Thursday, September 3, 2015

Why I'm Quitting Facebook

I've decided to delete my Facebook account because it's no longer adding to the sum total of my happiness. I enjoy being able to keep in touch with distant friends and relatives, but there are other ways to do that. Besides, look at your own Facebook feed and tell me whether most of the content has anything to do with that. I looked at the first 100 items in my current feed and only 15 were direct posts from actual friends, as opposed to ads, commercial posts from organizations I made the mistake of following, and indirect posts ('liked by', 'commented on', 'tagged in', etc. etc.). That's a miserable ratio of things I asked for to things I didn't ask for, far worse than the ratio of programming to commercials on TV.

I'm certainly not the first to observe the strange and probably harmful worldview found in commercial media --- commercial defined as something you read, watch or listen to that you didn't directly pay for. It's a loose definition; I pay for Netflix but it has many of the same problems. That worldview goes something like this:

- You are an awesome and unique creation and will become even awesomer by reading this story/clicking on this link/buying this product.

- Every illness has a cure if we could only raise money/spread awareness/educate people

- The normal human condition is to be very happy every day, and if you're not, you need to take some kind of action which we will help you with, for a price.

- All conflicts can be resolved if we just get to know each other.

- You are unique in your awesomeness, but also much like other awesome and amazing people we will now tell you about.

- Every person has unlimited, and therefore equal, potential.

- The race is not always to the swift nor the battle to the strong. You also have to have a compelling personal backstory.

- Your life will follow a story arc in which problems will be encountered and then overcome. After your to-do list has expanded and then tapered to zero, you will enter a type of nirvana.

- Life is laden with meaning. Death is a meaningful event that happens to other people.

- When something goes wrong, it is usually the fault of another person.

- People do wrong not because they are acting out of self-interest that conflicts with your own, but because they are inherently evil like the Riddler or Lex Luthor

I could go on.

I don't think it's healthy to be bombarded with this stuff for hours a day. You may think you're smart enough to see through the bullshit, but think again. Do you think you can outsmart professionals who spend millions of dollars conducting ads and media campaigns that exploit every weakness, appeal to your vanity and greed, pander to your biases, and keep you in a perpetual state of unbalance and dissatisfaction in order to get you to act how they want you to act? I think not.

When my kids were watching TV and a commercial came on, I used to tell them, "The product is you." It's time I took my own advice.



Saturday, August 29, 2015

Basilica San Clemente

I just got back from Rome. At the risk of turning this blog into a travelogue, I have to write a few words about a site that was so interesting and full of history, the trip would have been worth it if I had only visited that one place.

The place is the Basilica of San Clemente. It's not far from the Colosseum, a short way up the Coelian Hill. It's a church operated by the Irish Dominicans ever since the Pope gave it to them in the 1600s as a refuge from the persecutions of Cromwell. Like many medieval churches in Rome, you can just walk in during the day and look at the architecture and art. The current active structure was built in the 12th century. There's a guy asking for money near the door, but I wasn't quite sure whether he was actually affiliated with the church, so I didn't put any money on his plate.

Once you're inside the church, there's a small ticket office where you can pay 10 euros to see the "archaeological area" as they (under)state it. For God's sake, do it. It was the best 10 euros I spent on the whole trip.

What is the "archaeological area," you ask? In 1857, the Prior decided to excavate under the basilica. Why? Maybe he was just a bored Irishman making his own fun, as the Irish will do. One imagines there were rumors of ancient chambers under the structure, but there are probably rumors like that about every building in Rome. Perhaps he was talked into it by de Rossi, an archaeologist who supervised the excavations with him.

From some maps I bought in the bookshop, it looks like they initially dug into the floor of the sacristy along an interior wall. It turned out that the wall was the outer wall of an entire earlier basilica (the sacristy protrudes from the floor plan of the earlier basilica.) That basilica, which was actually somewhat larger than the current structure, was built in the 4th century. After several decades of excavation, they had nearly completely uncovered the 4th-century basilica. They observed that  columns supporting the roof of the old basilica had been incorporated into foundation walls, the rooms had been filled with rubble, and the walls of the new basilica had been built more or less directly on top of the lower walls.

Unfortunately the floor of the new basilica was built slightly lower than the ceiling of the old one, such that a lot of late-antiquity mosaics and frescoes were cut off about 3/4 of the way up. I am no judge of medieval religious art, but they are said to be quite significant. It is suggested that one fresco is a portrait from life of Theodora (500-548), the controversial wife of the Emperor Justinian. The bottom of one badly deteriorated fresco reads, "Whosoever may read these letters of my name, let him say: God have mercy on unworthy John." I read those letters and said what he asked!

Oh, by the way, it is believed that St. Cyril was buried in a corner of the 4th-century basilica. You know, St. Cyril, who with his brother Methodius brought Christianity to the Slavs, including a translation of the Bible using the first Slavonic alphabet, which they invented and which evolved into Cyrillic? There were a couple of Russians there to see Cyril's original burial place. The remains were lost in 1798 but supposedly some were returned in 1963.

There's also a fresco containing what is claimed to be the oldest existing written Italian, as opposed to Classical Latin. The sentences contain the phrase, "sons of bitches."

My favorite thing was a marble slab with a pagan inscription on one side that was later flipped over and re-used with a Christian inscription on the other side. They have the thing mounted on an axle so you can turn it over and see each side. That's almost too perfect - I wonder if it is some kind of fake.

After digging out the 4th-century basilica, the archaeologists realized that it was actually the converted second story of a commercial building dating from the 1st century. So they dug out a portion of the ground floor of that building, a narrow alleyway, and another building across the alleyway. The other building was a private home that contained a Mithraeum --- an altar of the Mithraic religion, which was briefly a competitor to Christianity in the waning days of the Roman religion.

Apparently the Mithras cult always worshipped in secret, underground, so the Mithraeum was probably in use at the same time as the 4th-century basilica, after the 1st-century street level had been raised one story. It would have been situated as the basement of the building across the street from the basilica. The Mithraeum would have been abandoned in the late 4th century when the emperor Theodosius banned all pagan religions.

The Mithraeum

In the very bottom corner of the 1st-century structure, a large natural spring issues forth and drains through a duct built in 1937 that joins with a larger discharge, the preclassical Cloaca Maxima, that runs under the Forum to the Tiber River. Before that duct was built, the lower level was full of water and unreachable.

I only relate here the things that made a big impression on me. There is a lot more to it, and in fact, a lot more that could be excavated if they had the funds. You can learn more and donate at the basilica's website.

San Clemente is not exactly obscure (I learned about it from a TV show) but I bet not one in a thousand visitors to Rome goes there. At times in the 1st-century level, I could not see or hear another person, and it's dark and damp. I'd call it creepy, but a better word perhaps is ominous. I could feel the presence of others. This place made an enormous impression on me. It is the kind of thing we simply cannot experience anywhere in the New World.  

Saturday, June 27, 2015

Slaves to Authority

You used to hear a lot about the East Coast being traditional and hidebound, in contrast to the freewheeling West Coast. I always thought this was malarkey. Maybe it was true 100 years ago, when you had to be kind of an adventurer to make it west of the Rockies, but it couldn't be true any more, what with coast-to-coast air travel being so cheap.

Well, after living in both places, I have to say it's all too true. I don't need to give examples of weird and eccentric behavior from California, but what you may find more interesting are examples of Easterners being absolute slaves to tradition and authority.

1. I had some contractors move a window as part of a kitchen renovation. They found a bundle of TV and phone cables running toward the second floor, across the location the window was supposed to be moved to. I told them to just cut the wires, because we don't have any TVs or phones upstairs, and if we wanted them in the future, they would be on Wi-Fi. They absolutely did not want to do it. They called their boss and he told them not to do it. I said I would sign a note giving them the OK to cut the wires, but that wasn't enough. It was either cut the wires or cancel the whole kitchen job, because if the window could't be moved, it would disrupt the whole layout of the new kitchen. It took an hour of arguing over the phone before they finally relented. I'd have cut the damn things myself but I was at work at the time.

