Archive for the ‘Nonsense I’ve spouted’ Category

The Rubio Gambit

Friday, June 10th, 2016

Senator Rubio folded the newspaper and let out a brief sigh.  The press had been merciless in their criticism of his decision to endorse Donald Trump and support him at the convention, after he had adamantly and unequivocally opposed Trump during the primaries.  They called him a coward, a “finger-in-the-air politician” who was shamelessly chasing popular opinion.

The Senator pressed the intercom button on his desk, and a moment later Sofia Chesterfield, his trusted aide, appeared at the door.  Rubio gestured for her to take a seat across from his desk.  He remained silent until she was seated.  She saw the headline on the newspaper he was still holding, and looked concerned.  He noticed her expression, and set the newspaper aside.

“The press bought it,” he began.  “And this morning I heard from the man himself — he wants me to introduce him at the convention.  I’m supposed to try to get him back in the good graces of the Mexicans, or something like that.”

“Are you sure you want to do this?  I mean, go through with this?” Sofia asked.

“I talked to Ryan and Priebus.  They’ll cover for me.  It’ll be OK, eventually.”

“Sir, I’m not sure I can do this.  I mean, I’ll support your decision, but I don’t know if I can be a part of this.  I think there’s going to be fallout.”

“If you want to resign, I’ll write you a glowing letter of recommendation.  You’ve done a superb job here.  You won’t have any trouble getting another job.  But before you go, I’d like you to help me set up a meeting with Jon Favreau and Gregory Bell.  I’d like their help with something.”

Sofia noticed that he was smiling.


Carolina Panthers still optimistic about Super Bowl rings

Wednesday, June 8th, 2016

Despite scoring fewer points than their opponents in Super Bowl 50 on February 7th, many of the Carolina Panther players and fans remain optimistic that their team will receive the Super Bowl rings that will be awarded on June 12th, in a ceremony in Denver.

“We know we didn’t outscore [the Denver Broncos] back in February, and most of the other statistics weren’t in our favor,” wrote an anonymous spokesman, “But we feel confident that the ring makers will ignore that and take into account that we are a better team now, and will be going forward into the coming season, particularly now that Peyton Manning has retired.  What happened back in February shouldn’t rule us out from winning in the end.”

Panthers fans, even more than the players themselves, are vehement that the Super Bowl rings should be awarded to the Panthers, rather than the more likely outcome, as reported universally by the corporate-owned mainstream media, that the rings will be awarded to the winners of the Super Bowl.  Their outrage was summed up by blogger #StillPanthers:

“The Broncos won on the field, on paper, and especially in the press, but we simply don’t trust them.  The Broncos were favored all along by the establishment.  There’s something really fishy about how Manning recovered at the end of the season — really fishy.  And some of those calls?  The only possible explanation is that the officials were rigging the game.  We will be vindicated in the end.  Our struggles continue.”

A small sample set

Sunday, March 8th, 2015

Later today, my daughter will compete in the US Gymnastics Association state championships for Massachusetts, as she has done for the past two years.  She qualified for the state championships in her first year as a gymnast — a bit of an accomplishment — and has qualified again each following year, each time at a higher level (although thanks to the confusing reworking of the rating system two years ago, this means that technically she repeated a numerical level when they renumbered nearly all of the skills).

Most parents would probably wait until they see the scores come out later today before they decide whether to boast about their child’s performance, or whether to let it pass without mention on facebook and other venues where modern parents share the triumphs and travails of their children.  I’m not like most parents, however.  I think I have a lot to be proud of already, even if she stumbles during her routine or the judges give her a low score for faults that are invisible to my non-expert eyes.

Competitive gymnastics is set up like most sports: at the beginning levels, almost everyone goes home with a trophy or a medal, sometimes for doing little more than showing up in a leotard.  The notion is that the competitors will be discouraged if all they ever do is lose.  It doesn’t help the sport if you have a competition with 50 kids and 49 of them feel bad at the end.  You need those 49 to feel enough encouragement to stick with it long enough to see whether they can improve.  If nothing else, the girl who won the blue ribbon needs to have those 49 other girls nipping at her heels, to challenge her to continue to improve.

The ranks start to thin out quite quickly, however, particularly at the older age groups (and my daughter, at 12, is one of the older girls at her level in the league).  It gets harder to win a medal at each level, and it gets harder to qualify for the states.  Two years ago, I think everyone on her team at her level qualified; this year, only about a third of them did (by my guess).

When I was a kid, I did competitive swimming, which is very different from gymnastics in some important aspects.  For several years — virtually all of my competitive career — I swam the same races.  I got stronger and I learned new techniques, and as a result I got faster, but the description of the events never changed: dive in and swim a certain number of lengths of the pool, using a particular stroke or combination of strokes.  Gymnastics is different; at each level, you need to master a new set of skills.  You don’t just do the same routine at each level — it’s different each year.  Doing the same routine as you did last year will get you disqualified.

That’s why I’m proud of my daughter.  Last year, she had a hard time doing a kip, and now it’s second nature.  A year ago, she couldn’t do a cartwheel on the beam, or an aerial, or a back handspring tuck, but now she can.  It wasn’t always easy, and she struggled with some of these skills, and the conditioning was hard, but she kept going, working toward her goals.

Whether she does well today is almost beside the point.  Her performance on a given day, and the scores awarded by a small number of judges, is a small sample set.  If she scores well, that’ll be nice, but it doesn’t capture how much progress she has made.  By showing up at every practice, working hard, and sticking with it, she’s already accomplished everything I could ask of her.

On shoulder surgery

Sunday, February 22nd, 2015

I recently had shoulder surgery, and found the experience and its effects quite a bit different than I’d expected.  I’ve therefore decided to share my thoughts about these experiences and provide advice to anyone facing a similar procedure.  Unlike my usual blog postings, which are generally intended (with varying results) to amuse, this posting is intended to be informative, and perhaps even didactic.  I’m going to tell you the things I wish I’d known ahead of time, along with a few things I knew but didn’t really take to heart.  It might not be humorous, but it might be useful.

I must begin with an important list of caveats: there are many reasons to have shoulder surgery; there are many different procedures that your surgeon might choose to perform; and there are many possible outcomes and followup treatments.  I am in no position to offer any medical advice about what might be best for you.  If my advice differs from that of your surgeon, physician, physical therapist, or other medical professional, you should probably take their advice — they’ve probably done this dozens or hundreds of times, and I’m in the middle of doing it for my first time.  Similarly, if your experiences differ from mine, the differences are most likely to be explained by the differences in procedures and ordinary variability in outcomes, and you shouldn’t interpret it to mean that something went wrong with your surgery.  Your mileage may vary, as they say.

If you think there’s anything missing or incorrect about my advice, please let me know!  You can email me at  (You can also leave a comment below, but with all the procedures I need to use to keep the spammers from overrunning this site, it’s a bit cumbersome for non-spammers to register and leave comments…)

You can’t do this alone

The most important thing you can do to prepare for shoulder surgery is find someone, or a rotating team of people, to take care of you for at least a few days, if not longer.  You will be quite helpless for a few days after the surgery, and somewhat helpless for perhaps several additional weeks.  You will need someone to help with all sorts of things — things that require using two hands, or flexing your shoulders in certain ways.  The list of such things is much longer than most people will guess.  You don’t require 24/7 attention, but there are simple things that you will not be able to do for yourself, at least not in the usual way.

  • Dressing/undressing yourself.  See notes below about clothing.
  • Cooking/cleaning up after meals.
  • Shaving, bathing (particularly toweling off afterward).
  • Laundry.
  • Driving.

You’ll be surprised, amazed, and dismayed at how many activities you think of as requiring one hand actually require two.  That other hand might be doing something simple — like holding something you’re trying to cut — but essential.

If you live in an area that gets snow, you’re going to have to find someone to shovel the snow for you — hire someone, if necessary.  It would not be wise to attempt any shoveling or attempting to wrestle with a  snowblower any time soon.

Even if you’re a total masochist, and hate to rely on anyone, there’s no way you’re going to get the bandages off by yourself.

Don’t (always) think for yourself

In addition to the errands your helper(s) will going to run for you (picking up prescriptions and groceries, etc), you also might need someone to help you think and remember things.  When you get out of your surgery, the surgeon will probably tell you all sorts of interesting and useful things about how it went and what to expect, not properly taking into account that you’re still dopey from all the anesthetic and won’t remember more than 10% of the conversation in an hour.  Then he or she will schedule a follow-up appointment or two with you, and give you an appointment card, which within two hours you will forget ever existed.  You need someone whose brain is fully functional to make note of any special instructions that the surgeon gives you, and makes sure that followup appointments get on your calendar, etc.  You’re asking for trouble if you expect to have your wits about you until the fog of anesthesia has completely lifted…  and after it does, you might be sleep-deprived for a while, which isn’t much better.  It’s a good idea to have a brain-buddy to keep track of things.  It’s a good idea to have someone go to the follow up appointments with you and take notes.

I’m going to repeat that for good measure — you are going to be sleep-deprived.  You will forget things, and you may make bad decisions.  Another person can help.


I didn’t tell a lot of people about my surgery ahead of time, and before I had shoulder surgery, I didn’t know many people who had had a similar procedure.  After I had the surgery, and it became impossible to hide that I’d had the surgery done, it seemed like people who had advice about shoulder surgery, either first-hand or from someone close to them, were everywhere.

If you tell people that you’re going to get this surgery done before you have it done, you’ll probably find yourself with lots of good advice that I never got.

Wear loose-fitting clothing

In the day-of-your-surgery instructions, it said to bring a loose-fitting shirt of some kind to wear after the surgery.  This is more important than you might think, and requires some prep.  I think it’s perfectly reasonable to acquire a new shirt for this specific purpose; a shirt that you might never wear again but will be happy to have for the few days you need it.

If you’re anything like me (tall, broad shoulders, and more than a little bit roly-poly) then the idea of a loose-fitting shirt may seem strange, so you might have to order something from big-and-tall shop or an athletic supplier — maybe one of those shirts that football players wear over their pads, perhaps.  For people who are of more ordinary dimensions, a shirt one or two sizes larger than normal is probably adequate, but don’t skimp.

If your procedure is like mine, here’s what’s going to happen to the shirt: after the procedure, they’re going to put an enormous bandage on your shoulder, and your shirt is going to need extra space in the shoulder and arm area to fit over this bandage, and getting the shirt arm is going to take some extra maneuvering room because your arm is going to be completely immobile.  Then you’re going to wear the shirt for the next few days, because it’s too much effort to take it off, and in the meanwhile your arm and shoulder are going to swell up quite a bit.

Long story short, I wore my largest, loosest-fitting shirt, and after two days I was seriously considering cutting it off my arm with scissors because it was uncomfortably tight and I believed it was beginning to cut off the circulation to my forearm.

I recommend a zip-up or quarter-zip hoodsie.  Or maybe a large bathrobe.

More loose-fitting clothing

Sweatpants or other pants with an elastic waist are a good idea for the time when you’re lounging around the house.  The benefit is that you can dress yourself (and use the toilet) without assistance.  Perhaps this is specific to my shoulder injury, but the motions of fastening buttons on my pants (or zipping my fly) and tightening my belt were just impossible.

More on clothing

Although most people I’ve heard from about shoulder surgery have been men, it’s not unheard of for women to get shoulder injuries as well, and women have an additional issue that men do not: bras.  If you normally wear a bra, you’re not going to be able to wear it after a serious shoulder injury and/or surgery, and figuring out how to unhook it when you do wear one might present new challenges — a front clasp might help.  I don’t have any concrete advice about how to deal with this, but if you’re a woman you probably have an idea or two.

A comfy reclining chair

One of the most difficult things for me to do after my surgery was sleep, despite the fact that it’s the thing I wanted to do more than anything else.  It’s difficult to find a comfortable position, and even more difficult to get into that position, because hard to get into bed or move around in bed without using your shoulder.

I do not have a recliner, but what I’ve heard is that they’re the best approach — especially the ones with the electric motors that raise and lower the chair.  You probably want to have pillows and blankets of various sizes to help hold your body in the right position — whatever is comfortable.

If you don’t have a recliner, at least try to sleep on a reasonably stiff mattress.  If you have one of those memory foam things, remove it for a few weeks.  I find that the softer the mattress, the more difficult it is to roll over and to sit up, because I sink in to it.  You’ll have a hard enough time moving around to begin with, and if you’re fighting to get out of a hole you’ve sunk down into, you might find it almost impossible.

Your experiences may vary — they almost certainly will.  The important thing is to find a way to get comfortable, which may require some inventiveness.  I recommend having a lot of pillows of various firmness and sizes available so you can construct whatever sort of support you need.

My physical therapist has told me several times that the first person to figure out the ideal way for people to sleep after shoulder surgery will be richer than the dreams of avarice.  I understand why.

A nightstand

Because getting up is going to be challenging for the first few days, you are going to want to have a few things closer at hand than usual:  tissues, reading glasses, books, e-reader, something to drink, telephone, snacks, medications, etc.

Some of the medications you might be prescribed should not be taken on an empty stomach, so it’s good to have them at hand, even if you wouldn’t ordinarily dream of eating in bed.

Household prep

Put new batteries in the TV remote.  You’re not going to be able to do this one-handed.

Vacuum.  Clean up.  This might be your last chance for a while.

One reader suggests getting a block of foam and cutting out slots for your smartphones, tablets, and other gadgets.  The idea is that this will make it easier to deal with these one-handed: put the gadget into the slot, and then it’s held steady and immobile so you can insert the power cable much more easily.

Pain management

Pain management is one of the things that is most likely to vary from person to person, from what I’ve been told.

The pain wasn’t horrible for me.  Annoying, but not agonizing.  It was enough to keep me from sleeping well, however, and it’s unhealthy when things interfere with your sleep over long periods of time.

I was given a prescription for hydrocodone, which didn’t seem to do anything to dull the pain.  (I suppose I could have tried a higher dosage, but at the recommended levels it didn’t seem to have any effect.)  I’ve heard that this is not unusual.  Pain killers are good for certain kinds of pain, but “bone pain” (if there is such a thing) isn’t one of them.  Fortunately, ordinary over-the-counter ibuprofen seems to help, and even-more-ordinary ice packs help even more.

Don’t get addicted to painkillers.  Those opioids will literally kill you.  Use what you need, but having a prescription for painkillers is not an excuse to get recreational with them.  As you’re reading this, you’re probably thinking to yourself “of course I’m not going to do anything as totally fucking stupid as that” and you’re probably right.  But after two weeks of not being able to sleep for more than a few minutes at a time, you may see things differently.  That is when people start to do totally fucking stupid things.

Ice bags

If your fridge doesn’t have an ice-maker, figure out some other way to stock up on ice.  Consider getting a special-purpose ice pack for your shoulder.  Start icing as soon as you get the big bandage off.


