The world’s most expensive trash truck

Bloomberg reported today that SpaceX won the contract to bring down the International Space Station. The idea is for a spacecraft to grab hold of the ISS and set it on a trajectory to burn up in the atmosphere. Truck it to the incinerator, as it were.

That makes me nervous. I don’t know what the likelihood of failure is here, but the cost of failure can be pretty high. Something goes wrong and pieces of the ISS start raining down on a populated area. Back in March, some junk from the ISS that was supposed to burn up in the atmosphere crashed through two floors of a family home in Florida. The family has filed a claim with NASA, requesting that they pay for damages.

The debris that fell on the house in Florida was part of a 2.9 ton pallet of batteries. The International Space Station weighs something like 460 tons, and it’s not just one solid piece. Undoubtedly pieces would break off as it’s falling through the atmosphere, and some of those pieces could fail to burn up. Whereas I suspect whoever came up with this idea has taken that into account, I don’t see how they’re going to solve that problem.

I especially don’t see how they’re going to solve that problem within the constraints of the budget: $843 million.

It’ll be interesting to understand how SpaceX is planning to do this. I just don’t see how they could deorbit the station intact and expect it all to burn up in the atmosphere. And I don’t see how they can disassemble the station into smaller parts and deorbit them individually for less than a billion dollars. How will they guarantee that pieces won’t fall to Earth in populated areas?

I wonder. Is it possible to deorbit the station on a trajectory that doesn’t pass over populated areas, and has a very low likelihood of shedding pieces that would deviate dangerously from that trajectory? I’ll have to look into that.

Fun with the piggy bank

Debra and I have a jar in which we put our spare change. When we fill it, about once every two years or so, we take the jar to the bank, where they pour the contents into their coin counter/sorter. We take the cash and splurge on something. It’s not a huge amount of money: usually around $200.

When the jar fills up, I like to dump it on the living room floor and count the money. Sifting through those coins brings back memories of my grandmother, who was a coin collector. I’m also reminded of watching the pinball machine service guys coming to Dad’s bowling center. And the brief period when I worked for my dad at the vending company, or emptying the coins from the vending machines we owned in our motels. Yeah, sifting through coins is a happy trip down memory lane for me.

While I was counting today, I got to thinking about the expected percentages of the different coins, and whether I could accurately estimate the amount of money in a change jar just by counting a single type of coin. So if I had, say, $100 in quarters, then how much money should I expect to be in the jar? How would I go about estimating that?

First, I have to make some assumptions.

  1. When I purchase something, I always get the optimum number of coins in change. That is, if I pay 75 cents for something, I’ll get a quarter back: never two dimes and a nickel, etc. This, in my experience, is a pretty safe assumption.
  2. I always pay for things in even dollar amounts. That is, if something costs $2.03, I give the cashier an even dollar amount and expect change. I never give, say, $5.03, and expect $3.00 back. I actually do that sometimes, but most often I don’t have any change in my pocket.
  3. I never take money out of the jar except for when I’m emptying it completely. That’s almost certainly true these days, because I don’t use the vending machines at work anymore. There’s no need for me to filch quarters.
  4. Each change amount is equally likely. That is, I’m just as likely to get 23 cents in change as I am to get 99 cents in change. This is probably a bad assumption. Cashiers often give me a quarter in change when the actual amount due is 24 cents. Rounding up one or two cents is common. Although this assumption doesn’t hold true, the percentage error it causes is likely small.

With those assumptions, how do I estimate how many coins of each type are in the jar?

The standard “counting up” method of making change is proven optimum. That is, if somebody pays $1.00 for an item that costs $0.33, then the change is two pennies, a nickel, a dime, and two quarters. If we write out the coins required to make change for every amount from $0.01 to $0.99, we end up with:

200 pennies (42.55% of coins)
40 nickels (8.51%)
80 dimes (17.02%)
150 quarters (31.91%)

$100 is 400 quarters. Given 400 quarters, I would expect the jar to hold (400/0.3191), or  1,253 coins, with this distribution:

533 pennies ($5.33)
106 nickels ($5.30)
213 dimes ($21.30)
400 quarters ($100.00)

(You’ll notice there’s a rounding error: the count of coins above is only 1,252.)