2. Had a new slide-in stove delivered, and I had to also pay them to install it, because my wife wouldn't let me make the gas connection. When the installers showed up with the stove on a truck, they said they would not install it, because they do not install slide-in stoves as a matter of policy. They were afraid of getting in trouble for damaging the countertop. I said (a) this particular stove doesn't actually touch the countertop, and (b) why did they bring the stove all the way out to my house if they weren't gonna install it? I couldn't get it through their thick skulls, so they left. Later, I talked to the people I ordered the stove from, and they gave me the excuse that the opening wasn't the right size. The installers never even measured the opening! And they must have noticed that the old stove already in the opening was the same size and make of the new stove. They really tried to twist and turn to get out of installing the stove. Mind you I was paying them a fee to do this. Finally I got it through to the manager that it was in their interest to at least try to install the stove, that is if they wanted me not to cancel the freaking order.

Now I'm trying to get our local school system to let my son do independent study in math instead of taking their standard course. He would still take the exams, but he'd study with me because I could move him about twice the normal speed. I don't need to tell you that when I brought this up with the math department, you would think I'd asked them to let him bring a pet cobra to class. Absolutely out of the question. The frustrating thing is, if I'd brought them a doctor's note saying he had to be given triple the standard time on tests due to a learning disability, plus had to be allowed to submit his answers in Old Church Slavonic, they would have allowed it, because the Authorities say you must let students do those kinds of things.

Wednesday, May 20, 2015

Being There

When I was a kid I used to dream about being involved in space launches and designing jet engines and things like that. They were big but achievable dreams, and in fact I have achieved them. At certain moments I stop being my adult self who carries around a history of gradual effort and advancement, and I go back to being my kid self and I just say, "I can't believe I'm doing this." For example, when I gave a presentation to NASA on how to fix a certain part of the Shuttle after the Columbia accident, for a few seconds I became my 12-year-old self who launched model rockets from the backyard, and I said, "I can't believe I'm doing this." That was also the time I am sure I felt my grandpa standing behind me, in his high boots, all covered in coal dust.

I have several friends who must have had the same beautiful and frightening experience, like my friend from high school the standup comic who did a set on Leno. I bring this up not to brag --- my dreams probably sound boring to some people, and that isn't the point.  I bring it up to make the point that there are certain experiences money cannot buy. It's not just greeting-card bullshit. You cannot buy the experience of discovering a law of physics or painting a masterpiece.

You may say, well, Elon Musk spent $1 billion because he wanted to build his own rocket. That's true, but the $1 billion by itself didn't get him all the way there. He didn't just give some people $1 billion to go off and design a rocket he could slap his name on, he actually designed the damned thing. (With help from a lot of other people, of course, but he was the driving force.) When the rocket launches, it is primarily by his own hand.

This is what I try to explain to my kids when they talk about careers. Like most kids, they would prefer to get rich, but what is the point of money if not to enable you to have certain experiences, even if it's just the experience of living in a 5th Avenue penthouse? But there are experiences that money can't buy. Lots of people have donated money to try to cure cancer, but they cannot buy the experience of actually curing it. Would you rather be the billionaire whose money enables cancer to be cured, or would you rather be the person who cures it?

Come to that, you can't buy the experience of living every day of your own life, whether your situation is happy or sad. You are the one who gets to live it --- or choose not to do so, I guess. This is what Steve Jobs meant when he said "Your time is limited, so don't waste it living someone else's life."



Saturday, May 16, 2015

Election 2016 Special!

I don't take electoral politics seriously. Most government policy is made by unelected bureaucrats who can create whatever regulations they feel like, the law be damned.

Most people either vote a straight party-line ticket or choose a candidate based on superficial things like height, a good speaking voice, physical fitness, a serious but not grave demeanor, and a lack of facial hair. In addition to these qualities, I also feel that a politician should provide entertainment. (It has been said that politics is show business for ugly people.)

It is very hard for the politician him- or herself to be entertaining, because politicians are carefully trained not to outrage even the most strange and bizarre opinions. It's hard to tell a funny joke that doesn't offend someone somewhere.

This is where Presidential brothers come in. We have a great tradition of goofy Presidential brothers - Billy Carter, Roger Clinton, Neil Bush. I don't remember much about the Carter Administration except for the hostages in Iran, and a drunken Billy Carter having peed on an airport runway in the presence of the news media.

So, I plan on voting for the candidate with the brother most likely to make an ass of himself. Here's a rundown of the potential for brotherly embarrassment for some of the major candidates for 2016.

Hillary Clinton: We have some real potential right off the bat here, with brother Hugh Rodham. He had to give back $400,000 he got from a guy who Bill Clinton pardoned. As a bonus, he is both fat and sloppy, which adds color to any comical missteps. The only trouble with Rodham is that he may have learned to stay out of trouble based on his experience during the Bill Clinton administration.

Elizabeth Warren: She has three older brothers, but they keep a low profile. All I could find was them supporting Warren's discredited claim about being part Indian.

Rand Paul: He has two brothers, but what interests me is his dad, Ron Paul, who was himself a candidate the last time around. Ron Paul was generally regarded as the most conservative Congressman of his time, and now he's retired and doesn't have to stand for office any more. He is both a free and original thinker, as well as a very likely source of gaffes and embarrassing associations.

Jeb Bush: Neil Bush is still the likeliest Bush brother to do something entertaining. George is far too savvy (don't be fooled by that down-home personality.) But like Hugh Rodham, Neil Bush has had time to sharpen his game, so he may be less likely to go off message.

Jim Webb: He has a brother, but I couldn't find anything on him. Webb himself may be the more likely source of entertainment. He likes to say what's on his mind, which is why he couldn't be a senator any more and why I don't see him making it far in the primaries.

Bernie Sanders: Now here is where it gets interesting. Bernie Sanders has a brother, Larry, who moved to England years ago and was recently defeated in an election as a Green Party candidate. Bernie Sanders himself is an actual socialist, so his brother is probably a real flake.

Lincoln Chafee: He doesn't have a brother, and moreover, is from an old-line New England political family. Bor----ing.

We have several strong contenders here. Will Larry Sanders tell a British tabloid that his brother's favorite song is the "Internationale"? Will one of Elizabeth Warren's low-profile brothers be caught on video saying "We Chinese, we play joke, we go pee-pee in your Coke"?  Or will Hugh Rodham show us all that he hasn't learned from his mistakes? Only time will tell.










Saturday, April 18, 2015

Warning: Dangerous Post

Recently I went through an experience familiar to most people with jobs: the dreaded annual safety training. I work in an office building and spend most of my day either sitting at my desk or at a table in a meeting room. Once a week or so I might go down to the lab, where they are so worried about peoples' eyes getting injured that they give you a brand new pair of safety glasses every time you go into the lab, and you can just throw them away afterwards. No expense is spared to keep your eyes safe.

My building is climate-controlled, handicapped-accessible and in strict compliance with all safety regulations of the State of New York. But, once a year, I have to spend an hour or two looking at web-based safety training so that I do not trip over a loose rug, strain my back trying to lift a parcel, accidentally guzzle a bottle of whiteboard cleaner with my lunch, or run like a maniac through a plate glass window when the fire alarm sounds.

Things have really changed since 1989, when I worked as a construction laborer to earn money for college. In that job, I dug holes, moved lumber, broke up skids, and ran a power grinder. This was in a high-rise, and several of the upper floors were still unfinished and open to the four winds. I could and did go onto the the roof of the building, which had no safety railing whatsoever.