It’s good to have something to pass the time after your surgery.  Books are good, but only if you can do them one-handed.  I find an old-fashioned Kindle to work well (the kind with the button to flip the page, instead of the swiping motion).  Having some sort of or lap-desk thing might help.  (Some people are comfortable holding a book in one hand and turning the pages with a thumb, but if I do this for more than a few hours it provokes tendonitis, and more joint problems are something I just don’t need.)

Save something to binge-watch on Netflix or whatever streaming video service you like.  Something brainless.  Laughter is the best medicine; Archer got me through some tough hours, but again your mileage may vary.

After the surgery

Chances are good that you’ll be intubated during the surgery.  In simple terms, they’re going to snake a tube down your throat to make sure you can breath.  The problem is that in some cases, when they snake the tube down your throat, it requires a little force, leaving small scratches, which feels like a sore throat and can cause you to cough up small amounts of blood.  (This is the sort of thing you should definitely call your surgeon about, if you experience it, but it’s not uncommon and you shouldn’t panic immediately.)

You want to take this into consideration when figuring out what to eat for your first few meals after the surgery.

Don’t be an idiot like me and eat a handful of tortilla chips the minute you get home from the hospital.  You might regret this very much.


Stop using the sling as soon as you can.  You’re not trying to get exercise yet, but you want to start moving the shoulder a little bit.  Don’t let it get frozen.  Keep it loose.

Of course, if your surgeon gives you a shoulder brace or immobilizer, then that’s a different story.  Do whatever your surgeon says; mine said to lose the sling as quickly as possible.

Don’t throw away the sling, however.  Bring it everywhere you go.  It’s very handy when you’re interacting with people who ordinarily want you to hold doors open for them, or shake hands, or pass them something, or otherwise expect you to do something with your shoulder that you’re just not ready to do.  Nobody is going to give you a welcome-back-from-your-surgery hug when you’re wearing a sling, but if you’re not wearing a sling and your arm is just hanging down at your side, then your injury is, for all practical purposes, invisible.  A sling is a convenient way to let people know that you’re not yourself yet.

Body glide

My arm swelled up to the point where the skin in my armpit was rubbed raw, because there was so much pressure on it when I moved my arm.  This just added to my misery.  Blisters on your pectorals from your biceps rubbing against them is even less fun than it sounds.

There is a product called “Body Glide”, which is probably available at your local pharmacy or market, that helps with this.  It’s meant for runners or other athletes who have problems with body parts rubbing together on long runs or whatever; there are probably similar products with other names, but this is the one I used.  It was very handy for a few weeks while the swelling abated.

Do the physical therapy

You’re going to ask yourself questions like “Does it really matter whether I do shoulder rolls six times a day or seven?” or “Why should I swing my arm back and forth every two hours?  It doesn’t seem to do a thing.”

Do them anyway.  Just do them.  It might seem like nothing is happening, but it is.  The progress might be so slow that it doesn’t seem like progress at all, and some days are going to be worse than the day before, but in a month or two you’ll find yourself doing things that seemed impossible just a few weeks earlier — first it will be small things like scratching your own ear, or putting on deodorant, but soon it will be major things.  Before you know it, you will stop thinking about your shoulder all the time and start using your arm and hand without wincing in anticipation.

Recovery is the hardest part.  The surgery is the simple part; you slept through it.  Keeping with the program of exercises and stretches and whatever else your physical therapist specifies is the hard part.  Keep with it.



Friday, February 20th, 2015

It was my turn to cook the dinner for Chinese New Year this year.

We didn’t want anything too elaborate.  It was already a busy day.  Most of the traditional foods, therefore, were omitted.

At 7:15 I began by mincing an ounce of fresh ginger, and then placing it in a small glass bowl and combining with rice wine vinegar, soy sauce, a touch of white pepper, and a dash of sugar. I wanted to let the vinegar work on the ginger for a while, so that the flavor would infuse the liquid. I would have chopped some scallions to add to the mix, but I had none on hand.

Then I dinked around on fb for a little while.

Around 7:40, I started a large pot of water boiling, and then started to clean a pile of Chinese broccoli. I then removed the stems, separating them from the leaves, and set each aside in different bowls. I cut the stems into two-inch segments.

Around 7:45, I heated a small amount of olive oil in our large wok. When it was hot enough to make water dance, I added the broccoli stems and stir-fried them for a minute, and then added a bit of sriracha sauce, and then a few lumps of black-beans and garlic sauce. When the sauce had liquified, I reduced the heat and added a few ounces of water to the wok and covered it for a few moments to let it steam. After a few minutes of intermittent stirring, I placed the broccoli and reduced sauce in a covered bowl so it would not be cold by the time we sat down to eat.

Around 7:50, I heated a larger amount of corn oil in the wok, and then introduced the broccoli leaves, stirring them constantly until each leaf was coated with the hot oil.  I then reduced the heat, added a bit of salt and fresh black pepper, and a small amount of fermented black bean sauce.  I let it simmer for a few moments until all most of the moisture was out of the leaves.

While the broccoli simmered, I started to heat oil in frying pan to cook dumplings.  We did store-bought dumplings this year; my wife didn’t want to go through the rigamarole of making them from scratch.  It’s the sort of thing that requires time from the whole family, at least in the incompetent labor-intensive way we make them.

I removed the broccoli from the wok and place it in a second bowl.  I then lined the frying pan with pork and shrimp dumplings and covered the pan while it slowly heated up.

By this time, the pot of water was at a steep boil.  I added a dollop of oil and a dash of salt to keep the dumplings from sticking, and then dumped in a bunch of chicken dumplings.  (My older daughter does not eat pork, and she prefers her dumplings boiled instead of pan-fried.)  I then increased the heat to bring the water back to a boil, and then turned my attention back to the frying pan.  I checked every minute or so to see whether the dumplings had started to brown on the bottom, and whether the oil was getting too hot.  When the dumplings started to show signs of browning, I added half a cup of water, which made its usual dramatic sizzle, and then covered the pan to let them steam.

I checked on the pot.  It wasn’t boiling again yet, nor were the dumplings floating yet.  I stirred them gently to make sure they weren’t clumping together too much.

After a few minutes, the water from the frying pan had mostly evaporated, and the skin of the pan-fried dumplings was soft.  I added a second half-cup of water and let them steam a little longer.

My older daughter finished setting the table and poured drinks for everyone.

Soon the dumplings in the pot were starting, one by one, to rise to the top, and the water neared boiling.  I added a cup of cold water and waited for them to boil again.  In a few minutes, they were ready to serve.  I fished them out of the water with a slotted spoon and placed them in a serving bowl, and them placed them on the table, in front of my older daughter’s place.  She sat at the table, eying them hungrily.

I removed the cover from the frying pan and let the last moisture evaporate from the pan.  As it started to sizzle again, I turned off the heat and placed them in a serving bowl.

At 8:15, my wife and younger daughter had come home from gymnastics and were washing their hands.  As they seated themselves, I placed pan-fried dumplings and the ginger sauce on the table.

Then we feasted on the dumplings and broccoli.

At approximately 9:00, my wife lamented that she had forgotten to tell me that she’d also bought some dragon fruit.  I guess we’ll have that tonight.

Agent Carter of Mars

Sunday, February 15th, 2015

I expected to like the television show Agent Carter.  At first glance, it appears to have all the ingredients of a television show that I would make an effort to reserve space for on my DVR — it takes place in the Marvel Universe; the apparent storyline is woven around events of importance in that universe; the titular character, Peggy Carter, seemed promising when we saw her in the Captain America movies, and I’m a sucker for a period piece.  Honestly, I’d probably tune in just to see the postwar cars and clothing.

And I feel that I was probably expected to like the show for these reasons, and so perhaps the writers and producers thought that was enough and didn’t bother to provide the real reason people like me watch these shows, which is because we find the characters interesting and want to learn more about them.  An essential, proven element in a superhero tale is the origin story.  What makes the hero willing and able to the things that he or she does?  What makes them different?  What inner conflict motivates them?  Who are they?  Why should we care what happens to them?

None of these questions have been addressed about Peggy Carter, not even glancingly.

In Agents of S.H.I.E.L.D, the other show that shares the timeslot with Agent Carter, there is a similar situation — we don’t know much about most of the main characters, particularly Skye.  But unlike Agent Carter, Agents of S.H.I.E.L.D uses this mystery as motivation, and most of the episodes so far have revealed, in at least a small way, some important information about at least one of the characters.  The characters are interested in each other and we watch them reveal their pasts — or have the secrets of their past torn away.  We’ve known since early in season one that Skye is some sort of space alien mutant star child, but deep into season two we still don’t know whether this is a good thing or a bad thing.

Peggy Carter isn’t interesting.  Nobody is trying to find out more about her.  There’s only one character — a waitress in a diner that Peggy frequents — who even seems to have any interest in her as a human being.  We don’t know where she’s from, besides having a sort of watered-down British accent.  We don’t know if her parents are living or dead, or whether she has any siblings.  We don’t know where she went to school, although this would probably be interesting because she seems remarkably well educated on many subjects and is fluent in a surprising number of languages.  We don’t know how or why she entered the military, or how she ended up attached to an American unit, although again this would probably be interesting.  We don’t know why she chose to return to New York City after the war, since she appears to have no friends there and she was only stationed there briefly during the war — why didn’t she return home and work for an agency like MI-5 that might better appreciate her talents?  We don’t know where she picked up her extraordinary hand-to-hand combat skills — the sort of skills that would typically require many years of dedicated effort (starting long before the war) to acquire, or some sort of latent supernatural ability.  Either way, it’s conceivable that there’s a story there, and we’re not hearing it.  She could be from Mars, for all we know.

And there’s nothing to suggest that we are ever going to learn more.  Unless there’s a sudden change in the narrative, Peggy Carter has the unenviable role as the least interesting, most predictable person in her own show.

The truly broken thing about this situation is that the writers haven’t completely abandoned the concept of the origin story — they just haven’t given Peggy one.  They’ve teased us with tidbits of the backstory of Jarvis, Howard Stark’s butler, who has also shown something resembling character development.

Maybe they’ll do a show about him.

Winter weather

Monday, February 9th, 2015

The current string of snowstorms we’re experiencing around Boston has reached historic proportions — I supposed it’s possible that people will compare future snowstorms to the weather of this month for years to come — but this isn’t the worst or most disruptive snowstorm I’ve lived through.  And it certainly isn’t the most magical.  That title seems secure.

Perhaps it was the same storm as the Blizzard of ’78.  It was around that time, but I don’t remember precisely.  In any case, if it was the same storm, I experienced it differently because at that time I lived far from Boston.  Instead of deep, drifting snow, the storm began with rapidly-falling, heavy snow, followed by a brief period of heavy rain, clearing skies, and then temperatures falling to well below freezing overnight.

The next morning, everything looked glazed, in the most literal sense.  All edges were smoothed by a coat of ice.  The glare of the sun was brilliant across the empty fields, their features smoothed away by a foot of snow and ice.

The coat of ice on top of the snow was strong enough that I could stand on it, and it was so slippery that it was challenging to keep my footing.  It was like walking on oiled glass.

Falling on the ice didn’t break the crust.  I tried breaking through the ice by stamping on it, but that didn’t break it either.  Similarly, the runners of our sled didn’t break through, which meant that the sled was unbelievably fast — and it was also very difficult to climb any hills to sled down, because it was so slippery.  I had to get down on all fours and climb the hills on my hands and knees, since the fabric of my pants and gloves provided more friction to the ice than my galoshes.  Hills that were scarcely taller than my own height would let the sled run for hundreds of yards.

I don’t know where the idea came from, but I’m going to claim it as my own.  It’s the kind of hair-brained, irresponsible thing that I would have done.  I looked at the rolling hills of the golf course behind our house, and I looked at the seemingly impenetrable crust of ice covering them, and I went and put on my ice skates and spent a magical day cross-country skating.



Wednesday, January 7th, 2015

When asked what sort of work he did, my father used to tell the following parable.

The employees of a certain company seemed to have low morale, and the president of that company desired to raise their morale.  The president asked one of his trusted lieutenants — a man renowned for his intelligence and integrity — to suggest how this could be accomplished.

The lieutenant prepared a thorough and well-crafted questionnaire about life at the company, and every employee dutifully filled out the questionnaire, answering every question honestly, frankly, and candidly.  The questionnaire was textbook neutral (as we all know, how a question is asked can have a profound effect on the answers!) and the resulting data set was beyond reproach.

Because this is a parable, however, the data set exhibited none of the interesting noise that one usually sees.

Exactly half of the employees complained about the cafeteria, and the other half complained about the lighting in their offices.  Nobody complained about anything else.

The lieutenant quickly assembled estimates for how much it would cost to address each issue, and found that both costs were exactly the same, and each cost was exactly what the president was willing to spend to increase morale.

As I’ve mentioned before, this is a parable, and I don’t want to distract the reader with details, so somehow all of these quantities are precisely the same.

At this point the lieutenant presented his results to the president, and the president decided, by flipping a coin, whether to improve the cafeteria or improve the lighting in the offices.  Or perhaps the president decided that since either choice only placated half his employees, neither was worth the price.

In either case, the decision was ill-informed, because it lacked perspective.  The lieutenant did not survey employees at other companies to establish a baseline.  What the lieutenant did not take realize is that (according to decades of data gathered by business consultants and legions of DBA students, and then carefully tabulated and interpreted by people like my father) it is simply part of the human condition to complain about the company cafeteria.  It is unusual for people to like the cafeteria, and if there’s some other issue that employees complain about as much as they complain about the cafeteria, that issue is verging on a crisis.

On the other hand, when employees complain about the lighting in their offices, it means that the lighting is terrible.  This is an unusual thing to complain about.

Given the proper perspective, it would have been obvious that the president should have had the office lighting fixed.

In short, my father’s profession was figuring out what “normal” is, which is much more subtle and complex than most people appreciate.

— — —

The author works for a company that has recently changed its office lighting and renovated its cafeteria in ways that he thinks were ill-advised and lack perspective.


Zombie mathematics

Sunday, July 13th, 2014

When the kids are out of the house for a few hours, and Netflix is in a cooperative mood, I am provided with a rare opportunity to catch up with popular culture by watching an R-rated film or television show. Today I finally got around to seeing World War Z, which Netflix kindly provided in its unrated form.

If you haven’t seen World War Z yet, then what you are about to read might spoil some of the aspects of the movie — but only if you don’t have any idea whatsoever what the movie is about and tend to watch movies without reading any of their reviews.  These are very high-level spoilers.