That gives me a total of $131.93. So I should be able to count the value of the quarters, add 30%, and have a pretty decent estimate of the amount of money in the jar.

I just happened to write down the contents of our change jar:

840 pennies ($8.40) (38.85% of coins)
330 nickels ($16.50) (15.26%)
402 dimes ($40.20) (18.59%)
590 quarters ($147.50) (27.29%)

That’s 2,162 coins, with a total value of $212.60. If I add 30% to the value of the quarters, I get $191.75, which is about 10% below the actual amount of money in the jar. The percentages of dimes and pennies are pretty close. The jar is light on quarters, and heavy on nickels.

A 10% error by counting only 27% of the coins, though, isn’t bad.

If you have a change jar and are willing to play along, I’d like to know your results. You don’t have to give me actual dollar amounts: just tell me the percentage error, and whether it’s high or low.

Something else I just noticed. The theoretically perfect jar has 1,252 coins, with a total value of $131.93. Our jar had 2,162 coins with a total value of $212.60. In both cases, if you divide the number of coins by 10, you come very close to the total value in the jar. $125.20 is only about 5% shy of the $131.93 actual total. And $216.20 is only 1.5% higher than the actual total in of $212.60 in our jar. Freaky.

Jerome J. Mischel, Jr (Jay): April 12, 1960 – January 31, 2018

My brother Jay passed away this afternoon, after a year-long fight with sarcoma, a rare and aggressive form of cancer. He was 57 years old.

Jay was the second of five children, and the oldest boy; 18 months older than I. As children, we were pretty much inseparable. At least that’s how I remember it. My fondest memories of early childhood include him. We began to drift apart when I was nine or ten, about the time he started going to junior high school. Although he did look out for me when we went on Boy Scout camping trips together. I went off to military school a few years later, and we didn’t see much of each other after that. We worked together with my dad for a few years in the late 1980s and early 1990s, but went our separate ways again after Dad died.

From his early teens on, Jay was something of a rebel. He had his own idea of what made a happy and successful life, and it was decidedly different from what Dad had in mind. Early on, he tried to fit in to conventional expectations. After graduating from St. John’s Military School, he worked for a few years and then enlisted in the U.S. Marine Corps, where he served for four years. Following his stint in the Corps, he went to work with Dad, building and operating small motels in Colorado, Arizona, and New Mexico. But his heart really wasn’t in it. Jay’s passion was music, and when Dad died he began to follow that passion.

Jay lived for 25 years in the Branson, MO and Eureka Springs, AR areas, working sound and lights for shows, and working at various other businesses. He struggled financially at times, but he enjoyed his life. Jay was a good man who kept mostly to himself, but his friends could count on him for help whenever they needed it. He was a true fan of music, a talented lights and sound man, and a singer/songwriter. We kept in touch, but weren’t especially close. More my loss than his, I think.

Jay struggled with medical issues: a heart attack and bypass surgery when he was 43, gallbladder surgery a few years later, and a motorcycle accident that fractured his pelvis and permanently damaged one foot. A year ago he began having trouble with his leg, and in May the doctors discovered the sarcoma. Two surgeries, chemotherapy, and radiation were unsuccessful in eliminating the cancer, and in December it became clear that he had little time left. Several of us visited him at Christmas as well as last weekend. Mom was there for over a month. Our sister was with him at the end.

Jay asked that there be a private family service, and that if you want to remember him, make a donation to your favorite charity, “or just be good to each other.”

His last words to me, as I was leaving Tuesday evening, were “See you on the flip side, bro.” Ditto, my friend. We miss you.

Live like our ancestors?

I’ve heard people say, during discussions of the evils of modern life, that we should endeavor to “live like our ancestors.” I wonder which of our ancestors they’re talking about.

I wonder if they think we should go back to my childhood, where we lived in constant fear of nuclear war, where there was a single phone in the house, calls out of your immediate area (long distance) were very expensive, and there was no such thing as overnight delivery or even fax machines. If you were lucky you got more than three channels on your television. Fresh fruit and vegetables were seasonal luxuries, and if you were lucky you got two days’ notice of potential hurricanes and floods. Food was more expensive and less plentiful. Airline travel was a very expensive luxury. If you wanted to go across the country it took you several days by train or perhaps a week by bus. And even a rumor of being homosexual could destroy your career and get you killed. A gay man was labeled a pervert, and wouldn’t find any public support. People didn’t acknowledge that gay women existed.