They were using cranes to lift big slabs of very nice pink marble, like 10 by 20 feet, that formed the outer face of the building. These must have weighed several tons each. Frequently I would have to walk directly under the slabs as they hung from the crane. I also had to walk under ironworkers who were working on the framework above me. Once a guy dropped an enormous wrench that must have weighed ten pounds, from thirty feet above me. If it had landed on my head, it would have driven me about a foot into the ground like a big nail.

Once I and another guy had to use an acetylene torch to trim off several vertical beams that were sticking up through the roof, while standing near the edge of the roof at least fifty feet above the ground. Then for good measure we hauled a pile of torn-up fiberglass insulation to a dumpster. We just picked up big strips of it with our hands and threw it in the dumpster. It itched. One of my jobs was to empty waste barrels into a big rollaway in the basement. Whenever I did that, a big cloud of some kind of dust would blow up into my face. Not to gross you out, but I used to hack up black phlegm at night.

The safety training for that job consisted of the foreman handing me a hard hat and telling me to be careful.

But even by 1989, industrial safety was advanced. They already had the concept of a "confined space"; if you needed to go someplace you couldn't get out of right away in an emergency, you were given a special briefing and someone had to stand watch until you got out. In contrast, I was watching an old movie of some guys building a solid rocket motor in 1956, and two guys shimmied right into the bore of the motor, which was about a foot and a half in diameter. Now, that's a confined space, but if something had gone wrong, no amount of training would have saved them.

I worked at a solid rocket motor plant for a couple of years. When a solid rocket is built, the propellant is cast right into the motor, so there were literally tons of live propellant in many of the buildings. They obviously needed a lot of safety precautions. My favorite was that if you parked your car outside a building where they were handling a lot of propellant, you were supposed to park with the car heading away from the building, with the keys left in the ignition. Then, if something went wrong while you were in the building, you were supposed to bust through the nearest breakout panel (thin plywood panels built into the walls every 50 feet or so), jump in your car, and gun the throttle to get away from the building as fast as possible. They didn't say we had to yell "Waaaaaaaa!" but I would have. I wanted to do that at least once, just for fun, but never came up with a fake reason to.


Here's the building I worked on in 1989. It's the William Green Building in Columbus, Ohio.  I used to go up on the roof (the pyramid-looking thing on the top is just an open framework) and throw paper airplanes.



Tuesday, April 7, 2015

Fads and Fashions in Computing

When I was in high school, we had an IBM PCjr. Despite what you've heard, it was a pretty decent computer. No, it didn't have a GUI, but neither did any other computer of the day except for the Mac, which cost $2495. I think the PCjr was about $1200 including a big color monitor. They both shipped with 128K.

The funny thing about the PCjr was how all the newspapers and magazines complained about the "chiclet" keyboard. They didn't like all the space between the keys; said it wasn't ergonomic. The New York Times said reporters "gasped with dismay" when they first caught sight of it. They said, "Its keyboard is not designed for extended typing." Of course, in the same story, they claimed a 16-bit computer is faster than an 8-bit computer because it can process more bits at one time. That sounds like common sense, but it's completely incorrect.

Anyway, here's the "horrible" chiclet keyboard of the PCjr:




here's the ideal keyboard of that time, the big 101-key Keytronic keyboard.





aaaaand here's a standard Apple keyboard from 2015.

I'd say the PCjr was about thirty years ahead of its time. We used to be such snobs about keyboard quality, and now we type with our thumbs on a flat piece of glass.

Everything old is new. In the early days of the Internet, all the snobs looked down on amateur web pages with flashing type, meaningless counters, animated GIFs, and disorganized or confusing layout.  The worst offense was to have your webpage automatically play a song when it loaded. What if you're surfing the 'net on your lunch hour? Do you want to risk everyone hearing your computer play a MIDI version of "Dixie" when you visit a Civil War website?

Let's see...flashing type, distracting sidebar items, and autoplaying audio. Sounds like pretty much every news site I visit now. It looks a lot slicker, with Flash and whatnot, but it's the same old crap people were complaining about in 1995. The old-timers may have been wrong about the keyboard, but they were right about this.

On a similar note, I was forced to learn Pascal my freshman year in college. Language of the future, they said. FORTRAN's days are numbered, they said. Fortunately, I paid just barely enough attention in that class to get a B, and then immediately forgot Pascal. Sometimes laziness does pay off.

Sunday, March 22, 2015

Robotic Cars and Your Basic Human Dignity

As an engineer, I really hesitate to criticize Elon Musk. This is a guy who, when it's all over with, will probably have done more for technological progress than anyone since Edison. So this is like Joe Shlabotnik criticizing Mickey Mantle. But success can breed hubris. Musk thinks that, for safety reasons, it should eventually become illegal for people to drive cars. All cars will be driven automatically by an algorithm.

Cue the satire.

Banning human-driven cars? Not a moment too soon, I say. Over 30,000 people a year are killed in car accidents in the U.S. If there's one thing that made this country great, it's the avoidance of all possible risks. Who can forget the great Federal Actuarial Council of 1968 that calculated a 10% risk of death for the Apollo astronauts, and pulled the plug on the foolhardy moon mission? Or the Over-land Travel Committee of 1840 that made it illegal to cross the Mississippi without 180 days' hard rations, six draft animals per person and a federally approved wagon? That stroke of genius stopped what would have been a disastrous mass movement to the west. Experts say that without that act, America would have eventually taken California from Mexico. When you look at the miserable standard of living in, say, Palo Alto these days, I consider that to have been a bullet dodged. America the Safe.

Anyway, robotic cars are still driven by humans, they're just driven indirectly by humans. Someone still has to design the car and determine how the steering algorithm functions. But let's face it, most humans are unqualified to decide the safe speed for a car, and they're getting worse by the day. The average person has little understanding of rigid-body dynamics. The navigation of cars should be restricted to those who can write the Lagrangian for a mass-spring-damper model of an automobile and derive the equations of motion.  

The Google self-driving car

The self-driving car from Sleeper by Woody Allen

I say let's take it to the next logical step. Many car trips are unnecessary anyway. The best way to avoid an accident is to just stay home! If your car can control which route to take and how fast to go in getting to the destination you select, then certainly it can just refuse to start at all, if its algorithms determine you don't need to be taking the trip. It should be very simple to track how many trips to the grocery store you made this week. Let's face it, if you can't get your groceries in two trips, you should just order out. In fact, it should be illegal to drive to the grocery store at all. It's much more efficient and safe, and easier to control your food consumption, for the grocery store to make delivery rounds with an automated van. And I hardly need to tell you how many people are abusing their driving privileges to attend demonstrations, visit the wilderness and annoy government officials in their places of work. Enough is enough.

Call me a dreamer, but I envision a day when nobody will leave the house at all. We can just stay inside, happily consuming infotainment and food of scientifically calibrated goodness.  

Libertarian extremists think everyone has the right to choose his own level of risk. But that kind of anarchy has led to the situation we have today, where maniacs think that just because it's a clear, dry day free of heavy traffic and they are late for their daughter's wedding, that it's OK to go 73 miles an hour down a rural interstate. What's next, the return of do-it-yourself auto repairs? Yeah, like I really want to drive on streets filled with cars whose oil was changed by shade tree mechanics instead of ASE certified automotive technicians.

The future looks bright. Instead of the constant, day-to-day grind of having to make decisions in the face of incomplete and uncertain information, people will be freed to live tranquil lives in which the only course of action permitted is that determined as optimal by algorithms created and approved by a central body of experts. You'll wake up and a message on a screen will tell you which color pants to put on.

Satire concluded.

The question you have to ask yourself is: are you using technology help you live, or are you using it to live life for you?



Saturday, February 14, 2015

The Time I Almost Got Killed in a Car Accident

When I was 22 years old and working at my first real job, I of course bought my first new car. I was a single guy making engineer money and looking for something to spend it on. I bought the car that had the lowest ratio of 0-60 time to purchase price. Yes, this is really how I made the decision. I still think this way.

