commission in the navy, I thought. I could fight the good fight against Ikea.

There wasn’t much to do back at the hotel except swim. My dad challenged me to a few races. I gave him a crash course to the butterfly. Then we stewed in the jacuzzi a while. As he lounged, I practiced holding my breathe. First trial: 70 seconds; then: 63; third: 71; and finally: 82. I laid on my stomach with my arms and legs extended and my eyes closed. I tried to imagine what it’s like to be dead. I aimed to last longer at the start of each go and to be more convincing, at least to me, of my death. I let my limbs go limper than before. Over time I found muscles I hadn’t realized her tense and relaxed them. The bubbles turned me onto one side. I floated. I felt free.

Janice and Andrew left for the pool just as dad and I returned. Now there wasn’t anything left to do. I played a little Tito Puente in the background and started my routine of push-ups and crunches. My mother isn’t stable enough even to be a candidate for a heart transplant. The first from a collection short stories by Judy Budnitz, Flying Leap, crept into my mind.

In this story, a woman needs a heart transplant. Her sisters cajole their nephew, the woman’s son, to donate his. At the end of the story, the woman lives and thanks the son, who promptly dies. I’ve read most of the other stories in the book, and heard this one on NPR, and even installed an AC for the author’s sister a few weeks ago, but I just can’t get into it. Magic realism just isn’t my thing.

Tonight my sister made her signature boiled dinner. Tomorrow I may be in Ontario. Check me out if you’re in the Greater Sudbury area.

Motivated by shame, I’ve taken up Dan Aaron’s challenge to read more original work by giants who laid the foundations of my field. Being a hack mathematician with physicist tendencies, I’ve turned to René Descartes—the man who married geometry and algebra to give us Cartesian coordinates, among other very important things—and his Discourse on Method. In the first part of the Discourse, he situates the reader a bit, explains his personal history, and how it led him to his approach to problem-solving. He tries very hard to be humble and sometimes he almost succeeds, but we know Descartes was a genius. He knew it, too. And even he can’t hide his high opinion of himself.

Descartes claims that the work of several authors is usually inferior in quality to that wrought by a single hand: it’s the old “too many cooks spoil the soup” theory. That’s how he justifies denouncing centuries of philosophers and their work: he had to do it start on his own from scratch; it’s impossible to sort through the ideas of others with any systematic clearity. But he stays out of the kitchen in his metaphor, instead traveling to the city:

Thus we notice that buildings conceived and completed by a single architect are usually more beautiful and better planned than those remodeled by several persons using ancient walls that had originally been built for quite other purposes. Similarly, those ancient towns which were originally nothing but hamlets, and in the course of time have become great cities [think London], are ordinarily very badly arranged compared to one of the symmetrical metropolitan districts which a city planner has laid out on an open plain according to his own designs [Brasilia, say: it looks like a bird or airplane]. It is true that when we consider their buildings one by one, there is often as much beauty in the first city as in the second, or even more; nevertheless, when we observe how they are arranged, here a large unit, there a small; and how the streets are crooked and uneven, one would rather supppose that chance and not the decisions of rational men had arranged them.

Now, Descartes’ philosophy aside, there’s a pretty interesting observation in there. Even though a very complicated system, such as a city, maybe be very orderly on small-scales, the over-all effect is painfully complex. I’ve declared more than a few times, proudly to visitors, that the streets of Boston were once the random paths of wandering cattle. So this Fathers’ Day, when my dad and sister came to visit my new digs, I had to remind them to look in all—not both—directions when crossing the street. “The streets around here are so wacky, that the cars going one way can be stopped at a red and still you can be hit in three other directions.” We all made it across, a little bit hurried but safe. Meanwhile, Manhattans live on a grid and seem to like it. Some have even claimed to prefer it.

A similar phenomenon exists in economics. A while back someone was awarded a Nobel Prize for showing that even though each person may act rationally, the market as a whole still might act irrationally. I don’t know much about how this works, but I can tell you about an analogue in math.

There are several competing definitions of chaos in mathematics, depending on just which subfield you subscribe to. One of the most tractable definitions comes from one-dimensional, real, discrete dynamics; that is, the study of iterated functions that live on the real number line. Simply, take a function, which is only a fancy word for a rule, which takes in a number (like 3) and spits out another (say 1.5) and repeat it over and over again. We say that a function is chaotic if it exhibits the following three behaviors:

• The function has a dense set of periodic points. Periodic points are orderly; their trajectories are predictable. They start at one location. The function moves a periodic point to another point; another application of the function moves it again to another, and another, and another. Eventually, though, the point needs to wind up where it started. Think of periodic points as travelers on a multi-city, round-trip itinerary. A salesman might start in Boston, go to Denver, follow-up in Phoenix, stop short to family visit in D.C., but at the end of it all, he’s got to go home to Boston. In the language of discrete dynamics, our salesman is a periodic point. Dense is just a mathematician’s way of saying most. So, if you blindly pick out a number, it’ll most likely be a periodic point. And if it’s not, there are plenty of periodic points nearby. On a plane, not every passenger is needs to be a travelling salesman like the one in our example. But near each passenger there should be a few of them close by.

Notice that the definition of a chaotic map (or system or function—these terms all refer to the same thing) demands lots of order. Periodic points are simple. We know exactly where they go and exactly where they’ll end up: they travel in loops forever. However, chaos requires a little bit more.

• The function displays sensitivity with respect to initial conditions. This requirement ensures that points which start out close don’t stay that way forever. You can think of functions which are sensitive to initial conditions as those maps which mix points up. Sensitive functions are not very tolerant of approximation. They hate playing horse-shoes, for example. And they’re very hard to plot on computers due to rounding errors. Even though we might be very accurate, a chaotic function will churn the points about so wildly that we cannot guarantee that anything we learn about one point will shed any insight on the whereabouts its neighbor.

So far, we require chaotic maps to be, on the one hand, very orderly—by way of a multitude of periodic points—, and simulatenously jumbled, on the other hand—in an indirect way, through its sensitivity. In a modern treatment, we could stop here. But to really drive things home, let’s add in a third requirement.

• The function is topologically transitive. Topological transitivity is a mathematician’s way of saying that the function meanders. Pick any two points A and B. If the function is topologically transitive, then I can find another point as close to A as you want that eventually makes its way as close to B as you want.

One of the simplest examples of a chaotic maps is the so-called logistic map. It’s a quadratic (there are squares in there):

x_n+1= x_n (1-x_n)/2.

Its continuous conterpart crops up in population dynamics as one of the simplest, foundational models. Some examples within the logistic equation’s domain include colonies of bacteria, blades of grass on a lawn, or frogs in a pond with no predators to eat them.

So, as long ago as 1637, Descartes noticed, very carelessly, that order can breed chaos. Let this be a warning to those of you neat-freaks who work tirelessly to assure everything is in its place. Also, Descartes might argue that cities provide evidence against the precepts of Intelligent Design. I know that’s how I read it.

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