Or how about my parents’ generation, where children regularly died of measles, polio, and other infectious diseases that were mostly a thing of the past when I was growing up? People died of simple infections because modern antibiotics (even penicillin) didn’t exist. Life expectancy was about 65 years in the developed world. My dad recounted stories of trudging through the snow in the middle of the night to the outhouse. That sounds like a great time. Wouldn’t it be just peachy to live in a time when the law enforced discrimination against black people? Air travel didn’t exist for most people. Family vacations were perhaps a trip to the lake in the summer. If you were lucky there was a telephone in the house. If you didn’t live in a city, you might not even have electricity. Refrigeration involved somebody delivering a block of ice to your house every week, so you could put it in the ice box along with the few bits of food you wanted to preserve.

My grandparents grew up on farms. No electricity, running water, telephones, or cars. Going into town involved hitching up the horse and wagon and spending the whole day getting to town and back. Radio didn’t even exist when my grandparents were kids. Children were born at home, without a physician in attendance. X-rays were unknown. Half the population of the United States spent more than half their time just growing and hunting enough food to live. Average life expectancy was about 50 years. In the early 1900s, the infant mortality rate in the U.S. was about 150 out of 1,000. By contrast, the infant mortality rate in Afghanistan today is about 112 of 1,000. Today in the U.S. it’s less than 6 out of 1000. Yeah, it’d be just grand to live in that time period.

Want to go back further? Until 1865 the law allowed people to own slaves. Yes, another person could be your personal property to do with as you pleased. Sounds fun, huh? Average life expectancy was about 40 years. If you lived to be 10, you were lucky to make it to 50. In 1800, close to 40% of children never lived to be five years old. Go back another 50 years or so and parents were lucky if half their children lived to adulthood. In Colonial America, 90% of people were subsistence farmers; they spent nearly all their time just growing and foraging for food. And it was grueling, backbreaking work.

The further back you go, the harder life gets. As hard as anybody thinks life is today, it was much harder for our ancestors. You don’t have to go back very far to find your forebears living in caves and wearing nothing but animal skins. I don’t know about you, but that doesn’t sound to me like a good time.

Those who suggest it don’t really want to live like their ancestors lived. They want to live in a bubble with all their modern conveniences and the benefits of a technological society, while the world outside conforms to some unrealistic notion of the idyllic life their ancestors lived in. Our ancestors did not have it better then than we do now. You’re fooling yourself if you believe that they did.

Wikipedia: Trust, but verify

A recent question on Stack Overflow asked why Quicksort is called Quicksort, even though it sometimes exhibits O(n2) behavior whereas Merge sort and Heap sort are both O(n * log(n)) in all cases. (For those unfamiliar with the terminology, he’s asking why it’s called “Quicksort,” when other algorithms are theoretically faster.) It’s a reasonable question for a beginner to ask.

One person commented that the answer to the question can be found in the Quicksort article on Wikipedia. But the person asking the question rejected that source because “My professor said Wikipedia is not an authentic site.”

I doubt that’s what the professor said, because a college professor telling students not to use Wikipedia would be, at best, irresponsible. I suspect that the professor said Wikipedia should not be cited as a primary source in formal writing, and the student took that to mean Wikipedia is not a reliable source of information. It seems a prevalent opinion among many. I know intelligent people who will not use Wikipedia. At all. For anything. I cannot understand that behavior.

In my experience, Wikipedia is a highly reliable source of information on fact-based topics (historical events, general science, algorithms and data structures, mathematics, astronomy, etc.), and a good introduction when it comes to political, religious, or other emotionally-charged topics. If I want to know what something is or was, then Wikipedia probably has an article about it, and that article will be accurate enough for me to get the general idea. Quickly skimming an article gives me a shallow understanding: enough that I don’t feel completely ignorant when somebody starts talking to me about the topic.