The car was a Plymouth Laser, the two-wheel-drive turbo version. Ha, you say, a Plymouth? This thing was a rocket ship. It was a really light, small car with 190 hp, and handled like an American sports car, which is to say not very well. When the turbo kicked in, the torque steer would yank the wheel out of your hands.

I bought the car from a dealer in Columbus, Ohio - I picked out the options and they had it shipped over from another dealer somewhere else in Ohio. When the car came in, I went down to pick it up and the salesman started writing up the deal using the sticker price of the car. Whoa, I says, I'm not paying sticker price. He said, oh, OK, how much are you going to offer? I don't remember exactly what I paid but it wasn't sticker. What I do remember is the salesman, who was extremely fat, like 450 lbs, telling me about how he walked a paper route on his off day to "keep in shape and earn extra money." He was good, this salesman.

Anyway, I had fun driving the car all summer. I used to have to drive over to the Transportation Research Center for work, and it had a long driveway on its private property, maybe a mile long with only a couple of gentle curves in it, so you could really get up some speed. I had it up to 115 once and was still accelerating but chickened out because the wipers started lifting off the windshield.

The TRC driveway where I went 115

That winter, one Friday night some of us at work decided to get together at a roadhouse in a tiny town called Broadway, which was a few miles north of the office. We never made it to Broadway. We pulled out of the office around dusk. (At that time, the entire American Honda design department fit into one room in a low building now occupied by the Honda Federal Credit Union, on State Route 739. I had badge 125; they must be close to 10,000 by now. But I digress. )

So three of us, myself and Jim and Tim (not their real names), went busting up 739 toward Broadway. I was way ahead of both of them and didn't notice the curve until it was way too late. I was probably going 80 on the straightaway and maybe braked down to 60 by the time I hit the curve, so there was no way I was going to stay on the road. It would have been OK except there was a drainage ditch along the road, and when I went off the road, the ditch flipped me. I think I went over three times, but don't really know. It was definitely more than once. Time really does slow down to give you a chance to think about your lifelong regrets in a situation like that.


Route to near-oblivion, also known as State Route 739

Luckily, I came to rest wheels-down and still strapped into my seat. If I hadn't been wearing a seat belt, you would not be reading this blog. I was kind of dazed, but actually not hurt at all, except for some small cuts on my head from flying glass that I didn't notice until the next day. Gradually I regained my senses as the mangled windshield wipers came spontaneously to life, working back and forth over the empty frame where the windshield used to be. There was not a square foot of that car that didn't have damage on it. I remember calling in the claim to my insurance company and them asking me if it was a total, and I said, "Uh, yeah...I'm pretty sure."

I could see Tim running to the car in the darkness, and he stopped about 50 feet away, I know because he was afraid of what he was going to see in the car. So I had to yell to him that I was OK. Somebody called an ambulance, and I took a ride to the Marysville Hospital (they gave me oxygen over my objections and then charged me $10 for it) where they let me go after checking me out. I called my girlfriend and she came out and picked me up. When we went out into the parking lot, I discovered both my jacket pockets were filled with tiny bits of shattered glass.

After the accident, Jim gave me the single best piece of advice I've ever gotten. I was already paying a risk premium on my insurance because of previous automotive-related indiscretions, so this accident would probably have made me uninsurable. Jim told me to immediately lease a car through the employee lease program. The lease came with its own insurance, and if I did it before my court date, the insurance company wouldn't know about the accident. The idea worked like a charm. Jim also let me drive "loaner" cars for the 30 days or so until my lease was ready. (At work they would buy competitors' cars and have employees put miles on them, then take them apart to see how well they held up. Jim was in charge of these cars.) Later I was able to pay Jim back by helping him with a couple of roofing jobs, but I came out far ahead on the deal. Jim, if you're out there, you know who you are --- thanks! When the two-year lease was up, I had two years of clean driving and was able to get regular insurance again.

I did get convicted of reckless operation and had my license suspended for a month, with driving privileges only to work. In the 22 years since, I've had a total of one speeding ticket (55 in a 35) and no accident claims. But I had to learn the hard way.





Tuesday, February 3, 2015

The Truth About STEM Careers

Back when I had more free time, I used to do a lot of "STEM outreach" --- judging science fairs, busing kids to NASA, that sort of thing. In my mind, the idea was to show science and technology to kids in a positive and realistic way, so they had good information to base a career decision on. I never tried to talk a kid into being a scientist. The only persuasion I did was to convince kids they could be scientists if that was what they really wanted. I also hoped to create an appreciation for science in kids who weren't going to be scientists (i.e. most kids), but who would likely come to have some influence over whether science will continue to be supported in our society.

The truth is that the vast majority of people would be unhappy with a career in science or technology. Not only unhappy, but disappointed, because of what they hear about how great STEM careers are supposed to be from various interested parties like big companies and universities.

First, it is totally untrue that there is a shortage of scientists and engineers. On the whole, it is no easier to get and keep a job in STEM than in any other field that requires a college degree. Certainly, companies would like as many STEM workers as possible to choose from, because then they can get more productive workers without having to pay high salaries. But true shortages are really rare - the ones I can think of were for aerospace engineers in the late 1950s and for anyone who knew anything about the Internet in the late 1990s. At those times, you could get multiple offers and signing bonuses. But even in times of high STEM unemployment, you still hear about this supposed worker shortage. People have heard it for so long that they don't question it anymore.

I do believe that having more STEM workers productively engaged in advancing the state of the art must be good for the country. But it is not as if there are projects going stale for lack of engineers. The investment just isn't there. That is a totally different problem than not having enough workers.

Another issue is the way STEM careers are portrayed by well-meaning adults who want kids to go into STEM. Here's a site that presents storm chasers, robotics researchers and and astronauts as sort of typical STEM careers. The reality is that most STEM jobs are nowhere near as fun as that, and the competition for the really fun jobs is very stiff.

When I was thinking about a career, I had the idea that going into STEM was sort of a short-cut to a high-prestige, professional career like law or medicine, but without having to go to graduate school. I didn't really know any scientists or engineers when I was a kid, so all my knowledge came from the media. My "STEM outreach" work was partly to help other kids not be in that position of ignorance.

With a bachelor's degree from a "not top ten" university, you are not going to be designing or inventing much of anything. I know, because I was there once. You're going to be doing things like keeping track of which parts go on which washing machine or lawnmower, figuring out how to save 3 cents a part by reducing the thickness of some material, and writing user manuals.

Now, doing that for a living maybe is not so bad compared to, say, road maintenance or moving boxes in a warehouse. But when you look at what it takes to even get a bachelor's degree in engineering, it doesn't seem worth it. For example, to get a BS in engineering, you'll have to pass a course in differential equations. I reckon that you need to be in the top 5% of mathematical ability to even stand a chance of doing that. And once you do, wouldn't you want to use that knowledge? In the job I had with only a bachelor's, I barely did algebra, let alone calculus. I had a calculator, but only ever used it to add up costs! Probably the average accountant does as much math as BS engineers. A lot of engineers got suckered into getting BS degrees, thinking they'd be designing Corvette engines or something. Twenty years later, they've designed a lot of pipes and brackets and they're wondering where the time went.

So getting a BS in engineering is no short cut to professional prestige. To get the really fun jobs, you need a Ph.D., which is certainly harder than law school and might be about as hard as med school. I think you have to be smarter than the average med student to get a STEM Ph.D., but you probably don't have to work as hard unless you have a real asshole as a research advisor. You do get paid (very little) to go to grad school instead of having to take out loans as in law or med school. If you find yourself paying your own way through a STEM Ph.D., you should really just forget it. Go to culinary school or become a llama rancher.  