The Z in World War Z stands for “Zombie”, and it’s not really a war.  It’s more of a headlong flight.  The zombies strongly desire to bite people, and people who are bitten turn into zombies, who strongly desire to bite people as well.  Unlike most of the zombie movies you’ve already seen, or have avoided seeing, these zombies are not hungry (they don’t eat you — they just nip at you a bit) and they don’t stumble about in a slow shambling manner: these zombies are fast.  In fact, each zombie seems to be stronger and faster than the person he or she was pre-zombification, which makes it hard to outrun them, even if you’re not Danny O’Bigbelly.  I think even Milla Jojovich might have a hard time with these zombies.

The most important difference between these zombies and the canonical zombie from the scientific literature is how long it takes to become a zombie after being bitten.  In the movie, the transformation happens in about ten seconds.

This aspect is played up again and again: a small number of zombies can overwhelm a large number of people by converting those people into zombies very quickly.  There’s a particularly memorable sequence where the defenses of a large, well-defended city are breached by a handful zombies, and the city is overrun in essentially the same amount of time it takes for people to flee from one side of the city to the other.  By the time the fleeing populace reaches the opposite side of the city, they’re all zombies.

But is that realistic?

Fortunately, mathematicians have been thinking about problems of this sort for some time, and therefore we know how to answer this question.

Let’s say that you have a single zombie and a crowd of people at time T.  The people are constrained in their movements somehow (let’s say they’re on a moving bus, or an airplane, or something like that, just to spice things up).  The zombie attacks someone, and after some struggle, manages to nip him or her, say after ten seconds have gone past.  So at time T+10, there’s one zombie and one infected person.  In our model, the zombie is particularly diligent, and immediately attacks a second person.  After another ten seconds, the zombie manages to nip its second victim, and the first victim has become a fully functional zombie.  So at time T+20, we have two zombies, and one infected person.  The two zombies immediately attack two other people, and at time T+30, we have three zombies and two more infected people.  Oh, and people are probably running around screaming and whatnot, but we can ignore that for now and build a table of how things progress:

Time (s) Zombies Bitten
T+0 1 0
T+10 1 1
T+20 2 1
T+30 3 2
T+40 5 3
T+50 8 5
T+60 13 8

People who are familiar with Fibonacci sequences will recognize this immediately: the number of zombies at during the next time interval is the sum of the number of zombies from the previous two time intervals.  Even though Fibonacci’s original research was about vampires or rabbits or something like that, the theory still applies: if you have a number that increases according to a construction like this (i.e., creating more zombies by biting more humans, and more zombies can bite more humans), then it can be modeled as a simple recurrence.  In this case, the number of zombies at time X is equal to the number of zombies at time X-10 (the previous number of zombies) plus the number of zombies at time X-20 (the number of people bitten at that time, who will become zombies by time X).

Interestingly, as the numbers grow, the ratio between the number of zombies at each ten-second interval becomes closer and closer to the Golden Ratio (approximately 1.618034) which is ubiquitous in both art and nature — proof, if ever one was needed, that zombies are a fundamental property of our world.  Or maybe it’s vampires?  Probably both.

In any case, the fact that the ratio between the number of zombies at time X and X-10 is, for a suitably large X, approximately 1.618034, which means that the number of zombies is increasing by this factor every ten seconds.  So after a second minute has gone by, we will have increased by this ratio six more times, or a factor of a smidgeon less than 18, giving us 233 zombies.  So a full bus might last more than a minute, but at the end of two minutes, a zombie can work its way through a large airplane.  The passengers of a large cruise ship would be zombified in three minutes, with another ten seconds to take care of the crew as well.

Now, maybe I’m being too generous to the victims.  Most people wouldn’t be able to put up a fight for ten seconds, perhaps.  In that case, things would be much worse.  What if a zombie could run down and nip each of its victims in less time than it takes for the zombie transformation?  That makes the math a little more fun.

Let’s consider a simple case: it takes five seconds for the zombie to inflict its bite, and then another ten seconds for that person to turn into a zombie.  After five seconds, we have one zombie, and one bitten person.  After ten seconds, the bitten person is transforming, and the zombie has bitten another person. After 15 seconds, the transforming person is a zombie (so now we have two), the bitten person is transforming, and the original zombie has bitten yet another person.

It looks like this:

Time (s) Zombies Transforming Bitten
T+0 1 0 0
T+5 1 0 1
T+10 1 1 1
T+15 2 1 1
T+20 3 1 2
T+25 4 2 3
T+30 6 3 4
T+35 9 4 6
T+40 13 6 9
T+45 19 9 13
T+50 28 13 19
T+55 41 19 28
T+60 50 28 41

It isn’t the canonical Fibonacci sequence, but with a little observation, we can see that it’s a different Fibonacci sequence.  The number of people bitten at time X+5 is the number of zombies at time X, and the number of people transforming at time X+5 is the number of people who were bitten at time X, and the number of zombies at time X+5 is the number of zombies at time X plus the number of people transforming at time X-5, which is the same as the number of people who where bitten at time X-10, which is the same as the number of zombies at time X-10. This gives us a recurrence that we can use to solve for the number of zombies five seconds from now, if we know how many there are now and how many there were ten seconds ago:

Zombies at time X+5 = (Zombies at time X) + (Zombies at time X-10)

For a person trapped in a confined area with a zombie and a group of other people, this is a bit of a problem.  After one minute has gone by, a single zombie has become 50 zombies, with an additional 69 people well on their way to being zombies.  The number of zombies grows by a factor of 50 every minute.  At this time, there are approximately 6 billion people on the planet (give or take), and 6 billion is about 20 * 50 * 50 * 50 * 50 * 50 , which gives humanity  a smidgeon more than five minutes to sort things out, assuming that all of humanity is clumped within a five-minute run of the position of the first zombie.

Fortunately, these numbers are bit pessimistic for a number of reasons.  First, people are dispersed, and tend to flee, making it impossible for zombies to find unbitten people to bite as quickly as used in our model. This is good news for people in Montana, or who live on small islands, but if you find yourself sitting next to a zombie in coach on a long flight, it’s not very comforting.

Second, some people fight back, which both reduces the number of zombies and lengthens the time required for a zombie to overpower a victim and bite him or her.  The bitten do not always succumb; some, knowing full well what is about to happen to them, choose to destroy themselves instead.

And finally, there is a crowding issue; once the number of surviving humans drops below a certain percentage of the number of zombies, the zombies tend to get in each other’s way in their zeal to chase down the remaining humans.

There are a number of analyses we could do: if the victims fought back with a given probability of killing a zombie during each time period, how would that change things?  How should people disperse themselves in order to form the most effective zombie-fighting units?  Does it matter which weapons are available?  The ancient phalanx formation is an example of an arrangement that permits the most offensive advantage for a given defensive perimeter, exposing very few people to be bitten while protecting them with the maximum number of spears.  But spears and interlocking shields are not something everyone has, unfortunately, and we need to fight the zombie apocalypse with the weapons we have, not the weapons we want.

If the humans are able to alter their tactics by working in teams to quickly dispatch the singleton zombies that try to attack them, they might survive for a considerable period of time.  The zombies, of course, might also alter their tactics so that instead of attacking by ones and twos, they could attack in a coordinated manner to increase the likelihood of converting more people quickly, before their attack is rebuffed.  It’s clear that zombie attacks are not effective if they are nipped quickly in the bud, but if the exponential infection rate gets a handhold, the zombies are going to win.  This is the sort of thing that mathematicians think about as well, with applications to many fields.

This is all very interesting, and I plan to spend some time thinking about how the different scenarios might play out.

I’m certainly not going to be falling asleep any time soon.

A sleeping baby

Thursday, May 15th, 2014

I have a number of friends who have very recently been, or shall very soon be, blessed with the birth of their first child. This seems as good a time as any, therefore, to tell the story about how I used to put my younger daughter to sleep in her crib.

Every night for more than year, we followed the same ritual.

After all the usual preparations — diaper, story, singing, etc — I would dim the lights and carry her to the crib. Carrying her in a horizontal attitude, with one hand under her rump, thighs, and lower back, and the other cupping her head neck, and shoulders (she was tiny, and I have large hands), I would lower her slowly and with great care until she was on her back on the mattress in the crib. As I lowered her, she would raise both arms up over her face until her hands were resting on her forehead. During this entire process, we maintained eye contact. At approximately the same moment that her heels touched the fitted sheet, she would close her eyes, and immediately fall asleep. I would let go and gently pull my hands out from beneath her. Then I would confirm that the baby monitor was on, and quietly leave her room.

Then I would have several hours of peace and quiet before she woke up.

The reason why I’m telling this story now is in the hope that some of my friends who will soon be putting their own babies to sleep for the first time will read this story and understand that it it is perfectly natural for new parents, over the course of the next year or two, to feel insanely jealous of me.

Sourdough honey bread

Tuesday, May 13th, 2014

I’ve been making sourdough bread for a few weeks, experimenting with various techniques, and using a starter that I created myself. I’ve been using my coworkers and friends as a convenient and green way to dispose of the results, with glowingly positive results. People have begun to ask me for the recipe, and even some of my starter.

For the sake of convenience, I’m going to post the basic Danny O’Bigbelly Sourdough Honey Bread recipe here.

If you don’t have your own sourdough starter, let me know and I’ll try to set you up.

Just to fend off the inevitable question: this recipe is not gluten-free. In fact, it’s almost entirely gluten. I don’t think more gluten could be added. Now, I’ve heard rumors that it’s possible to make bread without using gluten, and I do acknowledge that it is amazing what science can accomplish these days, but I’ve never tried my hand at that kind of alchemy.

Note that you’ll need a scale in order to follow this recipe. If you don’t have a scale, you can probably wing it, but I don’t recommend it. I recommend that you get a kitchen scale. Once you own one, you’ll find yourself using it all the time. It can even be handy for cooking.

In a large glass bowl, combine 100g of sourdough starter, 100g of warmish (not hot, and not cold) water, 30g of honey, and 3-5g of salt. Mix gently until the ingredients are completely blended. The general appearance will be somewhat disgusting, but get over it.

Add 200g of bread flour. You can use ordinary all-purpose flour if that’s all you have on hand. I’m not sure whether the difference between bread flour and all-purpose flour can be determined without the assistance of Walter White, but there’s no question that the bread smells and tastes better when made from ingredients that require a special trip to the store.

Gently mix in the flour. Any sudden movements at this point will dust the surrounding area with flour, which can be detected by all ants and cockroaches within a three-block radius. A word to the wise.

I like to use a steel dessert fork for mixing the dough, since it’s short and stubby, and soon the dough will become a sticky, awful mess of goo. Note that it is normal and expected that the dough be somewhat stickier and tackier than the dough or ordinary bread made with baker’s yeast: sourdough has a different consistency. Don’t add more flour to try to make it less tacky. You will ruin everything. Trust the scale.

Because the dough is tackier than ordinary bread dough, I don’t recommend kneading it by hand. Whenever I do this, half the dough ends up stuck to my hands and the working surface. Working the dough with a dessert fork works well for me.

There are various rules of thumb about when the dough is ready: for example, when it stretches out a certain distance without breaking, or the strands separate a certain way. My rule of thumb is that when I get bored and my hand starts to ache from trying to drag the fork through the goo, it’s probably good enough. It always comes out the same anyway.

Dribble a little olive oil (a tablespoon or so) into the bowl and roll the dough around in it until it is coated on all sides.

Grease a bread pan, sprinkle it with corn meal, and then plop the dough into it and cover it. Place in an oven with the light on (to warm things up a little) and go do something else for 6-10 hours.

The technique of covering it is one that I still have not perfected. The easiest thing is to drape some plastic wrap over the top of the pan, but if the dough rises enough to touch the plastic, it will stick to it like glue and detaching the dough from the wrap will cause trauma to the delicately puffy dough, spoiling the otherwise pillow-like shape. What I’ve done recently instead is to put the bread pan into a larger dutch oven. I’ll explain later why this might have an additional benefit.

I don’t recommend punching down the dough in the middle of this process. This dough is going to be relatively slow-rising to begin with, and punching it down in the middle just makes it even slower. Still, it’s a free country, and if you like punching dough, that’s none of my business.

When the dough appears to have stopped making any forward progress on rising, pop it in the oven at 350F for 45 minutes or until it looks done, whichever is more correct.

There are legends that say that the secret to a nice brown sourdough crust is in exposing the crust to steam when baking. If you’re using the dutch open technique, this is simple to do: pour half a cup or so of water into the bottom of the dutch oven, and put the lid back on before putting the whole thing in the oven to bake. The water will boil, and you’ll have a few minutes of steam, which should help.

Personally, I like my sourdough on the pale and soft side, so I usually don’t bother.

After removing the bread from the oven, let it cool for at least 30 minutes (depending on the properties of your bread pan, it may be shorter or longer) and then shake the bread out of the pan.


Sunday, May 4th, 2014

A lot of people in my department have things that once belonged to Charlie.

A while back, part of my group moved to offices on a different floor of our building. I was acquainted with the woman who was going to move into my old office, so I asked her if I could leave some of my plants on her windowsill until my move was complete. I wanted to move them myself, rather than have the movers do it, because the plants are fragile. I promised I’d come and fetch them first thing the next day.

The next morning, I saw another pot on the windowsill next to my pots in my old office. In a four-ounce pot were four small groups of four leaves, each leaf no more than five inches long. They looked like amaryllis leaves, but were very small — I thought they might, perhaps, be paper-whites. The new occupant of my office noticed my curiosity.

“I got those from Charlie,” she said. “I don’t think they’re doing very well. I always forget to water them.”

“What are they?”

She mentioned that they were the same kind of plant that another one of our co-workers had in his office, but she didn’t know the details.

“Your plants seem pretty happy,” she continued. “Maybe you’d like to take care of my plant? I’m probably just going to kill it.”

I took the plant, promising to try to care for it, and promising to return it later. I had room on my new windowsill.

Plant possession is often a transient thing in my office. When people change offices, their new office might not have enough light for their plants, or too much direct sun, and therefore sometimes plants stay with offices rather than move with their offices. I’d left a trail of plants behind as I moved offices — some cacti that only flourished on the southern side of the building, a jade plant that liked facing west, a few flowers that seemed to require a particular kind of blind to climb — and I’d picked up plants from other people whose new offices weren’t compatible with them. It wasn’t the first time I’d taken in a coworkers plant.

Now that I think about it, there’s not a single plant in my office that I actually bought. My plants are all refugees from other offices, and the plants I bought are all elsewhere, decorating other windowsills.

Later that day, I talked to the co-worker who allegedly had the same plant. He told me that it was indeed an amaryllis. This was useful information, because now I knew how to find advice for how to take care of the plants.

He also told me that he’d also gotten his from Charlie.

The office move continued over the next day; as offices were vacated, other people were moved into them, and as their offices were vacated, people were moved into them, and so on. As people packed their offices, items that hadn’t seen daylight for years came to the surface. One woman found a pile of puzzles tucked away on a shelf; she thought my children might enjoy them.

It turns out that she had gotten the puzzles from Charlie.