More critical reading not only supplies details, but also gives me a feel for points of controversy. Because Wikipedia articles, especially articles on current events or highly charged topics, are often edited by multiple people, it’s difficult for any single person or group to present a completely one-sided viewpoint. It’s also fairly easy to determine when a topic has been edited to remove any hint of controversy.

The best thing about Wikipedia is that it contains mostly reliable articles on almost every topic of any import. The second best thing is that those articles cite their sources. Every article has a “references” section in which it lists the sources for factual statements made in the article. If a factual statement does not have a reference, there is an annotation saying so. If the article lacks references in general, there’s a big note at the top of the article saying so.

With the references listed, one can easily spend a few minutes reading the primary source material to get more details, or to see if the article presents an accurate summation of the material. A Wikipedia article, like a well-written research paper, is verifiable. Contrast that with a printed encyclopedia, which rarely cites sources.

There are pretty high standards for Wikipedia articles, and the community of editors does a very good job of ensuring that articles meet those standards. If an article does not, there are prominent annotations in the text. If an article appears to be opinion-based, presents only one side of a controversial topic, lacks references, appears to be purely anecdotal, or runs afoul of any number of standards, there is a clearly marked indication of that in the article itself. I’ve seen things like, “this article lacks references” at the top of an article. Or “reference needed” when an unsupported assertion is made. Countless articles say, “This article does not meet standards.”

In short, a Wikipedia article gives you all the tools you need to gauge the reliability of the information presented. Certainly much more than a newspaper, television news channel, printed encyclopedia, magazine article, random Web site, your favorite politician, etc. Of those, only Wikipedia makes it a point to give you the resources you need to verify the information that’s presented.

Other than scientific journals, I can’t think of a general information source that I trust more than Wikipedia. It’s the first stop I make if I want to learn about anything.

Not that I take everything on Wikipedia as gospel. Like any other source of information, there are inadvertent mistakes and deliberate falsehoods in Wikipedia articles. But my experience has been that the number of such incidents is much smaller than in any other source of general information that I’m familiar with. More importantly, such things are typically identified and corrected very quickly.

trust information from Wikipedia articles, but I also verify it through other means. By contrast, I’ve come to distrust information from most news sources, and use other means to determine the veracity of their articles. The primary differences here are that Wikipedia articles tell me where I can verify the information, and I’m usually able to verify it. News outlets pointedly do not reveal their sources, and very often I find that their versions of events are, to be kind, not entirely accurate.

Pickle crack

When I was young–10 years old or even younger–Mom used to make this dill pickle dip. It was creamy, tasty stuff with chunks of dill pickle in it. It was my favorite dip for potato chips. It was a real treat whenever Mom would whip up a batch.

I used to think that Mom got the recipe from somebody who created a knock-off of a dip that you could buy in stores. I later learned that this was something Mom developed when she was a teenager. She called it “Dill Pickle Dip.”

When Debra and I were planning a pool party here shortly after we bought the house, I got to thinking about that dip and called Mom to see if she still had the recipe. She did, and I wrote it down. I think I’ve since lost that piece of paper, but the recipe is real simple. Debra and I make it from time to time. Some friends say it’s addictive and they’ve named it “Pickle crack.”

Here’s what you need:

  • 16 ounces of cream cheese
  • 16 ounces of sour cream
  • A 24 ounce jar of kosher dill pickles
  • Garlic powder (not garlic salt!) or fresh garlic
  • Dill weed (fresh if you like, but the dried stuff works great)
  • A mixing bowl that will hold a bit more than a quart
  • A fork (for mixing)
  • A knife (for cutting pickles)
  • A bag of potato chips (for taste testing)

It’s easier if you leave the cream cheese out of the refrigerator for an hour or two before you start. That’ll soften it up. But it’s not necessary.

Dump the cream cheese into the mixing bowl and start smashing it with the fork. I suspect there’s some technical term other than “smashing.” What I’m doing is making the stuff more spreadable. Otherwise it tends to clump. When the cream cheese is nice and creamy, add about half of the sour cream and mix it in. Once that’s thoroughly mixed, add the other half of the sour cream and mix it in until you have a nice uniform mixture.