It might be possible to short-cut that process by getting involved in startups. But that option is not available to most people; it certainly wasn't to me. You have to have savings or rich and generous parents to tide you through those lean times when your startup is unable to give you a paycheck.

Having thrown all this cold water on STEM careers, you might be expecting me to say I don't like my job. On the contrary, I love it. And to any kid who really likes science and technology, I say: you'll love it, too. But you need to be ready for a long slog. Like the song goes...




Tuesday, January 27, 2015

After my post yesterday about the mine wars, a friend asked about the Sid Hatfield murder. Sid Hatfield was the Chief of Police in Matewan, WV in 1920. Some mine "detectives" came to town to evict strikers from their company-owned houses, and Hatfield got together a posse, saying he would kill the detectives. There were several confrontations, the last resulting in a shootout that left seven detectives and three townspeople dead, including the mayor, Cab Testerman.

Some said Hatfield boasted about pulling the trigger on the head detective, Albert Felts, while others said they saw him track an injured Felts into the post office and finish him off. Two weeks later, Hatfield married Testerman's widow, leading to speculation that the whole shootout was a pretext to get Testerman killed so Hatfield could have his wife.  Hatfield took over Testerman's jewelry store and turned it into a firearm supply shop for union men.

Hatfield was tried, but beat the murder charges by claiming self-defense. He said Felts fired the first shot, at Testerman. Highly unlikely, not because Felts was an especially honorable man, but because he was a professional detective who had no particular reason to shoot a town official.

Soon after, Hatfield was charged with another shooting at Mohawk, for which he was supposed to stand trial in Welch. He had also been accused of blowing up a tipple and rifle-butting the superintendent of the Stone Mountain Coal Company when that company's mines were being struck by the UMWA. This was not all the trouble Hatfield was in, but I want to wrap this up.

When Hatfield went to Welch to stand trial, Everett Lively, a secret agent working for the mine operators, shot him dead on the courthouse steps in front of his new wife, the erstwhile Widow Testerman.  Hatfield, who was clearly what we today would refer to as a total dirtbag, became an instant martyr to the UMWA.

Anyway, my friend asked whether Hatfield's family had been killed with him. They were not, but I wondered whether he was thinking of the Jock Yablonski murder in 1969. Yablonski had just been elected president of the UMWA as a "reform" candidate. The former president, Tony Boyle, hand-picked successor to John L. Lewis, hired a hitman using embezzled union funds to kill Yablonski and his wife and daughter. Such a nice group of people.

I wrote yesterday that the mine wars were started by the UMWA on behalf of competing coal companies. They sent organizers, but things quickly spun out of control. After the 1921 "Battle of Blair Mountain," which resulted in a visit from the U.S. Army, including a wing of bombers, the UMWA tried to wash their hands of the situation, but they should have known what they were getting into. (The Army did not actually drop bombs on the union. That was done by planes privately hired by the Sheriff of Logan County.)

The union men tied red bandannas around their necks and called themselves rednecks, although the word already meant exactly what it means now. Are rednecks prone to violence? Not really. The violent crime rate in Mingo County, WV today is lower than the national average. It is 2.07, compared to a national average of 3.8. For comparison, the rate in Chicago is 9.00. But crime seems to come in waves, when there are are rival groups. Rednecks do not shoot each other over shoes or video games; there has to be some kind of group dynamic going on. This was well known when the UMWA went into WV, because the Hatfield-McCoy and other feuds that were mainly an aftermath of the Civil War had just died down. The UMWA going into West Virginia, and playing groups off one another, is like Nike trying to market shoes by getting the Rolling 60's to adopt them as a gang uniform. You don't think personal grudges played a role? Everett Lively and the officers of the UMWA local were childhood friends turned enemies!

Anyway. I wanted to say one last thing about John L. Lewis, the so-called hero of the UMWA. Here is a typical miner's house





and here is John L. Lewis's house











Monday, January 26, 2015

Another Book About the Mine Wars

I'm reading a new history of the West Virginia mine wars by historian James Green, called The Devil Is Here in These Hills: West Virginia's Coal Miners and Their Battle for Freedom. The story, though told many times, is still exciting.
From the front page of the New York Times, August 2, 1921

Prof. Green says he is an "activist scholar," and his career has been one of advocacy for collectivism.  It is no surprise, then, that the book paints the union organizers, who were generally associated with the United Mine Workers of America, as heroic defenders of the working man. As for myself, I am no historian, just the descendant of "company men" who were caught in the middle of the so-called mine wars. When UMWA members were stockpiling guns and ammunition, blowing up tipples and killing company officials in 1921, my grandfather was working miles from home, because the mines back near his home in Ottawa, Boone County, were shut down by strikes. Later that year he was called back to Ottawa to help with an armed defense of the mines and to stop the miners' army from getting through to Logan County to continue wreaking havoc. So you can expect that I have a somewhat different take.

Apparently, public TV has bought the rights to this book and plans to make an American Experience episode out of it. You probably also know about the movie Matewan. A thousand times more people will read the book and see the TV show than read this blog, but still, one must try. It's not my contention that unions are always wrong and companies are always right. In fact, I would never have been born were it not for the UMWA hospital at Welch, West Virginia. But I will make the case that the mine wars were a tragic waste of lives and property that had little to do with workers' rights per se.

Like Green's book, most histories of these events uncritically support the union men. The only really objective one I know of is Bloodletting in Appalachia by Howard Lee. Nearly all the others see the conflict as a moralistic good-versus-evil battle pitting a grassroots movement of saintly miners against oppressive mine operators straight out of a Dickens novel. These kinds of fairy tales are not only condescending, they are by now boring.

You have to realize what a strike meant in the early 1900s. Today, a strike means a picket line. Back then, a strike meant shutting down an operation by beating or killing people on their way to work and by destroying equipment. It is easy to criticize the mine operators for hiring private armies to break strikes if you have the modern kind of strike in mind, instead of what strikes were really like in those days.

By 1912, both the mine operators and the union were using tactics that have no place in decent society. The operators were running company towns like lords over a medieval manor, firing and blacklisting any miners who spoke or acted in ways that displeased management. For their part, the union was using guns and dynamite to shut down nonunion mines.

The natural question is, who started it? Who set off the chain of events that spun out of control until the Army had to be called in?

Contrary to Green's telling, the mine wars were anything but grassroots in origin and anything but ignited by oppression. In 1898, a coal cartel called the "Central Competitive Field" was formed, covering Ohio, Indiana, Illinois and western Pennsylvania. It sought to preserve profits by limiting production, exactly like an OPEC for coal, preventing price competition that would have reduced the cost of coal to consumers. Ultimately, the CCF was willing to pay whatever wage the UMWA demanded and just pass it all onto the consumer. The trouble is, the plan could only work if it were extended over the whole industry, otherwise other mines could undercut the cartel. In exchange for high wages, the UMWA promised the CCF it would unionize West Virginia, which would stop mines there from selling cheap coal. Green claims this is a "conspiracy theory," but alas it was a real conspiracy, not just a theory. Here is a high official of the UMWA, complaining to Congress in 1921 that the CCF operators were not helping them carry out this very promise:

Let me point to the fact that the United Mine Workers of America have diligently and aggressively attempted to carry out the promise made in Chicago in 1898 that they have done everything in their power to redeem any promise they may have made to organize West Virginia. Since 1898 our organization has at various times spent hundreds of thousands of dollars trying to unionize West Virginia. We have also sacrificed human life in the attempt to redeem that promise. In view of the fact that we have spent hundreds of thousands of dollars and that our organizers, our members who have gone there as missionaries in an attempt to redeem that promise have sacrificed their lives and their liberties, we should be given credit for what we have done. I want to ask the operators how much money they have spent and what they have done to aid us to organize West Virginia? 