Later that day, I went up to my old office, curiosity piqued, and asked its new occupant who Charlie was.

Charlie had worked in the group before I joined. He had some unusual habits; you might describe him as eccentric, but in a positive way. His office had been filled with plants, toys, games, and puzzles, in addition to the usual collection of high-tech equipment. He was remembered very fondly.

One of Charlie’s eccentricities was that nobody seemed to know where he lived, and there was some speculation that he didn’t have a home phone. In any case, nobody knew how to reach him. What I was told is that one day he went to the hospital because he wasn’t feeling well; they ran some tests, and he went home to rest. When the results of the test came back, it turned out to be something very serious. The hospital tried to reach Charlie immediately, but Charlie was dead before the hospital could find anyone who knew how to contact him.

After his death, I imagine people in the department visiting his office and taking a small keepsake. Or perhaps they simply kept whatever plant or puzzle or book Charlie had already loaned them. By all accounts, he was generous, and liked sharing his toys. In any case, it seems like all the old-timers in the department have something that belonged to Charlie — something that they keep; something that never gets thrown away during the office moves, but something that they’re willing to share with someone else. Charlie’s mementoes are passed along, but never abandoned.

If you’re reading this, you’re using part of Charlie’s legacy. In a very real sense, he was one of the people who shaped what the Internet is. We’ll be using technologies he worked on for decades to come — but outside the network research community, it seems that few people knew of his work, or remember his name today, and when they do remember him, they don’t remember him primarily as an engineer. They remember him as a friend.

After a few weeks of sun and regular watering, the amaryllis started to grow new leaves. I repotted it, and let it grow. After several months, I repotted it again. The four bulbs, which had been the size of marbles when I repotted them the first time, were now the size of billiard balls. They were gnarled together and I didn’t try to separate them, but instead left them together. Last autumn, I repotted the bulbs a final time. (under normal circumstances, amaryllis like to be root-bound, and their bulbs reach a certain size and stop growing — so it seems likely that the bulbs won’t ever need to be repotted again, except perhaps for aesthetic reasons because their current pot is a bit ugly)

In the autumn, when the sunlight started to diminish and the air grew colder and drier, all the leaves began to wither. This is a normal part of the lifecycle of an amaryllis; they need to have a dormant period before each growing season. I tried to encourage the dormant resting period (a hardcore amaryllis grower will actually keep the bulbs in a refrigerator for a month or two), but in a few weeks, new leaves began to appear and I reluctantly returned the pot to my windowsill. I didn’t think that the bulbs could possibly be ready for another season already, but the leaves grew wildly, reaching almost a yard in length.

My (limited) experience with amaryllis is that they bloom immediately when they come out of their dormant period, and these plants were showing no signs of blooms. There were no stems at all.

Their owner had told me that Charlie grew these plants from seed. I knew that this was possible, but few people did this; from what I’d read, ordinarily they are propogated by bulbils. I’d heard that amaryllis seeds often do not produce flowers, so I was disappointed, but not surprised, to not see stems.

A few weeks ago, as I was tending to them, I noticed new stems growing up from two of the bulbs, joined a week later by a third. They have been growing ever since, and the stems are more than two feet long. Yesterday the buds began to open, and tomorrow, with any luck, I’ll finally find out what what color they’ll be.

I think people in my department will be delighted to see them.

Another look

Sunday, February 9th, 2014

You might have noticed that my blog looks a bit different today.

There’s a reason for that, and it’s a dull and boring one. There is no need to look for a hidden meaning in this, although I suppose there’s no harm in it either.

The hosting site that serves my blog decided recently to update a bunch of their software, with the side effect that some of the themes I use, and minor tweaks I made to my site software, no longer work, or work in some slightly different way.

I don’t know if it’s worth trying to restore them. The current functionality is adequate, although I miss the bright orange banner.

Gorilla Barilla

Friday, September 27th, 2013

Boycotting Barilla Pasta is a stupid, shortsighted idea. I shall explain why.

For those of you haven’t been reading the news below the fold, Guido Barilla, chairman and part owner of the Barilla Group, a global, privately-held, family-owned food producer with assets worth 3B euros and a yearly income, after all taxes have been paid, of more than 75M euros, is a jackass with antiquated views on social issues, which I will not dignify by describing here. It has been suggested, by people who don’t really think things through, that people who disagree with his views should boycott the products that make up a small percentage of his company’s sales.

Let’s imagine, for a moment, that the boycott succeeds beyond expectations: Barilla goes out of business tomorrow, and Guido never earns another cent, but instead is forced to live on his savings. The unfortunate man will have to make due with a mere billion or so. Perhaps, if things get really rough, he’ll have to sell off that Picasso he bought for $100M in 2004 — it might even be worth more today. $100M will keep the lights on for a while.

While the boycotters celebrate ex-Chairman Barilla’s early retirement, they might do well to also consider the fate of the other 14,000 employees of the Barilla Group, including the people who actually make the product, drive the trucks, and all the other things that need to get done and that the members of the Barilla Group board do not do themselves. They’re out of work, and they don’t have hundreds of millions of dollars to cushion their landings. They, and their families, are the ones who will suffer. Guido might be annoyed, but, as the song goes, he’s never going to know the joy of a welfare Christmas.

Puzzling behavior

Saturday, September 21st, 2013

This morning I finished a 1,000-piece puzzle that I’ve been working on, in spare moments (in short supply these days!) since Labor Day weekend. It probably takes me a lot longer than most people to do a puzzle like this because I don’t have enough table-top space in any one room to do the puzzle in one place; I have two small tables in two different rooms. I dump out all the pieces in one room and start to assemble them, and then take the assembled bits into the other room. When I get a fixed idea of what, say, the next ten pieces I need look like, then I go back to the other room to hunt for them, but usually I end up finding something else, etc. I can’t keep more than about a dozen puzzle pieces in my memory at one time, so there are many trips back and forth.

It also probably slows me down that I don’t spend much time looking at the box to see what the puzzle is supposed to look like. (In fact, back when my vision was better and I had more time, I used to enjoy doing puzzles upside down and then flipping them over to see what the picture was, a game invented and mastered by one of my grand-aunts.) My wife uses the opposite strategy — she spends a lot of time looking at the box and figuring out exactly where each piece goes, so she can put a piece exactly where it’s supposed to go even if she hasn’t found its neighbors. I don’t know where things go in the final image, but I know which pieces are their neighbors. I tend to do things like blue skies, snowy fields, and other monochromatic areas first, because anything that distracts my eye from the shapes slows me down. As I have mentioned before, my eyesight isn’t what it used to be.

I think my younger daughter uses the same sort of method as my wife, but it all happens too frighteningly fast to be sure. She can put together a puzzle of a painting in less time than it took to paint the original.

A side effect of the way that I do puzzles is that I tend to start at one end and fill in or expand out.  In this case, I started near middle of the puzzle, where there is a river in the image, and all of the pieces have a characteristic color. In the foreground, on the near side of the river, are some farmers, and a little past them, in the distance, are some people strolling along a river. Beyond them, there is a boat on the river. I finished this part of the puzzle — which contains all the people — by Labor Day. Today I finished the top part of the tree that dominates the entire image, and then stepped back and viewed the image in its entirety. I had been focussing so much on the tree that I’d almost forgotten about the people in the image.

p.s. I’ve done this puzzle before; you might have seen the photos I posted. You can find an image of the original work here. It’s a wonderful work and I’m thinking of buying a large copy to hang in our dining room.


Friday, August 16th, 2013

In the past few months, I’ve received an ever-increasing volume of requests to subscribe to this blog.  This would be flattering, if they weren’t all spammers.

If you do not have your own blog, or haven’t been doing this for a while, then your first thought might be that attention from spammers is a form of flattery, because it wouldn’t make sense for spammers to target unpopular or abandoned blogs.  You might think that they would only want to focus their limited energies on blogs where their spam would receive a wide, gullible audience.

My readership is neither wide nor gullible, but the spammers don’t care.  They are not even aware of my existence in any ordinary sense; their computers make all the decisions and do all the work, and it is so inexpensive to add another blog to their stable that economists aren’t sure whether it makes sense to try to measure it (yes, there are economists who study spam — as if the dismal science wasn’t already dismal enough!), particularly when the computers, network connections, and power are usually stolen anyway.    Their computers tirelessly scan the web, looking for blogs where they can post their undisguised advertisements.  I’m sure you’ve seen them: comments of the form “I think you are making a good point.  You might also find this interesting: (link to a site that sells something).”

Somewhat perversely — either due to a bug in their scripts, or perhaps due to a heuristic to prefer sites where the owner doesn’t seem to be paying attention — these scripts appear to target sites that have not been updated in a long time, and I suspect that this is part of the reason why I am seeing such an increase in “people” who want to subscribe and post comments on this blog.

Hence this posting.

L: a project

Friday, November 23rd, 2012

Today is my birthday.  One year from now, I’ll be 50.

Different people react in different ways to such milestones, and if there’s one thing on which people who know me universally agree, it’s that I’m different.  I’m probably not going to buy a convertible.  Instead, I’m going to write a novel.

I strongly believe that the success or failure of my effort depends on you, the reader, providing a small amount of help before I get underway.  The simplest and most direct form of help would be a short but compelling argument proving that this is a terrible idea that I should abandon immediately.  I am hoping for a different sort of help, however, but one that will require more thought on your part.

The strength of my writing, such as it is, is not in plot and character; it’s in exposition.  The stories I come up with on my own tend to be dry and uninteresting, but they are told in an entertaining manner.  Challenges given to me by other people (such as “write a story about a baby being fed, from the perspective of the spoon”) turn out to be more engaging than things that I come up with on my own.  They’re also a lot more fun for me to write, and, given my unusually high author-to-reader ratio, I think my own enjoyment should be given extra weight.

Please send me your thoughts.  They might be as simple as “name a character after me!” or as complex as “rewrite The Pirates of Penzance from the perspective of Sullivan’s deaf tailor.”  You can leave a comment here, or on facebook, or send me email (, or PM me on facebook or any one of a number of sites.

Preface to the Paperback Edition

Saturday, October 27th, 2012


Dorothy Parker is quoted as saying, in regard to a book with which she had spent more time than she desired, “This is not a novel to be tossed aside lightly.  It should be thrown with great force.”  I believe that she would hesitated to say the same thing about the electronic version of this book, because “deleted with great force” simply doesn’t sing with the same poetry.  Perhaps a twenty-first century successor to Dorothy Parker will extend the canon of criticism with new metaphors suitable to succinctly characterize self-published electronic books, but until then I feel that is is only fair to make my work available in a format that may be critiqued in familiar terms.

There are unquestionably many virtues that paper books possess that electronic books have not yet attained.  While good books are, with some unimportant exceptions, just as enjoyable in electronic form as paper, bad paper books lend themselves to uses that electronic books simply cannot. The worse a book is, the greater the relative benefit from owning it on paper.  Paper books make good paperweights and fly swatters; their individual pages may be used as kindling, to line birdcages, or as a repository of grocery lists, to-do-lists, or other quick notes; they can be used to level uneven furniture, prop up other books, or as coasters to protect more valuable possessions from the evils of condensation.  Physical books may be casually forgotten, lost, misfiled, or loaned to a forgetful friend in such a way that one may easily and plausibly deny ever possessing them.  In the limiting case, the simple joy of feeding the collected works of Dan Brown through a paper shredder, making a papier-mâché piñata with the resulting chaff, and delegating its destruction to a sugar-deprived mob of schoolchildren more than justifies the necessary carbon offset.

Despite the many virtues of publishing on paper, when I prepared the first edition of this book for electronic publishing, I believed that a paper edition was unnecessary; it seemed like the world of print on paper was already well past the verge of being replaced by the world of pixels.  A number of my potential readers, however, expressed their dismay with my decision, and made it clear that they would have preferred that I had published my book in an ordinary paper form.  Some believed that reading on a small screen would give them headaches; others mentioned the increased sense of emotional attachment they associate with physical objects, and a few even declared that they would not be happy with any embodiment of the book that I would not be able to sign personally for them.

This edition of “The Corrected Danny O’Bigbelly” is a response to my friends who regretfully declined to purchase a copy in electronic format, but who promised that they would purchase a copy if I made it available in paper form.  This edition would not exist without their kind words of badgering encouragement.  To those who purchase this edition, I hope it provides them with many hours of enjoyment.

For the rest of them, I’ve called their bluff.

Two years before the bell

Tuesday, June 26th, 2012

My term as President of the local Rotary Club ended this morning. Below is my farewell address, written at the last minute to fill an unexpected gap in the agenda.

– – – –

A bit more than a year ago, incoming District Governor Subbiah Doraiswami asked me for ideas for his installation speech. I shared a few ideas with him, but I didn’t think that it was likely that he used any of them verbatim for the simple reason that our personal styles differ so greatly. A year later, I have had time to refine my thoughts, and I’d like to take a few moments to share them with you this morning, as my last act as your President.

As we prepare for the installation of new officers and to write the next paragraph in the history of our clubs, our district, and Rotary International, I would like to take a moment to reflect on the past, the present, and the future of Rotary.

Rotary was founded on February 23rd, 1905, which is just a few months more than 107 years ago. Rotary was born in a larger world; a world where parts of the map had not yet been filled in. Let us take a moment and consider some of the changes that have taken place since then.

In 1905, the world population was approximately the same as the current population of China, and less than the current population of India.

The life expectancy at birth for an average person born in 1905 was less than 32 years; today it is approaching 70.

Cars were rare and expensive in 1905; the first Ford Model T was three years in the future.

Telephones were novelties and useful only locally; the first transcontinental telephone call was still ten years away.

Radios had been invented, but the first commercial and news broadcasts would have to wait another fifteen years.

The first practical antibiotics were more than twenty years away. Most of the people who were alive in 1905 did not live to see vaccines for measles, mumps, chickenpox, meningitis, polio, and many other common diseases. Many of those people died of diseases that are no longer familiar names, or considered a threat to anyone with access to basic medical care or medicines that are now available for pennies per dose.

In 1905, Albert Einstein published several papers that established a foundation for a remarkable number of developments in physics, electrical engineering, and materials science, and providing mankind our first deep understanding of the true nature of the physical universe.

Politically and socially, the world was different as well. The median age of an American in 1905 was 23; today it is more than 35. In the United States, women would not be able to vote until more than another decade passed, and some minorities would not be guaranteed a fair vote for another sixty.

There is little question that we have come a long way, and it is a simple fact that Rotarians have played some role in a surprising number of these accomplishments. There is also little question that there is still far to go. While we should take pride in the progress of the last century, let us not congratulate ourselves prematurely or lose our focus. May these accomplishments not serve as labels for the pinnacles of our achievement, but rather milestones along the way, evidence of a steady habit, practiced daily, with diligence, persistence, and patience.