Put that aside, open the pickle jar, and grab your knife. Start dicing pickles. 1/4 inch (6 mm) chunks are good. You can go smaller if you like. Or larger, if that’s your thing. I like to stay around 1/4 inch, but this is definitely a matter of taste. Debra likes to use the onion chopper to dice the pickles. That works, but I kind of like cutting them with a knife.

In any event, chop up a bunch of pickles and mix them in with the sour cream and cream cheese. I like my dip really chunky, so I typically chop all the pickles in the jar and throw them in. Others might like a little less pickle.

If the mixture is too thick (again, it’s a matter of taste), you can pour some pickle juice from the jar into the mixture to thin it a bit. Be careful, though. This is dip for potato chips, not for a veggie tray. Although I have put it on a veggie tray once or twice. Carrots dipped in pickle dip is pretty good.

If you like garlic, add some garlic powder. Or, if you prefer fresh garlic, chop up a few cloves. Start with just a bit. Mix it in. Taste it. Maybe add some more. Same with the dill. If you want to accentuate the dill taste, throw in a bunch of dill weed. I suggest you exercise restraint, though. Mix the stuff up real good and then set it in the refrigerator overnight for the flavors to permeate. Pull it out in the morning and mix it up. Taste it. Add more seasoning as you see fit.

This stuff is quick to make and people really do seem to like it. Give it a try if you’re looking for a new taste treat for your potato or other chips.

Drawing attention to or hiding errors

I started my programming career writing COBOL programs for banks. One of my early tasks had me writing a program that would send a letter to all of our loan customers, informing them of a change in the payment notices. Included in that letter was to be a sample of the new payment coupon, which was to be clearly marked as a sample so that nobody would think it was bill and send a payment.

My design for the sample coupon included the words NOT AN INVOICE and NO PAYMENT REQUIRED and DO NOT PAY FROM THIS SAMPLE printed in several places. In addition, the account number printed on the coupon was something innocuous like “123-456-789”, and the customer’s name and address on all the coupons was the same:

Stanley Steamroller
123 Main St.
Thule, Greenland

And the amount due was “$123.45”.

My boss had me take that to the branch manager for approval. The manager praised my good thinking for including the NOT AN INVOICE and other wording, and the obviously fake name and address. His comment: “I was worried that customers might complain about an extra payment notice, but what you have here is clearly a sample. Nobody will be confused by this.”

To my knowledge, nobody called to complain that they had already made their payment and that they didn’t appreciate this erroneous invoice. We did, however, receive several checks for $123.45, with the account number 123-456-789 written in the Memo field, nicely packaged up with the sample payment coupon. It’s fortunate that the checks had the senders’ addresses on them. Otherwise we would not have known who to contact.

The first lesson I learned from this experience is that some people see only what they expect to see ( “Oh, look, a loan payment notice from the bank. Guess I’ll pay it.”). Later (with a similar mailing some months later) I learned that if you want people to stop and think about what they’re looking at, make a glaring error. If I had made that amount $7,743,926.59, I suspect nobody would have sent a check. We might have had a few calls from irate customers saying that they couldn’t possibly owe seven million dollars on their $15,000 loan, but it’s likely that they’d examine the notice a little more carefully before picking up the phone.

If you want people to notice something in a document, make an error that’s impossible to miss. That’ll force them to look more carefully at the rest of the page.

Oddly enough, the converse of that is also true in some situations. When preparing for room inspections at military school, I’d purposely leave something out of order. I wouldn’t make it too obvious, but it’d be something that the upperclassmen always looked for, and that was commonly in error. I found that if I tried to make my room perfect, those guys would spend entirely too much time looking for something wrong. But if I made one or two easy-to-find errors, they’d find the discrepancy, mark it down, and then leave the room happy that they did their jobs.

I think the difference is expectation. When somebody sends you information that you assume to be correct (like a statement from your bank), a glaring error makes you examine the rest of the information more carefully. But an upperclassman who’s looking for an opportunity to gig a subordinate will stop as soon as he’s found an error or two. He has proven his superiority and he has other rooms to inspect.