I can guess that the CCF would respond by saying that it was ultimately their mines that were the source of every one of the hundreds of thousands of dollars mentioned above. In effect, the CCF gave the workers a raise, a good portion of which went to the UMWA's strike fund, which had a double function as a sabotage operation against the CCF's competitors. The CCF agreement is a much more convincing explanation of when and why the mine wars happened in West Virginia than any spontaneous uprising of oppressed miners.

It is worse than that. Not only were the "mine wars" sponsored by the CCF, they actually achieved nothing but to rain death and destruction on operators and miners alike. There is no definitive tally of deaths, but in reading these histories, there are one or two killed here, and ten killed there, and a powerhouse blown up here, and children starving in strike colonies there, so it adds up to a lot of suffering.

In the end, the strikes and violence did nothing to unionize southern West Virginia. It was unionized (in 1933) by the federal government, when Roosevelt's NIRA was passed. And once again, the welfare of the workers was incidental to the real goal. The NIRA was drafted by another cartel, this one covering much of American manufacturing. Even liberals came to recognize that the NIRA was crony capitalism at its worst. Most of it was found unconstitutional in 1935, but the labor provisions were retained by subsequent legislation.

The role of the UMWA and its leader, John L. Lewis, is outlined here:

Northern coal-operator associations joined John L. Lewis...in helping to draft Section 7(a) of the NIRA. Because most northern mines had been unionized long before 1933 and could not be deunionized, their owners had long sought the unionization of Appalachia's mines as the ultimate solution to Appalachia's low coal prices...Lewis accepted what amounted to price fixing under the NIRA...in exchange for labor leaders' treasured Section 7(a) of the legislation. Lewis reportedly said at this time that he was only looking out for current miners. Miners' sons, he reportedly said, would have to look for work in the cities. Lewis was manifestly not, however, looking out for all current miners, His initial proposal for a nationwide daily minimum wage of five dollars for all coal miners would have ruined many Appalachian operations, throwing their miners out of work.

Let's think about this. In the depths of the Depression, with people breaking up furniture and burning it in their fireplaces to keep warm, the main concern of the federal government is...that there is too much cheap coal being mined in Appalachia. That is some kind of crazy.

The UMWA, like all unions, promoted the idea that workers have a claim on profits which only the union can help them get. But the CCF and NIRA episodes show that the miners' gains didn't come out of existing profits, they came out of coal prices paid by the public that were inflated by monopolies set up with the connivance of the UMWA. It sort of undermines the whole union narrative.

The UMWA and its allies in the press tried to drum up support for the union by depicting the desperate conditions that existed at times in the mining camps as luridly as possible. It is true that life was desperate at times in the West Virginia mining camps. But whose fault was that? The papers complained that families were living in tent colonies with little to eat. But they failed to point out that those same families had been living in houses with a regular wage until the UMWA induced them to strike. And the very worst times in the coalfields happened in the late 1930s, after unionization.

The saddest chapter is that the UMWA sold out the miners partially after the 1921 battle and completely in 1951 when John L. Lewis accepted the mechanization of the mines in exchange for higher wages for existing miners. It fulfilled his threat that miners' sons would have to look for work in the cities. Mechanization was of course inevitable, and beneficial to the consumers of coal, but that argument would not have garnered any support from the miners, had they been asked.

Green acknowledges this repeated betrayal by the UMWA, which started the whole mess back in 1898, but ends the book by describing a utopian scene of union solidarity in which West Virginia miners enjoy safe working conditions, job security, and sunny days forever. In fact, that lasted about ten years, because the UMWA was bleeding the mines dry. Green says he went to West Virginia recently to see Blair Mountain, where the UMWA battled the coal operators and the police. Do you know what he didn't see? Any of my grandfather's seven kids or their descendants, because they had to disperse from West Virginia to five different states in order to make a living.

Somebody will say that West Virginia's problems were due to the decline of the coal industry, which the union couldn't control. Not so. Even with recent moves to restrict coal-burning power plants, more bituminous coal is being mined now than before unionization, but the industry supports only a small fraction of the families it used to. The UMWA didn't stop the process or even try to slow it down. So what did the violence achieve? Do we really need to hold up this blood-soaked history as something to be proud of, or as an inspiration to today's workers? Blair Mountain should be protected from mountaintop removal and preserved in the interest of history, but as caution, not inspiration.



Saturday, January 17, 2015

Math Extra #3: Functions

Ten months ago I posted Math Extras #1 and 2 which I wrote for my son. At long last, here is Math Extra #3. This is for kids taking algebra. By the way, I solved the problem of how to typeset math in Blogger by using MathJax. It isn't perfect, but it's a whole lot better than the alternatives.

Functions

In the later stages of algebra, and on into calculus, we start to study functions a lot. A function is just a rule for generating a value from an input. The input is called an argument. Usually, the function is an algebraic expression, like $x^2-10$. For an input or argument of $x=1$, the value is $1^2-10$, which is $-9$. Sometimes we want to refer to functions by name instead of explicitly. First I'll talk about why we would want to do this. Then I'll give some examples and problems.

The following shows the difference between writing a function explicitly and referring it to by name:

Explicitly: ``The function $y=x^2+x-6$ has the value zero for $x=2$ and $x=-3$."

By name

  •  First we give the function a name: $f(x) \equiv x^2+x-6$
  •  Then we can refer to it by name: ``$f(x)=0$  for $x=2$ and $x=-3$."

The explicit statement of the function above uses the dependent variable $y$. Don't confuse the name of the function with the dependent variable. We can use any dependent variable we want; for example, we could write $y=f(x)$, meaning $y=x^2+x-6$, or we could write $z=f(x)$, meaning $z=x^2+x-6$. You say $f(x)$ like this: ``f of x."

Naming a function makes it easy to talk about different arguments. We can write $f(5)$ when we mean $5^2+5-6$. We can also write $f(x+2)$ when we mean $(x+2)^2+(x+2)-6$. Eventually, you will study functions that have more than one argument, such as $f(x,y,z)$.  You would say this as, ``f of x, y and z."

Did you notice that when I named the function, I used the symbol $\equiv$ instead of $=$? The three lines are on purpose. They indicate that this is a definition, just giving something a name. That's a completely different idea than stating two things are equal to each other. Not everyone is careful about this. They might give the definition as $f(x)= x^2+x-6$. But I think you can see that $f(x)=2$ is an equation, and doesn't have anything to do with the definition $f(x)\equiv x^2+x-6$. An explicit way to write that equation is $x^2+x-6=2$.

This naming may seem like too much trouble, but functions can become very lengthy and we may want to refer to them again and again. For example,

``The gamma function is defined as $\Gamma(t)\equiv\int_0^\infty x^{t-1} \text{e}^{-x} \, \text{d}x.$ It satisfies the identity $\Gamma(t+1)=t\Gamma(t)$. It is closely related to the factorial, because for integer arguments, $\Gamma(n)=(n-1)!$"

It's not important to understand what the preceding sentence means, just to appreciate that it would have been a lot longer and more confusing if we had to refer to the gamma function explicitly instead of as just $\Gamma(t)$.

Giving a function a name enables abstraction, which is what math is all about. By abstraction, I mean talking about the general properties of something instead of just specific examples. You already know that a variable can be used to represent a number, as in $x=5$. And you also know that we can make statements such as $x+y=y+x$. That equation expresses the commutative property of addition. It's true no matter what the specific values of $x$ and $y$ are. If you think about it, this simple statement contains a tremendous, in fact infinite, amount of information. To write it without using variables, you would have to write
\begin{align}
1 + 2 &= 2 + 1 \\
1 + 3 &= 3 + 1 \\
1 + 4 &= 4 + 1 \ldots
\end{align}
and so on, covering all possible sums of two numbers. Without using variables, it would literally require an infinite number of specific examples to completely define the commutative property of addition.  