Because there is still much to do.

There is still war in the world. In recent years we have seen tyrants toppled by cell phones and laptops instead of by guns and bombs, but there are people dying violently this very morning at the hands of other tyrants.

There is still disease in the world. We are very close to conquering polio, and have made a start on malaria, but there are new diseases, like AIDS, treatment-resistant tuberculosis, and widespread obesity, each virtually unknown a generation ago, that are as dangerous.

There is still famine in the world. There is still injustice. There is still inequality. There is still ignorance, prejudice, and hatred. There is still much to do.

Where shall we begin? I have a suggestion.

One the defining characteristics of Rotary is the inclusive nature of our membership. Although this has, admittedly, not always been true in the past, at the current time Rotary is remarkably inclusive and free from discrimination. There are Rotarians from every imaginable nationality, religion, political philosophy, ethnicity, and other demographic category. But there are people who do not fit the mold of Rotarians, whose philosophies cannot be aligned with the principles of Rotary, and who feel no desire to become Rotarians or to take part in the sort of work that Rotarians seek to do. Who are these people, and why must we concern ourselves with them?

These are people who believe that there is nothing practical that they can do that will make any lasting and positive difference in the world. You may call them fatalists or nihilists, but most people in this category would not identify themselves as either. They are simply overwhelmed by a world in which most people feel, or are made to feel, inconsequential or powerless. They do not vote. They are not active in their community. They may be dissatisfied with some aspects of their world, but they feel that there is nothing worth the effort required to change anything. They feel that there is nothing they can do that will make them feel better about themselves, improve their lives, or make the world a better place. They turn inward, and become passive.

These are not bad or lazy people. They may be kind, honest, hard-working, and intelligent; good parents, good neighbors, and loyal friends.  What they are missing is the realization that they are surrounded by easy opportunities to improve their world.  They lack vision, or they lack direction, or they lack a support network. They have made the mistake of believing that world events are something they watch on TV; that history is something they learned in school; that progress, or simply change, is the responsibility of someone else.

They are mistaken.

Neither change nor progress is inevitable. Their history is influenced by their choices, and never in history has the average man had more opportunity to change the world and influence events, for better or for worse, than at this moment.

As I step down from my office, I offer you a challenge, a challenge that I feel that Rotary must accept if it is to remain vigorous and relevant for another hundred years. It is not to conquer a new disease or bring an end to illiteracy, or any one of the many other laudable goals that Rotary has set for itself. Other people will lead those efforts, and I wish them godspeed.  My challenge is simpler, and less glamorous. I have not found a way to express as an elegant or inspirational slogan, but perhaps one of you will.

My challenge is this: spread the message of Rotary. Show the world that people working together on sustained, coordinated projects can make the world a better place. We have long lists of successful projects; more than a century of evidence that shows this to be true time and time again.

Spread the word. Spread the word that projects such as the eradication of polio are not difficult — in fact, in many ways they are remarkably easy, given the right vision, planning, and people. Find another million Rotarians, or another ten million. Teach the attitude that change is possible and that people working together toward a common goal can change the world in remarkable ways.

Many hands make light work, and we have much left to do.

Bill and I

Wednesday, April 25th, 2012

The annals of literature are filled with stories of authors who labored alone and unrecognized, or in some cases had to overcome great or small adversity, to create legacies that become treasured as masterpieces by readers for generations upon generations.

The annals of literature are not filled with stories of authors who, despite every advantage, can’t seem to connect the dots.  I’m sure that the stories are out there, but they’re not literature; they don’t captivate.

Did Shakespeare have a support network?  If he did, it apparently wasn’t very important, because there are serious scholars who still debate whether Shakespeare actually existed or whether the name is only a nom de plume of one or more other authors.  He didn’t seem to leave much of a footprint, except for his writing, which is required reading from high school through college hundreds of years later.

I have a great support network of people who make it possible for me to write, and who even help proof what I’ve written.  There are also an enormous number of people who will testify that I do, in every possible sense of the word, exist.  It doesn’t seem to help me sell books, however.

The Corrected Danny O’Bigbelly

Saturday, April 21st, 2012

Over the past several months, I’ve stitched together a number of my blog entries and other short pieces, along with a few new essays to fill some holes, and the result is a sort of book-like collection of essays. After removing most of the worst kinds of typos, stilted prose, and factual errors, and punching up some of the jokes, I’ve published it on Amazon:

The Corrected Danny O’Bigbelly

Note that this book is available as part of the loaning program, which means that if you are member of Amazon Prime, or your local library participates in this program (I think) then you can enjoy this book for no additional cost.

If you find my writing amusing, I think that you’ll find that this book is even more amusing.  If you do, I hope that you’ll consider writing a positive review and, much more importantly, sharing this information with your friends.  Word of mouth, or tweet, or status update, etc, are the only ways that anyone will learn about this book.

If you don’t like it, you can write a review to warn people not to buy the book, or at least describe why reading it might be a poor use of their time, and I can’t do anything about it except accept your critique.  Amazon takes customer reviews seriously, and so do I.

Introduction to TBD

Sunday, April 1st, 2012

A few years ago, I joined a small but rapidly-growing social web site called facebook. You might have heard of it; it was very popular in its day.

As soon as I filled in my profile information, facebook showed me an advertisement for another social web site, named “TBD”, which, according to the advertisement, was intended for the 40-plus crowd, or, as I remember, “for the rest of us.”

Like many other such free sites, facebook’s business model was focused on selling advertising, in much the same manner as other entertainment media. Unlike broadcast media, however, the advertisements shown to each facebook user were chosen specifically for that user using criteria based on information provided directly by the user or by observation of their browsing patterns while they were logged in – information from their profile (age, location, educational background, workplace, favorite pithy sayings, etc), keywords in their posts, the general demographics of the friends with which they interacted most often, and so forth. The goal was to show users advertisements to which the viewers would be most likely to respond (and for which facebook would be paid the most money). For example, if you’ve told facebook that you are male, 40-something and married and then later post as your facebook status that you are looking for a florist where you can buy roses at 10:00pm on a weeknight, facebook might choose to show you advertisements for divorce lawyers and discrete dating sites. If no such advertisers were currently retaining the services of facebook, then perhaps you might also see ads for florists.

I couldn’t tell if it was simply hubris for facebook to show me advertisements for one of its competitors, or whether facebook was politely hinting that perhaps we’d both be happier apart.

To make a long story short, I clicked on the ad and I didn’t come back to facebook for a long time.

TBD wasn’t the first such site that I’d joined, nor would it be the last, but it has been the only site that significantly changed the way that I think about such sites and the way that I spend my free time.

Most social sites are tailored to a specific combination of demographics and topics. On some sites, the expectation is that the people with whom you associate on the site are people with whom you associate in real life – family, neighbors, classmates, colleagues, and the like. These sites provide a convenient way to share information and keep in touch with people you already know. On other sites, the expectation is that you don’t know anyone, and are there to find new friends, business leads, or perhaps romantic partners.

TBD did not focus on a specific purpose or type of relationship that it expected its members to have, but instead focused on attracting a specific type of member and then letting the interactions that developed take their course. TBD’s target demographic was the over-40 adult who was looking for dialog and companionship. People who had never met, and would be unlikely to ever cross paths in the real world, joined TBD and became acquainted. It drew people from every part of the US and several other English-speaking areas of the world.

An organization that reaches out to the lonely and makes them feel welcome might sound superficially like a cult, but TBD was the opposite of a cult in every important aspect. In a cult, there is a leader who makes the rules, and dissent is forbidden; in TBD, the rules were minimal and dissent was mandatory. People without strong, independent personalities and the ability to articulate and defend their opinions while tolerating and respecting the opinions of others did not enjoy TBD and tended to depart quickly for other sites.

Although some of the TBD members knew each other in other contexts, and some of the members used their real names, my impression is that the majority of the active users of the site used pseudonyms and fictitious avatars. The advantage – if not necessity – of anonymity is obvious on such web sites; until you get a sense of who else is reading your postings and what their motivations and intents are, it is foolish to provide too much information about yourself – there are strange, unpleasant, and even dangerous people who wander the web. I started with an anonymous name, Danny O’Bigbelly (or DannyO), and stuck with it because it was easy to remember and I didn’t want to go to the hassle of changing avatar names, which was an awkward procedure on TBD. Ironically, although I never revealed my true name, appearance, home town, employer, or type of work I do, I believe that the people who know me as DannyO on TBD know me as well as almost anyone outside of my family.

Although I quickly felt that I’d established a connection with several of the people I’d met on TBD, I also knew that purely online friendships can be difficult to gauge; just as some people can behave very badly when given anonymity and a large audience, other people (or sometimes the same people) find it easy to be friendly, well-mannered or simply hide their true opinions behind a veneer of politeness as long as there is nothing real at stake. I was curious to meet the people I’d met on TBD in a real-world setting and see whether these relationships could survive a face-to-face conversation, so I organized several dinners and invited any TBD members living near Boston to attend. To my surprise and delight, people came from hundreds of miles away to meet each other, and everyone had a great time. Instead of being disappointed to discover that we weren’t all as charming and witty in real life as we were online, we were only disappointed that we hadn’t planned a get-together sooner.

Within TBD, there were a number of different groups formed by self-organizing and self-regulating clusters of users and topics, each with its own style of interaction and topics of discussion. Users were free to wander from one group to another, but most tended stay within a relatively small number of groups. In my case, I would have spent more time exploring new groups if I had had the free time, but since my free time was limited I tended to spend most of it in a few groups where I had become familiar with the local inhabitants and customs. My favorite area was the front page, where the discussions were seen by the most viewers and tended to be the most fast-paced, and fostered interaction (not all of it amiable) with the greatest number of people.

Several of the popular areas had a question-oriented format. Anyone could post a question, and anyone could answer – including the asker. Some of the questions were practical requests for factual answers, while others were more open-ended, thought-provoking and intended to spur discussion. Some were intended to be humorous, and others raised deep philosophical questions that sparked debates that lasted for months and whose transcripts grew to over a hundred pages of dense text.

I found that writing short essays to answer the questions, or to build on the answers of others, was habit-forming. It was a style of writing that appealed to me because of the range of possible approaches to the questions: a quick, off-the-cuff answer written in the morning while I should have been helping my wife get our children ready for school, or a thoughtful, structured essay written in the evening after mulling over a question during the quiet moments of the day. Some of the more interesting questions became the topics of blog entries, which then evolved into chapters of this book.

TBD only lasted a few years before the company that ran the site went out of business and closed the site. Although I don’t know the details of the business aspects of the site, I am certain that the failure wasn’t due to any lack of enthusiasm from its members. The popularity and vitality of the site continued, unabated, until the bitter end, including many discussions, started by members, about how the member community might somehow save the site. Today there are still several active sites where refugees from the TBD diaspora gather, reminisce about the old times, and attempt to recapture the chemistry of the original TBD.

A few months before I learned that TBD was going to close, I visited San Francisco on business. Realizing that my hotel was was only a few blocks from the offices of TBD, I sent TBD’s CEO (who I knew only from our interaction on the site) an email saying that I’d be in town and I hoped to meet her and some of her colleagues face-to-face. She invited me to visit for lunch. We ate take-out Schezhuan food off paper-plates, tech start-up style, with most of the rest of the TBD staff, in an open office space TBD shared with another fledgling company, and had a far-ranging conversation that I would have gladly continued for the rest of the afternoon, but we all had to get back to work. When I left, I thanked them for lunch, and I thanked them for creating TBD.

But I couldn’t possibly have thanked them enough.

A passing grade

Sunday, February 5th, 2012

As seems to happen with greater and greater frequency with each passing year, I recently received an email asking for reminisces or memories about a former teacher who recently passed away.

In this case, it was Catherine Boczkowski, my third-form chemistry teacher.

I was fortunate enough to attend a high school whose faculty contained — and continues to contain — many beloved teachers who possessed the rare blend of expertise, dedication, and compassion required to be a great educator. Even in this cohort, however, Dr. Catherine Boczkowski was recognized as a luminary.

I don’t doubt that there will be many people who provide stories about her warmth, humor, dedication to her students and her responsibilities within the department, and her flawless skill at the blackboard. Therefore I will not add to these, but instead will share a story that I believe may be unique, and that I haven’t shared before.

I came to the school in my third form, and enrolled in the standard introductory third form chemistry class. Dr. B. was my teacher. I had had no former experience with chemistry, and I found the subject both challenging and interesting. Dr. B. praised my rapid adjustment to the rigors of the school, and urged me to pursue studies in the field. In my heart, I knew that I’d never be a chemist, because the smells in the lab always gave me a headache, but I couldn’t refuse her encouragement. None of my other teachers had ever hinted that my performance in the classroom might actually lead to some sort of career.

My marks for assignments during the term were strong, but I knew I needed a good grade on the exam in order to achieve an A for the term, and therefore I was determined to do well on the final examination. The night before, I secretly studied well past lights-out. In the morning, I overslept and barely reached the field house in time to start the test.

For readers unfamiliar with the school during that era, many of the final examinations, particularly for the larger courses, were proctored in the field house. Long rows of desks filled the basketball courts and the wrestling areas, and students from different courses were intermixed in a complicated pattern to ensure that students were not tempted to cheat. While you were solving an equation, the student on your right might be translating passages from Latin and the student on your left might be writing an essay on post-war Japan.

I arrived late, and a proctor ushered me to one of the few remaining chairs, and asked me what class I was in.

“Dr. B.’s chemistry, I answered.”

He reached into his folder, fished out a test and handed it to me. I began working through it immediately, thankful that I hadn’t been locked out on account of my tardy arrival.

The first problem, which is traditionally just an ice-breaker, was difficult. The second and third problems were harder. The fourth problem seemed familiar in form, but required math that I hadn’t seen before to balance the equations. I started to worry, but I worked through the problem and eventually solved it.

It was clear that I had not studied enough, but I was determined to do my best. After taking so long on the fourth problem, I was certain that I was far behind the pace and would not be able to complete the exam. Therefore, instead of continuing on through the problems in order, I decided to skip ahead and answer the questions that looked easy first, to assure that I’d have all the easy points tucked away before time ran out.

Unfortunately, there weren’t many easy questions, and eventually I reached a question that I didn’t even know how to start. The question contained several terms that were unfamiliar, and weren’t mentioned anywhere else in the exam. I was completely stumped.

It was permitted to ask the teachers for clarification on the problems after some time had elapsed. I could see some of my classmates scattered around the room. I was sure that some of them must have reached this question already, but none of them had asked for clarification. I hadn’t noticed them asking any questions at all. I could see them writing steadily. They didn’t seem puzzled. I was thinking for long moments before trying each new approach, while answers were flowing out of their pencils as quickly as they could write.

I’d always had some doubts about whether I truly deserved a seat at this school, and now these doubts ran rampant. I was utterly out of my depth.

