Math is Hard

Every year at work I am required to take a refresher training course in the often-bewildering ethics rules. For two out of every three years, the training consists of certifying that I have looked at a web page. However, every third year the training is in person. This is such a year for me.

In order to keep attendees paying attention, the ethics folks organize some kind of a game. One year it was “football,” in which correct answers would move the ball some random number of yards down the field. Another year it was a version of “Who Wants to be a Millionaire?” I seem to recall a version of “The Weakest Link” as well. This year it was “Deal or No Deal.” For those who haven’t seen the game show, the key feature is that the contestant selects an object of unknown value and he or she can play for the value of the object or can take the offer of some known amount of money. The offer is usually somewhere around the mean value of the remaining objects. (As an example, if the contestant knows that his object is worth either $100 or $1000, the banker might offer $525, slightly under the mean value of the two choices.)

Frankly, my aim is to get out of the room in no more than an hour, and I don’t care about the outcome of the game. My colleagues, however, are so competitive they are constitutionally unable to help themselves. This year they even argued about some of the answers in a legalistic, hair-splitting manner. As a result, one would think everyone should be strategizing about both the answer and the bet - taking the “deal” or not.

As we got to the last two questions, my team was up by about $900 and would get the last question. All of the objects near the average value were gone - all that remained were some low-valued objects ($100, $200, and $600, if I recall correctly) and some high-valued ones (three more in the $2000 range). The “banker” offered around $1000 - enough to get ahead of my team if the other team answered the question correctly. Take the deal? There was a 50% chance that the object would be worth less than $900, and thus the team would lose regardless of whether it got the question right. There was a 50% chance the object would be worth a lot, although the team would still have to get the question right to climb ahead of my team. At that point, we’d still get a chance to answer one more question for the win, and we would know whether we’d have to roll the dice on the object in order to get enough money to win.

Taking the $1000 offer by the banker is straightforward: to win, the other team needs to answer the question and hope we blow our question. If the probability of answering correctly is 50%, then the odds of the other team winning are 25%. Rejecting the offer is more complicated. Half the time the object will be worth too little, and the team loses with certainty. Half the time the object will be worth more than enough to get ahead. Depending on the draw, we might be able to win by taking the banker’s offer and answering the question - the same odds as if the other team took the $1000 banker’s offer. The rest of the time we’d be forced to reject the banker’s offer and hope for a good outcome. We don’t know the odds of this outcome, but if we’re in that branch of the decision tree there’s some chance the other team will win regardless of how we answer the question; otherwise, it still comes down to whether we can answer the question correctly. In short, the only way this choice is better is if the odds are high the first team gets a good draw and the second team gets a bad draw from the remaining objects, because all the other possible outcomes are no better (and some are substantially worse) than just taking the banker’s offer. Yet we could all see the distribution of remaining objects, so the “first team’s draw is good, second team’s draw is bad” outcome is unlikely.

Naturally, the economist-free team rejected the banker’s offer and got an object worth $600. Game over. In the end, I’d like to think I re-learned some of the ethics rules and the other team learned a little about probability theory.

Farewell to Venexia and Goatswood

From Ziki Questi’s blog, I see that two photogenic role-playing sims are about to fade from the grid: Venexia and Goatswood. I never made it to Venexia, despite some good intentions, or if I did I neglected to memorialize my visit in this Journal, but I did report on my visit to Goatswood here.

A Journey to the Ninth Circle of Hell

In Dante’s Inferno, the Ninth Circle, the lowest level of Hell, is reserved for the traitors. Frank Lefravre has re-created Dante’s vision in Cocytus: the Ninth Circle of Hell. (My thanks to Inara Pey for chronicling the exhibit.) A latter-day Virgil starts by crossing a wooden bridge and then descending into the caves.



The circle has four concentric rings, starting with the Caina, named after Cain, and containing the traitors to relations.



The next circle is Antenora, after a Trojan nobleman who betrayed the city to the Greeks, and contains political traitors.



The third circle is Ptolomaea, after the governor of Jericho in the second century BC, who killed his dinner guest (and father-in-law), and is reserved for traitors to their guests.



The fourth area is named Judecca, after Judas Iscariot, and contains traitors to their benefactors. These traitors are completely encased in ice.



At the center of Hell is Satan, condemned for treachery against God. Satan stands waist-deep in ice, beating his wings but unable to escape.



Dante and Virgil escape Hell by climbing down Satan and through the center of the earth, before emerging in Purgatory. Fortunately, one need not take that particular perilous journey; a teleport is all that is needed to escape this particular Hell.