Using named functions enables a similar kind of abstraction. For example, a fact about functions from calculus is
\begin{equation}
\frac{\text{d}}{\text{d}t}f(x(t))=\frac{\text{d}}{\text{d}x}f(x)\frac{\text{d}}{\text{d}t}x(t)
\end{equation}
This is true no matter what the functions $f$ and $x$ are. For now, you don't need to know what all the d's are doing, but you can see that this would be impossible to write without being able to refer to functions by name instead of explicitly. This example also shows that the argument of a function can be a function itself.


Examples

Let $f(x)\equiv x^2+2x-3$. If $x=0$, then $f(x)=-3$. Another way to write this is $f(0)=-3$. On the other hand, $f(-1)=-4$. The values of $x$ for which $f(x)=0$ are called the zeros or roots of $f(x)$.  Note that these are not $f(0)$.  They are the solutions of the equation $f(x)=0$.  The roots of this $f(x)$ are $x=1$ and $x=-3$. Not every function has roots.

A function that has the same value for both signs of an argument is called an even function. $g(x)=x^2$ is an example of an even function. Its value is 4 for both $x=2$ and $x=-2$. If a function has the same value except with the sign flipped, it is called an odd function. $h(x)=x^3$ has the value $h=27$ for $x=3$ and $h=-27$ for $x=-3$. Therefore, it is an odd function. The function $f(x)$ as defined above is neither even nor odd.

It's important to understand the difference between the value of a function and the function itself. Let $f_1(x)\equiv 4x-4$ and $f_2(x)\equiv 3x-3$. It is true that $f_1(1)=f_2(1)=0$. However, $f_1(x)\neq f_2(x)$ otherwise. They are two different functions.

Sometimes we can draw conclusions about a function even if we don't know exactly what it is. ``Forget" the definition of $f(x)$ we stated above, so that we can re-use the name $f$. Now, if $f(x)=3f(2x)$, and $f(6)=-5$, then $f(3)=-15$. How do we know this? Let $x=3$ and evaluate $f(x)$ and $f(2x)$.  In this paragraph, we have discarded the old definition of $f(x)$. You have to be careful to understand when a function has been redefined. Math books or exams will typically be very careful about this. When they talk about $f(x)$ in a single problem or explanation, they usually mean the same definition of $f(x)$. Science books might not be so careful about it. When they say ``If $f(x)=\ldots$", they probably only intend that definition of $f(x)$ to hold in that particular statement.

The name we give to the argument doesn't matter in some situations. If $x$ and $z$ are two unknown numbers, then writing $f(x)$ is pretty much the same as writing $f(z)$ unless we know something about $x$ and $z$.  The only thing to be careful of is not to use the same name for the argument as for the value of the function, unless you really mean it. If you write $y=f(x)$, there is a value of $y$ corresponding to each possible value of $x$. But if you write $x=f(x)$, you've written an equation that may be solvable for $x$. For example, if $f(x)\equiv 5x-3$, then the equation $x=f(x)$ has one solution, $x=3/4$.

Because the important thing is the form of the function, and not the names of the variables, sometimes people write functions as $f(\bullet)$. That means any name could be used for the argument. This is because, for example, $f(x)\equiv 4x^2-x+1$ and $f(z)\equiv 4z^2-z+1$ are really the same function. Everything that is true of $f(x)$ is also true of $f(z)$, as long as there is nothing special about $x$ and $z$.

When the argument of a function is itself a function, the overall function is called the composition of two functions. It can just be written as $f(g(x))$, or it can be written more formally as $f \circ g$. For example, if $f(x)\equiv 2x-1$ and $g(x)\equiv -x+8$, then $f(g(x))=2(-x+8)-1=-2x+15.$

When a function is raised to a power, say the power of 2, it's written $f^2(x)$, not $f(x)^2$. Note that $f^2(x)$ is not the same thing as $f(x^2)$.


Problems

1. If $f(x)\equiv x+3$ and $g(x)\equiv 2x-3$, for what value or values of $x$ does $f(x)=g(x)$?

2. Is $g(x)\equiv x^4+x^2+3$ even, odd or neither?

3. What are the roots of $f(x)\equiv x^2-36$?

4. Suppose $f(x)$ is odd and $g(x)=3f(x)$. If $f(2)=-4$, then what is $g(-2)$?

5. If $\phi(y)\equiv 3y$, what is $\phi^3(z)$?

6. If $f(x)\equiv 4x+9$ and $g(x)\equiv x^2+3x+7$, what is $f \circ g$ for $x=0$?

7. If $f(x)$ and $g(x)$ are both even, and $f(5)=1$ and $g(-1)=5$, then what is $f \circ g$ if $x=1$?

8. Is composition of functions commutative? Hint: Let $g(x)\equiv -x$ and $f(x)\equiv x^2$. What is $f \circ g$? What is $g \circ f$? If you have trouble keeping track of the signs, substitute in a specific value like $x=1$.


Extra Info

You have probably seen things like $\sin(x)$ and $\log(x)$ on your calculator or elsewhere. These are named functions. They have fixed definitions (not given here) that everyone in math accepts. Whenever anyone writes $\sin(x)$, everyone knows it is the sine function from trigonometry. So don't choose names for your functions that are the same as the standard ones. But aside from the fact that these are standard functions, they work just like the functions you name yourself.

One thing about the standard functions is that their names are always typeset in Roman font, whereas the variables are always written in italics. This helps people not get confused into thinking that $\sin(x)$ means $s$ times $i$ times $n$ times $x$. One can argue that functions we name ourselves should also be in Roman font: $\text{f}(x)$ instead of $f(x)$. But nobody ever does this.

Usually, people omit the parentheses from standard functions. They write $\sin x$ instead of $\sin(x)$. They only use the parentheses in cases where there could be some confusion, such as $\tan (3x+6)$. That clarifies that the argument is $3x+6$. If you wrote $\tan 3x+6$ someone might think you meant $\tan(3x)+6$. But you never write $f x$. It always has to be $f(x)$ or else people will think you mean $f$ times $x$.

When picking names for functions, people usually start with $f$ (for ``function"), then go to $g$ and $h$. After that, practices vary. If you run out of Roman letters, you can use Greek letters like $\Gamma$ (capital gamma), or Gothic letters like $\mathfrak{F}$ or whatever. Avoid using calligraphic letters like $\mathcal{F}$, script letters like $\mathscr{F}$ or bold letters like $\mathbb{F}$. Those are usually used for other kinds of mathematical objects.

Other ways to write the definition of a function are $f(x) \triangleq 2x-7$ and $f(x)$ ${\scriptsize{\text{def}}}\atop{=}$ $ 2x-7$. A really formal way to do it is
\begin{equation}
f(x): x \rightarrow 2x-7.
\end{equation}
This formal way is called a ``mapping". It means that the function $f(x)$ ``maps" any argument $x$ to a different number $2x-7$.

In the beginning, I said that a function is usually an algebraic expression, but doesn't have to be. It could just as well be defined by a table, like this:


$x$     $f(x)$

$-2$     $2$
$-1$     $0$
$0$     $-2$
$1$     $-4$
$2$     $-6$

The function defined by this table is only defined for the specific arguments listed; that is, the integers between $-2$ and 2. $f(10)$ has no meaning, and neither does $f(0.5)$.
A function can also be defined in words, like this: ``For any real number $x$, let $f(x)$ be the next biggest integer." For example, $f(4.66)=5$. You can then use $f(x)$ in discussions.

Some algebra books say that a function can have only one value for any given argument, or else it technically isn't a function. For example, if $f(x) \equiv \sqrt{x}$, then for $x=9$, $f(x)=3$ and $-3$. They would say $\sqrt{x}$ is an expression, but not a function. This is a matter of words, not mathematics. Almost every book after algebra doesn't bother with this kind of hairsplitting. You might say that $f(x)$ is  multi-valued, but you'd still call it a function. If you want to get technical, you can say that $f(x)=\sqrt{x}$ is not a one-to-one mapping.