I raised my hand, and Dr. B. came over to my desk.

“I don’t remember this word,” I whispered, pointing to the mysterious passage on the exam. “Is it a typo? Or can you give me an example?”

She leaned close to read the test, and then stepped back, shaking her head. A smile flashed across her face, and then was replaced by a look of serious concern.

“Danny, oh, Danny,” she whispered, “What are you doing here?”

I had been asking myself the same question.

“I mean,” she continued, “Why are you sitting in the row for my Advanced Placement students?”

She took the paper from me, and handed me the proper test.

“Better hurry,” she whispered. “You don’t have much time left.”

The questions on the third form introductory chemistry seemed much easier, and there were no unfamiliar terms. From time to time, I looked up and saw Dr. B. reading through my first test, making notes, showing it to another chemistry teacher, who seemed to find it amusing.

It took every second of the exam period, but I finished all of the questions. As we were dismissed from the examination room, Dr. B. stopped me.

“How did it go?” she asked. I was embarrassed by my mistake, but proud that I’d finished exam.

“I think I did OK.”

“I think you probably did too. By the way, you might think of taking Advanced Placement Chemistry in a few years. Once you’ve taken the prerequisites, of course. After all, you’ve already passed the final.”

Rest in peace, Master Catherine Boczkowski.

What’s it all about?

Sunday, November 20th, 2011

It’s been a long time since anyone stopped me during one of my long ambles around the campus (for that matter, it’s been a while since I ambled around the campus–or any campus) to ask me, in a polite but insistent manner, what Gravity’s Rainbow is “about”.  The world has moved on to other questions; such is the way of all things.

And not only other questions, but other ways of answering questions.  It’s no longer hip to be distant and aloof; today public blogs are all the rage.  I’ve stayed away from blogging about my personal life in any deep manner because I’d much rather have a conversation with someone than pontificate to an audience that is, from what I can tell, either largely anonymous and passive, or completely absent.  I don’t usually like to pontificate, but when I do I like to have the feeling that someone is listening, and possibly taking notes, perhaps even weighing my words carefully in the hope that they will give them some insight into topics relevant to their attempts to pander to the whims and prejudices of the graders of their term papers.

But I can change–and I have.

If you were to ask me–and even if you haven’t, which is closer to the truth–what Gravity’s Rainbow is about, here’s what I would tell you.

The novel begins in London, at a time near the end of the second world war.  V2 rockets are raining down on the city at irregular intervals.  These weapons are terrifying because they arrive almost without warning (only a few minutes between their launch in Holland and impact in London) and their apparently arbitrary pattern of impact.  People are very interested to know where the rockets are going to strike next; it’s a simple Poisson distribution, created by the accumulation of errors in the guidance system and dynamics of each rocket, but that’s not very comforting or informative.

So, perhaps you could say that this book is about the tendency of people to look at random distributions and see patterns that arguably exist only in their minds–conspiracies, the hand of the divine, things of that nature.  But where would the fun be in that?  There are already books about that.  They’re dull and boring.  A dose of real conspiracy–and perhaps real divine intervention as well–make things more fun.  Besides, we have eight hundred pages to go, and it’s going to be tedious if it’s all about psychology and conditional probability.

Tyrone Slothrop is an American soldier attached to an English unit based in London.  I forget exactly why, or what he’s supposed to be doing.  It doesn’t really matter, except for the detail that whatever it is, it seems to provide him with plenty of free time, which he spends doing touristy things; traveling around London, seeing points of interest, and meeting various people.  He keeps a map of London pinned to the wall of his office, and on this map he marks places that he feels are notable for whatever arbitrary reason he chooses.

To the untrained eye, his map looks random.  Fortunately for the plot, there are plenty of trained eyes available, and therefore it is eventually noted–not by Tyrone, who is oblivious to all of this–that the pattern of markings on Tyrone’s map is nearly identical to the pattern of markings on the maps of the people who are keeping track of the impact points of the V2 rockets.  There is one important difference, however, and it is this what attracts attention: Tyrone updates his maps before the rockets hit.  It’s not a map of where the rockets have fallen; it’s a map of where the rockets shall fall.

How Tyrone accomplishes this trick is never made entirely clear, but there are hints and theories.  When Tyrone was an infant, he was subjected to a series of Pavlovian experiments as part of a research study whose techniques and goals are never provided in any useful detail.  The basic structure of Pavlov’s conditional experiments is simple and designed to show that the mind can form connections between stimuli with indirect relations, and these connections could continue long after the relationships were broken.  For example, if dogs hear a bell before they receive their food, then they will learn to begin to salivate when they hear the ringing of the bell, and this will occur when they hear the bell whether or not food arrives afterward.

When performing these experiments on people, is only fair to break these relationships after the experiment is over; to “untrain” the subject.  Infant Tyrone was given conditioning to extinguish the response, but perhaps it was a bit too extinguished, or the untraining went awry.  In any case, Tyrone now seems to start salivating, so to speak, before the bell.

Plus there’s a bunch of other stuff with characters and plot and whatnot; if you can’t find something in this novel that you can prattle on about for a few blue books, perhaps the problem is with you, not the book.

Be that as it may, this is what I used to tell people who asked me what the book was about.  I ran into one of those people again a few years later, and he told me that I’d misled him somewhat.

“That’s sort of where the plot begins,” he began.  “But then it goes all over the place, introducing all sorts of other plots and characters, while in the background that plot continues,” he continued.

“Yes,” I agreed.  “I acknowledge that my sketch of the plot lacked detail,” I summarized, “but what would you say the book is about?”

He shrugged, smiled, and then turned and walked away.



The unforeseen

Wednesday, September 28th, 2011

Now that nerd culture has been embraced into mainstream media, I have been given a golden opportunity to use my intimate–if not embarrassing–knowledge of arcane lore to offend a wider audience than ever before.

My mother always taught me that it is an error in judgment to squander an opportunity.  Or something like that…  something about squandering, anyway, and I’m fairly sure it was my mother.  Reasonably sure.  I wouldn’t put a lot of money on it, but it seems plausible.

I shall begin with the first of three annoying essays.

While I was still in the midst of reading through the books for the first time, I was already story-boarding epic movies based on The Lord of the Rings.  I knew that they’d be impossible to render on film, because of the scope of the scenery in the books is enormous; imagine a cast of somewhere in the vicinity of 80,000 characters, including walking trees, trolls, monsters of various kinds, and sets the size of a geosyncline.   A few decades later, computers solved all these problems, and the movies were made, using brilliant CGI to illustrate things that could never possibly be rendered in the real world.

Unfortunately, the movies were awful in a number of ways.  I understand that they are among the highest-grossest, most-viewed movies in history–and presumably this implies that many people really enjoyed them and considered their money well-spent–but they were not nearly as good as they could have been.

I have ranted before about the way that script writers combined and conflated characters so that key bits of dialogs ended up coming out of the mouths of different people, in ways that fundamentally change their characters and/or confuse the bejesus out of anyone paying attention.  Consider the following dialog from the battle in Moria:

Movie version:

Leogolas: “What the heck is that thing?  It’s scary.”

Gandalf: “It’s a Balrog, you silly teenager.  We’re boned.”

Book version:

Gandalf: “What the heck is that thing?  It nearly kicked my ass!”

Leogolas: “It’s a Balrog, junior.  We’re boned.”

If you look carefully, I’m sure that you’ll be able to detect the slight difference in nuance… but, as I’ve said before, I’ve already ranted about this, and I won’t rant about it again today.

The movie is peppered with other changes from the books; enough to fuel many arguments between people who have only seen the movie and people who have devoured the books.  Many of these I chalk up to simple poetic license–the scriptwriters felt that they needed to make some changes in order to create a movie that appealed to a wider audience, and to trim digressions in the plot in order to fit in the given budget/running time.  Hence we have the hearth-throb elf prince instead of the ancient scion of an ancient house; the wise-cracking, pattering dwarf instead of the dour, taciturn dwarf prince; an attempt to make Gandalf a more vulnerable, sympathetic character and the Witch King more frightening by having the Witch King taunt Gandalf and break his staff in a confrontation that never appears in the book, and which, all readers agree, would have ended quite differently–if Gandalf and the Witch King ever did fight one-on-one, all the smart money says that the fight would be brief, and there wouldn’t be enough left of the Witch King to bury in a match box when it was over.

Non-central characters are removed or coalesced; women are given more lines.  Geography is redrawn so that characters can pop up at unlikely and logic-defying times.  In the book, the heroes find that while they were off fighting the war, the war came to their home; their village has been ransacked and their friends and neighbors tortured and killed, while in the movie the heroes come home to a heroes welcome and they all live happily ever after.

I could revisit my usual rant about the dog’s breakfast that the writers made out of the characters and their dialog, but instead I will dwell on their second tragic mistake.

On their behalf, I have to say that I understand their reason for the abandonment of the backbone of the narrative structure of the books.  It would make a difficult movie, and people don’t like difficult movies.  People don’t like uncertainty, and in any case there is a strange paradox that suspense that can be sustained for hundreds of pages in a decently written novel comes across as trite and obvious in a 30-minute sitcom.  And so the books, which are written from the perspective of the characters, who frequently don’t know what the other characters are doing, and generate a lot of angst wondering whether so-and-so is dead or coming to help or whatever turns into a movie where the audience sees every one of the sub-plots unfold concurrently.  All of the uncertainty and suspense is completely lost.

For example, in one of the climactic arcs of the novels, we have three characters–who for the sake of argument, I’ll call Gandalf, Aragorn, and Theoden, who part ways to perform separate errands that are central to the plot.  They’ve learned that a city occupied by their friends and allies is about to be attacked.  Gandalf rides to a city, which is besieged almost as soon as he arrives.  Aragorn goes off in a different direction, looking for help, on an errand that he doesn’t explain in any detail to anyone before leaving, but his implied destination is known to be so utterly perilous that people believe that he has undertaken a suicide mission; some actually begin grieving over him.  Theoden has promised to gather his army and ride to the assistance of the city, but is unaware that the road to the city is held by an enemy force that is stronger than his own and has prepared an elaborate ambush; Gandalf has no way to tell Theoden that he is riding into a trap.

It looks grim.  All reports are that the road is impassable; Theoden cannot help, and Aragorn is lost in the wilderness.

The enemy assaults the city, and the siege goes on for a few days.  Eventually the enemy breaks the gate and prepares to sack the outer city and assault the inner citadel.  All flee the outer city in terror, except Gandalf.  Alone in the square behind the shattered remnants of the main gate, he calmly waits, alone, for the enemy to enter, his pulse presumably a steady 68 beats per minute.

This looks grim, but it also holds great promise.  I had been waiting for several hundred pages to see what happenes when Gandalf lets Narya and Glamdring off their leash, and this certainly appears to be a perfect opportunity for this to happen.  The reader has been hearing second-hand accounts of the astonishing feats that Gandalf has performed, but they always happen out of view of the narrator (and any other witness–at least, any witness who survives to tell the tale), and Gandalf uses such a terse, sketchy, and self-denigrating way of describing his feats that the reader is given very little idea how or what, exactly, Gandalf did.  We only get glimpses of what he can do; it seems like foreshadowing, building toward some epic confrontation.

This is that confrontation!  This time it’s all going to happen right out in the open.  The narrator is right there.  We’ve got ring-side seats!

But no.  Gandalf does nothing except be nonchalant.  We have been teased.

Theoden arrives with his army, extremely unexpectedly, and the assaulting army regroups to deal with this annoyance.  This is all very mysterious, because we don’t know how Theoden could have gotten there in the nick of time, much less have arrived in full force–explanations come later.  Gandalf races off in an unsuccessful attempt to prevent the king of the city, who believes that all is lost, from killing himself before the enemy can take him.  Gandalf never even crosses swords with any of the enemy.

Theoden and his army attempt to break the siege, and are nearly successful, but are overmatched by the superior numbers and placement of the enemy.  For a moment the battle looks like it could go either way, but then Theoden is slain, followed by another terrible setback–an enormous number of enemy reinforcements are observed sailing toward the city.

Things are looking fairly hopeless once again, but as the ships get closer it becomes apparent that they are flying Aragorn’s flag, and carry reinforcements for the city instead of the enemy.   This is again all very mysterious, because we don’t know how Aragorn could have gotten there in the nick of time, much less have captured the ships of the enemy–explanations come much later.

There’s suspense.  You really don’t know how the characters are going to survive.  You know that some of them will–the title of the volume gives a pretty strong hint that Aragorn will survive the battle–but it’s clear that Tolkien is an author who is more than capable of killing off major characters, and he certainly puts them in situations where the means of their survival is less than predictable.

And now for a bonus–when we do find out how Theoden managed to sneak around the army sent to block his path, it’s still a good read.  There’s still suspense, because don’t know how he’s going to do it, and things happen along the way, etc.  Similarly, Aragorn’s story is riveting, when one of his companions relates it to the narrator.

But let’s compare this to how it unfolds in the movie: Gandalf, Aragorn, and Theoden part ways.  A short sequence of scenes shows each of their progresses toward the city.  The people in the city are worried–Theoden won’t make it!  The viewer is unconcerned, because he just watched Theoden sneaking around in the woods.  The people are worried–Aragorn is certainly dead!  The viewer is unconcerned, because they just saw him negotiating with the head of a rogue army.  Oh, where is Theoden?  He’s got his army, and they’re riding, riding, riding toward the city.  Oh, where is Aragorn?  He’s taken a bunch of the enemy ships and is sailing toward the city!  Oh, where is Theoden, now that the gate is about to be broken?  No worries; he’s busy giving his army a pep talk before they attack.  And where is Aragorn?  Sailing up to the city, just like he said he would in the previous scene.

Without much question about how things are going to unfold, there’s no tension in the scene where Gandalf waits alone to stop the enemy army, and therefore the scene doesn’t occur in the movie.  It’s one of the moments that every reader comes back to revisit and stage in the theater of his or her mind, and they couldn’t find a way to write it into the movie at all.

For shame.

I’m still waiting for someone to make a movie based on The Lord of the Rings.


Wednesday, September 14th, 2011

A popular tradition, at least here in the West, is to make resolutions around New Years with the hope that the changing of the calendar will help to bring changes in ones life.  I have never been very good at making New Years resolutions, or resolute about keeping those that I have made.  The end-of-the-year holidays are too chaotic to permit the quiet reflection that I require before I can do any serious thinking about the future.

It has instead become a pattern that I think deeply about such matters when I am on my late-summer vacation, which in current years has been spent down the cape at the end of August, prior to the beginning of the school year.  The end of the summer and the beginning of school has been a much more meaningful time of transition than an arbitrarily-chosen cold day shortly after the Winter solstice (although of course it is also somewhat arbitrary) and the vacation gives me time to think.