I’ve heard that the tactic works for tax auditors, too: give him an obvious reason to make you pay a little extra tax, and he’ll give the rest of your records a cursory glance before declaring everything in order. He’s proven his worth, so he can pack up his calculator and head off to torture his next victim.

Notes from the commute

As I mentioned this morning, I’m testing out commuting options. Today’s experiment was to ride the train from Lakeline Station to downtown, and then make the return trip (20 miles) on my bike. The train ride in was, as usual, uneventful. The in-train bike rack is easy enough to use. I rode the six blocks from the downtown station to the office, and was able to store the bike in a corner out of the way.

The ride home is best described as a series of short notes.

  • Jim’s first rule of bicycle commuting is, “You forgot something.” I forgot my sunglasses. A pretty minor omission, really. Not like forgetting my helmet or shoes.
  • I waited five minutes for the elevator before I got annoyed and walked the bike out to the parking garage and just rode down the ramp. Next time I’ll go directly to the parking garage.
  • Most of the ride back to Lakeline is along a route that I used to travel regularly when I worked at the State Capitol 10 or 12 years ago.
  • Riding in downtown Austin is okay as long as you stay in the bike lanes and stay alert.
  • The street after 39th Street is 39-1/2 street, not 40th Street as one would expect. I don’t recall seeing 38-1/2 Street. Guess I should pay better attention to street signs.
  • A long section of Shoal Creek Blvd. is closed for road construction. Fortunately there are detour signs.
  • If you value your life, do not ride Allendale Road during rush hour, regardless of what the detour signs tell you.
  • Due to traffic signals and construction detours, the first third of the ride takes almost half the time.
  • The hills are taller and steeper than they were the last time I rode that route.
  • There are more bike lanes than there used to be.
  • Two bottles of water is not enough when it’s hot. That’s what convenience stores are for.
  • A quart of bottled water costs 50% more than it did 10 years ago.
  • 20 miles on one of the hottest days of the summer (over 100 degrees) probably isn’t how I should have started after not riding for almost a year.
  • Good thing I had a meeting until 5:30. If I had left at my normal time an hour earlier, I might have melted.
  • Google Maps did a credible job of mapping the route for me. I made a few small changes.
  • My legs are tired. They’ll be sore tomorrow.

All that said, I’m hopeful that I can make the same ride on Thursday, although I might cut the trip short: ride to one of the train stations closer to downtown, and take that up to Lakeline. It depends on how my legs feel Thursday.

Three rides for the price of two

I got a new job recently, doing server-side programming for a mobile games company. The big change is that the company’s office is in downtown Austin, about 25 miles from our house. More importantly, it’s a 40 minute drive in light traffic. In normal rush hour traffic the drive is … well, it could be 45 minutes or it could be two hours if there’s a wreck. But even relatively light rush hour traffic is hard on the nerves.

So I’ve started riding the train to work. It’s a six mile drive from the house to the train station, a 40 minute ride to downtown, and a six block walk to the office. I get to the office with a fresh mind, rather than being frazzled by dealing with traffic. And the trip home is pretty relaxing. Most days my brain actually comes through the door with my body.

The only possible drawback is the cost. A one-way ticket on the train is $3.50, and a 24-hour rail pass is $7.00. So for the last two weeks my daily commute has cost $7.00 for the train and about a half gallon of gas getting to and from the train station. Not terrible, really, as driving to work and back would cost me about two gallons of gas. At the current price of $2.50 per gallon, that makes the train trip $8.25 and driving about $5.00. If I had to pay for parking in downtown Austin, the cost of driving would be prohibitive. Fortunately, the company I work for pays for garage parking.

I didn’t take into account wear and tear on the vehicle, but that’s not going to add up to $3.00 per day. On a purely financial level, driving to work is less expensive than riding the train. It’s hard to put a number on my mental health, though. I seriously dislike driving in traffic. I don’t know if Debra has noticed it, but I feel much more relaxed and less irritable on the days I ride the train.