Saturday, January 10, 2015

Separated at Birth


Mr. Van Driessen from Beavis and Butt-head

Teacher from a brochure recently sent to my son

Friday, January 9, 2015

The Dope Filter

Mario Cuomo died this week, so he was in the news. Something that caught my eye was the following thing he said: "You're telling me that the Mafia is an organization, and I'm telling you that's a lot of baloney."

Now, Mario Cuomo was obviously a very able and intelligent person, so I can't imagine he really believed that. But was he lying? For normal people the answer would be yes. For politicians, though, the answer is more complicated.

I believe Cuomo was employing what you might call the "dope filter". Good politicians know how to use it. The dope filter is what you pass your real beliefs through before stating them for public consumption. Cuomo certainly knew that the Mafia is a real organization, but that most Italians are law-abiding. But he also knew that many voters can't understand that both of those statements can be true at the same time. For them, it's one or the other.




Given the limited ability of many people to deal with subtlety, Cuomo chose the path of least harm. He said the Mafia wasn't an organization not because it was true, but to preserve the fact that most Italians are law-abiding.

Most average people don't really care enough about the Mafia to get upset if some politician pretends it doesn't exist. The ones who do can be divided into two groups: Italians and "law-and-order" types. There is of course some overlap between the two groups, but only the "law-and-order" types would take issue with what Cuomo said. And when they did, he could easily deflect it by constructing some weird definition of an organization that the Mafia doesn't meet, or say that he really meant they have five organizations in New York and others in other cities, and they aren't all masterminded by one guy, so therefore it isn't "an organization", or other weaselings.

Don't get the idea that I am looking down on dopey voters. (Well, I am a little.) If you ask me why the Columbia burned up, I'm just going to say the heat shield was damaged by a piece of ice. I'm not going to get into the fact that this had happened many times previously, so the real cause was a flawed means of assessing the damage, blah blah blah, because it's just going to obscure the basic facts.

Sometimes I worry that people are using the "dope filter" on me. I'm a very literal person, so I don't catch on to body language and tone of voice as well as other people. I can imagine that people have to adopt a special, unusually direct way of talking when they talk to me, for fear of not communicating. They have to turn down the bandwidth a little, so there are things they can't communicate to me that they might be able to communicate to others.




Monday, January 5, 2015

We Who Write Bad Books

I read some interesting quotes by George Kennan, the diplomat and historian, so on impulse I bought his diary and a short book he wrote called Around the Cragged Peak, which was sort of a grab bag of his personal musings on politics, foreign relations, culture and whatnot. I figured anything he wrote would be worth reading, because he lived so long (101 years) and was involved in so many momentous events of the Cold War, an era I've always taken an interest in.

Well, I figured wrong. The diary was so whiny that I wished I hadn't ordered the book, but it was already done. I understand that a lot of diaries are whiny, but you shouldn't publish the ones that are. One thing I did learn was why the military has always been uncomfortable with the State Department. Guys like Kennan, Dulles (both of them) and James Jesus Angleton were so literate and glib that they could say one thing and then convince you they'd meant the exact opposite and that it was your fault for misunderstanding.

The book was better than the diary, but man, was it long-winded. He takes about four pages to say that nationalism is good as long as you don't take it too far. You know how Strunk and White say to omit needless words, like "at this juncture it is perhaps not inappropriate to point out that"? He must have skipped that chapter. I've come to dislike that sort of excessively precise writing, like "He had had a serious operation" instead of just "He had a serious operation". If you need to support your ideas with so many props and ornaments, maybe you had better consider whether they are good ideas. I think I mostly agreed with Kennan's politics. I think.

Come to that, I've lost interest in the "magnum opus". I used to think it would be cool to write a magnum opus; you know, put down on paper the sum total of your views on some topic of importance. But why? The theme of a magnum opus isn't the ideas, it's the author. And let's face it, most of us aren't that interesting, except to people who know us personally. If you want to write a magnum opus, you should give it away free to your friends and family, not charge a stranger money for it.

The technical equivalent of the magnum opus is the textbook or handbook. When I see a textbook with a grandiose title like Fracture: An Advanced Treatise, I just want to run in the other direction. Geezus, a treatise? The worst one is The Structure of Evolutionary Theory by Gould. The fact that he didn't just call it Evolution should be a warning to you.

I got drafted into writing a chapter of one of these magisterial handbooks about five years ago. The trouble with handbooks is that they usually can't get the best people to contribute, because the best people are too busy to write handbook chapters. I happened to be in a slow spot in my career where I had some free time and was looking for something to do, so I finished my chapter right away, and the editors used it to get the whole project greenlighted for publication. You can guess that all the big shots who were supposed to write the other chapters took a lot longer, and in fact the book is still not done. At this rate, the material will be obsolete before it ever hits the presses. If you think you need a handbook, my advice is to find a good review article written by a bona fide expert.








Saturday, January 3, 2015

I Stole A Bike

Once upon a time, I stole a bike. Sort of.

It was a weekend morning in the spring of 1990 and I was walking from my apartment on East Norwich Avenue in Columbus to the Ohio State football ticket office, which I believe was in French Field House at the time. Spring is when you buy your discounted student football ticket at Ohio State, and in those days, you had to do it in person. I was almost there, around some bike racks near some dormitories, in the area now occupied by the College of Business.

That's when I saw it - a bike I had to have. It wasn't even locked to the rack, and it was so early there was hardly anyone around. You certainly didn't have to worry about security cameras in those days. So I hopped on the bike and took off. I had it back at my apartment in just a few minutes. Then I walked back to the ticket office and bought my ticket. I figured it was a little too soon to be riding around that same area on the bike.

You know there's going to be more to the story. The reason I had to have that particular bike was that it was in fact my bike. Or, it had been my bike, depending on your point of view. It was a beat-up 10-speed I'd had since high school and had brought down to campus the previous spring. I'd stored it, chained and locked, on the bike rack in front of Taylor Tower where I lived.

During the two- or three-week break between spring quarter and summer quarter, I'd left the bike on the rack in front of Taylor, but when I'd come back to campus for summer classes, it was gone. I had heard there was a campus rule against leaving bikes on the racks during breaks, so maybe the campus police cut the chain and took it away. But it's not like there was a sign to that effect. It's also possible that someone just stole it. At that time all over campus you'd see front wheels chained to racks but with the rest of the bike stolen, because people had run the chain only through the wheel and not the frame of the bike. Or, at the kind of rack where you set the front wheel into a big slot, some idiot would lean on the bike until the wheel bent, so there were these old, rusty bent front wheels all over the place.

I also seem to remember that the campus police would sell bikes they'd confiscated for not having a sticker or whatever, so maybe someone had paid the police for my bike. But I might be remembering incorrectly about that.

Anyway, someone had my bike for almost a whole year. The day I was going to the ticket office, I spotted the bike and knew it was mine, not just someone's similar bike, because there was a rip in the seat that I'd fixed with some of that sneaker repair goo that comes in a tube. It was definitely mine. I had the bike all that summer, but not long after, it got stolen again, this time for good. I didn't have another bike until spring of the next year, when my girlfriend (wife-to-be) bought me a nice mountain bike for my birthday. Wisely, I chained the bike frame itself, not the wheel, to the rack outside my apartment, but they just stole the wheel. Eventually someone came with a bolt cutter and took the rest of the bike, too.  It is as if people considered bikes to be communal property.

So, overall I left Ohio State down two bikes. But it felt good getting the first bike back for a while. It halfway felt like stealing, so it was kind of exciting when I took off on it, but how can you steal your own bike? Just because I hadn't seen it in a year didn't make it any less my bike, did it? Who the hell knows.