This year my vacation was truncated by the passage of Hurricane Irene (a mere tropical storm by the time it reached us, but still more than sufficient to disrupt a vacation in a cottage whose elevation above sea level can be conveniently measured in inches).  Instead of relaxing week followed by a leisurely trip home, it was a week of mounting tension as the storm approached, followed by a hurried departure, more than a day early, so we could get off Cape Cod before everyone else had the same idea and/or the bridges were closed.  When we arrived home, things became more frantic as we prepared for the storm–moving all of the plants and other items off of the patio, rearranging the contents of the basement to get everything off of the floor and elevate the most important items to the second shelf or higher on the basement shelves, patching cracks in the basement to try to keep the water out, running to the store to buy milk and a UPS, searching for batteries, candles and matches, replacing parts of flashlights, and drawing water just in case.

The storm did not do much damage in our area (although other areas were far less fortunate) and in the end, after all of our preparations, it was little more than a severe thunderstorm for us.  We emerged from the house, cleared the fallen limbs from the yard, replaced the plants and the propane grill on the patio, took a deep breath, and headed back to work, where I learned that the project that I had more or less expected to be working on for the next four years will not be funded.

And thus I am in mid-September without a clear plan for the year.

Beside the point

Wednesday, July 20th, 2011

My previous posts resulted a few comments that questioned the mental well-being of the arctic explorer who had, in the opinion of the commentators, a strange form of “paranoia”.

These are presumably the same people who feel deep sympathy for the man who has only one coin of each type and wonders, for some reason that defies rational explaination, how many ways he can make change.  They are also baffled by the woman who boards a train in Chicago, heading east, and wants to know where the westbound train leaving Buffalo an hour later will pass by her window.  They are infuriated by the cruel physician who thinks first about Bayes rule before giving medicine with a high probability of serious side effects that treats a rare disease to an ailing child.  They’re appalled at someone who would enjoy thinking about sealing a live cat and a flask of poison to be released at some random and unknowable time in a box.

Basically, they don’t like math in the form of word problems.  Maybe they just don’t like math.  Or maybe it’s the problems they don’t like.

Well, admittedly Schrödinger could have picked a less gruesome thought experiment–the cat is really immaterial.  The real question isn’t whether the cat is alive or dead, it’s whether the flask is released (or, to be pedantic, whether or not the Cesium atom has decayed).  I guess Schrödinger didn’t like cats.

It’s possible to restate the ‘arctic explorer in need of a match’ problem with equations, but it would be horrible to behold and most people wouldn’t even be able to read it.  The prose version is nicer.

Trust me.

A fair coin

Wednesday, June 22nd, 2011

After some thought, let us return to the shop to buy some matches.

What strategy should you employ, knowing that the clerk has full knowledge of your strategy?

One strategy is to buy a lot of matches and hope that the clerk hasn’t had time to ruin them all.  This strategy might work in the real world, but it doesn’t work in our world.  The clerk has all the time he needs to ruin any number of matches–even all of them, if he chooses to do so.  You will leave the store, staggering under the burden of all of the matches, and then die at the end of your journey because none of the matches will light.

Another strategy is to buy a bunch of boxes of matches, and then carefully open each box and try the first match from each box.  If the match lights, then you assume that the box was not tampered with, and that the rest of the matches in that box are good.  If you run out of boxes, then you buy more.  This won’t work because the clerk knows that you’re planning to try the first match in each box, and therefore makes that match the only match that lights.  Therefore, having lighted the only working match in each box, you then set off into the wilderness with a box that contains 99 ruined matches, having chosen the one good match, and the die at the end of your journey because none of the remaining matches will light.

You can make things a little harder for the clerk by introducing some randomness–instead of choosing the first match in each box, choose one at random.  The clerk doesn’t know which match you’ll choose, but his strategy doesn’t have to change.  If he puts one working match in the box, then there are still only two possible outcomes for each box: you’ll either choose that match (and it will light and you’ll take that now-useless box), or you’ll throw away that box and try again.  It’s likely that you will have to try many boxes before you draw out a match that works.   The more boxes you try, the more obvious it is that the clerk is trying hard to kill you–and knows your strategy, and in the end you will eventually be fortunate, pick out the one working match, and then march off to your doom.

Every strategy that has this basic form is doomed, no matter how clever.  Consider the following refinement to this procedure: buy a box of matches, select half of the matches at random, and try to light them all.  If they all light, take the remaining matches.  Otherwise, try the whole process again.  The clerk can still attempt to kill you by filling the box with half good and half ruined matches, but the probability that you will randomly select exactly the half that light is astronomically small–the same probability as flipping a fair coin 50 times and having it come up heads every time.  This will happen by blind chance one time in 1125899906842624.  If that isn’t good enough for you–after all, your life is hanging in the balance–buy two boxes, pour out the contents of both into a big heap, and try to light 100.  The probability of success for you (lighting 100 successfully) and success for the clerk (lighting exactly the correct 100) is now one in 1267650600228229401496703205376.  In layman’s terms, this ain’t gonna happen, but if you’re very worried, or there are computers involved, you can always add more boxes of matches until the probability that the clerk will trick you successfully is as close to zero as you like.

This approach ensures that if the clerk is trying to kill you, you’ll probably never leave the store because it is extremely likely that you will catch the clerk every time he gives you a box of matches that would result in your death.  You’re probably not going to die on your expedition, but you’re also probably going to die of old age in the store.

The problem is that we’re giving the clerk as many tries as he needs to get lucky and arrange things in the one way that will send you off to your doom, and since the clerk knows your strategy and therefore knows exactly how to prepare the boxes of matches so that you will either buy another box or leave the store with a box that has no working matches.

Every strategy of this sort–where we give the clerk the opportunity to provide us with only exactly enough matches to pass the test and won’t leave the store until our conditions, which the clerk knows, are satisfied–will fail.  I’m going to make this claim without any proof–in the worst possible example of mathematical rigor, since I’ve only bothered to describe one type of strategy, and there are many.  In this family of strategies, you’ll either buy another box (because you think the box you have is bad), or you’ll leave the store with a box containing nothing but matches that don’t work.  By fine-tuning your strategy, you can make it more “difficult” for the clerk, but this just means that you have to buy a lot more matches before we stumble into the unlikely situation where you accept the box of matches that the clerk offers, and then wander off to die in the wilderness.

The fundamental problem is that we’ve designed a game with only one (eventual) outcome: going on the expedition.  If that’s the only choice, and the clerk controls the matches, then we’re dead.  The clerk doesn’t need intelligence or luck; he only needs patience.

At this point, it would seem like a better idea to simply abandon the expedition and stay home.  In any case it would be quicker.

This insight provides the path to a solution.

Keep in mind that the clerk wants to kill you.  He wants you to go on your expedition, and he will do whatever he can to make you think that you have a working match.  He doesn’t want you to give up and stay home and quietly live out the rest of your life.

In order to suceed, you need a different strategy: one that gets you out of the shop in a reasonable period of time, go on your trip, with a reasonable chance of survival.  Most importantly, however, you must provide the clerk with an attractive opportunity to kill you.  Remember that the clerk can simply ruin every match in the store, if he chooses to do so.  You might be able to detect that he’s done this, but there’s no way to prevent it.  You want to give the clerk an incentive–specifically, the opportunity to kill you–to leave some of the matches in working order, and you want to come up with a test for whether there are any working matches that is unlikely to consume all of them.

Buy some number of boxes of matches–let’s say 20.  After they are safely in your possession (and can’t be modified by the clerk), divide them into two piles by flipping a coin for each box.  There will be approximately ten boxes in each pile; if chance is against you and there are only a small number of boxes in one pile, start again.   Open all of the boxes in the heads pile and try to light matches until you either find one that works, or discover that they are all ruined.  If  some number of the boxes (i.e., 5) in the heads pile contain a working match, take the tails boxes with you on your trip.  Note that there’s no point in taking the remnants of the heads pile–you might have used up all of the good matches; there might have only been one good match in each box.  If any of the boxes in the heads pile do not contain at least one working match, stay home.  Don’t go on the trip.  Once you’ve purchased the 20 boxes, the game is essentially over from the perspective of the clerk; you won’t buy any more boxes, no matter what the outcome is.

In order for the clerk to kill you, he needs to guess correctly which boxes will be in the heads pile (and put at least one good match in five of them) and which boxes will be in the tails pile (and put no working matches in any of them).   This is possible, but unlikely, and if the clerk attempts it then what is far more likely is that at least one of the boxes containing a working match will end up in the tails pile.  Since this is the clerk’s one and only chance to kill you, he will need to prepare enough boxes of matches that contain at least one good match that you’ll be confident that it’s safe to go on your trip (or else he’ll lose his chance to kill you), and he’ll have to be very lucky (or else you’ll end up with at least one of the working matches).

I won’t work through the probabilities that if there are twenty boxes and only five of them contain working matches that all five will end up in the heads pile, but you can do it for yourself and explore how the numbers change if you use larger numbers of boxes, different success criteria, or a biased coin.  You can make the probability as high as you like that if you leave the store thinking that you probably have a working match, that you actually do, and decrease the probability that you won’t stay home if you actually have a good match.  You can’t eliminate the possibility that the clerk will be lucky and you’ll end up dead, but then again the arctic is not without its perils.

If you think about it long enough, I’m sure you’ll find a better solution.

Chance favors the prepared mind

Monday, June 20th, 2011

One of my professors gave this problem as a homework question a while ago.  By now I would expect that it is in wide circulation, but just in case you haven’t seen it already, please enjoy.

Imagine that you are an arctic explorer.  You are about to leave town to head into the wild, for some irrelevant reason, and when you get to your destination, you will need to light a fire in order to survive.  If you can’t light a fire when you get there, then you will die.  At your destination there is plenty of fuel and a fool-proof furnace that always lights on the first try, so you don’t need to worry about that.  The thing that you need to worry about is getting there with a match to light the furnace.  Unfortunately, you don’t have any matches yet.

In the town there is a store that sells matches.  The clerk of the store is the only other inhabitant of the town.  You have enough money to buy many boxes of matches, and the clerk in the store is happy to sell you as many boxes of matches as you like.  Each box is guaranteed to contain 100 matches.  If you are worried that the clerk will sell you a box filled with nothing, you can open each box and count them before you buy them.  The clerk won’t mind.

However, there is a twist.  For reasons that are beyond the scope of this problem, the clerk wants to kill you, and you are well aware of this fact.  You also know that the clerk has found a way to undetectably remove matches from a matchbox, tamper with them so that they don’t light and put them back into the box.  The only way to tell whether a match has been tampered with is to try it–if it lights, then it was good, but it’s no longer good.  Each match can only be used once, so the only way to find out whether a match is good or bad is to destroy it.  The matches are 100% reliable when they arrive at the store; the only ones that will fail are the matches that the clerk has ruined.

So, the problem really boils down to this: you need to buy matches from the clerk.  If you leave the store with at least one working match, you live.  Otherwise, you’re dead.

Your honest and pacifist beliefs prevent you from killing the clerk, stealing his matches, or trying to influence him in any other way.  The clerk, for similar reasons, can only kill you by selling you boxes of matches that he’s carefully manipulated.  The only interaction you can have is to make sure that each box contains the expected number of matches, buy boxes of matches, and try them.

What’s a good strategy?

This might all seem a little contrived, but hey, it’s a math problem.

Well, actually it’s not only a math problem.  It’s also related to cryptography, and so we’re going to make it a little more difficult.

The clerk knows your strategy.  You can’t keep any secrets from him, even though he can keep secrets from you.  He will know what steps you are going to take before you do.  He can practice and hone his strategy to increase his effectiveness at killing you.

This is exactly what cryptographers have to deal with.  Their adversaries can buy or acquire duplicates of the systems that they want to break and spend as much time as they need studying the system before they make their real attack.  When a burglar picks the lock of your door, it isn’t beginners luck–he’s been practicing opening locks just like yours for months.

And just to make things a little more interesting, let’s throw in a little game theory.  Let’s say that you don’t really need to go on your expedition.  You could skip the whole thing and stay home.  You’ll give up your chance for fortune and glory, but you’ll probably live to a ripe old age and die comfortably, surrounded by loved ones, rather than cursing the name of the clerk while you freeze to death in the middle of nowhere.

What to do?

I’ll let you think about it for a little while, but before I do I’m going to drop a bunch of clues.  You should stop reading now if you would prefer to bash your head against this problem for a while.

There are certain kinds of mathematical problems that nobody knows how to solve–or at least, if anyone knows how to solve them, they aren’t saying so.  This may be because some of the problems have the property that being able to solve these kinds of problems could be enormously valuable to certain people and/or governments.

Despite the temptation, I will avoid describing any of these problems in depth, and will only mention one quickly and without any rigor.

Given a very large number (say, several hundred digits in length) that is the product of two large primes (a few hundred digits in length), there is no known efficient way to discover those two primes.  If you can keep those primes secret, it is extremely unlikely that someone else will be able to figure them out, and since there are a mind-numbing number of such large primes, the probability that someone else will stumble across one is not even worth mentioning.  (they only need to find one, because after they’ve found one, they can find the other by dividing the product by it to find the second.)

This is an example of a particular kind of problem that is very hard to solve, but very easy to verify the solution.  Another example is opening a safe; for any given sequence of numbers, it’s easy to check whether they open the safe, but there’s no way to find the right sequence short of trying many, many sequences.

All of this would be no more than a mathematical curiosity, however, if it wasn’t for a second fact.  Large numbers that are the product of two large primes can be used as the building blocks for mathematical structures that behave in some ways like ordinary numbers and in other ways quite differently.  Most importantly, it is impossible to interpret the results in a meaningful way without knowing the prime factors.

I’m sure that mathematicians are cringing by now, but that’s OK.  They’re probably inured to this sort of casual imprecision from the hoi polloi.

So, if you know the prime factors, you can do calculations that nobody else will be able to understand.  By paths that I will not cover, I will assert that this can be used to create secret codes that are unbreakable by anyone who can’t find the primes, which is, as far as anyone knows, everyone.

This has all been known for a long time, but it had very little practical use until relatively recently, because there was a terrible problem that remained to be solved: finding large primes is as difficult as factoring large numbers.   The only way to prove that a number is prime is by showing that it has no non-trivial factors, and the only way to do that is by trial and error.  For large numbers, that’s a lot of trials and errors.

Primes were so hard to find, and so incredibly valuable–since they could be used to create nearly unbreakable codes–that some of them were considered state secrets.

Fortunately, a way was discovered around this.

Gary Miller discovered (or observed, or whatever) that there are certain functions that can test with absolute certainty whether a number is not a prime.  Instead of the usual “yes” or “no” that we expect from most tests, these functions have the outcomes “I don’t know” or “no”.  If the Miller test answers “no”, then the number is absolutely not a prime.  This doesn’t tell us what its factors are (in the general case) but we know that it’s not a prime.