Discount passes are available. For $26.50 I can get a 7-day commuter pass, or about $5.30 per working day. For a little less than $100, I can get a 30-day pass. If you figure 22 working days a month, that works out to around $4.50 per day. That’s cheaper than driving, even at today’s low gas prices. I think I can get that monthly pass through the cafeteria plan with pre-tax dollars, which would reduce it to something like $75, or about $3.50 per working day. The only drawback to these commuter passes is that I incur a commitment. For the weekly pass, I lose money if I don’t ride the train at least four days out of the week. The monthly pass at retail would require me to ride 15 days out of the month, or 11 days if I can get it pre-tax.

It occurred to me last week that I can adjust my schedule just a bit and save some money on train rides. Remember that my daily commuting ticket is actually a 24 hour pass: it’s good for 24 hours from the time I buy it. So if I were to buy the pass at 7:00 AM Monday, I can ride the train to work and back. But the pass is still good until 7:00 AM Tuesday. If I catch one of the two earlier trains (6:08 AM or 6:49 AM), I don’t have to pay for a ticket!

Tuesday afternoon I buy a ticket for the late (5:30) train and ride home. Wednesday morning I take the train in, and Wednesday afternoon my ticket is still good as long as I catch a train before 5:30. All told, I’ve made three round trips for the price of two: a 33% discount. If I go the whole week like that, I end up paying for three round trips and one one-way (the trip home Friday night), for a total for $24.50, or $4.90 per day. That’s cheaper than driving, and I don’t incur a long-term commitment.

But I can do better. What happens if I take my bike on the train on Tuesday morning, and ride the bike back to the station that evening rather than riding the train? If I do the same thing on Thursday, then I end up buying three tickets per week (total, $21.00). For that I get five morning trips to downtown and three trips home. Riding my bike home isn’t a particular hardship unless it’s cold or raining, and I need the exercise anyway. So my commuting cost is $21.00 per week, or $4.20 per day. That’s cheaper than driving and cheaper than the monthly rail pass, but not as good as the pre-tax plan. But I also I get a 20 or 25 mile bike ride in twice per week, and it only costs me a little extra time. Sounds like a win to me.

I’m testing that this week. Monday morning I took the later (7:00 AM) train to the office, and today I brought my bike along when I caught the 6:08 AM train. So this afternoon I either buy a return ticket or I ride the bike back. It’s going to be hot, but I don’t mind. I have plenty of water.

A chance meeting

Debra and I went to Phoenix last week to attend a court hearing (a family matter), and to get some things she had in storage. The trip itself was not exceptional except for one thing.

When we arrived at the court house on Tuesday, Debra went to the information desk to find out which room the hearing would be held in. I was seated not far away answering a work-related mail message on my phone, but within earshot. I could hear that people were talking and even pick out Debra’s voice, but I wasn’t paying attention to what was being said. But then I heard another voice that I sounded very familiar.

When I looked up Debra was walking away from the information desk, and the familiar voice was coming from a Sheriff’s deputy at the desk who was looking in her direction: from my perspective facing more away than in exact profile. I suppose you could say that I was seeing his right rear quarter.

The voice, combined with the profile and the uniform, prompted me to walk toward him and say, “Bob?” He turned around and, sure enough, the deputy was indeed Bob: a guy I knew in military school. We’d met at a few reunions since then, and when I saw him eight or ten years ago he was a deputy with the Maricopa County Sheriff.

We chatted for a while and marveled at the unlikely meeting. Bob’s take on things was “It’s a small world,” and I couldn’t disagree.

But on the way back from the hearing I got to wondering, “what are the odds?” More precisely, what was the probability that I would run into that person at that time. At first it seemed highly unlikely, but then I did a little calculation.

The number of Sheriff’s deputies in Maricopa County is something less than 1,000. If you assume that we had to encounter a deputy, then the odds of it being Bob were, at worst, one in 1,000. That’s not so very unlikely. If you narrow it down to deputies who have that court duty (probably fewer than 100), then it’s only one in 100. And if you restrict it to deputies who have duty in that particular court building, then it’s probably better than one in ten.

Given the conditions, that I ran into Bob is not terribly surprising. It wouldn’t seem surprising at all if I lived in Phoenix and knew that his current assignment was at that building. In fact, I probably would have been looking for him when I entered the building and might even have been surprised if I didn’t see him.

Mathematics aside, a seemingly random encounter with an old friend was a pleasant surprise.