Dante’s Inferno is a popular theme in Second Life, it appears. Back in 2011 this Journal commented on such an exhibit.

Tallights

I don’t put that many miles on my car over the course of a year, but I do have a consistent weekday driving pattern to and from the nearest Metro station parking lot. It’s about 10 miles each way, usually under 20 minutes, depending on how I catch the traffic lights and how much congestion I run into. This gives me the opportunity to observe my fellow drivers in their natural habitat.

I’ve noticed some behavioral quirks among many of these drivers. First, and most irksome: far too many people sit in the left lane, often matching speeds with the car in the right lane. Most of the traffic on my route eventually turns left, but c’mon, guys, a left turn give miles down the road is no reason to move to the left lane now. These rolling road blocks are time-consuming and dangerous. Traffic builds around them and drivers become impatient. At the first sign of a passing opportunity - boom! - someone will take the chance.

A second pet peeve involves people who brake for no apparent reason. I drive a small car, and can’t see around the behemoth SUVs, pickups, and minivans ahead of me. When someone brakes, I anticipate slower traffic ahead. When someone brakes repeatedly, for no particular reason, the brake light starts to lose its ability to communicate useful information about road conditions.

I’m convinced many of the people engaged in spontaneous braking are using the brake to make small speed adjustments. Normal drivers would slow down one or two miles per hour by easing up on the gas and letting friction do its thing. Instead, I get the constant barrage of brake lights from drivers who must believe a car in motion has only two available modes, gas and brake, and stopping one activity involves starting the other.

And don’t get me started on the people yapping on the phone, texting, reading a map, reading the newspaper, performing personal grooming chores,...

The Hazards of a Good Walk

Tourists. God bless 'em.

I'm fortunate to be working a mere stone's throw (or within easy looting distance, for anyone who measures distances that way) of the National Mall, with its numerous museums and mostly car-free walking. Although I would take daily walks when I worked further up town, and that area gave me a more varied set of routes, it's really delightful to take 30 minutes, once or twice a day, to get out of the office and stretch my legs. Less delightful when the temperature is below 35 or above 85, but that's still a good chunk of the year to spend communing with Mother Nature - or at least zipping through the great outdoors before the office beckons. Three things put a bit of a damper on my enjoyment.

First, the drivers of cars, trucks, and, most especially, buses who don't obey traffic controls. I don't mean cruising through a light that's been yellow for a while, I mean people who refuse to believe that right turns on red are to be done *after* a stop, that "no left turn" means it, and, most importantly, that pedestrians in a crosswalk with the light have the right of way. I know it's congested, I know you're in a hurry and want to make the light, but sheesh, you're in a climate-controlled vehicle. Besides, your day would go downhill rapidly if you were involved in a pedestrian death.*

Second, bicyclists who ride, generally illegally, on sidewalks as though pedestrians don't exist. Yes, I know it's dangerous for cyclists to be on the roads with cars. When the sidewalks are largely empty, I'm all for looking the other way. When the sidewalks are choked with pedestrians, however, walk your bike or pedal very slowly. Zipping along ringing your little bell does nothing to improve safety. 

Third, hordes of tourists, especially group tours, especially school groups. I have nothing against tourists: I like going places, so I know what it's like to be in a strange city trying to enjoy the sights. Furthermore, tourists spend money, which is good for the city's economy. But let's all play nicely. If you want to take a picture, I'll walk behind you. In return, don't stand on one side of the sidewalk taking a picture across the sidewalk so that I have no chance to walk behind you. (And no, I'm not walking in the street.) If you're ambling along, I'll go around you; no need to change your speed or direction. But if you're in a group of four or more, please don't spread yourself across the sidewalk so that no one can get by. If you're in a group of 20 waiting for your tour on a crowded sidewalk, please stay to one side, rather than milling across the entire sidewalk. (The Crime Museum on 7th Street is particularly bad for this.) And school groups on the Mall should take up some reasonable amount of space - let's say 95% rather than 100% of the width of the sidewalk, leaving just enough room for one crotchety middle-aged person to get by.

Ah, who am I kidding? Bad drivers are going to drive badly, some cyclists are going to ride unsafely, and tour groups are going to do whatever the heck they want to do. Some days I even remember this, and try to smile as I make my way through the throngs.

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* Always look drivers in the eye if possible. That way you might be able to tell if one is already having a bad day and just doesn't care any more. Let that driver go.**

** The other day I was driving down the highway and passed a car that was moving a little erratically. It turned out that the driver was sobbing uncontrollably. Not good.