The Miller test takes a number and computes a function of that number and the candidate number.  If the number fails the test (when the answer is “no”) then it is called a witness to the non-prime nature of the candidate.

That’s not very useful yet–we could construct a test that did the same thing just by saying “I don’t know” nearly all of the time, except when it happened to stumble across a factor, and then it would say “no”.  This would not represent progress.

Miller wasn’t the first to develop such a test; Fermat had one, all the way back at the dawn of number theory, but it wasn’t very good and some composites actually didn’t have any witnesses at all.   Solovay and Strassen had a much better one–more witnesses–but Miller’s was the best because it said “no” much more often as “I don’t know” for most composites.  For an arbitrary large non-prime, approximately three quarters of the numbers less than the non-prime are witnesses.

Unfortunately, there was no telling where the witnesses might be.  They didn’t arrange themselves nicely, and instead were sometimes clumpy.

Rabin, in what in retrospect seems obvious but at the time was a completely new and ground-breaking idea, suggested using sampling to choose witnesses.  We don’t know where the witnesses are, but we know how approximately how many there are, and so we know the probability of selecting one at random.

Here is the Miller-Rabin test: select a potential witness at random, and try Miller’s test.  If the answer is “no”, then it’s a composite, end of story.  If the answer is “I don’t know”, however, then the probability that the number is prime is approximately 0.75.  Repeat; if the second potential witness doesn’t work out, then the probability that the number is prime is approximately 0.9375.  After three iterations, 0.984.  After ten, 0.999999.  After twenty, 0.999999999999.

After a few hundred iterations, if you haven’t found a witness then you can be reasonably certain that the number is prime, or that you are the unluckiest person to ever walk the earth.  If you’re not sure which, just tack on a few hundred more iterations.  Miller’s test is quick and easy to compute, even for ridiculously large numbers.

So, if you want to have your own crypto keys that nobody but you can ever crack, here’s what you do: pick a random number, and test to see whether it’s prime.  If so, keep it; otherwise ditch it and begin again.  Repeat until you have all the primes you need.  There are plenty of primes out there, so you’ll find a couple eventually.

Now you either have a practically unbreakable crypto scheme, or else you’re the unluckiest person imaginable.

Rabin’s insight was that there are certain problems that we can’t solve with complete certainty, but only with very high probability.  We can make that probability as close to 1.0 as we like, but we will never get there.

This way of thinking has made possible practical solutions to problems that would otherwise be unthinkably intractable.  Every once in a while–say perhaps once between now and when the last star in the sky winks out–they will give the wrong answer, but it’s worth that risk.

It’s no coincidence that Rabin was the professor who assigned this problem.

I will let you think about this for a moment or two.


They walk among us

Monday, May 30th, 2011

This morning I ran into an old friend who had just returned from his twenty-fifth college reunion. It turns out that back in 1986 he graduated from Harvard, a small liberal-arts college back East somewhere, probably in New England. You might have heard of it, but if not, no matter.  It’s just the backdrop to this tale.

He told me that he’d run into a bunch of his college friends, most of whom were his fellow bandmates, and I was quite surprised to learn about this aspect of his life. I’d never heard him play and instrument, or sing in the church choir, or even mention an interest in the performing arts. Even if he was no longer musically active, I was surprised that he’d never even mentioned being in a band. In my experience, this is the sort of experience that can leave an indelible mark on the participant.

I gently probed for more information, and he grew wistful. For a moment his eyes seemed to focus on infinity and his face took on the expression of a traveler, lost in a strange city at midnight, trying to figure out which highway lane has EZPass. And then he smiled, and told me a story I didn’t expect, a story so unusual and unique that I knew I that I could bank on getting several page-views from it.

He told me about the Harvard University Band.

I have to be careful in what I write, because he made me promise that I would not repeat any of his stories verbatim or connect the names of any of the many people, now living quiet and respectable lives, who might not want to have their names associated with actions they were said to have taken in their younger, wilder, more carefree days. There was too much rumor and innuendo; too many crazy stories. It couldn’t be true, of course; the tales of under-age drinking and wild parties were clearly pure nonsense. My friend, although kind and reliable, is a nerd’s nerd, and the idea that he could have played a role in such goings on is ridiculous.  There were even hints at recreational drug use, casual and spontaneous sex, the stealing of signs, and the violation of any number of university regulations and state and city ordinances against loud noises, buffoonery, and general jackassedness. All false, of course; he could not offer me a shred of evidence of any sort to support his claims. If signs had been stolen then there would be a room somewhere filled with them; if students had been arrested or angry letters written then there would be some written record of all of this.

I’ll give you an example of this–the friends of my friend used to tease him that they had to carry him home after a party in the Fall of his Freshman year because in the midst of the revelry he had been overtaken with fatigue. They continued to insist that this had happened, even though my friend has no memory of this event. Imagine having all of your friends come over to your dorm in the middle of the night and not being able to remember any part of it–unthinkable! How could this be?

But my friend is honest–even if his friends liked to pull his leg. I trust him, and I trust his judgment, and therefore I know that there must be some kernel of truth in his story. My job as a blogger is to embellish that kernel up in a long-winded monologue and pimp it out for you, dear reader, to enjoy, and so that’s exactly what I’m going to do. Between my friend’s story and my nimble Googling, I think I have enough to begin…

If you’re not from Harvard, or haven’t seen them perform, then it is very likely that the Harvard University Band is not what you think it is, except in the most superficial sense of a being a group composed of people who play music together and wear Harvard insignia.

A little history: the Harvard University Band (which I will refer to as “The Band” in future references, because that’s what Bandies, which is the polite name for people who have been in The Band, call it, except in the few cases where the term would be ambiguous, in which case they call it The Band) invented the notion of performing at football games. They invented the idea of performing at halftime. They invented the idea of playing on the field, and then the idea of arranging themselves in some formation other than a concert shell, and then the idea of moving from one formation to another during the course of a single show, and then the idea of having a running narrative to accompany these changes in formation in order to augment the expressive options. In short, if you have seen a band perform at halftime or between the periods of any sporting events, you’re seeing an art form that was invented at Harvard by The Band.

The Band is also considered in some circles to be pioneers in the field of exaggerating their importance and historical significance, although in my opinion their contributions in this crucial area of human endeavor, although notable, are overstated and in any case are utterly overshadowed by the accomplishments in this field of other organizations in their cohort at Harvard.

In any case, it doesn’t take an enormous amount of skill to get a large number of people to wear snappy uniforms, carry shiny instruments, and march around in formations while playing schmaltzy pop. It takes a few people who have good organizational skills, and a lot of people who are decent musicians, good at following directions, and have plenty of time to practice, practice, practice. When done well, the resulting spectacle is truly impressive and inspiring. There’s nothing wrong with the direction that precision marching bands, drum and bugle corps, and the like have taken. If you’re a member of one of these organizations and are waiting for me to say something insulting about them, you will be disappointed. I have complete respect for anyone who does something very well, even if it is a thing that I have chosen not to do.

One of the great lessons of Harvard (or any other decent college, of which there are allegedly several others) is that there isn’t very much value in doing things that other people can do. Competition is fun for a while, but steamrolling your competitors lets you sleep better at night. If you really want to set yourself apart, you need to find the thing that you can do that nobody else can do. And thus is was that The Band continued to evolve until it reached a form that no other organization has ever been able to successfully mimic.

The most notable and unequaled innovations by The Band can be loosely categorized into the areas of professionalism, rehearsal technique, rigorous selection of most talented and dedicated musicians, and strict adherence to a rigid code of moral conduct. The Band eschewed them all equally.

Most college bands have professional conductors, use professionally-arranged music, have professional choreographers, and a staff of other adults that make sure that travel arrangements are made, lodgings, booked, and the like. The Band is an entirely student-run organization. It writes its own shows, arranges and/or writes its own music, designs its own formations, makes its own travel arrangements, raises its own funds, recruits its own victims freshmen, etc.

Most bands rehearse incessantly, or at least give that appearance. They gradually build up a repertoire that culminates in a magnificent show at the end of the season, but if you attend their shows every week, they begin to seem very repetitive. The Band does a new show every week, written from scratch during the course of the week and fine-tuned, often at the last possible moment, depending on the weather, the instrumentation that shows up at the game, and whether they’ve been able to steal a copy of the script from the other opposing band. It is not unheard of to be handed a fresh piece of music, ink still wet, key signature a rumor passed from person to person along each rank, moments before stepping on to the field to sight-read in front of an audience of 50,000.

This sort of thing might sound like unpreparedness, but it is the exact opposite. A Bandie is always ready to adapt to changing situations, to abandon a bad plan when a better plan is offered. For example, at one game the weather was so cold that all of brass instruments–which typically play the lead and carry the melody, while the woodwinds provide counterpoint and harmony–were rendered inoperable, their slides and valves frozen solid. The opposing band was helpless; their music was unrecognizable crap, hollow and empty of melody. The Band’s clarinet players ad-libbed the trumpet parts, and it sounded like crap, but it sounded like recognizable crap and people could sing along with it.

As implied by the two previous paragraphs, which any decent expos teacher would ask me to restructure so that they followed this point instead of foreshadowing it, the defining characteristic of a successful Bandie is the ability to play fast and loose; to react to rapidly changing circumstances, and to get things done even when it’s not clear what is being done. One of the central principles of Taoism, principle of p’u–the uncarved block that can become anything; the water that has no shape of its own; these are familiar to any Bandie.

The cadets at West Point have a tradition of picking people up and passing them up through the stands. Usually it’s a cadet, but once they grabbed an unwilling and somewhat terrified Harvard student and began passing her up. A Bandie charged into the cadet section of the stands and retrieved her.

Someone will opine that the cadets were simply reacting politely to the protestations of the young woman and the effect of the Bandie on the outcome of the situation was probably negligible, but those people weren’t there. The cadets were young, horny boys in a foul mood–possibly because they weren’t permitted to sit down during the entire game, perhaps because their team wasn’t beating the spread, or perhaps because some unknown and unseen agent, allegedly harbored within The Band itself, had recently pelted them with dead fish. Any reliable witness or student of human nature would agree that the grope-less outcome hinged on the actions of the Bandie.

This was not an isolated incident–unusual things happened around The Band with some regularity–but there’s no training for something like this. You can either do it, or you can’t, and the outcome almost entirely depends on the ability to judge situations that are both challenging and highly dynamic and your belief that you will succeed. It is also useful to be slightly insane or inebriated.

The technical musical requirements for being in The Band were minimal when compared to other musical groups. It was necessary to be able to read music–particularly to sight-read music–and play the standards well. There is no excuse for screwing up The Star Spangled Banner or Fair Harvard.  The Harvard marches and fight songs–the staples of any parade or post-game performance–are not particularly hard in comparison to the standard repertoire of a college wind ensemble or concert band, but in my opinion they are considerably more challenging than the average college fight song. This the sort of thing that is to be expected when Leroy Anderson and Tom Leher write your college pep tunes, I guess. Nevertheless, the emphasis in The Band is not on virtuosity, but on playing ones role; not of standing out, but of filling in. There is no place for a high-strung prima donna soloist with a custom-built instrument on a cold October morning as freezing rain falls and a thousand intoxicated Dartmouth freshman rush the field in Hanover–there is only a place for a team player who has the trust of his rank-mates and understands that there are ways to use the length and heft of the brass he carries that were never mentioned anywhere in any of his Rubank method books; a man who watches the conductor instead of the onrushing mob, a man who has faith in the strange and inexplicable powers of the prop crew, those smiling ninjas in white, who seem to enjoy this sort of thing in some perverse way.

A trait that is more important that musical virtuosity is punctuality. With such limited rehearsal time (and gigs beginning and ending at times chosen by the whim of the football team), the worst thing that a Bandie can do is to show up late. Latecomers are singled out and publicly humiliated by being forced to act out Debbie Reynolds’ verse of the “Good Morning” show tune from “Singin’ in the Rain”, or something like that. I confess that I didn’t really understand this part and I half suspect that my friend was making this up, because none of it seemed to make any sense at all.

Finally, there is the irreverence. Some have called The Band obscene, profane, crass, lewd, rude, childish, immature, uncultured, disgusting, or even perverted. My sense is that the use of any of these words is misplaced, except in cases where they are preceded by some qualifier such as “very”, “extremely”, “notably”, “painfully”, or “excruciatingly”. There is a ready explanation, of course–they were just trying to be funny, and humor is different when done at the stadium scale than when performed more intimately. The same jokes don’t work. Grand gestures are necessary.

Unfortunately, decorum prevents me from describing any of the alleged grand gestures.

It is a documented fact that The Band often found itself in hot water with the Harvard administration. Very few student organizations had their scripts reviewed before every performance, but The Band did–and this was complicated by the very short lead time on the scripts. There was barely time during the weekly cycle to write a show, have it be reviewed by the appropriate Dean, rewrite the objectionable jokes, have the script re-reviewed and approved, and then figure out how to slip the original jokes back in somehow before finalizing the show. And all of this was done without the aid of computers or even Xerox machines, apparently. It seems like an enormous over-reaction, a symptom of some dreadful insecurity complex, that the administration would demand to oversee the entire process simply because The Band had mentioned that Radcliffe, Harvard’s sister school at the time, had a stronger linguistic tradition than Harvard. From what I can tell from some shallow Googling, the question is still considered open, even though the Harvard students, whom both sides acknowledge to be masters of debate, have begun to eat away at the edges of the argument.

So, where are they now? Where are these zany kids, these people about whom such crazy stories were told? When he saw them at the reunion, what were they like? Had they mellowed with age? Did he still recognize them? Did they recognize him?

When I asked him these questions, it took him a moment to gather his thoughts, and then he answered in a way that told me that I’d asked the wrong question.

They all seemed successful, in their own ways. Most had families, and despite the running jokes of the reunion about trophy wives (or trophy husbands), they mostly seemed to be in happy and long-term, stable relationships, several of which with other former Bandies.

The last night of the reunion, many of the Bandies who attended the reunion gathered at the big, climactic dance party. They drank and danced and told stories about the old days until the small hours of the morning, and then dragged themselves back to wherever they were staying and collapsed, exhausted.

Only a few hours later, early the next morning, was the memorial service for deceased classmates. My friend entered the church a little early, because he wanted to get a seat near an exit so he could slip out if his kids needed him. The church was very empty and very quiet when he arrived, unlike the crowded, deafening tent where the dance was held. Only a small fraction of the people who came to the reunion came to the memorial service, but as my friend waited for the service to begin, he watched people enter. One by one, he saw nearly all of his bandmates come in and be seated. Perhaps they all did; he couldn’t see all the entrances.

They were, as he described them, living in the moment; doing the right thing; showing up on time. They hadn’t changed in any way that seemed particularly important or significant to him. There wasn’t any reason for them to change; they are happy with who they are, and with very good reason.